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Op Amp Applications Handbook This page intentionally left blank Op Amp Applications Handbook Walt Jung, Editor with the technical staff of Analog Devices A Volume in the Analog Devices Series AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYO Newnes is an imprint of Elsevier Newnes is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA Linacre House, Jordan Hill, Oxford OX2 8DP, UK Copyright © 2005 by Analog Devices, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: [email protected] You may also complete your request on-line via the Elsevier homepage (http://elsevier.com), by selecting “Customer Support” and then “Obtaining Permissions.” Recognizing the importance of preserving what has been written, Elsevier prints its books on acid-free paper whenever possible. Library of Congress Cataloging-in-Publication Data Jung, Water G. Op Amp applications handbook / by Walt Jung. p. cm – (Analog Devices series) ISBN 0-7506-7844-5 1. Operational amplifiers—Handbooks, manuals, etc. I. Title. II. Series. TK7871.58.O618515 2004 621.39'5--dc22 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. For information on all Newnes publications visit our Web site at www.books.elsevier.com 04 05 06 07 08 09 10 9 8 7 6 5 4 3 2 1 Printed in the United States of America 2004053842 Contents Foreword ................................................................................................................vii Preface ....................................................................................................................ix Acknowledgments .....................................................................................................xi Op Amp History Highlights ...................................................................................... xv Chapter 1: Op Amp Basics ........................................................................................ 3 Section 1-1: Introduction ...............................................................................................5 Section 1-2: Op Amp Topologies .................................................................................. 23 Section 1-3: Op Amp Structures ................................................................................... 31 Section 1-4: Op Amp Specifications.............................................................................. 51 Section 1-5: Precision Op Amps ................................................................................... 89 Section 1-6: High Speed Op Amps ................................................................................ 97 Chapter 2: Specialty Amplifiers .............................................................................. 121 Section 2-1: Instrumentation Amplifiers ...................................................................... 123 Section 2-2: Programmable Gain Amplifiers ................................................................ 151 Section 2-3: Isolation Amplifiers ................................................................................. 161 Chapter 3: Using Op Amps with Data Converters .................................................... 173 Section 3-1: Introduction ........................................................................................... 173 Section 3-2: ADC/DAC Specifications ......................................................................... 179 Section 3-3: Driving ADC Inputs ................................................................................. 193 Section 3-4: Driving ADC/DAC Reference Inputs ......................................................... 213 Section 3-5: Buffering DAC Outputs ........................................................................... 217 Chapter 4: Sensor Signal Conditioning .................................................................... 227 Section 4-1: Introduction ........................................................................................... 227 Section 4-2: Bridge Circuits ........................................................................................ 231 Section 4-3: Strain, Force, Pressure and Flow Measurements ....................................... 247 Section 4-4: High Impedance Sensors ......................................................................... 257 Section 4-5: Temperature Sensors............................................................................... 285 Chapter 5: Analog Filters ...................................................................................... 309 Section 5-1: Introduction ........................................................................................... 309 Section 5-2: The Transfer Function ............................................................................. 313 v Contents Section 5-3: Time Domain Response .......................................................................... 323 Section 5-4: Standard Responses ................................................................................ 325 Section 5-5: Frequency Transformations ..................................................................... 349 Section 5-6: Filter Realizations.................................................................................... 357 Section 5-7: Practical Problems in Filter Implementation ............................................. 393 Section 5-8: Design Examples ..................................................................................... 403 Chapter 6: Signal Amplifiers .................................................................................. 423 Section 6-1: Audio Amplifiers ..................................................................................... 423 Section 6-2: Buffer Amplifiers and Driving Capacitive Loads ........................................ 493 Section 6-3: Video Amplifiers ..................................................................................... 505 Section 6-4: Communication Amplifiers...................................................................... 545 Section 6-5: Amplifier Ideas........................................................................................ 567 Section 6-6: Composite Amplifiers.............................................................................. 587 Chapter 7: Hardware and Housekeeping Techniques ................................................. 607 Section 7-1: Passive Components ............................................................................... 609 Section 7-2: PCB Design Issues ................................................................................... 629 Section 7-3: Op Amp Power Supply Systems ............................................................... 653 Section 7-4: Op Amp Protection................................................................................. 675 Section 7-5: Thermal Considerations .......................................................................... 699 Section 7-6: EMI/RFI Considerations .......................................................................... 707 Section 7-7: Simulation, Breadboarding and Prototyping............................................. 737 Chapter 8: Op Amp History .................................................................................. 765 Section 8-1: Introduction ........................................................................................... 767 Section 8-2: Vacuum Tube Op Amps .......................................................................... 773 Section 8-3: Solid-State Modularand Hybrid Op Amps ................................................ 791 Section 8-4: IC Op Amps ........................................................................................... 805 Index ................................................................................................................... 831 vi Foreword The signal-processing products of Analog Devices, Inc. (ADI), along with those of its worthy competitors, have always had broad applications, but in a special way: they tend to be used in critical roles making possible—and at the same time limiting—the excellence in performance of the device, instrument, apparatus, or system using them. Think about the op amp—how it can play a salient role in amplifying an ultrasound wave from deep within a human body, or measure and help reduce the error of a feedback system; the data converter—and its critical position in translating rapidly and accurately between the world of tangible physics and the world of abstract digits; the digital signal processor—manipulating the transformed digital data to extract information, provide answers, and make crucial instant-by-instant decisions in control systems; transducers, such as the life-saving MEMS accelerometers and gyroscopes; and even control chips, such as the one that empowers the humble thermometric junction placed deep in the heart of a high-performance—but very vulnerable—microcomputer chip. From its founding two human generations ago, in 1965, ADI has been committed to a leadership role in designing and manufacturing products that meet the needs of the existing market, anticipate the near-term needs of present and future users, and envision the needs of users yet unknown—and perhaps unborn—who will create the markets of the future. These existing, anticipated and envisioned “needs” must perforce include far more than just the design, manufacture and timely delivery of a physical device that performs a function reliably to a set of specifications at a competitive price. We’ve always called a product that satisfies these needs “the augmented product,” but what does this mean? The physical product is a highly technological product that, above all, requires knowledge of its possibilities, limitations and subtleties. But when the earliest generations—and to some extent later generations—of such a product appear in the marketplace, there exist few (if any) school courses that have produced graduates proficient in its use. There are few knowledgeable designers who can foresee its possibilities. So we have the huge task of creating awareness; teaching about principles, performance measures, and existing applications; and providing ideas to stimulate the imagination of those creative users who will provide our next round of challenges. This problem is met by deploying people and publications. The people are Applications Engineers, who can deal with user questions arriving via phone, fax, and e-mail—as well as working with users in the field to solve particular problems. These experts also spread the word by giving seminars to small and large groups for purposes from inspiring the creative user to imbuing the system, design, and components engineer with the nuts-and-bolts of practice. The publications—both in hard copy and on-line—range from authoritative handbooks, such as the present volume, comprehensive data sheets, application notes, hardware and software manuals, to periodic publications, such as “Solutions Bulletins” and our unique Analog Dialogue—the sole survivor among its early peers—currently in its 38th year of continuous publication in print and its 6th year of regular publication on the Internet. This book is the ultimate expression of product “augmentation” as it relates to operational amplifiers. In some senses, it can be considered a descendant of two early publications. The first is a 1965 set of Op Amp vii Foreword Notes (Parts 1, 2, 3, and 4), written by Analog Devices co-founder Ray Stata, with the current text directly reflecting these roots. Much less directly would be the 1974 first edition of the IC Op Amp Cookbook, by Walter Jung. Although useful earlier books had been published by Burr-Brown, and by Dan Sheingold at Philbrick, these two timely publications were seminal in the early days of the silicon era, advocating the understanding and use of IC op amps to a market in the process of growing explosively. Finally, and perhaps more important to current students of the op amp art, would be the countless contributions of ADI design and applications engineers, amassed over the years and so highly evident within this new book. Operational amplifiers have been marketed since 1953, and practical IC op amps have been available since the late 1960s. Yet, half a century later, there is still a need for a book that embraces the many aspects of op amp technology—one that is thorough in its technical content, that looks forward to tomorrow’s uses and back to the principles and applications that still make op amps a practical necessity today. We believe that this is such a book, and we commend Walter Jung for “augmenting” the op amp in such an interesting and accessible form. Ray Stata Daniel Sheingold Norwood, Massachusetts, April 28, 2004 viii Preface Op Amp Applications Handbook is another book on the operational amplifier, or op amp. As the name implies, it covers the application of op amps, but does so on a broader scope. Thus it would be incorrect to assume that this book is simply a large collection of app notes on various devices, as it is far more than that. Any IC manufacturer in existence since the 1960s has ample application data on which to draw. In this case, however, Analog Devices, Inc. has had the benefit of applications material with a history that goes back beyond early IC developments to the preceding period of solid-state amplifiers in modular form, with links to the even earlier era of vacuum tube op amps and analog computers, where the operational amplifier began. This book brings some new perspectives to op amp applications. It adds insight into op amp origins and historical developments not available elsewhere. Within its major chapters it also offers fundamental discussions of basic op amp operation; the roles of various device types (including both op amps and other specialty amplifiers, such as instrumentation amplifiers); the procedures for optimal interfacing to other system components such as ADCs and DACs, signal conditioning and filtering in data processing systems, and a wide variety of signal amplifiers. The book concludes with practical discussions of various hardware issues, such as passive component selection, printed circuit design, modeling and breadboarding, etc. In short, while this book does indeed cover op amp applications, it also covers a host of closely related design topics, making it a formidable toolkit for the analog designer. The book is divided into 8 major chapters, and occupies nearly 1000 pages, including index. The chapters are outlined as follows: Chapter 1, Op Amp Basics, has five sections authored by James Bryant, Walt Jung, and Walt Kester. This chapter provides fundamental op amp operating information. An introductory section addresses their ideal and non-ideal characteristics along with basic feedback theory. It then spans op amp device topologies, including voltage and current feedback models, op amp internal structures such as input and/or output architectures, the use of bipolar and/or FET devices, single supply/dual supply considerations, and op amp device specifications that apply to all types. The two final sections of this chapter deal with the operating characteristics of precision and high-speed op amp types. This chapter, itself a book-within-a-book, occupies about 118 pages. Chapter 2, Specialty Amplifiers, has three sections authored by Walt Kester, Walt Jung, and James Bryant. This chapter provides information on those commonly used amplifier types that use op amp-like principles, but aren't op amps themselves—instead they are specialty amplifiers. The first section covers the design and application of differential input, single-ended output amplifiers, known as instrumentation amplifiers. The second section is on programmable gain amplifiers, which are op amp or instrumentation amplifier stages, designed to be dynamically addressable for gain. The final section of the chapter is on isolation amplifiers, which provide galvanic isolation between sections of a system. This chapter occupies about 52 pages. Chapter 3, Using Op Amps with Data Converters, has five sections authored by Walt Kester, James Bryant, and Paul Hendriks. The first section is an introductory one, introducing converter terms and the concept of minimizing conversion degradation within the design of an op amp interface. The second section covers ADC and DAC specifications, including such critically important concepts as linearity, monotonicity, ix Preface missing codes. The third section covers driving ADC inputs in both single-ended and differential signal modes, op amp stability and settling time issues, level shifting, etc. This section also includes a discussion of dedicated differential driver amplifier ICs, as well as op amp-based ADC drivers. The fourth section is concerned with driving converter reference inputs, and optimal use of sources. The fifth and final section covers DAC output buffer amplifiers, using both standard op amp circuits as well as differential driver ICs. This chapter occupies about 54 pages. Chapter 4, Sensor Signal Conditioning, has five sections authored by Walt Kester, James Bryant, Walt Jung, Scott Wurcer, and Chuck Kitchin. After an introductory section on sensor types and their processing requirements, the remaining four sections deal with the different sensor types. The second section is on bridge circuits, covering the considerations in optimizing performance with respect to bridge drive mode, output mode, and impedance. The third section covers strain, force, pressure, and flow measurements, along with examples of high performance circuits with representative transducers. The fourth section, on high impedance sensors, covers a multitude of measurement types. Among these are photodiode amplifiers, charge amplifiers, and pH amplifiers. The fifth section of the chapter covers temperature sensors of various types, such as thermocouples, RTDs, thermistor and semiconductor-based transducers. This chapter occupies about 82 pages. Chapter 5, Analog Filters, has eight sections authored by Hank Zumbahlen. This chapter could be considered a stand-alone treatise on how to implement modern analog filters. The eight sections, starting with an introduction, include transfer functions, time domain response, standard responses, frequency transformations, filter realizations, practical problems, and design examples. This chapter is more mathematical than any other within the book, with many response tables as design aids. One key highlight is the design example section, where an online filter-builder design tool is described in active filter implementation examples using Sallen-Key, multiple feedback, state variable, and frequency dependent negative resistance filter types. This chapter, another book-within-a-book, occupies about 114 pages. Chapter 6, Signal Amplifiers, has six sections authored by Walt Jung and Walt Kester. These sections are audio amplifiers, buffer amplifiers/driving capacitive loads, video amplifiers, communication amplifiers, amplifier ideas, and composite amplifiers. In the audio, video, and communications amplifier sections, various op amp circuit examples are shown, with emphasis in these sections on performance to high specifications— audio, video, or communications, as the case may be. The “amplifier ideas” section is a broad-range collection of various amplifier applications, selected for emphasis on creativity and innovation. The final section, on composite amplifiers, shows how additional discrete devices can be added to either the input or output of an op amp to enhance net performance. This book-within-a-book chapter occupies about 184 pages. Chapter 7, Hardware and Housekeeping Techniques, has seven sections authored by Walt Kester, James Bryant, Walt Jung, Joe Buxton, and Wes Freeman. These sections are passive components, PCB design issues, op amp power supply systems, op amp input and output protection, thermal considerations, EMI/RFI considerations, and the final section, simulation, breadboarding and prototyping. All of these practical topics have a commonality that they are not completely covered (if at all) by the op amp data sheet. But, most importantly, they can be just as critical as the device specifications towards achieving the final results. This book-within-a-book chapter occupies about 158 pages. Chapter 8, the History chapter has four sections authored by Walt Jung. It provides a detailed account of not only the beginnings of operational amplifiers, but also their progress and the ultimate evolution into the IC form known today. This began with the underlying development of feedback amplifier principles, by Harold Black and others at Bell Telephone Laboratories. From the first practical analog computer feedback amplifier building blocks used during World War II, vacuum tube op amps later grew in sophistication, popularity x Preface and diversity of use. The first solid-state op amps were “black-brick” plug in modules, which in turn were followed by hybrid IC forms, using chip semiconductors on ceramic substrates. The first monolithic IC op amp appeared in the early 1960s, and there have been continuous developments in circuitry, processes and packaging since then. This chapter occupies about 68 pages, and includes several hundred literature references. The book is concluded with a thorough index with three pointer types: subject, ADI part number, and standard part numbers. Acknowledgments A book on a scale such as Op Amp Applications Handbook isn’t possible without the work of many individuals. In the preparation phase many key contributions were made, and these are here acknowledged with sincere thanks. Of course, the first “Thank you” goes to ADI management, for project encouragement and support. Hearty thanks goes next to Walt Kester of the ADI Central Applications Department, who freely offered his wisdom and counsel from many years of past ADI seminar publications. He also commented helpfully on the manuscript throughout. Special thanks go to Walt, as well as the many other named section authors who contributed material. Thanks go also to the ADI Field Applications and Central Applications Engineers, who helped with comments and criticism. Ed Grokulsky, Bruce Hohman, Bob Marwin and Arnold Williams offered many helpful comments, and former ADI Applications Engineer Wes Freeman critiqued most of the manuscript, providing valuable feedback. Special thanks goes to Dan Sheingold of ADI, who provided innumerable comments and critiques, and special insights from his many years of op amp experience dating from the vacuum tube era at George A. Philbrick Researches. Thanks to Carolyn Hobson, who was instrumental in obtaining many of the historical references. Thanks to Judith Douville for preparation of the index and helpful manuscript comments. Walt Jung and Walt Kester together prepared slides for the book, and coordinated the stylistic design. Walt Jung did the original book page layout and typesetting. Specific-to-Section Acknowledgments Acknowledged here are focused comments from many individuals, specific to the section cited. All were very much appreciated. Op Amp History; Introduction: Particularly useful to this section of the project was reference information received from vacuum tube historian Gary Longrie. He provided information on early vacuum tube amplifiers, the feedback experiments of B. D. H. Tellegen at N. V. Philips, and made numerous improvement comments on the manuscript. Mike Hummel provided the reference to Alan Blumlein’s patent of a negative feedback amplifier. Dan Sheingold provided constructive comments on the manuscript. Bob Milne offered many comments towards improvement of the manuscript. xi Preface Op Amp History; Vacuum Tube Op Amps: Particularly useful were numerous references on differential amplifiers, received from vacuum tube historian Gary Longrie. Gary also reviewed the manuscript and made numerous improvement comments. Without his enthusiastic inputs, the vacuum tube related sections of this narrative would be less complete. Dan Sheingold supplied reference material, reviewed the manuscript, and made numerous constructive comments. Without his inputs, the vacuum tube op amp story would have less meaning. Bel Losmandy provided many helpful manuscript inputs, including his example 1956 vacuum tube op amp design. He also reviewed the manuscript and made many helpful comments. Paul de R. Leclercq and Morgan Jones supplied the reference to Blumlein’s patent describing his use of a differential pair amplifier. Bob Milne reviewed the manuscript and offered various improvement comments. Steve Bench provided helpful comment on several points related to the manuscript. Op Amp History; Solid-State Modular and Hybrid Op Amps: Particularly useful was information from two GAP/R alumni, Dan Sheingold and Bob Pease. Both offered many details on the early days of working with George Philbrick, and Bob Pease furnished a previously unpublished circuit of the P65 amplifier. Dick Burwen offered detailed information on some of his early ADI designs, and made helpful comments on the development of the narrative. Steve Guinta and Charlie Scouten provided many of the early modular op amp schematics from the ADI Central Applications Department archival collection. Lew Counts assisted with comments on the background of the high speed modular FET amplifier developments. Walt Kester provided details on the HOS-050 amplifier and its development as a hybrid IC product at Computer Labs. Op Amp History; IC Op Amps: Many helpful comments on this section were received, and all are very much appreciated. In this regard, thanks go to Derek Bowers, JoAnn Close, Lew Counts, George Erdi, Bruce Hohman, Dave Kress, Bob Marwin, Bob Milne, Reza Moghimi, Steve Parks, Dan Sheingold, Scott Wurcer, and Jerry Zis Op Amp Basics; Introduction: Portions of this section were adapted from Ray Stata’s “Operational Amplifiers - Part I,” Electromechanical Design, September, 1965. Bob Marwin, Dan Sheingold, Ray Stata, and Scott Wayne contributed helpful comments. Op Amp Basics; Structures: Helpful comments on various op amp schematics were received from ADI op amp designers Derek Bowers, Jim Butler, JoAnn Close, and Scott Wurcer. xii Preface Signal Amplifiers; Audio Amplifiers: Portions of this section were adapted from Walt Jung, “Audio Preamplifiers, Line Drivers, and Line Receivers,” Chapter 8 of Walt Kester, System Application Guide, Analog Devices, Inc., 1993, ISBN 0916550-13-3, pp. 8-1 to 8-100. During the preparation of this material the author received helpful comments and other inputs from Per Lundahl of Lundahl Transformers, and from Arne Offenberg of Norway. Signal Amplifiers; Amplifier Ideas: Helpful comments were received from Victor Koren and Moshe Gerstenhaber. Signal Amplifiers, Composite Amplifiers: Helpful comments were received from Erno Borbely, Steve Bench, and Gary Longrie. Hardware and Housekeeping Techniques; Passive Components and PCB Design Issues: Portions of these sections were adapted from Doug Grant and Scott Wurcer, “Avoiding Passive Component Pitfalls,” originally published in Analog Dialogue 17-2, 1983. Hardware and Housekeeping Techniques; EMI/RFI Considerations: Eric Bogatin made helpful comments on this section. The above acknowledgments document helpful inputs received for the Analog Devices 2002 Amplifier Seminar edition of Op Amp Applications. In addition, Scott Wayne and Claire Shaw aided in preparation of the manuscript for this Newnes edition. While reasonable efforts have been made to make this work error-free, some inaccuracies may have escaped detection. The editors accept responsibility for error correction within future editions, and will appreciate errata notification(s). Walt Jung, Editor Op Amp Applications Handbook May 14, 2004 xiii This page intentionally left blank Op Amp History Highlights 1928 Harold S. Black applies for patent on his feedback amplifier invention. Operational amplifiers first referred to by name in Ragazzini’s key paper “Analysis of Problems in Dynamics by Electronic Circuits.” It references the Bell Labs work on what became the M9 gun director, specifically referencing the op amp circuits used. 1930 Harry Nyquist applies for patent on his regenerative amplifier (patent issued in 1933). 1937 Bardeen, Brattain, and Shockley of Bell Labs discover the transistor effect. U.S. Patent No. 2,102,671 issued to H.S. Black for “Wave Translation System.” 1948 B.D.H. Tellegen publishes a paper on feedback amplifiers, with attributions to H.S. Black and K. Posthumus. George A. Philbrick publishes article describing a single-tube circuit that performs some op amp functions. Hendrick Bode files for an amplifier patent, issued in 1938. 1949 Edwin A. Goldberg invents chopper-stabilized vacuum tube op amp. 1941 Stewart Miller publishes an article with techniques for high and stable gain with response to dc, introducing “cathode compensation.” 1952 Granino and Theresa Korn publish textbook Electronic Analog Computers, which becomes a classic work on the uses and methodology of analog computing, with vacuum tube op amp circuits. Testing of prototype gun director system called the T10 using feedback amplifiers. This later leads to the M9, a weapon system instrumental in winning WWII. 1953 First commercially available vacuum tube op amp introduced by GAP/R. Patent filed by Karl D. Swartzel Jr. of Bell Labs for a “Summing Amplifier,” with a design that could well be the genesis of op amps. Patent not issued until 1946. 1954 Gordon Teal of Texas Instruments develops a silicon transistor. 1946 George Philbrick founds company, George A. Philbrick Researches, Inc. (GAP/R). His work was instrumental in op amp development. 1956 GAP/R publishes manual for K2-W and related amplifiers, that becomes a seminal reference. Nobel Prize in Physics awarded to Bardeen, Brattain, and Shockley of Bell Labs for the transistor. Burr-Brown Research Corporation formed. It becomes an early modular solid-state op amp supplier. 1947 Medal for Merit award given to Bell Labs’s M9 designers Lovell, Parkinson, and Kuhn. Other contributors to this effort include Bode and Shannon. xv Op Amp History Highlights 1958 1968 The µA741 op amp, designed by Dave Fullagar, is introduced by Fairchild and becomes the standard op amp. Jack Kilby of Texas Instruments invents the integrated circuit (IC). 1959 1969 Jean A. Hoerni files for a patent on the planar process, a means of stabilizing and protecting semiconductors. Dan Sheingold takes over as editor of Analog Dialogue (and remains so today). 1962 1970 George Philbrick introduces the PP65, a square outline, 7-pin modular op amp which becomes a standard and allows the op amp to be treated as a component. Model 45 high speed FET op amp introduced by ADI. 1972 Russell and Frederiksen of National Semiconductor Corp. introduce an amplifier technique that leads to the LM324, the low cost, industry-standard general-purpose quad op amp. 1963 Bob Widlar of Fairchild designs the µA702, the first generally recognized monolithic IC op amp. 1965 1973 Fairchild introduces the milestone µA709 IC op amp, also designed by Bob Widlar. Analog Devices introduces AD741, a high-precision 741-type op amp. Analog Devices, Inc. (ADI) is founded by Matt Lorber and Ray Stata. Op amps were their first product. 1974 Ion implantation, a new fabrication technique for making FET devices, is described in a paper by Rod Russell and David Culner of National Semiconductor. 1967 National Semiconductor Corp. (NSC) introduces the LM101 IC op amp, also designed by Bob Widlar, who moved to NSC from Fairchild. This device begins a second generation of IC op amps. 1988 ADI introduces a high speed 36V CB process and a number of fast IC op amps. High performance op amps and op amps designed for various different categories continue to be announced throughout the 1980s and 1990s, and into the twenty-first century. Analog Dialogue magazine is first published by ADI. Chapter 8 provides a detailed narrative of op amp history. xvi CHAPTER 1 Op Amp Basics ■ Section 1-1: Introduction ■ Section 1-2: Op Amp Topologies ■ Section 1-3: Op Amp Structures ■ Section 1-4: Op Amp Specifications ■ Section 1-5: Precision Op Amps ■ Section 1-6: High Speed Op Amps This page intentionally left blank CHAPTER 1 Op Amp Basics James Bryant, Walt Jung, Walt Kester Within Chapter 1, discussions are focused on the basic aspects of op amps. After a brief introductory section, this begins with the fundamental topology differences between the two broadest classes of op amps, those using voltage feedback and current feedback. These two amplifier types are distinguished more by the nature of their internal circuit topologies than anything else. The voltage feedback op amp topology is the classic structure, having been used since the earliest vacuum tube based op amps of the 1940s and 1950s, through the first IC versions of the 1960s, and includes most op amp models produced today. The more recent IC variation of the current feedback amplifier has come into popularity in the mid-to-late 1980s, when higher speed IC op amps were developed. Factors distinguishing these two op amp types are discussed at some length. Details of op amp input and output structures are also covered in this chapter, with emphasis on how such factors potentially impact application performance. In some senses, it is logical to categorize op amp types into performance and/or application classes, a process that works to some degree, but not altogether. In practice, once past those obvious application distinctions such as “high speed” versus “precision,” or “single” versus “dual supply,” neat categorization breaks down. This is simply the way the analog world works. There is much crossover between various classes, i.e., a high speed op amp can be either single or dual-supply, or it may even fit as a precision type. A low power op amp may be precision, but it need not necessarily be single-supply, and so on. Other distinction categories could include the input stage type, such as FET input (further divided into JFET or MOS, which, in turn, are further divided into NFET or PFET and PMOS and NMOS, respectively), or bipolar (further divided into NPN or PNP). Then, all of these categories could be further described in terms of the type of input (or output) stage used. So, it should be obvious that categories of op amps are like an infinite set of analog gray scales; they don’t always fit neatly into pigeonholes, and we shouldn’t expect them to. Nevertheless, it is still very useful to appreciate many of the aspects of op amp design that go into the various structures, as these differences directly influence the optimum op amp choice for an application. Thus structure differences are application drivers, since we choose an op amp to suit the nature of the application—for example, single-supply. In this chapter various op amp performance specifications are also discussed, along with those specification differences that occur between the broad distinctions of voltage or current feedback topologies, as well as the more detailed context of individual structures. Obviously, op amp specifications are also application drivers; in fact, they are the most important since they will determine system performance. We choose the best op amp to fit the application, based on the required bias current, bandwidth, distortion, and so forth. 3 This page intentionally left blank SECTION 1-1 Introduction Walt Jung As a precursor to more detailed sections following, this introductory chapter portion considers the most basic points of op amp operation. These initial discussions are oriented around the more fundamental levels of op amp applications. They include: Ideal Op Amp Attributes, Standard Op Amp Feedback Hookups, The Non-Ideal Op Amp, Op Amp Common-Mode Dynamic Range(s), the various Functionality Differences of Single and Dual-Supply Operation, and the Device Selection process. Before op amp applications can be developed, some requirements are in order. These include an understanding of how the fundamental op amp operating modes differ, and whether dual-supply or single-supply device functionality better suits the system under consideration. Given this, then device selection can begin and an application developed. First, an operational amplifier (hereafter simply op amp) is a differential input, single-ended output amplifier, as shown symbolically in Figure 1-1. This device is an amplifier intended for use with external feedback elements, where these elements determine the resultant function, or operation. This gives rise to the name “operational amplifier,” denoting an amplifier that, by virtue of different feedback hookups, can perform a variety of operations.1 At this point, note that there is no need for concern with any actual technology to implement the amplifier. Attention is focused more on the behavioral nature of this building block device. POSITIVE SUPPLY IDEAL OP AMP ATTRIBUTES: • Infinite Differential Gain • Zero Common Mode Gain • Zero Offset Voltage • Zero Bias Current (+) INPUTS OP AMP OUTPUT (−) OP AMP INPUTS: • High Input Impedance • Low Bias Current • Respond to Differential Mode Voltag • Ignore Common Mode Voltages OP AMP OUTPUT: • Low Source Impedance NEGATIVE SUPPLY Figure 1-1: The ideal op amp and its attributes An op amp processes small, differential mode signals appearing between its two inputs, developing a single-ended output signal referred to a power supply common terminal. Summaries of the various ideal op amp attributes are given in Figure 1-1. While real op amps will depart from these ideal attributes, it is very helpful for first-level understanding of op amp behavior to consider these features. Further, although these initial discussions talk in idealistic terms, they are also flavored by pointed mention of typical “real world” specifications—for a beginning perspective. 1 The actual naming of the operational amplifier occurred in the classic Ragazinni, et al paper of 1947 (see Reference 1). However, analog computations using op amps as we know them today began with the work of the Clarence Lovell-led group at Bell Labs, around 1940 (acknowledged generally in the Ragazinni paper). 5 Chapter One It is also worth noting that this op amp is shown with five terminals, a number that happens to be a minimum for real devices. While some single op amps may have more than five terminals (to support such functions as frequency compensation, for example), none will ever have fewer. By contrast, those elusive ideal op amps don’t require power, and symbolically function with just four pins.2 Ideal Op Amp Attributes An ideal op amp has infinite gain for differential input signals. In practice, real devices will have quite high gain (also called open-loop gain) but this gain won’t necessarily be precisely known. In terms of specifications, gain is measured in terms of VOUT/VIN, and is given in V/V, the dimensionless numeric gain. More often, however, gain is expressed in decibel terms (dB), which is mathematically dB = 20 • log (numeric gain). For example, a numeric gain of 1 million (106 V/V) is equivalent to a 120 dB gain. Gains of 100 dB – 130 dB are common for precision op amps, while high speed devices may have gains in the 60 dB – 70 dB range. Also, an ideal op amp has zero gain for signals common to both inputs, that is, common-mode (CM) signals. Or, stated in terms of the rejection for these common-mode signals, an ideal op amp has infinite CM rejection (CMR). In practice, real op amps can have CMR specifications of up to 130 dB for precision devices, or as low as 60 dB–70 dB for some high speed devices. The ideal op amp also has zero offset voltage (VOS = 0), and draws zero bias current (IB = 0) at both inputs. Within real devices, actual offset voltages can be as low as 1 µV or less, or as high as several mV. Bias currents can be as low as a few fA, or as high as several µA. This extremely wide range of specifications reflects the different input structures used within various devices, and is covered in more detail later in this chapter. The attribute headings within Figure 1-1 for INPUTS and OUTPUT summarize the above concepts in more succinct terms. In practical terms, another important attribute is the concept of low source impedance, at the output. As will be seen later, low source impedance enables higher useful gain levels within circuits. To summarize these idealized attributes for a signal processing amplifier, some of the traits might at first seem strange. However, it is critically important to reiterate that op amps simply are never intended for use without overall feedback. In fact, as noted, the connection of a suitable external feedback loop defines the closed-loop amplifier’s gain and frequency response characteristics. Note also that all real op amps have a positive and negative power supply terminal, but rarely (if ever) will they have a separate ground connection. In practice, the op amp output voltage becomes referred to a power supply common point. Note: This key point is further clarified with the consideration of typically used op amp feedback networks. The basic op amp hookup of Figure 1-2 applies a signal to the (+) input, and a (generalized) network delivers a fraction of the output voltage to the (−) input terminal. This constitutes feedback, with the op amp operating in closed-loop fashion. The feedback network (shown here in general form) can be resistive or reactive, linear or nonlinear, or any combination of these. More detailed analysis will show that the circuit gain characteristic as a whole follows the inverse of the feedback network transfer function. The concept of feedback is both an essential and salient point concerning op amp use. With feedback, the net closed-loop gain characteristics of a stage such as Figure 1-2 become primarily dependent upon a set of external components (usually passive). Thus behavior is less dependent upon the relatively unstable amplifier open-loop characteristics. 2 Such an op amp generates its own power, has two input pins, an output pin, and an output common pin. 6 Op Amp Basics OP AMP INPUT FEEDBACK OUTPUT NETWORK Figure 1-2: A generalized op amp circuit with feedback applied Note that within Figure 1-2, the input signal is applied between the op amp (+) input and a common or reference point, as denoted by the ground symbol. It is important to note that this reference point is also common to the output and feedback network. By definition, the op amp stage’s output signal appears between the output terminal/feedback network input, and this common ground. This single relevant fact answers the “Where is the op amp grounded?” question so often asked by those new to the craft. The answer is simply that it is grounded indirectly, by virtue of the commonality of its input, the feedback network, and the power supply, as is shown in Figure 1-2. To emphasize how the input/output signals are referenced to the power supply, dual supply connections are shown dotted, with the ± power supply midpoint common to the input/output signal ground. But do note, while all op amp application circuits may not show full details of the power supply connections, every real circuit will always use power supplies. Standard Op Amp Feedback Hookups Virtually all op amp feedback connections can be categorized into just a few basic types. These include the two most often used, noninverting and inverting voltage gain stages, plus a related differential gain stage. Having discussed above just the attributes of the ideal op amp, at this point it is possible to conceptually build basic gain stages. Using the concepts of infinite gain, zero input offset voltage, zero bias current, and so forth, standard op amp feedback hookups can be devised. For brevity, a full mathematical development of these concepts isn’t included here (but this follows in a subsequent section). The end-of-section references also include such developments. 7 Chapter One The Noninverting Op Amp Stage The op amp noninverting gain stage, also known as a voltage follower with gain, or simply voltage follower, is shown in Figure 1-3. OP AMP G = VOUT/VIN = 1 + (RF/RG) RF VOUT VIN RG Figure 1-3: The noninverting op amp stage (voltage follower) This op amp stage processes the input VIN by a gain of G, so a generalized expression for gain is: G= VOUT VIN Eq. 1-1 Feedback network resistances RF and RG set the stage gain of the follower. For an ideal op amp, the gain of this stage is: G= RF + RG RG Eq. 1-2 For clarity, these expressions are also included in the figure. Comparison of this figure and the more general Figure 1-2 shows RF and RG here as a simple feedback network, returning a fraction of VOUT to the op amp (−) input. (Note that some texts may show the more general symbols ZF and ZG for these feedback components—both are correct, depending upon the specific circumstances.) In fact, we can make some useful general points about the network RF – RG. We will define the transfer expression of the network as seen from the top of RF to the output across RG as β. Note that this usage is a general feedback network transfer term, not to be confused with bipolar transistor forward gain. β can be expressed mathematically as: β= RG RF + RG Eq. 1-3 So, the feedback network returns a fraction of VOUT to the op amp (–) input. Considering the ideal principles of zero offset and infinite gain, this allows some deductions on gain to be made. The voltage at the (–) input is forced by the op amp’s feedback action to be equal to that seen at the (+) input, VIN. Given this relationship, it is relatively easy to work out the ideal gain of this stage, which in fact turns out to be simply the inverse of β. This is apparent from a comparison of Eqs. 1-2 and 1-3. 8 Op Amp Basics Thus an ideal noninverting op amp stage gain is simply equal to 1/β, or: 1 Eq. 1-4 β This noninverting gain configuration is one of the most useful of all op amp stages, for several reasons. Because VIN sees the op amp’s high impedance (+) input, it provides an ideal interface to the driving source. Gain can easily be adjusted over a wide range via RF and RG, with virtually no source interaction. G= A key point is the interesting relationship concerning RF and RG. Note that to satisfy the conditions of Eq. 1-2, only their ratio is of concern. In practice this means that stable gain conditions can exist over a range of actual RF – RG values, so long as they provide the same ratio. If RF is taken to zero and RG open, the stage gain becomes unity, and VOUT is then exactly equal to VIN. This special noninverting gain case is also called a unity gain follower, a stage commonly used for buffering a source. Note that this op amp example shows only a simple resistive case of feedback. As mentioned, the feedback can also be reactive, i.e., ZF, to include capacitors and/or inductors. In all cases, however, it must include a dc path, if we are to assume the op amp is being biased by the feedback (which is usually the case). To summarize some key points on op amp feedback stages, we paraphrase from Reference 2 the following statements, which will always be found useful: The summing point idiom is probably the most used phrase of the aspiring analog artificer, yet the least appreciated. In general, the inverting (−) input is called the summing point, while the noninverting (+) input is represented as the reference terminal. However, a vital concept is the fact that, within linear op amp applications, the inverting input (or summing point) assumes the same absolute potential as the noninverting input or reference (within the gain error of the amplifier). In short, the amplifier tries to servo its own summing point to the reference. The Inverting Op Amp Stage The op amp inverting gain stage, also known simply as the inverter, is shown in Figure 1-4. As can be noted by comparison of Figures 1-3 and 1-4, the inverter can be viewed as similar to a follower, but with a transposition of the input voltage VIN. In the inverter, the signal is applied to RG of the feedback network and the op amp (+) input is grounded. SUMMING POINT RG RF G = VOUT/VIN = − RF/RG VIN OP AMP VOUT Figure 1-4: The inverting op amp stage (inverter) 9 Chapter One The feedback network resistances RF and RG set the stage gain of the inverter. For an ideal op amp, the gain of this stage is: G=− RF RG Eq. 1-5 For clarity, these expressions are again included in the figure. Note that a major difference between this stage and the noninverting counterpart is the input-to-output sign reversal, denoted by the minus sign in Eq. 1-5. Like the follower stage, applying ideal op amp principles and some basic algebra can derive the gain expression of Eq. 1-5. The inverting configuration is also one of the more useful op amp stages. Unlike a noninverting stage, however, the inverter presents a relatively low impedance input for VIN, i.e., the value of RG. This factor provides a finite load to the source. While the stage gain can in theory be adjusted over a wide range via RF and RG, there is a practical limitation imposed at high gain, when RG becomes relatively low. If RF is zero, the gain becomes zero. RF can also be made variable, in which case the gain is linearly variable over the dynamic range of the element used for RF. As with the follower gain stage, the gain is ratio dependent, and is relatively insensitive to the exact RF and RG values. The inverter’s gain behavior, due to the principles of infinite op amp gain, zero input offset, and zero bias current, gives rise to an effective node of zero voltage at the (−) input. The input and feedback currents sum at this point, which logically results in the term summing point. It is also called a virtual ground, because of the fact it will be at the same potential as the grounded reference input. Note that, technically speaking, all op amp feedback circuits have a summing point, whether they are inverters, followers, or a hybrid combination. The summing point is always the feedback junction at the (–) input node, as shown in Figure 1-4. However in follower type circuits this point isn’t a virtual ground, since it follows the (+) input. A special gain case for the inverter occurs when RF = RG, which is also called a unity gain inverter. This form of inverter is commonly used for generating complementary VOUT signals, i.e., VOUT = −VIN. In such cases it is usually desirable to match RF to RG accurately, which can readily be done by using a wellspecified matched resistor pair. A variation of the inverter is the inverting summer, a case similar to Figure 1-4, but with input resistors RG2, RG3, etc (not shown). For a summer individual input resistors are connected to additional sources VIN2, VIN3, and so forth, with their common node connected to the summing point. This configuration, called a summing amplifier, allows linear input current summation in RF.3 VOUT is proportional to an inverse sum of input currents. The Differential Op Amp Stage The op amp differential gain stage (also known as a differential amplifier, or subtractor) is shown in Figure 1-5. Paired input and feedback network resistances set the gain of this stage. These resistors, RF–RG and RF′–RG′, must be matched as noted, for proper operation. Calculation of individual gains for inputs V1 and V2 and their linear combination derives the stage gain. 3 The very first general-purpose op amp circuit is described by Karl Swartzel in Reference 3, and is titled “Summing Amplifier.” This amplifier became a basic building block of the M9 gun director computer and fire control system used by Allied Forces in World War II. It also influenced many vacuum tube op amp designs that followed over the next two decades. 10 Op Amp Basics RG' RF' V2 for R F'/R G' ≡ RF/RG OP AMP VIN = V1 − V2 G2 G = VOUT/VIN = RF/RG VOUT V1 RF RG G1 Figure 1-5: The differential amplifier stage (subtractor) Note that the stage is intended to amplify the difference of voltages V1 and V2, so the net input is VIN = V1–V2. The general gain expression is then: VOUT Eq. 1-6 V1 − V2 For an ideal op amp and the resistor ratios matched as noted, the gain of this differential stage from VIN to VOUT is: R G= F Eq. 1-7 RG The great fundamental utility that an op amp stage such as this allows is the property of rejecting voltages common to V1–V2, i.e., common-mode (CM) voltages. For example, if noise voltages appear between grounds G1 and G2, the noise will be suppressed by the common-mode rejection (CMR) of the differential amp. The CMR however is only as good as the matching of the resistor ratios allows, so in practical terms it implies precisely trimmed resistor ratios are necessary. Another disadvantage of this stage is that the resistor networks load the V1–V2 sources, potentially leading to additional errors. G= The Nonideal Op Amp—Static Errors Due to Finite Amplifier Gain One of the most distinguishing features of op amps is their staggering magnitude of dc voltage gain. Even the least expensive devices have typical voltage gains of 100,000 (100 dB), while the highest performance precision bipolar and chopper stabilized units can have gains as high 10,000,000 (140 dB), or more. Negative feedback applied around this much voltage gain readily accomplishes the virtues of closed-loop performance, making the circuit dependent only on the feedback components. As noted above in the discussion of ideal op amp attributes, the behavioral assumptions follow from the fact that negative feedback, coupled with high open-loop gain, constrains the amplifier input error voltage (and consequently the error current) to infinitesimal values. The higher this gain, the more valid these assumptions become. 11 Chapter One In reality, however, op amps do have finite gain and errors exist in practical circuits. The op amp gain stage of Figure 1-6 will be used to illustrate how these errors impact performance. In this circuit the op amp is ideal except for the finite open-loop dc voltage gain, A, which is usually stated as AVOL. β network ZG ZF VOUT OP AMP * VIN * OPEN-LOOP GAIN = A G2 G1 Figure 1-6: Nonideal op amp stage for gain error analysis Noise Gain (NG) The first aid to analyzing op amps circuits is to differentiate between noise gain and signal gain. We have already discussed the differences between noninverting and inverting stages as to their signal gains, which are summarized in Eqs. 1-2 and 1-4, respectively. But, as can be noticed from Figure 1-6, the difference between an inverting and noninverting stage can be as simple as where the reference ground is placed. For a ground at point G1, the stage is an inverter; conversely, if the ground is placed at point G2 (with no G1) the stage is noninverting. Note, however, that in terms of the feedback path, there are no real differences. To make things more general, the resistive feedback components previously shown are replaced here with the more general symbols ZF and ZG, otherwise they function as before. The feedback attenuation, β, is the same for both the inverting and noninverting stages: β= ZG ZG + ZF Eq. 1-8 Noise gain can now be simply defined as: The inverse of the net feedback attenuation from the amplifier output to the feedback input. In other words, the inverse of the β network transfer function. This can ultimately be extended to include frequency dependence (covered later in this chapter). Noise gain can be abbreviated as NG. As noted, the inverse of β is the ideal noninverting op amp stage gain. Including the effects of finite op amp gain, a modified gain expression for the noninverting stage is: G CL 1 1 = × 1 β 1 + A β VOL Eq. 1-9 where GCL is the finite-gain stage’s closed-loop gain, and AVOL is the op amp open-loop voltage gain for loaded conditions. 12 Op Amp Basics It is important to note that this expression is identical to the ideal gain expression of Eq. 1-4, with the addition of the bracketed multiplier on the right side. Note also that this right-most term becomes closer and closer to unity, as AVOL approaches infinity. Accordingly, it is known in some textbooks as the error multiplier term, when the expression is shown in this form.4 It may seem logical here to develop another finite gain error expression for an inverting amplifier, but in actuality there is no need. Both inverting and noninverting gain stages have a common feedback basis, which is the noise gain. So Eq. 1-9 will suffice for gain error analysis for both stages. Simply use the β factor as it applies to the specific case. It is useful to note some assumptions associated with the rightmost error multiplier term of Eq. 1-9. For AVOLβ >> 1, one assumption is: 1 1+ 1 ≈ 1− A VOL β 1 A VOL β Eq. 1-10 This in turn leads to an estimation of the percentage error, ε, due to finite gain AVOL: ε (%) ≈ 100 A VOL β Eq. 1-11 Gain Stability The closed-loop gain error predicted by these equations isn’t in itself tremendously important, since the ratio ZF/ZG could always be adjusted to compensate for this error. But note however that closed-loop gain stability is a very important consideration in most applications. Closed-loop gain instability is produced primarily by variations in open-loop gain due to changes in temperature, loading, and so forth. ∆G CL ∆A VOL 1 ≈ × G CL A VOL A VOL β Eq. 1-12 From Eq. 1-12, any variation in open-loop gain (∆AVOL) is reduced by the factor AVOLβ, insofar as the effect on closed-loop gain. This improvement in closed-loop gain stability is one of the important benefits of negative feedback. Loop Gain The product AVOLβ, which occurs in the above equations, is called loop gain, a well-known term in feedback theory. The improvement in closed-loop performance due to negative feedback is, in nearly every case, proportional to loop gain. The term “loop gain” comes from the method of measurement. This is done by breaking the closed feedback loop at the op amp output, and measuring the total gain around the loop. In Figure 1-6 for example, this could be done between the amplifier output and the feedback path (see arrows). To a first 4 Some early discussions of this finite gain error appear in References 4 and 5. Terman uses the open-loop gain symbol of A, as we do today. West uses Harold Black’s original notation of µ for open-loop gain. The form of Eq. 1-9 is identical to Terman’s (or to West’s, substituting µ for A). 13 Chapter One approximation, closed-loop output impedance, linearity, and gain stability are all reduced by AVOLβ with the use of negative feedback. Another useful approximation is developed as follows. A rearrangement of Eq. 1-9 is: A VOL = 1 + A VOL β G CL Eq. 1-13 A VOL ≈ A VOL β G CL Eq. 1-14 So, for high values of AVOLβ, Consequently, in a given feedback circuit the loop gain, AVOLβ, is approximately the numeric ratio (or difference, in dB) of the amplifier open-loop gain to the circuit closed-loop gain. This loop gain discussion emphasizes that, indeed, loop gain is a very significant factor in predicting the performance of closed-loop operational amplifier circuits. The open-loop gain required to obtain an adequate amount of loop gain will, of course, depend on the desired closed-loop gain. For example, using Eq. 1-14, an amplifier with AVOL = 20,000 will have an AVOLβ ≈ 2000 for a closed-loop gain of 10, but the loop gain will be only 20 for a closed-loop gain of 1000. The first situation implies an amplifier-related gain error on the order of ≈ 0.05%, while the second would result in about 5% error. Obviously, the higher the required gain, the greater will be the required open-loop gain to support an AVOLβ for a given accuracy. Frequency Dependence of Loop Gain Thus far, it has been assumed that amplifier open-loop gain is independent of frequency. Unfortunately, this isn’t the case. Leaving the discussion of the effect of open-loop response on bandwidth and dynamic errors until later, let us now investigate the general effect of frequency response on loop gain and static errors. The open-loop frequency response for a typical operational amplifier with superimposed closed-loop amplifier response for a gain of 100 (40 dB), illustrates graphically these results in Figure 1-7. In these Bode plots, subtraction on a logarithmic scale is equivalent to normal division of numeric data.5 Today, op amp openloop gain and loop gain parameters are typically given in dB terms, thus this display method is convenient. A few key points evolve from this graphic figure, which is a simulation involving two hypothetical op amps, both with a dc/low frequency gain of 100 dB (100 kV/V). The first has a gain-bandwidth of 1 MHz, while the gain-bandwidth of the second is 10 MHz. • The open-loop gain AVOL for the two op amps is noted by the two curves marked 1 MHz and 10 MHz, respectively. Note that each has a –3 dB corner frequency associated with it, above which the openloop gain falls at 6 dB/octave. These corner frequencies are marked at 10 Hz and 100 Hz, respectively, for the two op amps. • At any frequency on the open-loop gain curve, the numeric product of gain AVOL and frequency, f, is a constant (10,000 V/V at 100 Hz equates to 1 MHz). This, by definition, is characteristic of a constant gain-bandwidth product amplifier. All voltage feedback op amps behave in this manner. 5 The log-log displays of amplifier gain (and phase) versus frequency are called Bode plots. This graphic technique for display of feedback amplifier characteristics, plus definitions for feedback amplifier stability were pioneered by Hendrick W. Bode of Bell Labs (see Reference 6). 14 Op Amp Basics Gain-bandwidth = 1MHz Gain-bandwidth = 10MHz dB AVOL β GCL Figure 1-7: Op amp closed-loop gain and loop gain interactions with typical open-loop responses • AVOLβ in dB is the difference between open-loop gain and closed-loop gain, as plotted on log-log scales. At the lower frequency point marked, AVOLβ is thus 60 dB. • AVOLβ decreases with increasing frequency, due to the decrease of AVOL above the open-loop corner frequency. At 100 Hz for example, the 1 MHz gain-bandwidth amplifier shows an AVOLβ of only 80 db – 40 db = 40 dB. • AVOLβ also decreases for higher values of closed-loop gain. Other, higher closed-loop gain examples (not shown) would decrease AVOLβ to less than 60 dB at low frequencies. • GCL depends primarily on the ratio of the feedback components, ZF and ZG, and is relatively independent of AVOL (apart from the errors discussed above, which are inversely proportional to AVOLβ). In this example 1/β is 100, or 40 dB, and is so marked at 10 Hz. Note that GCL is flat with increasing frequency, up until that frequency where GCL intersects the open-loop gain curve, and AVOLβ drops to zero. • At this point where the closed-loop and open-loop curves intersect, the loop gain is by definition zero, which implies that beyond this point there is no negative feedback. Consequently, closed-loop gain is equal to open-loop gain for further increases in frequency. • Note that the 10 MHz gain-bandwidth op amp allows a 10× increase in closed-loop bandwidth, as can be noted from the –3 dB frequencies; that is 100 kHz versus 10 kHz for the 10 MHz versus the 1 MHz gain-bandwidth op amp. Figure 1-7 illustrates that the high open-loop gain figures typically quoted for op amps can be somewhat misleading. As noted, beyond a few Hz, the open-loop gain falls at 6 dB/octave. Consequently, closed-loop gain stability, output impedance, linearity and other parameters dependent upon loop gain are degraded at higher frequencies. One of the reasons for having dc gain as high as 100 dB and bandwidth as wide as several MHz, is to obtain adequate loop gain at frequencies even as low as 100 Hz. 15 Chapter One A direct approach to improving loop gain at high frequencies, other than by increasing open-loop gain, is to increase the amplifier open-loop bandwidth. Figure 1-7 shows this in terms of two simple examples. It should be borne in mind however that op amp gain-bandwidths available today extend to the hundreds of MHz, allowing video and high-speed communications circuits to fully exploit the virtues of feedback. Op Amp Common-Mode Dynamic Range(s) As a point of departure from the idealized circuits above, some practical basic points are now considered. Among the most evident of these is the allowable input and output dynamic ranges afforded in a real op amp. This obviously varies with not only the specific device, but also the supply voltage. While we can always optimize this performance point with device selection, more fundamental considerations come first. Any real op amp will have a finite voltage range of operation, at both input and output. In modern system designs, supply voltages are dropping rapidly, and 3 V – 5 V total supply voltages are now common. This is a far cry from supply systems of the past, which were typically ±15 V (30 V total). Obviously, if designs are to accommodate a 3 V – 5 V supply, careful consideration must be given to maximizing dynamic range, by choosing a correct device. Choosing a device will be in terms of exact specifications, but first and foremost it should be in terms of the basic topologies used within it. Output Dynamic Range Figure 1-8 is a general illustration of the limitations imposed by input and output dynamic ranges of an op amp, related to both supply rails. Any op amp will always be powered by two supply potentials, indicated by the positive rail, +VS, and the negative rail, –VS. We will define the op amp’s input and output CM range in terms of how closely it can approach these two rail voltage limits. +VS VSAT(HI) VCM(HI) VCM OP AMP VCM(LO) VOUT VSAT(LO) −VS (OR GROUND) Figure 1-8: Op amp input and output common-mode ranges At the output, VOUT has two rail-imposed limits, one high or close to +VS, and one low, or close to –VS. Going high, it can range from an upper saturation limit of +VS – VSAT(HI) as a positive maximum. For example if +VS is 5 V, and VSAT(HI) is 100 mV, the upper VOUT limit or positive maximum is 4.9 V. Similarly, going low it can range from a lower saturation limit of –VS + VSAT(LO). So, if –VS is ground (0 V) and VSAT(HI) is 50 mV, the lower limit of VOUT is simply 50 mV. Obviously, the internal design of a given op amp will impact this output CM dynamic range, since, when so necessary, the device itself must be designed to minimize both VSAT(HI) and VSAT(LO), to maximize the output dynamic range. Certain types of op amp structures are so designed, and these are generally associated with designs expressly for single-supply systems. This is covered in detail later within the chapter. 16 Op Amp Basics Input Dynamic Range At the input, the CM range useful for VIN also has two rail-imposed limits, one high or close to +VS, and one low, or close to –VS. Going high, it can range from an upper CM limit of +VS – VCM(HI) as a positive maximum. For example, again using the +VS = 5 V example case, if VCM(HI) is 1 V, the upper VIN limit or positive CM maximum is +VS – VCM(HI), or 4 V. Figure 1-9 illustrates by way of a hypothetical op amp’s data how VCM(HI) could be specified, as shown in the upper curve. This particular op amp would operate for VCM inputs lower than the curve shown. VCM(HI) VCM(LO) Figure 1-9: A graphical display of op amp input common mode range In practice the input CM range of real op amps is typically specified as a range of voltages, not necessarily referenced to +VS or –VS. For example, a typical ±15 V operated dual supply op amp would be specified for an operating CM range of ±13 V. Going low, there will also be a lower CM limit. This can be generally expressed as –VS + VCM(LO), which would appear in a graph such as Figure 1-9 as the lower curve, for VCM(LO). If this were again a ±15 V part, this could represent typical performance. To use a single-supply example, for the –VS = 0 V case, if VCM(LO) is 100 mV, the lower CM limit will be 0 V + 0.1 V, or simply 0.1 V. Although this example illustrates a lower CM range within 100 mV of –VS, it is actually much more typical to see single-supply devices with lower or upper CM ranges, which include the supply rail. In other words, VCM(LO) or VCM(HI) is 0 V. There are also single-supply devices with CM ranges that include both rails. More often than not, however, single-supply devices will not offer graphical data such as Figure 1-9 for CM limits, but will simply cover performance with a tabular range of specified voltage. 17 Chapter One Functionality Differences of Dual-Supply and Single-Supply Devices There are two major classes of op amps, the choice of which determines how well the selected part will function in a given system. Traditionally, many op amps have been designed to operate on a dual power supply system, which has typically been ±15 V. This custom has been prevalent since the earliest IC op amps days, dating back to the mid-sixties. Such devices can accommodate input/output ranges of ±10 V (or slightly more), but when operated on supplies of appreciably lower voltage, for example ±5 V or less, they suffer either loss of performance, or simply don’t operate at all. This type of device is referenced here as a dual-supply op amp design. This moniker indicates that it performs optimally on dual voltage systems only, typically ±15 V. It may or may not also work at appreciably lower voltages. Figure 1-10 illustrates in a broad overview the relative functional performance differences that distinguish the dual-supply versus single-supply op amp classes. This table is arranged to illustrate various general performance parameters, with an emphasis on the contrast between single-and dual-supply devices. Which particular performance area is more critical will determine which type of device will be the better system choice. PERFORMANCE PARAMETER SUPPLY LIMITATIONS OUTPUT V RANGE INPUT V RANGE TOTAL DYNAMIC RANGE V & I OUTPUT PRECISION LOAD IMMUNITY VARIETY AVAILABLE DUAL SUPPLY SINGLE SUPPLY Best >10V, Limited <10V − Limited Best <10V, Limited >10V + Greatest − Limited + Greatest + Greatest − Least + Greater + Greatest + Greatest − Less − Less (growing) − Least + Greater − Less (growing) Figure 1-10: Comparison of relative functional performance differences between single and dual-supply op amps More recently, with increasing design attention to lower overall system power and the use of single rail power, the single-supply op amp has come into vogue. This has not been without good reason, as the virtues of using single supply rails can be quite compelling. A review of Figure 1-10 illustrates key points of the dual versus single supply op amp question. In terms of supply voltage limitations, there is a crossover region in terms of overall utility, which occurs around 10 V of total supply voltage. For example, single-supply devices tend to excel in terms of their input and output voltage dynamic ranges. Note that in Figure 1-10 a maximum range is stated as a percentage of available supply. Single-supply parts operate better in this regard, because they are internally designed to maximize these respective ranges. For example, it is not unusual for a device operating from 5 V to swing 4.8 V at the output, and so on. But, rather interestingly, such devices are also usually restricted to lower supply ranges (only), so their upper dynamic range in absolute terms is actually more limited. For example, a traditional ±15 V 18 Op Amp Basics dual-supply device can typically swing 20 V p-p, or more than four times that of a 5 V single-supply part. If the total dynamic range is considered (assuming an identical input noise), the dual-supply operated part will have four times (or 12 dB) greater dynamic range than that of the 5 V operated part. Or, stated in another way, the input errors of a real part such as noise, drift, and so forth, become four times more critical (relatively speaking), when the output dynamic range is reduced by a factor of 4. Note that these comparisons do not involve any actual device specifications, they are simply system-based observations. Device specifications are covered later in this chapter. In terms of total voltage and current output, dual-supply parts tend to offer more in absolute terms, since single-supply parts are usually designed not just for low operating voltage ranges, but also for more modest current outputs. In terms of precision, the dual-supply op amp has long been favored by designers for highest overall precision. However, this status quo is now beginning to be challenged, by such single-supply parts as the truly excellent chopper-stabilized op amps. With more and more new op amps being designed for single-supply use, high precision is likely to become an ever-increasing strength of this category. Load immunity is often an application problem with single-supply parts, as many of them use commonemitter or common-source output stages, to maximize signal swing. Such stages are typically much more load sensitive than the classic common-collector stages generally used in dual-supply op amps. There is now a greater variety of dual-supply op amps available. However, this is at least in part due to the ~30-year head start they have been enjoying. Currently, new op amp designs are increasingly oriented around one or more aspects of single-supply compatibility, with strong trends toward lower supply voltages, smaller packages, and so forth. Device Selection Drivers As the op amp design process is begun, it is useful to keep in mind the fact that there are several selection drivers, which can dictate priorities. This is illustrated by Figure 1-11. FUNCTION PERFORM PACKAGE MARKET Single, Dual, Quad Single Or Dual Supply Supply Voltage Precision Type Cost Speed Size Availability Distortion, Noise Low Bias Current Power Footprint Figure 1-11: Some op amp selection drivers Actually, any single heading along the top of this chart can, in fact, be the dominant selection driver and take precedence over all of the others. In the early days of op amp design, when such things as supply range, package type, and so forth, were fairly narrow in spread, performance was usually the major driver. Of course, it is still very much so and will always be. But, today’s systems are much more compact and lower in power, so things like package type, size, supply range, and multiple devices can often be major drivers of selection. As one example, if the only available supply voltage is 3 V, look at 3 V compatible devices first, and then fill other performance parameters as you can. 19 Chapter One As another example, one coming from another perspective, sometimes all-out performance can drive everything else. An ultralow, non-negotiable input current requirement can drive not only the type of amplifier, but also its package (a FET input device in a glass-sealed hermetic package may be optimum). Then, everything else follows from there. Similarly, high power output may demand a package capable of several watts dissipation; in which case, find the power handling device and package first, and then proceed accordingly. At this point, the concept of these “selection drivers” is still quite general. The following sections of the chapter introduce device types, which supplement this with further details of a realistic selection process. Classic Cameo Ray Stata Publications Establish ADI Applications Work In January of 1965 Analog Devices Inc. (ADI) was founded by Matt Lorber and Ray Stata. Operating initially from Cambridge, MA, modular op amps were the young ADI’s primary product. In those days, Ray Stata did more than administrative tasks. He served in sales and marketing roles, and wrote many op amp applications articles. Even today, some of these are still available to ADI customers. One very early article set was a two part series done for Electromechanical Design, which focused on clear, down-to-earth explanation of op amp principles.1 A second article for the new ADI publication Analog Dialogue was titled “Operational Integrators,” and outlined various errors that plague integrators (including capacitor errors).2 A third impact article was also done for Analog Dialogue, titled “User’s Guide to Applying and Measuring Operational Amplifier Specifications.”3 As the title denotes, this was a comprehensive guide to aid the understanding of op amp specifications, and also showed how to test them. Ray authored an Applications Manual for the 201, 202, 203 and 210 series of chopper op amps.4 Ray was also part of the EEE “Speaks Out” series of article-interviews, where he outlined some of the subtle ways that op amp specs and behavior can trap unwary users (above photo from that article).5 Although ADI today makes many other products, those early op amps were the company’s roots. 1 2 3 4 5 Ray Stata, “Operational Amplifiers − Parts I and II,” Electromechanical Design, Sept., Nov., 1965. Ray Stata, “Operational Integrators,” Analog Dialogue, Vol. 1, No. 1, April, 1967. See also ADI AN357. Ray Stata, “User’s Guide to Applying and Measuring Operational Amplifier Specifications,” Analog Dialogue, Vol. 1, No. 3, September 1967. See also ADI AN356. Ray Stata, Applications Manual for 201, 202, 203 and 210 Chopper Op Amps, ADI, 1967. “Ray Stata Speaks Out on ‘What’s Wrong with Op Amp Specs’,” EEE, July 1968. 20 Op Amp Basics References: Introduction 1. John R. Ragazzini, Robert H. Randall and Frederick A. Russell, “Analysis of Problems in Dynamics by Electronic Circuits,” Proceedings of the IRE, Vol. 35, May 1947, pp. 444–452. 2. Walter Borlase, An Introduction to Operational Amplifiers (Parts 1–3), September 1971, Analog Devices Seminar Notes, Analog Devices, Inc. 3. Karl D. Swartzel, Jr. “Summing Amplifier,” US Patent 2,401,779, filed May 1, 1941, issued June 11, 1946. 4. Frederick E. Terman, “Feedback Amplifier Design,” Electronics, Vol. 10, No. 1, January 1937, pp. 12–15, 50. 5. Julian M. West, “Wave Amplifying System,” US Patent 2,196,844, filed April 26, 1939, issued April 9, 1940. 6. Hendrick W. Bode, “Relations Between Attenuation and Phase In Feedback Amplifier Design,” Bell System Technical Journal, Vol. 19, No. 3, July, 1940. See also: “Amplifier,” US Patent 2,173,178, filed June 22, 1937, issued July 12, 1938. 7. Ray Stata, “Operational Amplifiers-Parts I and II,” Electromechanical Design, September, November 1965. 8. Dan Sheingold, Ed., Applications Manual for Operational Amplifiers for Modeling, Measuring, Manipulating, and Much Else, George A. Philbrick Researches, Inc., Boston, MA, 1965. See also Applications Manual for Operational Amplifiers for Modeling, Measuring, Manipulating, and Much Else, 2nd Ed., Philbrick/Nexus Research, Dedham, MA, 1966, 1984. 9. Walter G. Jung, IC Op Amp Cookbook, 3rd Ed., Prentice-Hall PTR, 1986, 1997, ISBN: 0-13-889601-1. 10. Walt Kester, Editor, Linear Design Seminar, Analog Devices, Inc., 1995, ISBN: 0-916550-15-X. 11. Sergio Franco, Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed. (Sections 1.2 – 1.4), McGraw-Hill, 1998, ISBN: 0-07-021857-9. 21 This page intentionally left blank SECTION 1-2 Op Amp Topologies Walt Kester, Walt Jung, James Bryant The previous section examined op amps without regard to their internal circuitry. In this section the two basic op amp topologies—voltage feedback (VFB) and current feedback (CFB)—are discussed in more detail, leading up to a detailed discussion of the actual circuit structures in Section 1-3. HIGH GAIN STAGE WITH SINGLE-POLE RESPONSE DIFFERENTIAL INPUT STAGE + OUTPUT STAGE A(s) = OPEN LOOP GAIN v ~ –A(s) v – Figure 1-12: Voltage feedback (VFB) op amp Although not explicitly stated, the previous section focused on the voltage feedback op amp and the related equations. In order to reiterate, the basic voltage feedback op amp is repeated here in Figure 1-12 (without the feedback network) and in Figure 1-13 (with the feedback network). VIN A(s) = OPEN LOOP GAIN + ~ v VOUT –A(s) v – R2 1 + R2 R1 VOUT R1 VIN = 1 + = 1 A(s) 1 + R2 R1 1 + R2 R1 1 + 1 A(s) β Figure 1-13: Voltage feedback op amp with feedback network connected It is important to note that the error signal developed because of the feedback network and the finite openloop gain A(s) is in fact a small voltage, v. 23 Chapter One Current Feedback Amplifier Basics The basic current feedback amplifier topology is shown in Figure 1-14. Notice that within the model, a unity gain buffer connects the noninverting input to the inverting input. In the ideal case, the output impedance of this buffer is zero (RO = 0), and the error signal is a small current, i, which flows into the inverting input. The error current, i, is mirrored into a high impedance, T(s), and the voltage developed across T(s) is equal to T(s) · i. (The quantity T(s) is generally referred to as the open-loop transimpedance gain.) This voltage is then buffered and connected to the op amp output. If RO is assumed to be zero, it is easy to derive the expression for the closed-loop gain, VOUT/VIN, in terms of the R1-R2 feedback network and the open-loop transimpedance gain, T(s). The equation can also be derived quite easily for a finite RO, and Figure 1-14 gives both expressions. + VIN T(s) = TRANSIMPEDANCE OPEN LOOP GAIN –T(s) i ×1 ×1 i VOUT T(s) i – RO 1 + R2 R1 VOUT VIN = 1 + R2 T(s) 1 + RO R1 + RO R2 R2 ASSUME R O << R1, AND R1 R1 VOUT VIN ≈ R2, THEN 1 + R2 R1 1 + R2 T(s) Figure 1-14: Current feedback (CFB) op amp topology At this point it should be noted that current feedback op amps are often called transimpedance op amps, because the open-loop transfer function is in fact an impedance as described above. However, the term transimpedance amplifier is often applied to more general circuits such as current-to-voltage (I/V) converters, where either CFB or VFB op amps can be used. Therefore, some caution is warranted when the term transimpedance is encountered in a given application. On the other hand, the term current feedback op amp is rarely confused and is the preferred nomenclature when referring to op amp topology. From this simple model, several important CFB op amp characteristics can be deduced. • Unlike VFB op amps, CFB op amps do not have balanced inputs. Instead, the noninverting input is high impedance, and the inverting input is low impedance. • The open-loop gain of CFB op amps is measured in units of Ω (transimpedance gain) rather than V/V as for VFB op amps. • For a fixed value feedback resistor R2, the closed-loop gain of a CFB can be varied by changing R1, without significantly affecting the closed-loop bandwidth. This can be seen by examining the simplified equation in Figure 1-14. The denominator determines the overall frequency response; and if R2 is constant, then R1 of the numerator can be changed (thereby changing the gain) without affecting the denominator—hence the bandwidth remains relatively constant. 24 Op Amp Basics The CFB topology is primarily used where the ultimate in high speed and low distortion is required. The fundamental concept is based on the fact that in bipolar transistor circuits currents can be switched faster than voltages, all other things being equal. A more detailed discussion of CFB op amp ac characteristics can be found in Section 1-5. Figure 1-15 shows a simplified schematic of an early IC CFB op amp, the AD846—introduced by Analog Devices in 1988 (see Reference 1). Notice that full advantage is taken of the complementary bipolar (CB) process which provides well matched high ft PNP and NPN transistors. +VS 7 Q5 Q6 CCOMP/2 IIN 3 Q3 IIN Q11 Q1 Q9 (+) INPUTS OUTPUT (−) 6 2 Q4 Q10 Q2 Q12 CCOMP/2 Q8 Q7 −VS 4 COMPENSATION Figure 1-15: AD846 current feedback op amp (1988) Transistors Q1–Q2 buffer the noninverting input (Pin 3) and drive the inverting input (Pin 2). Q5–Q6 and Q7–Q8 act as current mirrors that drive the high impedance node. The CCOMP capacitor provides the dominant pole compensation; and Q9, Q10, Q11, and Q12 comprise the output buffer. In order to take full advantage of the CFB architecture, a high speed complementary bipolar (CB) IC process is required. With modern IC processes, this is readily achievable, allowing direct coupling in the signal path of the amplifier. However, the basic concept of current feedback can be traced all the way back to early vacuum tube feedback circuitry, which used negative feedback to the input tube cathode. This use of the cathode for feedback would be analogous to the CFB op amp’s low impedance (–) input, in Figure 1-15. 25 Chapter One Current Feedback Using Vacuum Tubes Figure 1-16 is an adaptation from a 1937 article on feedback amplifiers by Frederick E. Terman (see Reference 2). Notice that the ac-coupled R2 feedback resistor for this two-stage amplifier is connected to the low impedance cathode of T1, the pentode vacuum tube input stage. Similar examples of early tube circuits using cathode feedback can be found in Reference 3. R2 T1 T2 VIN ZL R1 +V +V Adapted from: Frederick E. Terman, "Feedback Amplifier Design," Electronics , January 1937, pp. 12-15, 50. Figure 1-16: A 1937 vacuum tube feedback circuit designed by Frederick E. Terman, using current feedback to the low impedance input cathode (adapted from Reference 2) Dc-coupled op amp design using vacuum tubes was difficult for numerous reasons. One reason was a lack of suitable level shifters. Multistage op amps either required extremely high supply voltages or suffered gain loss because of resistive level shifters. In a 1941 article, Stewart E. Miller describes how to use gas discharge tubes as level shifters in several vacuum tube amplifier circuits (see Reference 4). A circuit of particular interest is shown in Figure 1-17. In the Figure 1-17 reproduction of Miller’s circuit, the R2 feedback resistor and the R1 gain setting resistor are labeled for clarity, and it can be seen that feedback is to the low impedance cathode of the input tube. The author suggests that the closed-loop gain of the amplifier can be adjusted from 72 dB–102 dB, by varying the R1 gain-setting resistor from 37.4 Ω to 1.04 Ω. What is really interesting about the Miller circuit is its frequency response, which is reproduced in Figure 1-18. Notice that the closed-loop bandwidth is nearly independent of the gain setting, and the circuit certainly does not exhibit a constant gain-bandwidth product as would be expected for a traditional VFB op amp. For a gain of 72 dB, the bandwidth is about 30 kHz, and for a gain of 102 dB (30 dB increase), the bandwidth only drops to ~15 kHz. With a 72 dB gain at 30 kHz VFB op amp, bandwidth would be expected to drop 5 octaves to ~0.9 kHz for 102 dB of gain. 26 Op Amp Basics GAIN (R1) 1.04Ω - 37.4Ω FEEDBACK RESISTOR (R2) (151kΩ) Adapted from: Stewart E. Miller, “Sensitive DC Amplifier with AC Operation,” Electronics, November 1941, pp. 27−31, 105−109 Figure 1-17: A 1941 vacuum tube feedback circuit using current feedback To clarify this point on bandwidth, a standard VFB op amp 6 dB/octave (20 dB/decade) slope has been added to Figure 1-18 for reference. Although there is no mention of the significance of this within the text of the actual article, it nevertheless illustrates a popular application of CFB behavior, in the design of high speed programmable gain amplifiers with relatively constant bandwidth. 6 dB / OCTAVE (20 dB / DECADE) SLOPE Adapted from: Stewart E. Miller, “Sensitive DC Amplifier with AC Operation,” Electronics, November 1941, pp. 27−31, 105−109 Figure 1-18: A 1941 feedback circuit shows characteristic CFB gain-bandwidth relationship 27 Chapter One When transistor circuits ultimately replaced vacuum tube circuits between the late 1950s and the mid1960s, the current feedback architecture became popular for certain high speed op amps. Figure 1-19 shows a fast-settling op amp designed at Bell Labs in 1965, for use as a building block in high speed A/D converters (see Reference 5). TO DC SERVO AMP VIN R2 R1 Adapted from: J. O. Edson and H. H. Henning, “Broadband Codecs for an Experimental 224Mb/s PCM Terminal,” BSTJ, Vol. 44, No. 9, November 1965, pp. 1887−1950 Figure 1-19: A 1965 solid- state current feedback op amp design from Bell Labs The circuit shown is a composite amplifier containing a high speed ac amplifier (shown inside the dotted outline) and a separate dc servo amplifier loop (not shown). The feedback resistor R2 is ac coupled to the low impedance emitter of transistor Q1. The circuit design was somewhat awkward because of the lack of good high frequency PNP transistors, and it also required zener diode level shifters, and nonstandard supplies. Hybrid circuit manufacturing technology, which was well established by the 1980s, allowed the use of fast, relatively well-matched NPN and PNP transistors, to realize CFB op amps. The Analog Devices’ AD9610 and AD9611 hybrids were good examples of these devices introduced in the mid-1980s. With the development of high speed complementary bipolar IC processes in the 1980s (see Reference 6) it became possible to realize completely dc-coupled current feedback op amps using PNP and NPN transistors such as the Analog Devices’ AD846, introduced in 1988 (Figure 1-15). Device matching and clever circuit design techniques give these modern IC CFB op amps excellent ac and dc performance without a requirement for separate level shifters, awkward supply voltages, or separate dc servo loops. Various patents have been issued for these types of designs (see References 7 and 8, for example), but it should be remembered that the fundamental concepts were established decades earlier. 28 Op Amp Basics References: Op Amp Topologies 1. Wyn Palmer, Barry Hilton, “A 500 V/µs 12-Bit Transimpedance Amplifier,” ISSCC Digest, February 1987, pp. 176–177, 386. 2. Frederick E. Terman, “Feedback Amplifier Design,” Electronics, January 1937, pp. 12–15, 50. 3. Edward L. Ginzton, “DC Amplifier Design Techniques,” Electronics, March 1944, pp. 98–102. 4. Stewart E. Miller, “Sensitive DC Amplifier with AC Operation,” Electronics, November 1941, pp. 27–31, 105–109. 5. J. O. Edson and H. H. Henning, “Broadband Codecs for an Experimental 224Mb/s PCM Terminal,” Bell System Technical Journal, Vol. 44, No. 9, November 1965, pp. 1887–1950. 6. “Op Amps Combine Superb DC Precision and Fast Settling,” Analog Dialogue, Vol. 22, No. 2, pp. 12–15. 7. David A. Nelson, “Settling Time Reduction in Wide-Band Direct-Coupled Transistor Amplifiers,” US Patent 4,502,020, Filed October 26, 1983, Issued February 26, 1985. 8. Royal A. Gosser, “DC-Coupled Transimpedance Amplifier,” US Patent 4,970,470, Filed October 10, 1989, Issued November 13, 1990. 29 This page intentionally left blank SECTION 1-3 Op Amp Structures Walt Kester, Walt Jung, James Bryant This section describes op amps in terms of their structures, and Section 1-4 discusses op amp specifications. It is hard to decide which to discuss first, since discussion of specifications, to be useful, entails reference to structures, and discussion of structures likewise requires reference to the performance feature that they are intended to optimize. Since the majority of readers will have at least some familiarity with operational amplifiers and their specifications, we shall discuss structures first, and assume that readers will have at least a first-order idea of the definitions of the various specifications. Where this assumption proves ill-founded, the reader should look ahead to the next section to verify any definitions required. Because single-supply devices permeate practically all modern system designs, the related design issues are integrated into the following op amp structural discussions. Single-Supply Op Amp Issues Over the last several years, single-supply operation has become an increasingly important requirement because of market demands. Automotive, set-top box, camera/camcorder, PC, and laptop computer applications are demanding IC vendors to supply an array of linear devices that operate on a single-supply rail, with the same performance of dual supply parts. Power consumption is now a key parameter for line or battery-operated systems, and in some instances, more important than cost. This makes low voltage/low supply current operation critical; at the same time, however, accuracy and precision requirements have forced IC manufacturers to meet the challenge of “doing more with less” in their amplifier designs. In a single-supply application, the most immediate effect on the performance of an amplifier is the reduced input and output signal range. As a result of these lower input and output signal excursions, amplifier circuits become more sensitive to internal and external error sources. Precision amplifier offset voltages on the order of 0.1 mV are less than a 0.04 LSB error source in a 12-bit, 10 V full-scale system. In a single-supply system, however, a “rail-to-rail” precision amplifier with an offset voltage of 1 mV represents a 0.8 LSB error in a 5 V full-scale system (or 1.6 LSB for 2.5 V full-scale). To keep battery current drain low, larger resistors are usually used around the op amp. Since the bias current flows through these larger resistors, they can generate offset errors equal to or greater than the amplifier’s own offset voltage. Gain accuracy in some low voltage single-supply devices is also reduced, so device selection needs careful consideration. Many amplifiers with ~120 dB open-loop gains typically operate on dual supplies—for example OP07 types. However, many single-supply/rail-to-rail amplifiers for precision applications typically have open-loop gains between 25,000 and 30,000 under light loading (>10 kΩ). Selected devices, like the OP113/OP213/OP413 family, do have high open-loop gains (>120 dB), for use in demanding applications. Another example would be the AD855x chopper-stabilized op amp series. Many trade-offs are possible in the design of a single-supply amplifier circuit—speed versus power, noise versus power, precision versus speed and power, and so forth. Even if the noise floor remains constant (highly unlikely), the signal-to-noise ratio will drop as the signal amplitude decreases. 31 Chapter One Besides these limitations, many other design considerations that are otherwise minor issues in dual-supply amplifiers now become important. For example, signal-to-noise (SNR) performance degrades as a result of reduced signal swing. “Ground reference” is no longer a simple choice, as one reference voltage may work for some devices, but not others. Amplifier voltage noise increases as operating supply current drops, and bandwidth decreases. Achieving adequate bandwidth and required precision with a somewhat limited selection of amplifiers presents significant system design challenges in single-supply, low power applications. Most circuit designers take “ground” reference for granted. Many analog circuits scale their input and output ranges about a ground reference. In dual-supply applications, a reference that splits the supplies (0 V) is very convenient, as there is equal supply headroom in each direction, and 0 V is generally the voltage on the low impedance ground plane. In single-supply/rail-to-rail circuits, however, the ground reference can be chosen anywhere within the supply range of the circuit, since there is no standard to follow. The choice of ground reference depends on the type of signals processed and the amplifier characteristics. For example, choosing the negative rail as the ground reference may optimize the dynamic range of an op amp whose output is designed to swing to 0 V. On the other hand, the signal may require level shifting in order to be compatible with the input of other devices (such as ADCs) that are not designed to operate at 0 V input. Very early single-supply “zero-in, zero-out” amplifiers were designed on bipolar processes, which optimized the performance of the NPN transistors. The PNP transistors were either lateral or substrate PNPs with much less bandwidth than the NPNs. Fully complementary processes are now required for the new breed of single-supply/rail-to-rail operational amplifiers. These new amplifier designs don’t use lateral or substrate PNP transistors within the signal path, but incorporate parallel NPN and PNP input stages to accommodate input signal swings from ground to the positive supply rail. Furthermore, rail-to-rail output stages are designed with bipolar NPN and PNP common-emitter, or N-channel/P-channel common-source amplifiers whose collector-emitter saturation voltage or drain-source channel on resistance determine output signal swing as a function of the load current. The characteristics of a single-supply amplifier input stage (common-mode rejection, input offset voltage and its temperature coefficient, and noise) are critical in precision, low voltage applications. Rail-rail input operational amplifiers must resolve small signals, whether their inputs are at ground, or in some cases near the amplifier’s positive supply. Amplifiers having a minimum of 60 dB common-mode rejection over the entire input common-mode voltage range from 0 V to the positive supply are good candidates. It is not necessary that amplifiers maintain common-mode rejection for signals beyond the supply voltages. But, what is required is that they do not self-destruct for momentary overvoltage conditions. Furthermore, amplifiers that have offset voltages less than 1 mV and offset voltage drifts less than 2 µV/°C are also very good candidates for precision applications. Since input signal dynamic range and SNR are equally if not more important than output dynamic range and SNR, precision single-supply/rail-to-rail operational amplifiers should have noise levels referred-to-input (RTI) less than 5 µV p-p in the 0.1 Hz to 10 Hz band. The need for rail-to-rail amplifier output stages is also driven by the need to maintain wide dynamic range in low supply voltage applications. A single-supply/rail-to-rail amplifier should have output voltage swings that are within at least 100 mV of either supply rail (under a nominal load). The output voltage swing is very dependent on output stage topology and load current. Generally, the voltage swing of a good rail-to-rail output stage should maintain its rated swing for loads down to 10 kΩ. The smaller the VOL and the larger the VOH, the better. System parameters, such as “zeroscale” or “full-scale” output voltage, should be determined by an amplifier’s VOL (for zero-scale) and VOH (for full-scale). 32 Op Amp Basics • Single Supply Offers: − Lower Power − Battery-Operated Portable Equipment − Requires Only One Voltage • Design Trade-Offs: − Reduced Signal Swing Increases Sensitivity to Errors Caused by Offset Voltage, Bias Current, Finite OpenLoop Gain, Noise, etc. − Must Usually Share Noisy Digital Supply − Rail-to-Rail Input and Output Needed to Increase Signal Swing − Precision Less than the best Dual Supply Op Amps but not Required for All Applications − Many Op Amps Specified for Single Supply, but do not have Rail-to-Rail Inputs or Outputs Figure 1-20: Single-supply op amp design issues Since the majority of single-supply data acquisition systems require at least 12-to 14-bit performance, amplifiers which exhibit an open-loop gain greater than 30,000 for all loading conditions are good choices in precision applications. Single-supply op amp design issues are summarized in Figure 1-20. 33 Chapter One Op Amp Input Stages It is extremely important to understand input and output structures of op amps in order to properly design the required interfaces. For ease of discussion, the two can be examined separately, as there is no particular reason to relate them at this point. Bipolar Input Stages The very common and basic bipolar input stage of Figure 1-21 consists of a “long-tailed pair” built with bipolar transistors. It has a number of advantages: it is simple, has very low offset, the bias currents in the inverting and noninverting inputs are well-matched and do not vary greatly with temperature. In addition, minimizing the initial offset voltage of a bipolar op amp by laser trimming also minimizes its drift over temperature. This architecture was used in the very earliest monolithic op amps such as the µA709. It is also used with modern high speed types, like the AD829 and AD8021. Although NPN bipolars are shown, the concept also applies with the use of PNP bipolars. VIN Low Offset: As Low as 10µV High Bias Currents: 50nA − 10µA Low Offset Drift: As Low as 0.1µV/ºC (Except Super-Beta: 50pA − 5nA, More Complex and Slower) Temperature Stable IB Medium Current Noise: 1pA/√Hz Well-Matched Bias Currents Matching source impedances minimize offset error due to bias current Low Voltage Noise: As Low as 1nV/√Hz Figure 1-21: A bipolar transistor input stage The AD829, introduced in 1990, is shown in Figure 1-22. This op amp uses a bipolar differential input stage, Q1–Q2, which drives a “folded cascode” gain stage which consists of a fast pair of PNP transistors, Q3–Q4 (see Reference 1). These PNPs drive a current mirror that provides the differential-to-single-ended conversion. The output stage is a two-stage complementary emitter follower. The AD829 is a wideband video amplifier with a 750 MHz uncompensated gain-bandwidth product, and it operates on ±5 V to ±15 V supplies. For added flexibility, the AD829 provides access to the internal compensation node (CCOMP). This allows the user to customize frequency response characteristics for a particular application where the closed-loop gain is less than 20. The RC network connected between the output and the high impedance node helps maintain stability, when driving capacitive loads. Input bias current is 7 µA maximum at 25°C, input voltage noise is 1.7 nV Hz , and input current noise is 1.5 pA Hz . Laser wafer trimming reduces the input offset voltage to 0.5 mV maximum for the “A” grade. Typical input offset voltage drift is 0.3 µV/°C. 34 Op Amp Basics +VS 7 Q3 Q4 CF R 15Ω 12.5pF 500Ω 6 OUTPUT (−) Q1 15Ω Q2 2 INPUTS 3 (+) 1.2mA −VS 4 VOS adj Ccomp BIAS CURRENT FOR AD829 = 7µA MAX @ +25°C INPUT VOLTAGE NOISE = 1.7nV/ √Hz INPUT CURRENT NOISE = 1.5pA/ √Hz Figure 1-22: AD829 op amp simplified schematic In an op amp input circuit such as Figure 1-22, the input bias current is the base current of the transistors comprising the long-tailed pair, Q1–Q2. It can be quite high, especially in high speed amplifiers, because the collector currents are high. It is typically ~3 µA, for the AD829. In amplifiers where the bias current is uncompensated (as true in this case), the bias current will be equal to one-half of the Q1–Q2 emitter current, divided by the HFE. The bias current of a simple bipolar input stage can be reduced by a couple of measures. One is by means of bias current compensation, to be described further below. Another method of reducing bias current is by the use of superbeta transistors for Q1–Q2. Superbeta transistors are specially processed devices with a very narrow base region. They typically have a current gain of thousands or tens of thousands (rather than the more usual hundreds). Op amps with superbeta input stages have much lower bias currents, but they also have more limited frequency response. Since the breakdown voltages of superbeta devices are quite low, they also require additional circuitry to protect the input stage from damage caused by overvoltage (for example, they wouldn’t operate in the circuit of Figure 1-22). Some examples of superbeta input bipolar op amps are the AD704/AD705/AD706 series, and the OP97/ OP297/OP497 series (single, dual, quad). These devices have typical 25°C bias currents of 100 pA or less. Bias Current Compensated Bipolar Input Stage A simple bipolar input stage such as used in Figure 1-22 exhibits high bias current because the currents seen externally are in fact the base currents of the two input transistors. 35 Chapter One VIN Poor Bias Current Match (Currents May Even Flow in Opposite Directions) Low Offset Voltage: As low as 10µV Low Offset Drift: As low as 0.1µV/ºC Higher Current Noise Temperature Stable Ibias Not Very Useful at HF Low Bias Currents: <0.5nA − 10nA Matching source impedances makes offset error due to bias current worse because of additional impedance Low Voltage Noise: As low as 1nV/√Hz Figure 1-23: A bias current compensated bipolar input stage By providing necessary bias currents via an internal current source, as in Figure 1-23, the only external current then flowing in the input terminals is the difference current between the base current and the current source, which can be quite small. Most modern precision op amps use some means of internal bias current compensation; examples would be the familiar OP07 and OP27 series. The well-known OP27 op amp family is good example of bias-compensated op amps (see References 2 and 3). The simplified schematic of the OP27, shown in Figure 1-24, shows that the multiple-collector transistor Q6 provides the bias current compensation for the input transistors Q1 and Q2. The “G” grade of the OP27 VOS adj 1 8 +VS 7 C2 Q6 Q22 C1 Q21 Q1A Q1B Q2B R23 R24 820? 820? Q2A R1 Q46 R12 Q23 (+) Q24 C3 Q20 OUTPUT Q19 3 6 INPUTS Q3 R5 R11 C4 Q45 (−) Q27 2 −VS 4 Q11 Q28 Q26 Q12 BIAS CURRENT FOR OP27G = ±80nA MAX @ 25°C INPUT VOLTAGE NOISE = 3nV/√Hz INPUT CURRENT NOISE = 0.4pA/√Hz Figure 1-24: OP27 op amp uses bias current compensated input stage 36 Op Amp Basics has a maximum input bias current specification of ±80 nA at 25°C. Input voltage noise is 3 nV Hz , and input current noise 0.4 pA Hz . Offset voltage trimming by “Zener-zapping” reduces the input offset voltage of the OP27 to 50 µV maximum at 25°C for the “E” grade device (see Reference 4 for details of this trim method). Bias-current-compensated input stages have many of the good features of the simple bipolar input stage, namely: low voltage noise, low offset, and low drift. Additionally, they have low bias current which is fairly stable with temperature. However, their current noise is not very good, and their bias current matching is poor. These latter two undesirable side effects result from the external bias current being the difference between the compensating current source and the input transistor base current. Both of these currents inevitably have noise. Since they are uncorrelated, the two noises add in a root-sum-of-squares fashion (even though the dc currents subtract). Since the resulting external bias current is the difference between two nearly equal currents, there is no reason why the net current should have a defined polarity. As a result, the bias currents of a bias-compensated op amp may not only be mismatched, they can actually flow in opposite directions. In most applications this isn’t important, but in some it can have unexpected effects. (For example, the droop of a sample-and-hold [SHA] built with a bias-compensated op amp may have either polarity.) In many cases, the bias current compensation feature is not mentioned on an op amp data sheet, and a simplified schematic isn’t supplied. It is easy to determine if bias current compensation is used by examining the bias current specification. If the bias current is specified as a “±" value, the op amp is most likely compensated for bias current. Note that this can easily be verified by examining the offset current specification (the difference in the bias currents). If internal bias current compensation exists, the offset current will be of the same magnitude as the bias current. Without bias current compensation, the offset current will generally be at least a factor of 10 smaller than the bias current. Note that these relationships generally hold, regardless of the exact magnitude of the bias currents. It is also a well-known fact that, within an op amp application circuit, the effects of bias current on the output offset voltage of an op amp can often be cancelled by making the source resistances at the two inputs equal. However, there is an important caveat here. The validity of this practice holds true only for bipolar input op amps without bias current compensation; that is, where the input currents are well matched. In a case of an op amp using internal bias current compensation, adding an extra resistance to either input will usually make the output offset worse. Bias Current Compensated Superbeta Bipolar Input Stage As mentioned above, the OP97/297/OP497-series are high performance superbeta op amps, that also use input bias current compensation. As a result, their input bias currents are ±150 pA max at 25°C. Note that in this case the “±" prefix to the bias current magnitude indicates that the amplifier uses internal bias current compensation. 37 Chapter One A simplified schematic of an OP97 (or one-quarter of the OP497) is shown in Figure 1-25. Note that the Q1–Q2 superbeta pair is protected against large destructive differential input voltages, by the use of both back-to-back diodes, and series current-limiting resistors. Note also that the Q1–Q2 superbeta pair is also protected against excessive collector voltage, by an elaborate bias and bootstrapping network. As a result of these clamping and protection circuits, the input common-mode voltage of this op amp series can safely vary over the full range of the supply voltages used. +VS NOTES: = SUPERBETA TYPE D2 (−) Q1 OUTPUT Q4 Q2 Q5 INPUTS D1 (+) Q3 −VS BIAS CURRENT FOR OP497F = ±150pA MAX @ 25°C INPUT VOLTAGE NOISE = 15nV/√Hz INPUT CURRENT NOISE = 20fA/√Hz Figure 1-25: The OP97, OP297 and OP497 op amp series uses superbeta input stage transistors and bias current compensation FET Input Stages Field-Effect Transistors (FETs) have much higher input impedance than do bipolar junction transistors (BJTs) and would therefore seem to be ideal devices for op amp input stages. However, they cannot be manufactured on all bipolar IC processes, and when a process does allow their manufacture, they often have their own problems. FETs have high input impedance, low bias current, and good high frequency performance. (In an op amp, the lower gm of the FET devices allows higher tail currents, thereby increasing the maximum slew rate.) FETs also have much lower current noise. On the other hand, the input offset voltage of FET long-tailed pairs is not as good as the offset of corresponding BJTs, and trimming for minimum offset does not simultaneously minimize drift. A separate trim is needed for drift, and as a result, offset and drift in a JFET op amp, while good, aren’t as good as the best BJTs. A simplified trim procedure for an FET input op amp stage is shown in Figure 1-26. 38 Op Amp Basics 1 DRIFT TRIM 2 OFFSET TRIM Offset as Low as 50µV IB doubles every 10°C Offset TC ~ 5µV/°C Tradeoff Between Voltage Noise and Input Capacitances Low Current Noise Bias Current as Low as 20fA Figure 1-26: Junction field effect transistor (JFET) input op amp stage showing offset and drift trims It is possible to make JFET op amps with very low voltage noise, but the devices involved are very large and have quite high input capacitance, which varies with input voltage, and so a trade-off is involved between voltage noise and input capacitance. The bias current of an FET op amp is the leakage current of the gate diffusion (or the leakage of the gate protection diode, which has similar characteristics for a MOSFET). Such leakage currents double with every 10°C increase in chip temperature so that a FET op amp bias current is one thousand times greater at 125°C than at 25°C. Obviously this can be important when choosing between a bipolar or FET input op amp, especially in high temperature applications where bipolar op amp input bias current actually decreases. Thus far, we have spoken generally of all kinds of FETs, that is, junction (JFETs) and MOS (MOSFETs). In practice, combined bipolar/JFET technology op amps (i.e., BiFET) achieve better performance than op amps using purely MOSFET or CMOS technology. While ADI and others make high performance op amps with MOS or CMOS input stages, in general these op amps have worse offset and drift, voltage noise, highfrequency performance than the bipolar counterparts. The power consumption is usually somewhat lower than that of bipolar op amps with comparable, or even better, performance. JFET devices require more headroom than do BJTs, since their pinch-off voltage is typically greater than a BJTs base-emitter voltage. Consequently, they are more difficult to operate at very low power supply voltages (1–2 V). In this respect, CMOS has the advantage of requiring less headroom than JFETs. 39 Chapter One Rail-Rail Input Stages Today, there is common demand for op amps with input CM voltage that includes both supply rails, i.e., rail-to-rail CM operation. While such a feature is undoubtedly useful in some applications, engineers should recognize that there are still relatively few applications where it is absolutely essential. These applications should be distinguished from the many more applications where a CM range close to the supplies, or one that includes one supply, is necessary, but true input rail-to-rail operation is not. In many single-supply applications, it is required that the input CM voltage range extend to one of the supply rails (usually ground). High side or low side current-sensing applications are examples of this. Many amplifiers can handle 0 V CM inputs, and they are easily designed using PNP differential pairs (or N-channel JFET pairs) as shown in Figure 1-27. The input CM range of such an op amp generally extends from about 200 mV below the negative rail (–VS or ground), to about 1 V–2 V of the positive rail, +VS. +VS +VS PNPs N-CH JFETs –VS –VS Figure 1-27: PNP or N-channel JFET stages allow CM inputs to the negative rail An input stage could also be designed with NPN transistors (or P-channel JFETs), in which case the input CM range would include the positive rail, and go to within about 1 V–2 V of the negative rail. This requirement typically occurs in applications such as high-side current sensing. The OP282/OP482 input stage uses a P-channel JFET input pair whose input CM range includes the positive rail, making it suitable for highside sensing. The AD823 is a dual 16 MHz (G = +1) op amp with an N-channel JFET input stage (as in Figure 1-27). A simplified schematic of the AD823 is shown in Figure 1-28. This device can operate on single-supply voltages from +3 V to +36 V. This range also allows operation on traditional ±5 V, or ±15 V dual supplies if desired. Similar devices in a related (but lower power) family include the AD820, the AD822, and the AD824. The AD823 JFET input stage allows the input common-mode voltage to range from200 mV below the negative supply to within about 1.5 V of the positive supply. Input offset voltage is 0.8 mV maximum at 25°C, input bias current is 25 pA maximum at 25°C, offset voltage drift is 2 µV/°C, and input voltage noise is 16 nV Hz . Current noise is only 1 fA Hz . The AD823 is laser wafer trimmed for both offset voltage and offset voltage drift as described above. A simplified diagram of a true rail-to-rail input stage is shown in Figure 1-29. Note that this requires use of two long-tailed pairs: one of PNP bipolar transistors Q1–Q2, the other of NPN transistors Q3–Q4. Similar input stages can also be made with CMOS pairs. 40 Op Amp Basics +VS Q43 VBE + 0.3V Q72 J1 Q58 Q61 Q44 A=1 Q49 Q57 A=19 J6 (+) R44 R28 INPUTS (−) S1P Q62 S1N OUTPUT Q60 VB Q48 Q53 Q59 A=1 Q17 A=19 Q35 Q56 I1 −VS BIAS CURRENT = 25pA MAX @ 25°C INPUT OFFSET VOLTAGE = 0.8mV MAX @ 25°C INPUT VOLTAGE NOISE = 15nV/√Hz INPUT CURRENT NOISE = 1fA/√Hz Figure 1-28: AD823 JFET input op amp simplified schematic +VS Q2 Q1 Q3 Q4 –VS Figure 1-29: A true rail-to-rail bipolar transistor input stage It should be noted that these two pairs will exhibit different offsets and bias currents, so when the applied CM voltage changes, the amplifier input offset voltage and input bias current does also. In fact, when both current sources remain active throughout most of the entire input common-mode range, amplifier input offset voltage is the average offset voltage of the two pairs. In those designs where the current sources are alternativelyswitched off at some point along the input common-mode voltage, amplifier input offset voltage is dominated by the PNP pair offset voltage for signals near the negative supply, and by the NPN pair offset voltage for signals near the positive supply. As noted, a true rail-to-rail input stage can also be constructed from CMOS transistors, for example as in the case of the CMOS AD8531/AD8532/AD8534 op amp family. Amplifier input bias current, a function of transistor current gain, is also a function of the applied input common-mode voltage. The result is relatively poor common-mode rejection (CMR), and a changing common-mode input impedance over the CM input voltage range, compared to familiar dual-supply devices. These specifications should be considered carefully when choosing a rail-to-rail input op amp, especially 41 Chapter One for a noninverting configuration. Input offset voltage, input bias current, and even CMR may be quite good over part of the common-mode range, but much worse in the region where operation shifts between the NPN and PNP devices, and vice versa. True rail-to-rail amplifier input stage designs must transition from one differential pair to the other differential pair, somewhere along the input CM voltage range. Some devices like the OP191/OP291/OP491 family and the OP279 have a common-mode crossover threshold at approximately 1 V below the positive supply (where signals do not often occur). The PNP differential input stage is active from about 200mV below the negative supply to within about 1 V of the positive supply. Over this common-mode range, amplifier input offset voltage, input bias current, CMR, input noise voltage/current are primarily determined by the characteristics of the PNP differential pair. At the crossover threshold, however, amplifier input offset voltage becomes the average offset voltage of the NPN/PNP pairs and can change rapidly. Also, as noted previously, amplifier bias currents are dominated by the PNP differential pair over most of the input common-mode range, and change polarity and magnitude at the crossover threshold when the NPN differential pair becomes active. Op amps like the OP184/OP284/OP484 family, shown in Figure 1-30, utilize a rail-to-rail input stage design where both NPN and PNP transistor pairs are active throughout most of the entire input CM voltage range. With this approach to biasing, there is no CM crossover threshold. Amplifier input offset voltage is the average offset voltage of the NPN and the PNP stages, and offset voltage exhibits a smooth transition throughout the entire input CM range, due to careful laser trimming of input stage resistors. +VS R3 Q16 R4 Q17 Q11 Q12 (+) Q1 Q2 INPUTS (−) Q4 Q7 Q3 Q8 Q10 OUTPUT CC2 Q9 R6 CFF Q13 Q5 R1 Q15 Q6 R5 CO Q14 CC1 R7 R2 Q18 R8 R9 R10 −VS Figure 1-30: OP284 op amp simplified schematic shows true rail-to-rail input stage In the same manner, through careful input stage current balancing and input transistor design, the OP184 family input bias currents also exhibit a smooth transition throughout the entire CM input voltage range. The exception occurs at the very extremes of the input range, where amplifier offset voltages and bias currents increase sharply, due to the slight forward-biasing of parasitic p-n junctions. This occurs for input voltages within approximately 1 V of either supply rail. When both differential pairs are active throughout most of the entire input common-mode range, amplifier transient response is faster through the middle of the common-mode range by as much as a factor of 2 for for JFET input stages. This is due to the higher transconductance bipolar input stages and by a factor of of two operating input stages. 42 Op Amp Basics Input stage gm determines the slew rate and the unity-gain crossover frequency of the amplifier, hence response time degrades slightly at the extremes of the input common-mode range when either the PNP stage (signals approaching the positive supply rail) or the NPN stage (signals approaching the negative supply rail) are forced into cutoff. The thresholds at which the transconductance changes occur are approximately within 1 V of either supply rail, and the behavior is similar to that of the input bias currents. In light of the many quirks of true rail-to-rail op amp input stages, applications that do require true railto-rail inputs should be carefully evaluated, and an amplifier chosen to ensure that its input offset voltage, input bias current, common-mode rejection, and noise (voltage and current) are suitable. Don’t Forget Input Overvoltage Considerations In order to achieve the performance levels required, it is sometimes not possible to provide complete overdrive protection within IC op amps. Although most op amps have some type of input protection, care must still be taken to prevent possible damage against both CM and differential voltage stress. This is most likely to occur, for example, when the input signal comes from an external sensor. Rather than present a cursory discussion of this topic here, the reader is instead referred to Chapter 7, Section 7-4 for a detailed examination of this important issue. Output Stages The earliest IC op amp output stages were NPN emitter followers with NPN current sources or resistive pull-downs, as shown in Figure 1-31A. Naturally, the slew rates were greater for positive-going than they were for negative-going signals. While all modern op amps have push-pull output stages of some sort, many are still asymmetrical, and have a greater slew rate in one direction than the other. Asymmetry tends to introduce distortion on ac signals and generally results from the use of IC processes with faster NPN than PNP transistors. It may also result in an ability of the output to approach one supply more closely than the other in terms of saturation voltage. In many applications, the output is required to swing only to one rail, usually the negative rail (i.e., ground in single-supply systems). A pull-down resistor to the negative rail will allow the output to approach that rail (provided the load impedance is high enough, or is also grounded to that rail), but only slowly. Using an FET current source instead of a resistor can speed things up, but this adds complexity, as shown in Figure 1-31B. (A) (C) (B) +VS NPN NMOS VOUT NPN +VS +VS NPN VOUT VOUT NMOS PNP –VS –VS –VS Figure 1-31: Some traditional op amp output stages 43 Chapter One With modern complementary bipolar (CB) processes, well matched high speed PNP and NPN transistors are readily available. The complementary emitter follower output stage shown in Figure 1-31C has many advantages, but the most outstanding one is the low output impedance. However, the output voltage of this stage can only swing within about one VBE drop of either rail. Therefore an output swing of 1 V to 4 V is typical of such a stage, when operated on a single 5 V supply. The complementary common-emitter/common-source output stages shown in Figure 1-32A and B allow the op amp output voltage to swing much closer to the rails, but these stages have much higher open-loop output impedance than do the emitter follower-based stages of Figure 1-31C. In practice, however, the amplifier’s high open-loop gain and the applied feedback can still produce an application with low output impedance (particularly at frequencies below 10 Hz). What should be carefully evaluated with this type of output stage is the loop gain within the application, with the load in place. Typically, the op amp will be specified for a minimum gain with a load resistance of 10 kΩ (or more). Care should be taken that the application loading doesn’t drop lower than the rated load, or gain accuracy may be lost. It should also be noted these output stages can cause the op amp to be more sensitive to capacitive loading than the emitter-follower type. Again, this will be noted on the device data sheet, which will indicate a maximum of capacitive loading before overshoot or instability will be noted. +VS (A) (B) PNP +VS PMOS VOUT VOUT NMOS NPN –VS –VS SWINGS LIMITED BY FET "ON" RESISTANCE SWINGS LIMITED BY SATURATION VOLTAGE Figure 1-32: “Almost” rail-to-rail output structures The complementary common emitter output stage using BJTs (Figure 1-32A) cannot swing completely to the rails, but only to within the transistor saturation voltage (VCESAT) of the rails. For small amounts of load current (less than 100 µA), the saturation voltage may be as low as 5 mV to 10 mV, but for higher load currents, the saturation voltage can increase to several hundred mV (for example, 500 mV at 50 mA). On the other hand, an output stage constructed of CMOS FETs (Figure 1-32B) can provide nearly true railto-rail performance, but only under no-load conditions. If the op amp output must source or sink substantial current, the output voltage swing will be reduced by the I × R drop across the FETs internal “on” resistance. Typically this resistance will be on the order of 100 Ω for precision amplifiers, but it can be less than 10 Ω for high current drive CMOS amplifiers. 44 Op Amp Basics For the above basic reasons, it should be apparent that there is no such thing as a true rail-to-rail output stage, hence the caption of Figure 1-32 (“Almost” Rail-to-Rail Output Structures). The best any op amp output stage can do is an almost rail-to-rail swing, when it is lightly loaded. Op amps built on foundry CMOS processes have a primary advantage of low cost. Also, it is relatively straightforward to design rail-to-rail input and output stages with these CMOS devices, which will operate on low supply voltages. Figure 1-33 shows a simplified schematic of the AD8531/AD8532/AD8534 (single/dual/quad) op amp, which is typical of these design types. The AD8531/AD8532/AD8534 operates on a single 2.7 V to 6.0 V supply and can drive 250 mA. Input offset voltage is 25 mV maximum at 25°C, and voltage noise 45 nV Hz . This type of op amp is simple and cost effective, and the lack of high dc precision is often no disadvantage. To the contrary, the high output drive available can be an overriding plus, particularly in AC-coupled applications. Figure 1-33: AD8531/AD8532/AD8534 CMOS rail-to-rail op amp simplified schematic Output Stage Surge Protection Most low speed, high precision op amps generally have output stages which are protected against short circuits to ground or to either supply. Their output current is limited to a little more than 10 mA. This has the additional advantage of minimizing self-heating of the chip (and thus minimizing dc errors due to chip temperature differentials). If an op amp is required to deliver both high precision and a large output current, it is advisable to use a separate output stage (within the loop) to minimize self-heating of the precision op amp. A simple buffer amplifier such as the BUF04, or a section of a nonprecision op amp can be used. Note that high speed op amps cannot have output currents limited to low values, as it would affect their slew rate and load drive ability. Thus most high speed op amps will source/sink between 50 mA–100 mA. Although many high speed op amps have internal protection for momentary shorts, their junction temperatures can be exceeded with sustained shorts. The user needs to be wary, and consult the specific device ratings. 45 Chapter One Offset Voltage Trim Processes The AD860x CMOS op amp family exploits the advantages of digital technology to minimize the offset voltage normally associated with CMOS amplifiers. Offset voltage trimming is done after the devices are packaged. A digital code is entered into the device to adjust the offset voltage to less than 1 mV, depending upon the grade. Wafer testing is not required, and the patented ADI technique called DigiTrim™ requires no extra pins to accomplish the function. These devices have rail-to-rail inputs and outputs (similar to Figure 1-33), and the NMOS and PMOS parallel input stages are trimmed separately using DigiTrim to minimize the offset voltage in both pairs. A functional diagram of the AD8602 DigiTrim op amp is shown in Figure 1-34. + – HIGH CM TRIM FUSE LOW CM TRIM CLOCK DATA IN TRIM DATA N FUSE ARRAY N VOS HIGH TRIM DAC N VOS LOW TRIM DAC N FUSE ARRAY Figure 1-34: AD8602 (1/2) CMOS op amp showing DigiTrim DigiTrim adjusts the offset voltage by programming digitally weighted current sources. The trim information is entered through existing pins using a special digital sequence. The adjustment values can be temporarily programmed, evaluated, and readjusted for optimum accuracy before permanent adjustment is performed. After the trim is completed, the trim circuit is locked out to prevent the possibility of any accidental re-trimming by the end user. The physical trimming, achieved by blowing polysilicon fuses, is very reliable. No extra pads or pins are required, and no special test equipment is needed to perform the trimming. The trims can be done after packaging so that assembly-related shifts can be eliminated. No testing is required at the wafer level because of high die yields The first devices to use this new technique are the Analog Devices’ AD8601/02/04 (single, dual, quad) railto-rail CMOS amplifiers. The offset is trimmed for both high and low common-mode conditions so that the offset voltage is under 500 µV over the full common-mode input voltage range. The bandwidth of the op amps is 8 MHz, slew rate is 5 V/µs, and supply current is only 640 µA per amplifier. At this point it is useful to review the other popular trim methods. Analog Devices pioneered the use of thin film resistors and laser wafer trimming for precision amplifiers, references, data converters, and other linear ICs (see Reference 5). Up to 16-bit accuracy can be achieved with trimming, and the thin film resistors themselves are very stable with temperature and can add to the thermal stability and accuracy of 46 Op Amp Basics a device, even without trimming. Thin film deposition and patterning are processes that must be tightly controlled. The laser trimming systems are also quite expensive. In-package trimming is not possible, so assembly-related shifts cannot be easily compensated. Nevertheless, thin film trimming at the wafer level provides continuous fine trim resolution in precision integrated circuits where high accuracy and stability are required. Zener zapping uses a voltage to create a metallic short circuit across the base-emitter junction of a transistor to remove a circuit element (see References 4 and 6). The base-emitter junction is commonly referred to as a zener, although the mechanism is actually avalanche breakdown of the junction. During the avalanche breakdown across the base-emitter junction, the very high current densities and localized heating generate rapid metal migration between the base and emitter connections, leading to a metallic short across the junction. With proper biasing (current, voltage, and time), this short will have a very low resistance value. If a series of these base-emitter junctions are arranged in parallel with a string of resistors, zapping selected junctions will short out portions of the resistor string, thereby adjusting the total resistance value. It is possible to perform zener zap trimming in the packaged IC to compensate for assembly-related shifts in the offset voltage. However, trimming in the package requires extra package pins. Alternately, trimming at the wafer level requires additional probe pads. Probe pads do not scale effectively as the process features shrink. Thus, the die area required for trimming is relatively constant, regardless of the process geometries. Some form of bipolar transistor is required for the trim structures, therefore a purely MOS-based process may not have zener zap capability. The nature of the trims is discrete since each zap removes a predefined resistance value. Increasing trim resolution requires additional transistors and pads or pins, which rapidly increase the total die area and/or package cost. This technique is most cost-effective for fairly large geometry processes where the trim structures and probe pads make up a relatively small percentage of the overall die area. It was in the process of creating the industry standard OP07 in 1975 that Precision Monolithics Incorporated pioneered zener zap trimming (Reference 6). The OP07 and other similar parts must be able to operate from over ±15 V supplies. As a result, they utilize relatively large device geometries to support the high voltage requirements, and extra probe pads don’t significantly increase die area. Link trimming is the cutting of metal or poly-silicon links to remove a connection. In link trimming, either a laser or a high current is used to destroy a “shorted” connection across a parallel resistive element. Removing the connection increases the effective resistance of the combined element(s). Laser cutting is similar to laser trimming of thin films. The high local heat from the laser beam causes material changes that lead to a nonconductive area, effectively cutting a metal or conductive polysilicon connector. The high-current link trim method works as an inverse to zener zapping—the conductive connection is destroyed, rather than created by a zener-zap. Link trim structures tend to be somewhat more compact than laser trimmed resistor structures. No special processes are required in general, although the process may have to be tailored to the laser characteristics if laser cutting is used. With the high-current trimming method, testing at the wafer level may not be required if die yields are good. The laser cutting scheme doesn’t require extra contact pads, but the trim structures don’t scale with the process feature sizes. Laser cutting of links cannot be performed in the package, and requires additional probe pads on the die. In addition, it can require extra package pins for in-package highcurrent trims. Like zener zapping, link trimming is discrete. Resolution improvements require additional structures, increasing area and cost. EEPROM trimming utilizes special, nonvolatile digital memory to store trim data. The stored data bits control adjustment currents through on-chip D/A converters. Memory cells and D/A converters scale with 47 Chapter One the process feature size. In-package trimming and even trimming in the customer’s system is possible so that assembly-related shifts can be trimmed out. Testing at the wafer level is not required if yields are reasonable. No special hardware is required for the trimming beyond the normal mixed-signal tester system, although test software development may be more complicated. Since the trims can be overwritten, it is possible to periodically reprogram the system to account for longterm drifts or to modify system characteristics for new requirements. The number of reprogram cycles possible depends on the process, and is finite. Most EEPROM processes provide enough rewrite cycles to handle routine recalibration. This trim method does require special processing. Stored trim data can be lost under certain conditions, especially at high operating temperatures. At least one extra digital contact pad/package pin is required to input the trim data to the on-chip memory. This technique is only available on MOS-based processes due to the very thin oxide requirements. The biggest drawback is that the on-chip D/A converters are large—often larger than the amplifier circuits they are adjusting. For this reason, EEPROM trimming is mostly used for data converter or system-level products where the trim D/A converters represent a much smaller percentage of the overall die area. Figure 1-35 summarizes the key features of each ADI trim method. It can be seen from that all trim methods have their respective places in producing high performance linear integrated circuits. PROCESS TRIMMED AT: SPECIAL PROCESSING RESOLUTION DigiTrim™ Wafer or Final Test None Discrete Laser Trim Wafer Thin Film Resistor Continuous Zener Zap Trim Wafer None Discrete Link Trim Wafer EEPROM Trim Wafer or Final Test Thin Film or Poly Resistor EEPROM Discrete Discrete Figure 1-35: Summary of ADI trim processes Op Amp Process Technologies The wide variety of op amp processes is shown in Figure 1-36. The early 1960s op amps used standard NPN-based bipolar processes. The PNP transistors of these processes were extremely slow and were used primarily for current sources and level-shifting. The ability to produce matching high speed PNP transistors on a bipolar process added great flexibility to op amp circuit designs. The first p-epi complementary bipolar (CB) process was introduced by ADI in the mid-1980s. The fts of the PNP and NPN transistors were approximately 700 MHz and 900 MHz, respectively, and had 30 V breakdowns. Since its original introduction in 1985, several additional CB processes have been developed at ADI designed for higher speeds and lower breakdowns. For example, a current 5 V CB process has 9 GHZ PNPs and 16 GHz NPNs. These CB processes are used in today’s precision op amps, as well as those requiring wide bandwidths. 48 Op Amp Basics • BIPOLAR (NPN-BASED): This is Where it All Started • COMPLEMENTARY BIPOLAR (CB): Rail-to-Rail, Precision, High Speed • BIPOLAR + JFET (BiFET): High Input Impedance, High Speed • COMPLEMENTARY BIPOLAR + JFET (CBFET): High Input Impedance, Rail-to-Rail Output, High Speed • COMPLEMENTARY MOSFET (CMOS): Low Cost Op Amps (ADI DigiTrim Minimizes Offset Voltage and Drift in CMOS Op Amps) • BIPOLAR (NPN) + CMOS (BiCMOS): Bipolar Input Stage adds Linearity, Low Power, Rail-to-Rail Output • COMPLEMENTARY BIPOLAR + CMOS (CBCMOS): Rail-to-Rail Inputs, Rail-to-Rail Outputs, Good Linearity, Low Power, Higher Cost Figure 1-36: Op amp process technology summary The JFETs available on the Analog Devices complementary bipolar processes allow high input impedance op amps to be designed suitable for such applications as photodiode or electrometer preamplifiers. These processes are sometimes designated as CBFET. CMOS op amps, generally have higher offset voltages and offset voltage drift than trimmed bipolar or BiFET op amps, however the Analog Devices DigiTrim process described above yields low offset voltage, while keeping costs low. Voltage noise for CMOS op amps tends to be larger, but the input bias current is very low. They offer low power and cost (foundry CMOS processes are typically used). The addition of bipolar or complementary devices to a CMOS process (BiMOS or CBCMOS) adds greater flexibility, better linearity, and lower power as well as additional cost. The bipolar devices are typically used for the input stage to provide good gain and linearity, and CMOS devices for the rail-to-rail output stage. In summary, there is no single IC process that is optimum for all op amps. Process selection and the resulting op amp design depends on the targeted applications and ultimately should be transparent to the customer. 49 Chapter One References: Op Amp Structures 1. “Video Op Amp,” Analog Dialogue, Vol. 24, No. 3, p. 19. 2. George Erdi, “Amplifier Techniques for Combining Low Noise, Precision, and High-Speed Perfomance,” IEEE Journal of Solid-State Circuits, Vol. SC-16, December, 1981 pp. 653–661. 3. George Erdi, Tom Schwartz, Scott Bernardi, and Walt Jung, “Op Amps Tackle Noise and for Once, Noise Loses,” Electronic Design, December 12, 1980. 4. George Erdi, “A Precision Trim Technique for Monolithic Analog Circuits,” IEEE Journal of SolidState Circuits, Vol. SC-10, December, 1975 pp. 412–416. 5. Richard Wagner, “Laser-Trimming on the Wafer,” Analog Dialogue, Vol. 9, No. 3, pp. 3–5. 6. Donn Soderquist, George Erdi, “The OP07 UltraLow Offset Voltage Op Amp,” Precision Monolithics AN-13, December, 1975. 7. Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 8. Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0-916550-17-6 (available for download at www.analog.com). 9. Walt Kester, Editor, Practical Analog Design Techniques, Analog Devices, 1995, ISBN: 0-916550-16-8. (available for download at www.analog.com). 50 SECTION 1-4 Op Amp Specifications Walt Kester, Walt Jung, James Bryant Most op amp specifications are largely topology independent. However, although voltage feedback and current feedback op amps have similar error terms and specifications, the application of each part warrants discussing some of the specifications separately. In the following discussions, this will be done where significant differences exist. Input Offset Voltage, VOS Ideally, if both inputs of an op amp are at exactly the same voltage, the output should be at zero volts. In practice, a small differential voltage must be applied to the inputs to force the output to zero. This is known as the input offset voltage, VOS. Input offset voltage is modeled as a voltage source, VOS, in series with the inverting input terminal of the op amp as shown in Figure 1-37. The corresponding output offset voltage (due to VOS) is obtained by multiplying the input offset voltage by the dc noise gain of the circuit (see Figure 1-3 and Eq. 1-2). − VOS + • • Offset Voltage: The differential voltage that must be applied to the input of an op amp to produce zero output. Ranges: − Chopper-Stabilized Op Amps: <1µV − General-Purpose Precision Op Amps: 50-500µV − Best Bipolar Op Amps: 10−25µV − Best FET Op Amps: 100−1,000µV − High Speed Op Amps: 100−2,000µV − Untrimmed CMOS Op Amps: 5,000−50,000µV − DigiTrim CMOS Op Amps: <1,000µV Figure 1-37: Input offset voltage Chopper stabilized op amps have a VOS that is less than 1 µV (AD8551 series), and the best precision bipolar op amps (super-beta or bias stabilized) can have offsets as low as 25 µV (OP177F). The very best trimmed FET types have about 100 µV of offset (AD8610B), and untrimmed CMOS op amps can range from 5 mV to 50 mV. However, the ADI DigiTrim CMOS op amps have offset voltages less than 1 mV (AD8605). Generally speaking, “precision” op amps will have VOS < 0.5 mV, although some high speed amplifiers may be a little worse than this. 51 Chapter One Measuring input offset voltages of a few microvolts requires that the test circuit does not introduce more error than the offset voltage itself. Figure 1-38 shows a standard circuit for measuring offset voltage. The circuit amplifies the input offset voltage by the noise gain of 1001. The measurement is made at the amplifier output using an accurate digital voltmeter. The offset referred to the input (RTI) is calculated by dividing the output voltage by the noise gain. The small source resistance seen by the inputs results in negligible bias current contribution to the measured offset voltage. For example, 2 nA bias current flowing through the 10 Ω resistor produces a 0.02 µV error referred to the input. As simple as this circuit looks, it can give inaccurate results when testing precision op amps, unless care is taken in implementation. The largest potential error source comes from parasitic thermocouple junctions, formed where two different metals are joined. This thermocouple voltage can range from 2 µV/ºC to more than 40 µV/ºC. Note that in this circuit additional “dummy” resistors have been added to the noninverting input, in order to exactly match/balance the thermocouple junctions in the inverting input path. R2, 10kΩ R1, 10Ω +VS ∼ – VOUT = 1 + VOS 10Ω R2 V OS R1 VOUT = 1001• VOS + –VS VOS = VOUT 1001 10kΩ For OP177F: V OS = 25µV max @ 25C VOS DRIFT = 0.1µV/°C maximum VOS STABILITY = 0.3µV/month typical Figure 1-38: Measuring input offset voltage The accuracy of the measurement also depends on the mechanical layout of the components and exactly how they are placed on the PC board. Keep in mind that the two connections of a component such as a resistor create two equal, but opposite polarity thermoelectric voltages (assuming they are connected to the same metal, such as the copper trace on a PC board). These will cancel each other, assuming both are at exactly the same temperature. Clean connections and short lead lengths help to minimize temperature gradients and increase the accuracy of the measurement. Note—see the Chapter 7 discussions on this general topic for more detail. In the test circuit, airflow should be minimal so that all the thermocouple junctions stabilize at the same temperature. In some cases, the circuit should be placed in a small closed container to eliminate the effects of external air currents. The circuit should be placed flat on a surface so that convection currents flow up and off the top of the board, not across the components, as would be the case if the board were mounted vertically. Measuring the offset voltage shift over temperature is an even more demanding challenge. Placing the printed circuit board containing the amplifier being tested in a small box or plastic bag with foam insulation prevents the temperature chamber air current from causing thermal gradients across the parasitic thermocouples. If cold testing is required, a dry nitrogen purge is recommended. Localized temperature cycling of the amplifier itself using a Thermostream-type heater/cooler may be an alternative, but these units tend to generate quite a bit of airflow that can be troublesome. 52 Op Amp Basics Generally, the test circuit of Figure 1-38 can be made to work for many amplifiers. Low absolute values for the small resistors (such as 10 Ω) will minimize bias current induced errors. An alternate VOS measurement method is shown in Figure 1-39, and is suitable for cases of high and/or unequal bias currents (as in the case of current feedback op amps). In this measurement method, an in amp is connected to the op amp input terminals through isolation resistors, and provides the gain for the measurement. The offset voltage of the in amp (measured with S closed) must then be subtracted from the final VOS measurement. Also, the circuit shown in Figure 1-44, for measuring input bias currents, can also be used to measure input offset voltage independent of bias currents. RP Figure 1-39: Alternate input offset voltage measurement using an in amp + DUT R1 − R2 1kΩ 1kΩ + S ∆VO = 1000VOS VO RG IN-AMP − G = 1000 Offset Adjustment (Internal Method) Many single op amps have pins available for optional offset null. To make use of this feature, two pins are joined by a potentiometer, and the wiper goes to one of the supplies through a resistor, as shown generally in Figure 1-40. Note that if the wiper is accidentally connected to the wrong supply, the op amp will probably be destroyed—this is a common problem, when one op amp type is replaced by another. The range of offset adjustment in a well-designed op amp is no more than two or three times the maximum VOS of the R1 +VS * R2 7 2 − 1 8 6 3 + 4 −VS • * Wiper connection may be to either +VS or –VS depending on op amp • R values depend on op amp. Consult data sheet • Use to null out input offset voltage, not system offsets • There may be high gain from offset pins to output — Keep them quiet • Nulling offset causes increase in offset temperature coefficient, µ V/°C for 1mV offset null for FET inputs approximately 4µ Figure 1-40: Offset adjustment pins 53 Chapter One lowest grade device, in order to minimize sensitivity. Nevertheless, the voltage gain of an op amp at its offset adjustment pins may actually be greater than the gain at its signal inputs. It is therefore very important to keep these pins noise free. Note that it is never advisable to use long leads from an op amp to a remote nulling potentiometer. As mentioned above, the offset drift of an op amp with temperature will vary with the setting of its offset adjustment. The internal adjustment terminals should therefore be used only to adjust the op amp’s own offset, not to correct any system offset errors, since doing so would be at the expense of increased temperature drift. The drift penalty for a FET input op amp is on the order of 4 µV/°C for each millivolt of nulled offset voltage. It is generally better to control offset voltage by proper device/grade selection. Offset Adjustment (External Methods) If an op amp doesn’t have offset adjustment pins (popular duals and all quads do not), and it is still necessary to adjust the amplifier and system offsets, an external method can be used. This method is also most useful if the offset adjustment is to be done with a system programmable voltage, such as a DAC. With an inverting op amp configuration, injecting current into the inverting input is the simplest method, as shown in Figure 1-41A. The disadvantage of this method is that some increase in noise gain is possible, due to the parallel path of R3 and the potentiometer resistance. The resulting increase in noise gain may be reduced by making ±VR large enough so that the R3 value is much greater than R1||R2. Note that if the power supplies are stable and noise free, they can be used as ±VR. Figure 1-41B shows how to implement offset trim by injecting a small offset voltage into the noninverting input. This circuit is preferred over Figure 1-41A, as it results in no noise gain increase (but it requires adding RP). If the op amp has matched input bias currents, RP should equal R1|| R2 (to minimize the added offset voltage). Otherwise, RP should be less than 50 Ω. For higher values, it may be advisable to bypass RP at high frequencies. R2 (A) R1 VIN R2 (B) R1 VIN – – VOUT VOUT + + NOISE GAIN = R3 RA –VR R2 1+ R1||(R3 + R A ||R B ) R3 RB RA +VR VOUT = – R2 VIN ± R2 VR R3 R1 –VR RP NOISE GAIN = R2 1 + R1 RB +VR VOUT = – R2 VIN ± 1 + R2 R1 R1 RP RP + R3 VR MAX OFFSET MAX OFFSET RP = R1||R2 IF IB+ ≈ IB- RP ≤ 50Ω IF IB+ ≠ IB- Figure 1-41: Inverting op amp external offset trim methods The circuit shown in Figure 1-42 can be used to inject a small offset voltage when using an op amp in the noninverting mode. This circuit works well for small offsets, where R3 can be made much greater than R1. Note that otherwise, the signal gain might be affected as the offset potentiometer is adjusted. The gain may be stabilized, however, if R3 is connected to a fixed low impedance reference voltage source, ±VR. 54 Op Amp Basics VIN + Figure 1-42: Noninverting op amp external offset trim methods VOUT – R2 R1 NOISE GAIN = 1 + R3 RA –VR R2 R1||(R3 + R A||R B ) RB +VR R2 R2 VOUT ≈ 1 + R1 VIN ± R3 VR MAX OFFSET FOR R3 >> R1 Input Offset Voltage Drift and Aging Effects Input offset voltage varies with temperature, and its temperature coefficient is known as TCVOS, or more commonly, drift. As we have mentioned, offset drift is affected by offset adjustments to the op amp, but when it has been minimized, it may be as low as 0.1 µV/°C (typical value for OP177F). More typical drift values for a range of general purpose precision op amps lie in the range 1−10 µV/°C. Most op amps have a specified value of TCVOS, but instead, some have a second value of maximum VOS that is guaranteed over the operating temperature range. Such a specification is less useful, because there is no guarantee that TCVOS is constant or monotonic. The offset voltage also changes as time passes, or ages. Aging is generally specified in µV/month or µV/1000 hours, but this can be misleading. Since aging is a “drunkard’s walk” phenomenon it is proportional to the square root of the elapsed time. An aging rate of 1 µV/1000 hour therefore becomes about 3 µV/year (not 9 µV/year). Long-term stability of the OP177F is approximately 0.3 µV/month. This refers to a time period after the first 30 days of operation. Excluding the initial hour of operation, changes in the offset voltage of these devices during the first 30 days of operation are typically less than 2 µV. Input Bias Current, IB Ideally, no current flows into the input terminals of an op amp. In practice, there are always two input bias currents, IB+ and IB– (see Figure 1-43). + IB+ Figure 1-43: Op amp input bias current IB− – • A very variable parameter • I B can vary from 60 fA (1 electron every 3 µs) to many µA, depending on the device. • Some structures have well-matched I B , others do not. • Some structures’ I B varies little with temperature, but a FET op amp’s I B doubles with every 10°C rise in temperature. • Some structures have I B that may flow in either direction. 55 Chapter One Values of IB range from 60 fA (about one electron every three microseconds) in the AD549 electrometer, to tens of microamperes in some high speed op amps. Op amps with simple input structures using BJT or FET long-tailed pair have bias currents that flow in one direction. More complex input structures (biascompensated and current feedback op amps) may have bias currents that are the difference between two or more internal current sources, and may flow in either direction. Bias current is a problem to the op amp user because it flows in external impedances and produces voltages, which add to system errors. Consider a noninverting unity gain buffer driven from a source impedance of 1 MΩ. If IB is 10 nA, it will introduce an additional 10 mV of error. This degree of error is not trivial in any system. If the designer simply forgets about IB and uses capacitive coupling, the circuit won’t work—at all. Or, if IB is low enough, it may work momentarily while the capacitor charges, giving even more misleading results. The moral here is not to neglect the effects of IB, in any op amp circuit. The same admonition goes for in amp circuits. Input bias current (or input offset voltage) may be measured using the test circuit of Figure 1-44. To measure IB, a large resistance, RS, is inserted in series with the input under test, creating an apparent additional offset voltage equal to IB × RS. If the actual VOS has previously been measured and recorded, the change in apparent VOS due to the change in RS can be determined, and IB is then easily computed. This yields values for IB+ and IB–. The rated value of IB is the average of the two currents, or IB = (IB– + IB–)/2. S1 100Ω – 10kΩ RS S2 – DUT 100Ω VO + RS + R2 RS >> 100Ω (100kΩ TO 1GΩ) S1 CLOSED TO TEST IB+ VO = 1+ R2 100 VOS + 1+ R2 100 IB+ RS – 1+ R2 100 IB− RS S2 CLOSED TO TEST IB− BOTH CLOSED TO TEST V OS BOTH OPEN TO TEST I OS Figure 1-44: Measuring input bias current The input offset current, IOS, may also be calculated, by taking the difference between IB– and IB+, or IOS = IB+ – IB–. Typical useful RS values vary from 100 kΩ for bipolar op amps to 1000 MΩ for some FET input devices. Note also that IOS is only meaningful where the two individual bias currents are fundamentally reasonably well-matched, to begin with. This is true for most VFB op amps. However, it wouldn’t, for example, be meaningful to speak of IOS for a CFB op amp, as the currents are radically unmatched. 56 Op Amp Basics Extremely low input bias currents must be measured by integration techniques. The bias current in question is used to charge a capacitor, and the rate of voltage change is measured. If the capacitor and general circuit leakage is negligible (this is very difficult for currents under 10 fA), the current may be calculated directly from the rate of change of the output of the test circuit. Figure 1-45 illustrates the general concept. With one switch open and the opposite closed, either IB+ or IB– is measured. S2 Figure 1-45: Measuring very low bias currents C IB– – VO DUT IB+ + ∆ VO ∆t C = IB = C IB C ∆ VO ∆t OPEN S1 TO MEASURE I B+ OPEN S2 TO MEASURE I B– It should be obvious that only a premium capacitor dielectric can be used for C, for example Teflon or polypropylene types. Canceling the Effects of Bias Current (External to the Op Amp) When the bias currents of an op amp are well matched (the case with simple bipolar op amps, but not internally bias compensated ones, as noted previously), a bias compensation resistor, R3, (R3 = R1||R2) introduces a voltage drop in the noninverting input to match and thus compensate the drop in the parallel combination of R1 and R2 in the inverting input. This minimizes additional offset voltage error, as in Figure 1-46. Note that if R3 is more than 1 kΩ or so, it should be bypassed with a capacitor to prevent noise pickup. Also note that this form of bias cancellation is useless where bias currents are not well-matched, and will, in fact, make matters worse. R2 Figure 1-46: Canceling the effects of input bias current within an application R1 – IB– IB+ VO + R3 = R1 || R2 VO = R2 (IB– – IB+ ) = R2 IOS = 0, IF IB+ = IB– NEGLECTING V OS 57 Chapter One Calculating Total Output Offset Error Due to IB and VOS The equations shown in Figure 1-47 are useful in referring all the offset voltage and induced offset voltage from bias current errors to either the input (RTI) or the output (RTO) of the op amp. The choice of RTI or RTO is a matter of preference. GAIN FROM = "A" TO OUTPUT B R1 IB– VOS A NOISE GAIN = R2 NG = 1 + R1 R2 ∼ – VOUT R3 IB+ + OFFSET (RTO) = VOS 1 + R2 R1 OFFSET (RTI ) = VOS + IB+ • R3 R2 GAIN FROM = – "B" TO OUTPUT R1 1+ R2 R1 + IB+ • R3 – IB– • R2 – IB– R1•R2 R1 + R2 FOR BIAS CURRENT CANCELLATION: OFFSET (RTI) = VOS R1•R2 IF IB+ = IB– AND R3 = R1 + R2 Figure 1-47: Op amp total offset voltage model The RTI value is useful in comparing the cumulative op amp offset error to the input signal. The RTO value is more useful if the op amp drives additional circuitry, to compare the net errors with that of the next stage. In any case, the RTO value is obtained by multiplying the RTI value by the stage noise gain, which is 1 + R2/R1. Before departing the topic of offset errors, some simple rules towards minimization might bear repetition: • Keep input/feedback resistance values low, to minimize offset voltage due to bias current effects. • Use a bias compensation resistance with VFB op amps not using internal bias compensation. Bypass this resistance, for lowest noise pickup. • If a VFB op amp does use internal bias current compensation, don’t use the compensation resistance. • When necessary, use external offset trim networks, for lowest induced drift. • Select an appropriate precision op amp specified for low offset and drift, as opposed to trimming. • For high performance low drift circuitry, watch out for thermocouple effects and used balanced, low thermal error layouts. 58 Op Amp Basics Input Impedance VFB op amps normally have both differential and common-mode input impedances specified. Current feedback op amps normally specify the impedance to ground at each input. Different models may be used for different voltage feedback op amps, but in the absence of other information, it is usually safe to use the model in Figure 1-48. In this model, the bias currents flow into the inputs from infinite impedance current sources. The common-mode input impedance data sheet specification (Zcm+ and Zcm–) is the impedance from either input to ground (NOT from both to ground). The differential input impedance (Zdiff) is the impedance IB+ IB– Zdiff – INPUT + INPUT Zcm – Zcm+ • Z cm+ and Z cm – are the common-mode input impedance. The figure on the data sheet is for one, not both, but they are approximately equal. Z diff is the differential input impedance. • They are high resistance (10 5 − 1012 Ω) in parallel with a small • shunt capacitance (sometimes as high as 25pF). • In most practical circuits, Z cm – is swamped by negative feedback. Figure 1-48: Input impedance (voltage feedback op amp) between the two inputs. These impedances are usually resistive and high (105 Ω–1012 Ω) with some shunt capacitance (generally a few pF, sometimes 20 pF–25 pF). In most op amp circuits, the inverting input impedance is reduced to a very low value by negative feedback, and only Zcm+ and Zdiff are of importance. A current feedback op amp is even more simple, as shown in Figure 1-49. Z+ is resistive, generally with some shunt capacitance, and high (105 Ω–109 Ω) while Z– is reactive (L or C, depending on the device) but has a resistive component of 10 Ω–100 Ω, varying from type to type. ×1 +INPUT – INPUT Z– Z+ • Z+ is high resistance (10 5 − 10 9Ω) with little shunt capacitance. • Z− is low and may be reactive (L or C). The resistive component is 10-100Ω. Figure 1-49: Input impedance (current feedback op amp) 59 Chapter One Manipulating Op Amp Noise Gain and Signal Gain Consider an op amp and two resistors, R1 and R2, arranged as shown in the series of figures of Figure 1-50. Note that R1 and R2 need not be resistors; they could also be complex impedances, Z1 and Z2. − IN R2 R1 − + R1 (B) R2 (C) − + R1 (A) + IN R2 IN R3 Signal Gain = 1 + R2/R1 Signal Gain = – R2/R1 Signal Gain = – R2/R1 Noise Gain = 1 + R2/R1 Noise Gain = 1 + R2/R1 Noise Gain = 1 + R2 R1||R3 • Voltage Noise and Offset Voltage of the op amp are reflected to the output by the Noise Gain. • Noise Gain, not Signal Gain, is relevant in assessing stability. • Circuit C has unchanged Signal Gain, but higher Noise Gain, thus better stability, worse noise, and higher output offset voltage. Figure 1-50: Manipulating op amp noise gain and signal gain If we ground R1 and apply a signal to the noninverting input, we see a signal gain of 1 + R2/R1, as in Figure 1-50A. If we ground the noninverting input and apply the signal to R1, we see a signal gain of –R2/R1, as in Figure 1-50B. In both cases, the voltage noise of the op amp itself (as well as the input offset voltage) sees a gain of 1 + R2/R1, i.e., the noise gain of the op amp, as discussed earlier in this chapter. This discussion is aimed at making the point that a stage’s noise gain and signal gain need not necessarily be equal. Some times it can be to the user’s advantage to manipulate them, so as to be somewhat independent of one another. But, importantly, it is the noise gain that is relevant in assessing stability. It is sometimes possible to alter the noise gain, while leaving signal gain unaffected. When this is done, a marginally stable op amp stage can sometimes be made stable, with the same signal gain. For example, consider the inverting amplifier of Figure 1-50B. If we add a third resistor to Figure 1-50B, it becomes Figure 1-50C. This dummy resistor R3, from the inverting input to ground, increases the noise gain to 1 + R2/(R1||R3). But, note the signal gain is unaffected; that is it is still −R2/R1. This provides a means of stabilizing an unstable inverting amplifier—at a cost of worse signal-to-noise ratio, less loop gain, and increased sensitivity to input offset voltage. Nevertheless, it is still a sometimes useful trick. Open-Loop Gain And Open-Loop Gain Nonlinearity Open-loop voltage gain, usually called AVOL (sometimes simply AV), for most VFB op amps is quite high. Common values are 100,000 to 1,000,000, and 10 or 100 times these figures for high precision parts. 60 Op Amp Basics Some fast op amps have appreciably lower open-loop gain, but gains of less than a few thousand are unsatisfactory for high accuracy use. Note also that open-loop gain isn’t highly stable with temperature. It can vary quite widely from device to device of the same type, so it is important that it be reasonably high. Since a voltage feedback op amp operates as voltage in/voltage out, its open-loop gain is a dimensionless ratio, so no unit is necessary. However, data sheets sometimes express gain in V/mV or V/µV instead of V/V, for the convenience of using smaller numbers. Or, voltage gain can also be expressed in dB terms, as gain in dB = 20 × logAVOL. Thus an open-loop gain of 1 V/µV is equivalent to 120 dB, and so on. CFB op amps have a current input and a voltage output, so their open-loop transimpedance gain is expressed in volts per ampere or ohms (or kΩ or MΩ). Values usually lie between hundreds of kΩ and tens of MΩ. From basic feedback theory, it is understood that in order to maintain accuracy, a precision amplifier’s dc open-loop gain, AVOL, should be high. This can be seen by examining the closed-loop gain equation, including errors due to finite gain. The expression for closed loop gain with a finite gain error is: G CL 1 1 = • 1 β 1 + A β VOL Eq. 1-15A Since noise gain is equal to 1/β, there are alternate forms of this expression. Combining the two right side terms and using the NG expression, an alternate one is: G CL = NG NG 1+ A VOL Eq. 1-15B Eqs. 1-15A and 1-15B are equivalent, and either can be used. As previously discussed, noise gain (NG) is simply the gain seen by a small voltage source in series with the op amp input, and is also the ideal amplifier signal gain in the noninverting mode. If AVOL in Eqs. 1-15A and 1-15B is infinite, the closed-loop gain becomes exactly equal to the noise gain, 1/β. However, for NG << AVOL and finite AVOL, there is a closed-loop gain error estimation: Closed loop error (%) ≈ NG • 100 A VOL Eq. 1-16 Note that the expression of Eq. 1-16 is equivalent to the earlier mentioned Eq. 1-11, when 1/β is substituted for NG. Again, either form can be used, at the user’s discretion. Notice from Eq. 1-16 that the percent gain error is directly proportional to the noise gain, therefore the effects of finite AVOL are less for low gain. Some examples illustrate key points about these gain relationships. 61 Chapter One In Figure 1-51, the first example for a NG of 1000 shows that for an open-loop gain of 2 million, the closedloop gain error is about 0.05%. Note that if the open-loop gain stays constant over temperature and for various output loads and voltages, the 0.05% gain error can easily be calibrated out of the measurement, and then there is then no overall system gain error. If, however, the open-loop gain changes, the resulting closed-loop gain will also change. This introduces a gain uncertainty. In the second example, AVOL drops to 300,000, which produces a gain error of 0.33%. This situation introduces a gain uncertainty of 0.28% in the closedloop gain. In most applications, when using a good amplifier, the gain resistors of the circuit will be the largest source of absolute gain error, but it should be noted that gain uncertainty cannot be removed by calibration. • “IDEAL” CLOSED LOOP GAIN = 1/β= NOISE GAIN (NG) • ACTUAL CLOSED LOOP GAIN = 1• 1 1 β 1+ A VOL β • CLOSED LOOP GAIN ERROR (%) ≈ = 1+ NG × 100 A VOL NG NG A VOL (NG << A VOL ) − Ex. 1: Assume A VOL = 2,000,000, NG = 1,000 % Gain Error ≈ 0.05% − Ex. 2: Assume A VOL Drops to 300,000 % Gain Error ≈ 0.33% − Closed Loop Gain Uncertainty = 0.33% – 0.05% = 0.28% Figure 1-51: Changes in open-loop gain cause closed-loop gain uncertainty Changes in the output voltage level and output loading are the most common causes of changes in the open-loop gain of op amps. A change in open-loop gain with signal level produces a nonlinearity in the closed-loop gain transfer function, which also cannot be removed during system calibration. Most op amps have fixed loads, so AVOL changes with load are not generally important. However, the sensitivity of AVOL to output signal level may increase for higher load currents. The severity of this nonlinearity varies widely from one device type to another, and generally isn’t specified on the data sheet. The minimum AVOL is always specified, and choosing an op amp with a high AVOL will minimize the probability of gain nonlinearity errors. Gain nonlinearity can come from many sources, depending on the design of the op amp. One common source is thermal feedback (for example, from a hot output stage back to the input stage). If temperature shift is the sole cause of the nonlinearity error, it can be assumed that minimizing the output loading will help. To verify this, the nonlinearity is measured with no load, and then compared to the loaded condition. An oscilloscope X-Y display test circuit for measuring dc open-loop gain nonlinearity is shown in Figure 1-52. The same precautions previously discussed relating to the offset voltage test circuit must also be observed in this circuit. The amplifier is configured for a signal gain of –1. The open-loop gain is defined as the change in output voltage divided by the change in the input offset voltage. However, for large values of AVOL, the actual offset may change only a few microvolts over the entire output voltage swing. Therefore the divider consisting of the 10 Ω resistor and RG (1 MΩ) forces the node voltage VY to be: R VY = 1 + G VOS = 100,001 • VOS ⋅ 10Ω 62 Eq. 1-17 Op Amp Basics VY 10kΩ NONLINEAR RG 1MΩ ±10V RAMP VOS VY = 100001•VOS 10kΩ +15V IDEAL – A VOL = 10kΩ –VREF (–10V) + +VREF 10kΩ VX VX 10Ω 10Ω ∆VX ∆VOS RL –15V (+10V) OFFSET ADJUST (Multi-Turn Film-Type) CLOSED LOOP GAIN NONLINEARITY ≈ NG • OPEN LOOP GAIN NONLINEARITY ≈ NG • 1 1 – A VOL,MIN A VOL,MAX Figure 1-52: Circuit measures open-loop gain nonlinearity The value of RG is chosen to give measurable voltages at VY, depending on the expected values of VOS. The ±10 V ramp generator output is multiplied by the signal gain, –1, and forces the op amp output voltage VX to swing from +10 V to –10 V. Because of the gain factor applied to the offset voltage, the offset adjust potentiometer is added to allow the initial output offset to be set to zero. The resistor values chosen will null an input offset voltage of up to ±10 mV. Stable 10 V voltage references such as the AD688 should be used at each end of the potentiometer to prevent output drift. Note also that the ramp generator frequency must be quite low, probably no more than a fraction of 1 Hz because of the low corner frequency of the openloop gain (0.1 Hz for the OP177). The plot on the right-hand side of Figure 1-52 shows VY plotted against VX. If there is no gain nonlinearity, the graph will have a constant slope and AVOL is calculated as follows: A VOL = ∆V R ∆V ∆VX = 1 + G X = 100,001 • X ⋅ ∆VOS 10 Ω ∆VY ∆VY Eq. 1-18 If there is nonlinearity, AVOL will vary dynamically as the output signal changes. The approximate openloop gain nonlinearity is calculated based on the maximum and minimum values of AVOL over the output voltage range: Open-Loop Gain Nonlinearity = 1 A VOL,MIN − 1 A VOL,MAX ⋅ Eq. 1-19 The closed-loop gain nonlinearity is obtained by multiplying the open-loop gain nonlinearity by the noise gain, NG: 1 1 Closed-Loop Gain Nonlinearity ≈ NG • − ⋅ A VOL,MIN A VOL,MAX Eq. 1-20 In an ideal case, the plot of VOS versus VX would have a constant slope, and the reciprocal of the slope is the open-loop gain, AVOL. A horizontal line with zero slope would indicate infinite open-loop gain. In an actual op amp, the slope may change across the output range because of nonlinearity, thermal feedback, and so forth. In fact, the slope can even change sign. 63 Chapter One Figure 1-53 shows the VY (and VOS) versus VX plot for an OP177 precision op amp. The plot is shown for two different loads, 2 kΩ and 10 kΩ. The reciprocal of the slope is calculated based on the end points, and the average AVOL is about 8 million. The maximum and minimum values of AVOL across the output voltage range are measured to be approximately 9.1 million, and 5.7 million, respectively. This corresponds to an open-loop gain nonlinearity of about 0.07 ppm. Thus, for a noise gain of 100, the corresponding closedloop gain nonlinearity is about 7 ppm. These nonlinearity measurements are, of course, most applicable to high precision dc circuits. But they are also applicable to wider bandwidth applications, such as audio. The X-Y display technique of Figure 1-52 will easily show for example, crossover distortion in a poorly designed op amp output stage. RL = 10kΩ VY 50mV/DIV. A VOL = VOS (0.5µV/DIV.) (RTI) –10V ?VX ∆V ?VOS ∆V RL = 2kΩ 0 VX = OUTPUT VOLTAGE A VOL (AVERAGE) +10V ≈ 8 million A VOL,MAX ≈ 9.1 million, A VOL,MIN ≈ 5.7million ≈ 0.07ppm OPEN-LOOP GAIN NONLINEARITY CLOSED-LOOP GAIN NONLINEARITY ≈ NG × 0.07ppm Figure 1-53: OP177 gain nonlinearity Op Amp Frequency Response There are a number of issues to consider when discussing the frequency response of op amps. Some are relevant to both voltage and current feedback op amp types, some apply to one or the other, but not to both. Issues that vary with type are usually related to small signal performance, while large-signal issues mostly apply to both. A good working definition of “large-signal” is where the output voltage swing/frequency limit is set by the slew rate measured at the output stage, rather than the pole(s) of the small signal response. We shall therefore consider large signal parameters applying to both types of op amp before we consider those parameters where they differ. Frequency Response—Slew Rate and Full-Power Bandwidth The slew rate (SR) of an amplifier is the maximum rate of change of voltage at its output. It is expressed in V/s (or, more probably, V/µs). We have mentioned earlier why op amps might have different slew rates during positive-and negative-going transitions, but for this analysis we shall assume that good fast op amps have reasonably symmetrical slew rates. If we consider a sine wave signal with a peak-to-peak amplitude of 2 Vp and of a frequency f, the expression for the output voltage is: V (t ) = Vp sin 2 πft. 64 Eq. 1-21 Op Amp Basics This sine wave signal has a maximum rate of change (slope) at the zero crossing. This maximum rate of change is: dV = 2 πfVp dt max Eq. 1-22 To reproduce this signal without distortion, an amplifier must be able to respond in terms of its output voltage at this rate (or faster). When an amplifier reaches its maximum output rate of change, or slew rate, it is said to be slew limiting (sometimes also called rate limiting). Thus, we can see that the maximum signal frequency at which slew limiting does not occur is directly proportional to the signal slope, and inversely proportional to the amplitude of the signal. This allows us to define the full power bandwidth (FPBW) of an op amp, which is the maximum frequency at which slew limiting doesn’t occur for rated voltage output. It is calculated by letting 2 Vp in Eq. 1-22 equal the maximum peak-to-peak swing of the amplifier, dV/dt equal the amplifier slew rate, and solving for f: FPBW = Slew Rate / 2 πVp Eq. 1-23 It is important to realize that both slew rate and full-power bandwidth can also depend somewhat on the power supply voltage being used, and the load the amplifier is driving (particularly if it is capacitive). The key issues regarding slew rate and full-power bandwidth are summarized in Figure 1-54. As a point of reference, an op amp with a 1 V peak output swing reproducing a 1MHz sine wave must have a minimum SR of 6.28 V/µs. • Slew Rate = Maximum rate at which the output voltage of an op amp can change • Ranges: A few volts/µs to several thousand volts/µs • For a sinewave, VOUT = Vp sin2πft dV/dt = (dV/dt) max = 2 πfV p cos2 πft 2πfV p • If 2V p = full output span of op amp, then Slew Rate = (dV/dt) MAX = 2π·FPBW·Vp FPBW = Slew Rate / 2 πVp Figure 1-54: Slew rate and full-power bandwidth Realistically, for a practical circuit the designer would choose an op amp with an SR in excess of this figure, since real op amps show increasing distortion prior to reaching the slew limit point. 65 Chapter One Frequency Response—Settling Time The settling time of an amplifier is defined as the time it takes the output to respond to a step change of input and come into, and remain within, a defined error band, as measured relative to the 50% point of the input pulse, as shown in Figure 1-55. OUTPUT ERROR BAND DEAD TIME SLEW RECOVERY TIME TIME SETTLING TIME FINAL SETTLING • Error band is usually defined to be a percentage of the step 0.1%, 0.05%, 0.01%, etc. • Settling time is nonlinear; it may take 30 times as long to settle to 0.01% as to 0.1%. • Manufacturers often choose an error band that makes the op amp look good. Figure 1-55: Settling time Unlike a DAC device, there is no natural error band for an op amp (a DAC naturally has an error band of 1 LSB, or perhaps ±1 LSB). So, one must be chosen and defined, along with other definitions, such as the step size (1 V, 5 V, 10 V, and so forth). What is chosen will depend on the performance of the op amp, but since the value chosen will vary from device to device, comparisons are often difficult. This is true because settling is not linear, and many different time constants may be involved. Examples are early op amps using dielectrically isolated (DI) processes. These had very fast settling to 1% of full scale, but they took almost forever to settle to 10 bits (0.1 %). Similarly, some very high precision op amps have thermal effects that cause settling to 0.001% or better to take tens of ms, although they will settle to 0.025% in a few µs. It should also be noted that thermal effects can cause significant differences between short-term settling time (generally measured in nanoseconds) and long-term settling time (generally measured in microseconds or milliseconds). In many ac applications, long-term settling time is not important; but if it is, it must be measured on a much different time scale than short-term settling time. Measuring fast settling time to high accuracy is very difficult. Great care is required in order to generate fast, highly accurate, low noise, flat-top pulses. Large amplitude step voltages will overdrive many oscilloscope front ends, when the input scaling is set for high sensitivity. The example test setup shown in Figure 1-56 is useful in making settling time measurements on op amps operating in the inverting mode. The signal at the “false summing node” represents the difference between the output and the input signal, multiplied by the constant k, i.e., the ERROR signal. Many subtleties are involved in making this setup work reliably. The resistances should low in value, to minimize parasitic time constants. The back-back Schottky diode clamps help prevent scope overdrive, and allow high sensitivity. If R1 = R2, then k = 0.5. Thus the error band at the ERROR output will be 5 mV for 0.1% settling with a 10 V input step. 66 Op Amp Basics ERROR R R2 − V1 R1 V2 + ERROR = k(V 1 − V2), k= R1 R1 + R2 Figure 1-56: Measuring settling time using a “false summing node” In some cases, a second (very fast) amplifier stage may be used after the false summing node, to increase the signal level. In any case, to ensure validity, testing of settling time must be done with a test setup identical to that used by the op amp manufacturer. Many modern digitizing oscilloscopes are insensitive to input overdrive and can be used to measure the ERROR waveform directly—this must be verified for each oscilloscope by carefully examining the operating manual. Note that a direct measurement allows measurements of settling time in both the inverting and noninverting modes. An example of the output step response to a flat pulse input for the AD8039 op amp is shown in Figure 1-57. Notice that the settling time to 0.1% is approximately 18 ns. OUTPUT 2mV (0.1%) / DIV INPUT 0.5V/DIV 5ns/DIV 18ns Figure 1-57: AD8039 G = +2 settling time measured directly In making settling time measurements of this type, it is also imperative to use a pulse generator source capable of generating a pulse of sufficient flatness. In other words, if the op amp under test has a settling time of 20 ns to 0.1%, the applied pulse should settle to better than 0.05% in less than 5 ns. 67 Chapter One This type of generator can be expensive, but a simple circuit, as shown in Figure 1-58, can be used with a reasonably flat generator to ensure a flat pulse output. The circuit of Figure 1-58 works best if low capacitance Schottky diodes are used for D1–D2–D3, and the lead lengths on all the connections are minimized. A short length of 50 Ω coax can be used to connect the pulse generator to the circuit; however, best results are obtained if the test fixture is connected directly to the output of the generator. The pulse generator is adjusted to output a positive-going pulse at “A” which rises from approximately –1.8 V to +0.5 V in less than 5 ns (assuming the settling time of the DUT is in the order of 20 ns). Shorter rise times may generate ringing, and longer rise times can degrade the DUT settling time; therefore, some optimization is required in the actual circuit to get best performance. When the pulse generator output “A” goes above 0 V, D1 begins to conduct, and D2/D3 are reverse biased. The “0 V” region of the signal “B” at the input of the DUT is flat “by definition”—neglecting the leakage current and stray capacitance of the D2–D3 series combination. The D1 diode and its 100 Ω resistor help maintain an approximate 50 Ω termination during the time the pulse at “A” is positive. “FLAT” REGION +0.5V 0V –1V –1.8V B A 50Ω COAX PULSE GENERATOR (50Ω OUTPUT) DIRECT CONNECTION PREFERRED D2 100Ω D3 D1 + DUT – 100Ω 100Ω R1 R2 MAKE AS SHORT AS POSSIBLE, USE GROUND PLANE Figure 1-58: A simple flat pulse generator Frequency Response—Voltage Feedback Op amps, Gain-Bandwidth Product The open-loop frequency response of a voltage feedback op amp is shown in Figure 1-59. There are two possibilities: Figure 1-59A shows the most common, where a high dc gain drops at 6 dB/octave from quite a low frequency down to unity gain. This is a classic single pole response. By contrast, the amplifier in Figure 1-59B has two poles in its response—gain drops at 6 dB/octave for a while, and then drops at OPEN LOOP GAIN dB 6 dB/Octave OPEN LOOP GAIN dB 6 dB/Octave 12 dB/ Octave LOG f LOG f Full Compensated Decompensated Figure 1-59: Frequency response of voltage feedback op amps 68 Op Amp Basics 12 dB/octave. The amplifier in Figure 1-59A is known as an unconditionally stable or fully compensated type and may be used with a noise gain of unity. This type of amplifier is stable with 100% feedback (including capacitance) from output to inverting input. Compare this to the amplifier in Figure 1-59B. If this op amp is used with a noise gain that is lower than the gain at which the slope of the response increases from 6 dB to 12 dB/octave, the phase shift in the feedback will be too great, and it will oscillate. Amplifiers of this type are characterized as “stable at gains ≥ X” where X is the gain at the frequency where the 6 dB/12 dB transition occurs. Note that here it is, of course, the noise gain that is being referenced. The gain level for stability might be between 2 and 25, typically quoted behavior might be “gain-of-five-stable,” and so forth. These decompensated op amps do have higher gain bandwidth products than fully compensated amplifiers, all other things being equal. So they are useful, despite the slightly greater complication of designing with them. But, unlike their fully compensated op amp relatives, a decompensated op amp can never be used with direct capacitive feedback from output to inverting input. The 6 dB/octave slope of the response of both types means that over the range of frequencies where this slope occurs, the product of the closed-loop gain and the 3 dB closed-loop bandwidth at that gain is a constant —this is known as the gain bandwidth product (GBW) and is a figure of merit for an amplifier. For example, if an op amp has a GBW product of X MHz, its closed-loop bandwidth at a noise gain of 1 will be X MHz, at a noise gain of 2 it will be X/2 MHz, and at a noise gain of Y it will be X/Y MHz (see Figure 1-60). Notice that the closed-loop bandwidth is the frequency at which the noise gain plateau intersects the open-loop gain. GAIN dB OPEN LOOP GAIN, A(s) IF GAIN BANDWIDTH PRODUCT = X THEN Y · f CL = X X Y WHERE f CL = CLOSED-LOOP BANDWIDTH f CL = NOISE GAIN = Y Y=1+ R2 R1 LOG f f CL Figure 1-60: Gain-bandwidth product for voltage feedback op amps In the above example, it was assumed that the feedback elements were resistive. This is not usually the case, especially when the op amp requires a feedback capacitor for stability. 69 Chapter One Figure 1-61 shows a typical example where there is capacitance, C1, on the inverting input of the op amp. This capacitance is the sum of the op amp internal capacitance, plus any external capacitance that may exist. This always-present capacitance introduces a pole in the noise gain transfer function. − R1 + R3 GAIN dB R2 1 + C1/C2 1 + R2/R1 NOISE GAIN C1 f CL C2 LOG f Figure 1-61: Bode plot showing noise gain for voltage feedback op amp with resistive and reactive feedback elements The net slope of the noise gain curve and the open-loop gain curve, at the point of intersection, determines system stability. For unconditional stability, the noise gain must intersect the open-loop gain with a net slope of less than 12 dB/octave (20 dB per decade). Adding the feedback capacitor, C2, introduces a zero in the noise gain transfer function, which stabilizes the circuit. Notice that in Figure 1-61 the closed-loop bandwidth, fcl, is the frequency at which the noise gain intersects the open-loop gain. The Bode plot of the noise gain is a very useful tool in analyzing op amp stability. Constructing the Bode plot is a relatively simple matter. Although it is outside the scope of this section to carry the discussion of noise gain and stability further, the reader is referred to Reference 1 for an excellent treatment of constructing and analyzing Bode plots. Second-order systems related to noise analysis are discussed later in this section. Frequency Response—Current Feedback Op Amps Current feedback op amps do not behave in the same way as voltage feedback types. They are not stable with capacitive feedback, nor are they so with a short circuit from output to inverting input. With a CFB op amp, there is generally an optimum feedback resistance for maximum bandwidth. Note that the value of this resistance may vary with supply voltage—consult the device data sheet. If the feedback resistance is increased, the bandwidth is reduced. Conversely, if it is reduced, bandwidth increases, and the amplifier may become unstable. In a CFB op amp, for a given value of feedback resistance (R2), the closed-loop bandwidth is largely unaffected by the noise gain, as shown in Figure 1-62. Thus it is not correct to refer to gain bandwidth product, for a CFB amplifier, because of the fact that it is not constant. Gain is manipulated in a CFB op amp application by choosing the correct feedback resistor for the device (R2), and then selecting the bottom resistor (R1) to yield the desired closed loop gain. The gain relationship of R2 and R1 is identical to the case of a VFB op amp (Figure 1-14). Typically, CFB op amp data sheets will provide a table of recommended resistor values that provide maximum bandwidth for the device, over a range of both gain and supply voltage. It simplifies the design process considerably to use these tables. 70 Op Amp Basics GAIN dB G1 G1 · f 1 G2 · f 2 G2 f1 f2 LOG f • Feedback resistor fixed for optimum performance. Larger values reduce bandwidth, smaller values may cause instability. • For fixed feedback resistor, changing gain has little effect on bandwidth. • Current feedback op amps do not have a fixed gain-bandwidth product. Figure 1-62: Frequency response for current feedback op amps Bandwidth Flatness In demanding applications such as professional video, it is desirable to maintain a relatively flat bandwidth and linear phase up to some maximum specified frequency, and simply specifying the 3dB bandwidth isn’t enough. In particular, it is customary to specify the 0.1 dB bandwidth, or 0.1 dB bandwidth flatness. This means there is no more than 0.1 dB ripple up to a specified 0.1 dB bandwidth frequency. Video buffer amplifiers generally have both the 3 dB and the 0.1 dB bandwidth specified. Figure 1-63 shows the frequency response of the AD8075 triple video buffer. Note that the 3 dB bandwidth is approximately 400 MHz. This can be determined from the response labeled “GAIN” in the graph, and the corresponding gain scale is shown on the left-hand vertical axis (at a scaling of 1 dB/division). 3dB BANDWIDTH ≈ 400MHz, 0.1dB BANDWIDTH ≈ 65MHz Figure 1-63: 3 dB and 0.1 dB bandwidth for the AD8075, G = 2, triple video buffer, RL = 150 Ω 71 Chapter One The response scale for “FLATNESS” is on the right-hand vertical axis, at a scaling of 0.1 d B/division in this case. This allows the 0.1 dB bandwidth to be determined, which is about 65 MHz in this case. The general point to be noted here is the major difference in the applicable bandwidth between the 3 dB and 0.1 dB criteria. It requires a 400 MHz bandwidth amplifier (as conventionally measured) to provide the 65 MHz 0.1 dB flatness rating. It should be noted that these specifications hold true when driving a 75 Ω source and load terminated cable, which represents a resistive load of 150 Ω. Any capacitive loading at the amplifier output will cause peaking in the frequency response, and must be avoided. Operational Amplifier Noise This section discusses the noise generated within op amps, not the external noise they may pick up. External noise is also important, and is discussed in detail in Chapter 7; in this section we are concerned solely with internal noise. There are three noise sources in an op amp: a voltage noise, which appears differentially across the two inputs, and two current noise sources, one in each input. The simple voltage noise op amp model is shown in Figure 1-64. The three noise sources are effectively uncorrelated (independent of each other). There is a slight correlation between the two noise currents, but it is too small to need consideration in practical noise analyses. In addition to these three internal noise sources, it is necessary to consider the Johnson noise of the external gain-setting resistors that are used with the op amp. – VN + • Input Voltage Noise is bandwidth dependent and measured in nV/√Hz (noise spectral density) • Normal Ranges are 1 nV/√Hz to 20 nV/√Hz Figure 1-64: Input voltage noise All resistors have a Johnson noise of where k is Boltzmann’s Constant (1.38 × 10–23J/K), T is the absolute temperature, B is the bandwidth, and R is the resistance. Note that this is an intrinsic property—it is not possible to obtain resistors that do not have Johnson noise. The simple model is shown in Figure 1-65. Uncorrelated noise voltages add in a “root-sum-of-squares” manner; i.e., noise voltages V1, V2, V3 give a summed result of . Noise powers, of course, add normally. Thus, any noise voltage that is more than 3 to 5 times any of the others is dominant, and the others may generally be ignored. This simplifies noise assessment. The voltage noise of different op amps may vary from under 1 nV Hz to 20 nV Hz, or even more. Bipolar op amps tend to have lower voltage noise than JFETs, although it is possible to make JFET op amps with low voltage noise (such as the AD743/AD745), at the cost of large input devices, and hence large input capacitance. Voltage noise is specified on the data sheet, and it isn’t possible to predict it from other parameters. 72 Op Amp Basics VNR R • ALL resistors have a voltage noise of VNR =√( 4kTBR) • T = Absolute Temperature = T(°C) + 273.15 • B = Bandwidth (Hz) • k = Boltzmann’s Constant (1.38 x 10 –23J/K) • A 1000 Ω resistor generates 4nV/√Hz @ 25°C Figure 1-65: Johnson noise of resistors Current noise can vary much more widely, dependent upon the input structure. It ranges from around 0.1 fA Hz (in JFET electrometer op amps) to several pA Hz (in high speed bipolar op amps). It isn’t always specified on data sheets, but may be calculated in cases like simple BJT or JFETs, where all the bias current flows in the input junction, because in these cases it is simply the Schottky (or shot) noise of the bias current. , where IB is the bias current (in amps) and q is the Shot noise spectral density is simply charge on an electron (1.6 × 10–19 C). It can’t be calculated for bias-compensated or current feedback op amps, where the external bias current is the difference of two internal currents. A simple current noise model is shown in Figure 1-66. − IN– IN+ + • Normal Ranges: 0.1fA/√Hz to 10pA/√Hz • In Voltage Feedback op amps, the current noise in the inverting and noninverting inputs is uncorrelated (effectively) but roughly equal in magnitude. • In simple BJT and JFET input stages, the current noise is the shot noise of the bias current and may be calculated from the bias current. • In bias-compensated input stages and in current feedback op amps, the current noise cannot be calculated. • The current noise in the two inputs of a current feedback op amp may be quite different. They may not even have the same 1/f corner. Figure 1-66: Input current noise Current noise is only important when it flows in an impedance, and thus generates a noise voltage. Maintaining relatively low impedances at the input of an op amp circuit contributes markedly to minimizing the effects of current noise (just as doing the same thing also aids in minimizing offset voltage). 73 Chapter One It is logical therefore that the optimum choice of a low noise op amp depends on the impedances around it. This will be illustrated with the aid of some impedance examples, immediately below. Consider for example an OP27, an op amp with low voltage noise (3 nV Hz ), but quite high current noise (1 pA Hz ). With zero source impedance, the voltage noise will dominate as shown in Figure 1-67 (left column). With a source resistance of 3 kΩ (center column), the current noise of (1 pA Hz) flowing in 3 kΩ will equal the voltage noise, but the Johnson noise of the 3 kΩ resistor is (7 nV Hz) and is dominant. With a source resistance of 300 kΩ (right column), the current noise portion increases 100 × to 300 nV Hz , voltage noise continues unchanged, and the Johnson noise (which is proportional to the resistance square root) increases tenfold. Current noise dominates. The above example shows that the choice of a low noise op amp depends on the source impedance of the signal, and at high impedances, current noise always dominates. EXAMPLE: OP27 Voltage Noise = 3nV/√Hz Current Noise = 1pA /√Hz T = 25°C + OP27 R CONTRIBUTION FROM AMPLIFIER VOLTAGE NOISE AMPLIFIER CURRENT NOISE FLOWING IN R VALUES OF R 0 3kΩ 3 3 3 0 3 300 0 7 70 300kΩ – R2 R1 Neglect R1 and R2 Noise Contribution JOHNSON NOISE OF R RTI NOISE (nV/√Hz) Dominant Noise Source is Highlighted Figure 1-67: Different noise sources dominate at different source impedances From Figure 1-68, it should be apparent that different amplifiers are best at different source impedances. For low impedance circuits, low voltage noise amplifiers such as the OP27 will be the obvious choice, since they are inexpensive, and their comparatively large current noise will not affect the application. At medium resistances, the Johnson noise of resistors is dominant, while at very high source resistance, we must choose an op amp with the smallest possible current noise, such as the AD549 or AD795. Until recently, BiFET amplifiers tended to have comparatively high voltage noise (though very low current noise), and were thus more suitable for low noise applications in high rather than low impedance circuitry. The AD795, AD743, and AD745 have very low values of both voltage and current noise. The AD795 specifications at 10 kHz are 10 nV Hz and 0.6 fA Hz , and the AD743/AD745 specifications at 10 kHz are 2.9 nV Hz and 6.9 fA Hz . These make possible the design of low-noise amplifier circuits that have low noise over a wide range of source impedances. The noise figure of an amplifier is the amount (in dB) by which the noise of the amplifier exceeds the noise of a perfect noise-free amplifier in the same environment. The concept is useful in RF and TV applications, where 50 Ω and 75 Ω transmission lines and terminations are ubiquitous, but is useless for an op amp that is used in a wide range of electronic environments. Noise figure related to communications applications is discussed in more detail in Chapter 6 (Section 6-4). Voltage noise spectral density and current noise spectral density are generally more useful specifications in most cases. 74 Op Amp Basics 100 100 RS = 100Ω 741 744 744 795 OP07 10 741 RS = 10k Ω OP27, 795 10 743 OP07, 743 OP27 1 1 10 100 1k 10k 10 100 1k 10k 10k RS = 1MΩ 741 ALL VERTICAL SCALES nV/√Hz ALL HORIZONTAL SCALES Hz OP27 1k 744 743 795 OP07 100 10 100 1k 10k Figure 1-68: Different amplifiers are best at different source impedances So far, we have assumed that noise is white (i.e., its spectral density does not vary with frequency). This is true over most of an op amp’s frequency range, but at low frequencies the noise spectral density rises at 3 dB/octave, as shown in Figure 1-69. The power spectral density in this region is inversely proportional to frequency, and therefore the voltage noise spectral density is inversely proportional to the square root of the frequency. For this reason, this noise is commonly referred to as 1/f noise. Note, however, that some textbooks still use the older term flicker noise. The frequency at which this noise starts to rise is known as the 1/f corner frequency (FC) and is a figure of merit—the lower it is, the better. The 1/f corner frequencies are not necessarily the same for the voltage noise and the current noise of a particular amplifier, and a current feedback op amp may have three 1/f corners: for its voltage noise, its inverting input current noise, and its noninverting input current noise. NOISE n/√Hz or µV/√Hz 3dB/Octave en , i n = k FC 1 f 1 CORNER f en , i n WHITE NOISE k FC LOG f • 1/f Corner Frequency is a figure of merit for op amp noise performance (the lower the better) • Typical Ranges: 2Hz to 2kHz • Voltage Noise and Current Noise do not necessarily have the same 1/f corner frequency Figure 1-69: Frequency characteristic of op amp noise 75 Chapter One The general equation which describes the voltage or current noise spectral density in the 1/f region is e n , i n , = k Fc 1 , f Eq. 1-24 where k is the level of the “white” current or voltage noise level, and FC is the 1/f corner frequency. The best low frequency low noise amplifiers have corner frequencies in the range 1 Hz–10 Hz, while JFET devices and more general-purpose op amps have values in the range to 100 Hz. Very fast amplifiers however may make compromises in processing to achieve high speed which result in quite poor 1/f corners of several hundred Hz or even 1 kHz–2 kHz. This is generally unimportant in the wideband applications for which they were intended, but may affect their use at audio frequencies, particularly for equalized circuits. Popcorn Noise Popcorn noise is so-called because when played through an audio system, it sounds like cooking popcorn. It consists of random step changes of offset voltage that take place at random intervals in the 10+ millisecond timeframe. Such noise results from high levels of contamination and crystal lattice dislocation at the surface of the silicon chip, which in turn results from inappropriate processing techniques or poor quality raw materials. When monolithic op amps were first introduced in the 1960s, popcorn noise was a dominant noise source. Today, however, the causes of popcorn noise are well understood, raw material purity is high, contamination is low, and production tests for it are reliable so that no op amp manufacturer should have any difficulty in shipping products that are substantially free of popcorn noise. For this reason, it is not even mentioned in most modern op amp textbooks. RMS Noise Considerations As was discussed above, noise spectral density is a function of frequency. In order to obtain the RMS noise, the noise spectral density curve must be integrated over the bandwidth of interest. In the 1/f region, the RMS noise in the bandwidth FL to FC is given by v n,rms (FL , FC ) = v nw FC FC 1 ∫ f df = v nw FL F FC ln C FL Eq. 1-25 where vnw is the voltage noise spectral density in the “white” region, FL is the lowest frequency of interest in the 1/f region, and FC is the 1/f corner frequency. The next region of interest is the “white” noise area which extends from FC to FH. The RMS noise in this bandwidth is given by v n,rms (FC , FH ) = v nw FH − FC Eq. 1-26 Eq. 1-25 and Eq. 1-26 can be combined to yield the total RMS noise from FL to FH: F v n,rms (FL , FH ) = v nw FC In C + (FH − FC ) FL Eq. 1-27 In many cases, the low frequency p-p noise is specified in a 0.1 Hz to 10 Hz bandwidth, measured with a 0.1 Hz to 10 Hz bandpass filter between op amp and measuring device. 76 Op Amp Basics The measurement is often presented as a scope photo with a time scale of 1s/div, as shown in Figure 1-70 for the OP213. 1s 100 90 .... .... .... .... .... .... .... .... .... .... 20nV/div. (RTI) 120nV 10 0 .... .... .... .... .... .... .... .... .... .... 20mV 1s/div. 900Ω − 100Ω TO SCOPE ACTIVE BPF 0.1 − 10Hz GAIN = 1000 OP213 G = 100 TOTAL GAIN = 1,000,000 + NOISE GAIN = 10 Figure 1-70: The peak-to-peak noise in the 0.1 Hz to 10 Hz bandwidth for the OP213 is less than 120 nV It is possible to relate the 1/f noise measured in the 0.1 Hz to 10 Hz bandwidth to the voltage noise spectral density. Figure 1-71 shows the OP177 input voltage noise spectral density on the left-hand side of the diagram, and the 0.1 Hz to 10 Hz peak-to-peak noise scope photo on the right-hand side. Eq. 1-26 can be used to calculate the total RMS noise in the bandwidth 0.1 Hz to 10 Hz by letting FL = 0.1 Hz, FH = 10 Hz, FC = 0.7 Hz, v nw = 10 nV Hz . The value works out to be about 33 nV RMS, or 218 nV peak-to-peak (obtained by multiplying the RMS value by 6.6—see the following discussion). This compares well to the value of 200 nV as measured from the scope photo. INPUT VOLTAGE NOISE, nV/√Hz 0.1Hz to 10Hz VOLTAGE NOISE 30 25 1/F CORNER FC = 0.7Hz 20 200nV 15 v nw (WHITE) 10 5 0.1 1 10 FREQUENCY (Hz) TIME - 1sec/DIV. 100 Vn,rms (FL , FH) = v nw FC ln FC FL + (FH – FC) For F L = 0.1Hz, FH = 10Hz, v nw = 10nV/√Hz, FC = 0.7Hz: Vn,rms = 33nV Vn,pp = 6.6 × 33nV = 218nV Figure 1-71: Input voltage noise for the OP177 77 Chapter One It should be noted that at higher frequencies, the term in the equation containing the natural logarithm becomes insignificant, and the expression for the RMS noise becomes: Vn,rms (FH , FL ) ≈ v nw FH − FL Eq. 1-28 Vn,rms (FH ) ≈ v nw FH Eq. 1-29 And, if FH >> FL, However, some op amps (such as the OP07 and OP27) have voltage noise characteristics that increase slightly at high frequencies. The voltage noise versus frequency curve for op amps should therefore be examined carefully for flatness when calculating high frequency noise using this approximation. At very low frequencies when operating exclusively in the 1/f region, FC >> (FH – FL), and the expression for the RMS noise reduces to: F Vn,rms (FH , FL ) ≈ Vnw FC 1n H ⋅ FL Eq. 1-30 Note that there is no way of reducing this 1/f noise by filtering if operation extends to dc. Making FH = 0.1 Hz and FL = 0.001 still yields an RMS 1/f noise of about 18 nV RMS, or 119 nV peak-to-peak. The point is that averaging results of a large number of measurements over a long period of time has practically no effect on the RMS value of the 1/f noise. A method of reducing it further is to use a chopperstabilized op amp, to remove the low frequency noise. In practice, it is virtually impossible to measure noise within specific frequency limits with no contribution from outside those limits, since practical filters have finite roll-off characteristics. Fortunately, measurement error introduced by a single pole low-pass filter is readily computed. The noise in the spectrum above the single pole filter cutoff frequency, fc, extends the corner frequency to 1.57 fc. Similarly, a two pole filter has an apparent corner frequency of approximately 1.2 fc. The error correction factor is usually negligible for filters having more than two poles. The net bandwidth after the correction is referred to as the filter equivalent noise bandwidth (see Figure 1-72). GAUSSIAN NOISE SOURCE SINGLE POLE LOWPASS FILTER, f C IDENTICAL LEVELS GAUSSIAN NOISE SOURCE SAME RMS NOISE LEVEL BRICK WALL LOWPASS FILTER, 1.57f C EQUIVALENT NOISE BANDWIDTH = 1.57 × f C Figure 1-72: Equivalent noise bandwidth 78 Op Amp Basics It is often desirable to convert RMS noise measurements into peak-to-peak. In order to do this, one must have some understanding of the statistical nature of noise. For Gaussian noise and a given value of RMS noise, statistics tell us that the chance of a particular peak-to-peak value being exceeded decreases sharply as that value increases—but this probability never becomes zero. Thus, for a given RMS noise, it is possible to predict the percentage of time that a given peak-to-peak value will be exceeded, but it is not possible to give a peak-to-peak value which will never be exceeded as shown in Figure 1-73. Nominal Peak-to-Peak % of the Time Noise will Exceed Nominal Peak-to-Peak Value 2 × rms 32% 3 × rms 13% 4 × rms 4.6% 5 × rms 1.2% 6 × rms 0.27% 6.6 × rms* 0.10% 7 × rms 0.046% 8 × rms 0.006% *Most often used conversion factor is 6.6 Figure 1-73: RMS to peak-to-peak ratios Peak-to-peak noise specifications, therefore, must always be written with a time limit. A suitable one is 6.6 times the RMS value, which is exceeded only 0.1% of the time. Total Output Noise Calculations We have already pointed out that any noise source that produces less than one-third to one-fifth of the noise of some greater source can be ignored, with little error. When so doing, both noise voltages must be measured at the same point in the circuit. To analyze the noise performance of an op amp circuit, we must assess the noise contributions of each part of the circuit, and determine which are significant. To simplify the following calculations, we shall work with noise spectral densities, rather than actual voltages, to leave bandwidth out of the expressions (the noise spectral density, which is generally expressed in , is equivalent to the noise in a 1 Hz bandwidth). 79 Chapter One If we consider the circuit in Figure 1-74, which is an amplifier consisting of an op amp and three resistors (R3 represents the source resistance at node A), we can find six separate noise sources: the Johnson noise of the three resistors, the op amp voltage noise, and the current noise in each input of the op amp. Each source has its own contribution to the noise at the amplifier output. Noise is generally specified RTI, or referred to the input, but it is often simpler to calculate the noise referred to the output (RTO) and then divide it by the noise gain (not the signal gain) of the amplifier to obtain the RTI noise. VN,R2 B VN,R1 ∼ VN 4kTR1 A VN,R3 ∼ R3 NOISE GAIN = R2 R1 4kTR2 IN– R1 GAIN FROM = “A” TO OUTPUT R2 ∼ ∼ NG = 1 + – CLOSED LOOP BW = f CL IN+ VOUT R2 GAIN FROM = – “B” TO OUTPUT R1 + 4kTR3 VN2 RTI NOISE = BW • + 4kTR3 4kTR1 + 4kTR2 2 R1•R2 + IN+2R32 + IN–2 R1+R2 RTO NOISE = NG • RTI NOISE + R2 R1+R2 R1 R1+R2 2 2 BW = 1.57 f CL Figure 1-74: Op amp noise model for single-pole system Figure 1-75 is a detailed analysis of how each of the noise sources in Figure 1-74 is reflected to the output of the op amp. Some further discussion regarding the effect of the current noise at the inverting input is warranted. This current, IN–, does not flow in R1, as might be expected—the negative feedback around the amplifier works to keep the potential at the inverting input unchanged, so that a current flowing from that pin is forced, by negative feedback, to flow in R2 only, resulting in a voltage at the output of IN– R2. We could equally well consider the voltage caused by IN– flowing in the parallel combination of R1 and R2 and then amplified by the noise gain of the amplifier, but the results are identical—only the calculations are more involved. NOISE SOURCE EXPRESSED AS A VOLTAGE MULTIPLY BY THIS FACTOR TO REFER TO THE OP AMP OUTPUT Johnson noise in R3: √(4kTR3) Noise Gain = 1 + R2/R1 Noninverting input current noise flowing in R3: IN + R3 Noise Gain = 1 + R2/R1 Input voltage noise: VN Noise Gain = 1 + R2/R1 Johnson noise in R1: √(4kTR1) –R2/R1 (Gain from input of R1 to output) Johnson noise in R2: √(4kTR2) 1 Inverting input current noise flowing in R2: IN – R2 1 Figure 1-75: Noise sources referred to the output (RTO) 80 Op Amp Basics Notice that the Johnson noise voltage associated with the three resistors has been included in the expressions of Figure 1-75. All resistors have a Johnson noise of , where k is Boltzmann’s Constant (1.38 × 10–23 J/K), T is the absolute temperature, B is the bandwidth in Hz, and R is the resistance in Ω. A simple relationship which is easy to remember is that a 1000 Ω resistor generates a Johnson noise of 4 nV Hz at 25ºC. The analysis so far assumes that the feedback network is purely resistive and that the noise gain versus frequency is flat. This applies to most applications, but if the feedback network contains reactive elements (usually capacitors) the noise gain is not constant over the bandwidth of interest, and more complex techniques must be used to calculate the total noise (see in particular, Reference 2 and Chapter 4, Section 4-4 of this book). The circuit shown in Figure 1-76 represents a second-order system, where capacitor C1 represents the source capacitance, stray capacitance on the inverting input, the input capacitance of the op amp, or any combination of these. C1 causes a breakpoint in the noise gain, and C2 is the capacitor that must be added to obtain stability. C2 C1 B VN,R1 VN,R2 R1 ∼ VN,R3 ∼ IN– VN 4kTR1 A R2 ∼ R3 4kTR2 ∼ – VOUT IN+ + 4kTR3 Figure 1-76: Op amp noise model with reactive elements (second-order system) Because of C1 and C2, the noise gain is a function of frequency, and has peaking at the higher frequencies (assuming C2 is selected to make the second-order system critically damped). Textbooks state that a flat noise gain can be achieved if one simply makes R1C1 = R2C2. But in the case of current-to-voltage converters, however, R1 is typically a high impedance, and the method doesn’t work. Maximizing the signal bandwidth in these situations is somewhat complex and is treated in detail in Section 1-6 of this chapter and in Chapter 4, Section 4-4 of this book. A dc signal applied to input A (B being grounded) sees a gain of 1 + R2/R1, the low frequency noise gain. At higher frequencies, the gain from input A to the output becomes 1 + C1/C2 (the high frequency noise gain). The closed-loop bandwidth, fcl, is the point at which the noise gain intersects the open-loop gain. A dc signal applied to B (A being grounded) sees a gain of –R2/R1, with a high frequency cutoff determined by R2-C2. Bandwidth from B to the output is 1/2πR2C2. The current noise of the noninverting input, IN+, flows in R3 and gives rise to a noise voltage of IN + R3, which is amplified by the frequency-dependent noise gain, as are the op amp noise voltage, VN, and the Johnson noise of R3, which is . The Johnson noise of R1 is amplified by –R2/R1 over a bandwidth of 81 Chapter One 1/2πR2C2, and the Johnson noise of R2 is not amplified at all but is connected directly to the output over a bandwidth of 1/2πR2C2. The current noise of the inverting input, IN–, flows in R2 only, resulting in a voltage at the amplifier output of IN–R2 over a bandwidth of 1/2πR2C2. If we consider these six noise contributions, we see that if R1, R2, and R3 are low, the effect of current noise and Johnson noise will be minimized, and the dominant noise will be the op amp’s voltage noise. As we increase resistance, both Johnson noise and the voltage noise produced by noise currents will rise. If noise currents are low, Johnson noise will take over from voltage noise as the dominant contributor. Johnson noise, however, rises with the square root of the resistance, while the current noise voltage rises linearly with resistance so, ultimately, as the resistance continues to rise, the voltage due to noise currents will become dominant. These noise contributions we have analyzed are not affected by whether the input is connected to node A or node B (the other being grounded or connected to some other low impedance voltage source), which is why the noninverting gain (1 + Z2/Z1), which is seen by the voltage noise of the op amp, VN, is known as the “noise gain.” Calculating the total output RMS noise of the second-order op amp system requires multiplying each of the six noise voltages by the appropriate gain and integrating over the appropriate frequency as shown in Figure 1-77. NOISE SOURCE EXPRESSED AS A VOLTAGE MULTIPLY BY THIS FACTOR TO REFER TO OUTPUT INTEGRATION BANDWIDTH Johnson noise in R3: √(4kTR3) Noise Gain as a function of frequency Closed-Loop BW Noninverting input current noise flowing in R3: IN+R3 Noise Gain as a function of frequency Closed-Loop BW Input voltage noise: VN Noise Gain as a function of frequency Closed-Loop BW Johnson noise in R1: √(4kTR1) –R2/R1 (Gain from B to output) 1/2πR2C2 Johnson noise in R2: √(4kTR2) 1 1/2πR2C2 Inverting input current noise flowing in R2: IN–R2 1 1/2πR2C2 Figure 1-77: Noise sources referred to the output for a second-order system The root-sum-square of all the output contributions thus represents the total RMS output noise. Fortunately, this cumbersome exercise may be greatly simplified in most cases by making the appropriate assumptions and identifying the chief contributors. Although shown, the noise gain for a typical second-order system is repeated in Figure 1-78. It is quite easy to perform the voltage noise integration in two steps, but notice that because of peaking, the majority of the output noise due to the input voltage noise will be determined by the high frequency portion where the noise gain is 1 + C1/C2. This type of response is typical of second-order systems. 82 Op Amp Basics C2 C1 OPEN-LOOP GAIN R1 B GAIN (dB) R2 – R3 + A 1 + C1/C2 1 + R2/R1 f CL = CLOSED-LOOP BANDWIDTH NOISE GAIN LOG f f CL Figure 1-78: Noise gain of a typical second-order system The noise due to the inverting input current noise, R1, and R2 is only integrated over the bandwidth 1/2πR2C2. Op Amp Distortion Dynamic range of an op amp may be defined in several ways. The most common are to specify harmonic distortion, total harmonic distortion (THD), or total harmonic distortion plus noise (THD + N). Other specifications related specifically to communications systems such as intermodulation distortion (IMD), intercept points (IP), spurious free dynamic range (SFDR), multitone power ratio (MTPR) and others are covered thoroughly in Chapter 6, Section 6-4. In this section, only harmonic distortion, THD, and THD + N will be covered. The distortion components that make up total harmonic distortion are usually calculated by taking the root sum of the squares of the first five or six harmonics of the fundamental. In many practical situations, however, there is negligible error if only the second and third harmonics are included. The definition of THD and THD + N is shown in Figure 1-79. • Vs = Signal Amplitude (RMS Volts) • V2 = Second Harmonic Amplitude (RMS Volts) • Vn = nth Harmonic Amplitude (RMS Volts) • Vnoise = RMS value of noise over measurement bandwidth • • THD + N = V22 + V32 + V42 + . . . + Vn 2 + Vnoise 2 Vs THD = V22 + V32 + V42 + . . . + Vn 2 Vs Figure 1-79: Definitions of THD and THD + N 83 Chapter One It is important to note that the THD measurement does not include noise terms, while THD + N does. The noise in the THD + N measurement must be integrated over the measurement bandwidth. In audio applications, the bandwidth is normally chosen to be around 100 kHz. In narrow-band applications, the level of the noise may be reduced by filtering. On the other hand, harmonics and intermodulation products which fall within the measurement bandwidth cannot be filtered, and therefore may limit the system dynamic range. Common-Mode Rejection Ratio (CMRR), Power Supply Rejection Ratio (PSRR) If a signal is applied equally to both inputs of an op amp, so that the differential input voltage is unaffected, the output should not be affected. In practice, changes in common-mode voltage will produce changes in output. The op amp common-mode rejection ratio (CMRR) is the ratio of the common-mode gain to differential-mode gain. For example, if a differential input change of Y volts produces a change of 1 V at the output, and a common-mode change of X volts produces a similar change of 1 V, the CMRR is X/Y. When the common-mode rejection ratio is expressed in dB, it is generally referred to as common-mode rejection (CMR). Typical LF CMR values are between 70 dB and 120 dB, but at higher frequencies CMR deteriorates. Many op amp data sheets show a plot of CMR versus frequency, as shown in Figure 1-80 for an OP177 op amp. 160 140 CMR dB 120 100 CMR = 20 log 10 CMRR 80 60 40 20 0 0.01 0.1 1 10 100 1k 10k 100k 1M FREQUENCY − Hz Figure 1-80: OP177 common-mode rejection (CMR) CMRR produces a corresponding output offset voltage error in op amps configured in the noninverting mode as shown in Figure 1-81. VIN = VCM + Figure 1-81: Calculating offset error due to common-mode rejection ratio (CMRR) VOUT – ERROR (RTI) = VCM = CMRR R1 R2 VOUT = 1 + R2 R1 ERROR (RTO) = 84 VIN + 1+ R2 R1 VIN CMRR VIN CMRR VIN CMRR Op Amp Basics Note inverting mode operating op amps will have negligible CMRR error, as both inputs are held at a ground (or virtual ground), i.e., there is no CM dynamic voltage. Common-mode rejection ratio can be measured in several ways. The method shown in Figure 1-82 uses four precision resistors to configure the op amp as a differential amplifier, a signal is applied to both inputs, and the change in output is measured—an amplifier with infinite CMRR would have no change in output. The disadvantage inherent in this circuit is that the ratio match of the resistors is as important as the CMRR of the op amp. A mismatch of 0.1% between resistor pairs will result in a CMR of only 66 dB—no matter how good the op amp. Since most op amps have a LF CMR of between 80 dB and 120 dB, it is clear that this circuit is only marginally useful for measuring CMRR (although it does an excellent job in measuring the matching of the resistors). R2 R1 − VIN VOUT DUT R1 + ∆VOUT = R2 ∆VIN CMRR (1 + R2 R1 ) RESISTORS MUST MATCH WITHIN 1 ppm (0.0001%) TO MEASURE CMRR > 100dB Figure 1-82: Simple common-mode rejection ratio (CMRR) test circuit The slightly more complex circuit, shown in Figure 1-83, measures CMRR without requiring accurately matched resistors. In this circuit, the common-mode voltage is changed by switching the power supply voltages. (This is easy to implement in a test facility, and the same circuit with different supply voltage connections can be used to measure power supply rejection ratio.) +25V +5V 10kΩ S1 10kΩ 100Ω + − 20kΩ A1 DUT 100Ω ±10V − ∆VOUT + 20kΩ CMRR = 101 20V ∆VOUT S2 –25V A1: HIGH GAIN, LOW V OS, LOW I B –5V Figure 1-83: CMRR test circuit does not require precision resistors 85 Chapter One The power supply values shown in the circuit are for a ±15 V DUT op amp, with a common-mode voltage range of ±10 V. Other supplies and common-mode ranges can also be accommodated by changing voltages, as appropriate. The integrating amplifier A1 should have high gain, low VOS, and low IB, such as an OP97 family device. If the supply of an op amp changes, its output should not, but it does. The specification of power supply rejection ratio or PSRR is defined similarly to the definition of CMRR. If a change of X volts in the supply produces the same output change as a differential input change of Y volts, the PSRR on that supply is X/Y. The definition of PSRR assumes that both supplies are altered equally in opposite directions—otherwise the change will introduce a common-mode change as well as a supply change, and the analysis becomes considerably more complex. It is this effect that causes apparent differences in PSRR between the positive and negative supplies. Typical PSR for the OP177 is shown in Figure 1-84. The test setup used to measure CMRR may be modified to measure PSRR as shown in Figure 1-85. The voltages are chosen for a symmetrical power supply change of 1 V. Other values may be used where appropriate. 160 140 120 PSR dB 100 PSR = 20 log 10 PSRR 80 60 40 20 0 0.01 0.1 1 10 100 1k 10k 100k 1M FREQUENCY − Hz Figure 1-84: OP177 power supply rejection +14V +15V 10kΩ S1 10kΩ 100Ω + − 20kΩ A1 DUT 100Ω 0V − ∆VOUT + 20kΩ PSRR = 101 1V ∆VOUT S2 –15V A1: HIGH GAIN, LOW V OS, LOW I B –14V Figure 1-85: Test setup for measuring power supply rejection ratio (PSRR) 86 Op Amp Basics Power Supplies and Decoupling Because op amp PSRR is frequency dependent, op amp power supplies must be well decoupled. At low frequencies, several devices may share a 10 µF–50 µF capacitor on each supply, provided it is no more than 10cm (PC track distance) from any of them. At high frequencies, each IC should have the supply leads decoupled by a low inductance 0.1 µF (or so) capacitor with short leads/PC tracks. These capacitors must also provide a return path for HF currents in the op amp load. Typical decoupling circuits are shown in Figure 1-86. Further bypassing and decoupling information is found Chapter 7. +VS + C3 = LARGE AREA GROUND PLANE < 10cm C1 = + C1, C2: LOCALIZED HF DECOUPLING, LOW INDUCTANCE CERAMIC, 0.1µF C3, C4: SHARED LF DECOUPLING, ELECTROLYTIC, 10µF TO 50µF – C2 < 10cm C4 + –VS LEAD LENGTH MINIMUM Figure 1-86: Proper low and high-frequency decoupling techniques for op amps Power Supplies and Power Dissipation Op amps have no ground terminal. Specifications of power supply are quite often in the form ±X Volts, but in fact it might equally be expressed as 2X Volts. What is important is where the CM and output ranges lie relative to the supplies. This information may be provided in tabular form or as a graph. Data sheets will often advise that an op amp will work over a range of supplies (from +3 V to ±16.5 V for example), and will then give parameters at several values of supply, so that users may extrapolate. If the minimum supply is quite high, it is usually because the device uses a structure requiring a threshold voltage to function (zener diode). Data sheets also give current consumption. Any current flowing into one supply pin will flow out of the other or out of the output terminal. When the output is open circuit, the dissipation is easily calculated from the supply voltage and current. When current flows in a load, it is easiest to calculate the total dissipation (remember that if the load is grounded to the center rail the load current flows from a supply to ground, not between supplies), and then subtract the load dissipation to obtain the device dissipation. Data sheets normally give details of thermal resistances and maximum junction temperature ratings, from which dissipation limits may be calculated knowing conditions. Details of further considerations relating to power dissipation, heatsinking, and so forth, can be found in Chapter 7, Section 7-5. 87 Chapter One References: Op Amp Specifications 1. James L. Melsa and Donald G. Schultz, Linear Control Systems, McGraw-Hill, 1969, pp. 196–220, ISBN: 0-07-041481-5. 2. Lewis Smith and Dan Sheingold, “Noise and Operational Amplifier Circuits,” Analog Dialogue, Vol. 3, No.1, pp. 1, 5–16. See also: Analog Dialogue 25th Anniversary Issue, pp. 19–31, 1991. 3. Thomas M. Frederiksen, Intuitive Operational Amplifiers, McGraw-Hill, 1988., ISBN: 0-07-021966-4. 4. Walter G. Jung, IC Op Amp Cookbook, 3rd Ed., Prentice-Hall PTR, 1986, 1997, ISBN: 0-13-889601-1. 5. J. K. Roberge, Operational Amplifiers-Theory and Practice, John Wiley, 1975, ISBN: 0-471-72585-4. 6. D. Stout, M. Kaufman, Handbook of Operational Amplifier Circuit Design, New York, McGrawHill, 1976, ISBN: 0-07-061797-X. 7. J. Dostal, Operational Amplifiers, Elsevier Scientific Publishing, New York, 1981, ISBN: 0-444-99760-1. 8. Paul R. Gray and Robert G. Meyer, Analysis and Design of Analog Integrated Circuits, 3rd Edition, John Wiley, 1993, ISBN: 0-471-57495-3. 9. Sergio Franco, Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., McGraw-Hill, 1998, ISBN: 0-07-021857-9. 10. Walt Kester, Editor, Linear Design Seminar, Analog Devices, Inc., 1995, ISBN: 0-916550-15-X. 11. Walt Kester, Editor, Practical Analog Design Techniques, Analog Devices, 1995, ISBN: 0-916550-16-8, (available for download at www.analog.com). 12. Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0-916550-17-6, (available for download at www.analog.com). 88 SECTION 1-5 Precision Op Amps Walt Kester, Walt Jung This section examines in more detail some of the issues relating to amplifiers for use in precision signal conditioning applications. Although the OP177 op amp is used for the “gold standard” for precision in these discussions, more recent product introductions such as the rail-to-rail output OP777, OP727, and OP747, along with the OP1177, OP2177, and OP4177 offer nearly as good performance in smaller packages. Precision op amp open-loop gains greater than 1 million are available, along with common-mode and power supply rejection ratios of the same magnitude. Offset voltages of less than 25 µV and offset drift less than 0.1 µV/°C are available in dual supply op amps such as the OP177, however, the performance in single-supply precision bipolar op amps may sometimes fall short of this performance. This is the trade-off that must sometimes be made in low power, low voltage applications. On the other hand, however, modern chopper stabilized op amps provide offsets and offset voltage drifts which cannot be distinguished from noise, and these devices operate on single supplies and provide rail-to-rail inputs and outputs. They, too, come with their own set of problems that are discussed later within this section. It is important to understand that dc open-loop gain, offset voltage, power supply rejection (PSR), and common-mode rejection (CMR) alone shouldn’t be the only considerations in selecting precision amplifiers. The ac performance of the amplifier is also important, even at “low” frequencies. Open-loop gain, PSR, and CMR all have relatively low corner frequencies; therefore, what may be considered “low” frequency may actually fall above these corner frequencies, increasing errors above the value predicted solely by the dc parameters. For example, an amplifier having a dc open-loop gain of 10 million and a unity-gain crossover frequency of 1 MHz has a corresponding corner frequency of 0.1 Hz. One must therefore consider the open-loop gain at the actual signal frequency. The relationship between the single-pole unity-gain crossover frequency, fu, the signal frequency, fsig, and the open-loop gain AVOL(fsig) (measured at the signal frequency) is given by: f A VOL f = u Eq. 1-31 (sig ) f sig In the example above, the open-loop gain is 10 at 100 kHz, and 100,000 at 10 Hz. Note that the constant gain-bandwidth product concept only holds true for VFB op amps. It doesn’t apply to CFB op amps, but then they are rarely used in precision applications. Loss of open-loop gain at the frequency of interest can introduce distortion, especially at audio frequencies. Loss of CMR or PSR at the line frequency or harmonics thereof can also introduce errors. The challenge of selecting the right amplifier for a particular signal conditioning application has been complicated by the sheer proliferation of various types of amplifiers in various processes (Bipolar, Complementary Bipolar, BiFET, CMOS, BiCMOS, and so forth) and architectures (traditional op amps, instrumentation amplifiers, chopper amplifiers, isolation amplifiers, and so forth) In addition, a wide selection of precision amplifiers which operate on single-supply voltages are now available which complicates the design process even further because of the reduced signal swings and voltage input and output restrictions. Offset voltage and noise are now a more significant portion of the input signal. 89 Chapter One Selection guides and parametric search engines, which can simplify this process somewhat, are available on the World Wide Web (www.analog.com) as well as on CDROM. Some general attributes of precision op amps are summarized in Figure 1-87. • Input Offset Voltage <100µV • Input Offset Voltage Drift <1µV/°C • Input Bias Current <2nA • Input Offset Current <2nA • DC Open-Loop Gain >1,000,000 • Unity Gain Bandwidth Product, fu 500kHz − 5MHz • Always Check Open Loop Gain at Signal Frequency • 1/f (0.1Hz to 10Hz) Noise <1µV p-p • Wideband Noise <10nV/√Hz • CMR, PSR >100dB • Trade-offs: − Single supply operation − Low supply currents Figure 1-87: Precision op amp characteristics Precision Op Amp Amplifier DC Error Budget Analysis In order to develop a concept for the magnitudes of the various errors in a high precision op amp circuit, a simple room temperature analysis for the OP177F is shown in Figure 1-88. The amplifier is connected in the inverting mode with a signal gain of 100. The key data sheet specifications are also shown in the diagram. We assume an input signal of 100 mV fullscale which corresponds to an output signal of 10 V. The various error sources are normalized to full-scale and expressed in parts per million (ppm). Note: parts per million (ppm) error = fractional error × 106 = % error × 104. VIN MAXIMUM ERROR CONTRIBUTION, + 25 °C FULLSCALE: V IN=100mV, V OUT = 10V 10kΩ – VOUT 100Ω VOS 25µV ÷ 100mV 250ppm IOS 100Ω ×1.5nA ÷ 100mV 1.5ppm A VOL (100/ 5×106) × 100mV 20ppm A VOL Nonlinearity 100 × 0.07ppm 7ppm 0.1Hz to 10Hz 1/f Noise 200nV ÷ 100mV 2ppm Total Unadjusted Error ≈ 12 Bits Accurate 280.5ppm Resolution Error ≈ 17 Bits Accurate 9ppm OP177F + SPECS @ 25°C: VOS = 25µV max IOS = 1.5nA max A VOL = 5 × 10 6 min A VOL Nonlinearity = 0.07ppm 0.1Hz to 10Hz Noise = 200nV RL 2kΩ Figure 1-88: Precision op amp (OP177F) dc error budget analysis 90 Op Amp Basics Note that the offset errors due to VOS and IOS and the gain error due to finite AVOL can be removed with a system calibration. However, the error due to open-loop gain nonlinearity cannot be removed with calibration and produces a relative accuracy error, often called resolution error. A second contributor to resolution error is the 1/f noise. This noise is always present and adds to the uncertainty of the measurement. The overall relative accuracy of the circuit at room temperature is 9ppm, equivalent to ~17 bits of resolution. It is also useful to compare the performance of a number of single-supply op amps to that of the “gold standard” OP177, and this is done in Figure 1-89 for some representative devices. Note that the Figure 1-89 amplifier list does not include the category of chopper op amps, which excel in many of the categories. These are covered separately, next. LISTED IN ORDER OF INCREASING SUPPLY CURRENT PART NO. VOS max VOS TC A VOL min NOISE (1kHz) INPUT I /AMP OUTPUT SY MAX OP293 250µV 2µV/°C 200k 5nV/√Hz 0, 4V 5mV, 4V 20µA OP196/296/496 300µV 2µV/°C 150k 26nV/√Hz R/R “R/R” 60µA OP777 100µV 1.3µV/°C 300k 15nV√Hz 0, 4V “R/R” 270µA OP191/291/491 700µV 5µV/°C 25k 35nV/√Hz R/R “R/R” 350µA 20µV/°C 500k 16nV/√Hz 0, 4V “R/R” 800µA *AD820/822/824 1000µV **AD8601/2/4 600µV 2µV/°C 20k 33nV/√Hz R/R “R/R” 1000µA OP184/284/484 150µV 2µV/°C 50k 3.9nV/√Hz R/R “R/R” 1350µA OP113/213/413 175µV 4µV/°C 2M 4.7nV/√Hz 0, 4V 5mV, 4V 3000µA OP177F (±15V) 25µV 0.1µV/°C 5M 10nV/√Hz N/A N/A 2000µA *JFET INPUT **CMOS NOTE: Unless Otherwise Stated Specifications are Typical @ 25°C VS = 5V Figure 1-89: Precision single-supply op amp performance characteristics 91 Chapter One Chopper Stabilized Amplifiers For the lowest offset and drift performance, chopper-stabilized amplifiers may be the only solution. The best bipolar amplifiers offer offset voltages of 25 µV and 0.1 µV/ºC drift. Offset voltages less than 5 µV with practically no measurable offset drift are obtainable with choppers, albeit with some penalties. A basic chopper amplifier circuit is shown in Figure 1-90. When the switches are in the “Z” (auto-zero) position, capacitors C2 and C3 are charged to the amplifier input and output offset voltage, respectively. When the switches are in the “S” (sample) position, VIN is connected to VOUT through the path comprised of R1, R2, C2, the amplifier, C3, and R3. The chopping frequency is usually between a few hundred Hz and several kHz, and it should be noted that because this is a sampling system, the input frequency must be much less than one-half the chopping frequency in order to prevent errors due to aliasing. The R1-C1 combination serves as an antialiasing filter. It is also assumed that after a steady state condition is reached, there is only a minimal amount of charge transferred during the switching cycles. The output capacitor, C4, and the load, RL, must be chosen such that there is minimal VOUT droop during the auto-zero cycle. CHOPPER SWITCH DRIVER VIN R1 R2 C2 S S = SAMPLE Z = AUTO-ZERO C3 R3 S VOUT AMP Z Z C1 C4 RL Figure 1-90: Classic chopper amplifier The basic chopper amplifier of Figure 1-90 can pass only very low frequencies because of the input filtering required to prevent aliasing. In contrast to this, the chopper-stabilized architecture shown in Figure 1-91 is most often used in chopper amplifier implementations. In this circuit, A1 is the main amplifier, and A2 is _ –IN VOUT A1 + +IN S NULL C1 S C2 Z S = SAMPLE Z = AUTO-ZERO Z _ NULL A2 + Figure 1-91: Modern chopper stabilized op amp 92 Op Amp Basics the nulling amplifier. In the sample mode (switches in “S” position), the nulling amplifier, A2, monitors the input offset voltage of A1 and drives its output to zero by applying a suitable correcting voltage at A1’s null pin. Note, however, that A2 also has an input offset voltage, so it must correct its own error before attempting to null A1’s offset. This is achieved in the auto-zero mode (switches in “Z” position) by momentarily disconnecting A2 from A1, shorting its inputs together, and coupling its output to its own null pin. During the auto-zero mode, the correction voltage for A1 is momentarily held by C1. Similarly, C2 holds the correction voltage for A2 during the sample mode. In modern IC chopper-stabilized op amps, the storage capacitors C1 and C2 are on-chip. Note in this architecture that the input signal is always connected to the output, through A1. The bandwidth of A1 thus determines the overall signal bandwidth, and the input signal is not limited to less than one-half the chopping frequency as in the case of the traditional chopper amplifier architecture. However, the switching action does produce small transients at the chopping frequency, which can mix with the input signal frequency and produce intermodulation distortion. A patented spread-spectrum technique is used in the AD8571/AD72/AD74 series of single-supply chopperstabilized op amps, to virtually eliminate intermodulation effects. These devices use a pseudorandom chopping frequency swept between 2 kHz and 4 kHz. Figure 1-92 compares the intermodulation distortion of a traditional chopper stabilized op amp (AD8551/AD52/AD54, left) that uses a fixed 4 kHz chopping frequency to that of the AD8571/AD72/AD74 (right) that uses the pseudorandom chopping frequency. AD8551/AD52/AD54 FIXED CHOPPING FREQUENCY: 4kHz AD8571/AD72/AD74 PSEUDORANDOM CHOPPING FREQ: 2kHz − 4kHz VS = 5V G = 60dB VS = 5V G = 60dB INPUT SIGNAL = 1mV RMS, 200Hz OUTPUT SIGNAL: 1V RMS, 200Hz GAIN = 60dB Figure 1-92: Intermodulation product: fixed pseudorandom chopping frequency 93 Chapter One A comparison between fixed and pseudorandom chopping on the voltage noise is shown in Figure 1-93. Notice for the fixed chopping frequency, there are distinct peaks in the noise spectrum at the odd harmonics of 4 kHz, whereas with pseudorandom chopping, the spectrum is much more uniform, although the average noise level is higher. AD8571/AD72/AD74 PSEUDORANDOM CHOPPING FREQUENCY 2kHz − 4kHz AD8551/AD52/AD54 FIXED CHOPPING FREQUENCY: 4kHz VS = 5V RS = 0Ω VS = 5V RS = 0Ω Figure 1-93: Voltage noise spectral density comparison: fixed versus pseudorandom chopping frequency The AD8571/AD8572/AD8574 family of chopper-stabilized op amps offers rail-to-rail input and output single-supply operation, low offset voltage, and low offset drift. As discussed above, the pseudorandom chopping frequency minimizes intermodulation distortion with the input signal. The storage capacitors are internal to the IC, and no external capacitors other than standard decoupling capacitors are required. Key specifications for the devices are given in Figure 1-94. • Single Supply: 2.7V to 5V • 1µV Typical Input Offset Voltage • 0.005µV/°C Typical Input Offset Voltage Drift • 130dB CMR, PSR • 750µA Supply Current/Op Amp • 50µs Overload Recovery Time • 50nV/√Hz Input Voltage Noise • Pseudorandom Chopping Frequency • 1.5MHz Gain-Bandwidth Product • Single (AD8571), Dual (AD8572) and Quad (AD8574) Figure 1-94: AD8571/AD72/AD74 chopper-stabilized rail-to-rail input/output amplifiers It should be noted that extreme care must be taken when applying all of the chopper-stabilized devices. This is because in order to fully realize the full offset and drift performance inherent to the parts, parasitic thermocouple effects in external circuitry must be avoided. See Chapter 4, Section 4-5 for a general discussion of thermocouples, and Chapter 7, Section 7-1 related to passive components. 94 Op Amp Basics Noise Considerations for Chopper-Stabilized Op Amps It is interesting to consider the effects of a chopper amplifier on low frequency 1/f noise. If the chopping frequency is considerably higher than the 1/f corner frequency of the input noise, the chopper-stabilized amplifier continuously nulls out the 1/f noise on a sample-by-sample basis. Theoretically, a chopper op amp therefore has no 1/f noise. However, the chopping action produces wideband noise which is generally much worse than that of a precision bipolar op amp. Figure 1-95 shows the noise of a precision bipolar amplifier (OP177) versus that of the AD8571/AD72/AD74 chopper-stabilized op amp. The peak-to-peak noise in various bandwidths is calculated for each in the table below the graphs. INPUT VOLTAGE NOISE, nV / √Hz 30 80 Bipolar: OP177 Chopper: AD8571/AD72/AD74 25 70 1/F CORNER FC = 0.7Hz 20 60 15 50 v nw (WHITE) 10 40 5 30 0.1 1 10 FREQUENCY (Hz) NOISE BW 0.1Hz to 10Hz 0.01Hz to 1Hz 0.001Hz to 0.1Hz 0.0001Hz to 0.01Hz 100 0.01 BIPOLAR (OP177) 0.238µV p-p 0.135µV p-p 0.120µV p-p 0.118µV p-p 0.1 1 FREQUENCY (Hz) 10 CHOPPER (AD8571/72/74) 1.3 µV p-p 0.41µV p-p 0.130µV p-p 0.042µV p-p Figure 1-95: Noise: bipolar versus chopper stabilized op amp Note from the data that as the frequency is lowered, the chopper amplifier noise continues to drop, while the bipolar amplifier noise approaches a limit determined by the 1/f corner frequency and its white noise. Notice that only at very low frequencies (<0.01 Hz) is the chopper noise performance superior to that of the bipolar op amp. In order to take advantage of the chopper op amp’s lack of 1/f noise, much filtering is required—otherwise the total noise of a chopper will always be worse than a good bipolar op amp. Choppers should therefore be selected on the basis of their low offset and drift—not because of their lack of 1/f noise. 95 Chapter One References: Precision Op Amps 1. Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN: 0-916550-10-9. 2. Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 3. Data Sheet for AD8551/AD8552/AD8554 Zero-Drift, Single-Supply, Rail-to-Rail Input/Output Operational Amplifiers, at www.analog.com. 4. Data Sheet for AD8571/AD8572/AD8574 Zero-Drift, Single-Supply, Rail-to-Rail Input/Output Operational Amplifiers, at www.analog.com. 5. Data Sheet for OP777/OP727/OP747 Precision Micropower Single-Supply Operational Amplifiers, at www.analog.com. 6. Data Sheet for OP1177/OP2177/OP4177 Precision Low Noise, Low Input Bias Current Operational Amplifiers, at www.analog.com. 96 SECTION 1-6 High Speed Op Amps Walt Kester Introduction High speed analog signal processing applications, such as video and communications, require op amps that have wide bandwidth, fast settling time, low distortion and noise, high output current, good dc performance, and operate at low supply voltages. These devices are widely used as gain blocks, cable drivers, ADC preamps, current-to-voltage converters, and so forth. Achieving higher bandwidths for less power is extremely critical in today’s portable and battery-operated communications equipment. The rapid progress made over the last few years in high speed linear circuits has hinged not only on the development of IC processes but also on innovative circuit topologies. The evolution of high speed processes using amplifier bandwidth as a function of supply current as a figure of merit is shown in Figure 1-96. (In the case of duals, triples, and quads, the current per amplifier is used.) Analog Devices BiFET process, which produced the AD712 (3 MHz bandwidth, 3 mA current) yields about 1 MHz per mA. 3000 AD8351 1000 AD8001 AD8011 BANDWIDTH−MHz 300 : CB XF 100 z MH 100 30 : CB 10 10 A AD811 m ER zP MH OP482 3 Rm PE B AD8009 AD847 AD817 A R PE Hz 1M T: E F I mA AD712, OP249 741 1 0.3 1 3 10 30 SUPPLY CURRENT (PER AMPLIFIER) −mA Figure 1-96: Amplifier bandwidth versus supply current for Analog Devices’ processes The CB (Complementary Bipolar) process (AD817, AD847, AD811, and so forth) yields about 10 MHz/mA of supply current. The fts of the CB process PNP transistors are about 700 MHz, and the NPNs about 900 MHz. The CB process at Analog Devices was introduced in 1985. The next complementary bipolar process from Analog Devices was a high speed dielectrically isolated process called “XFCB” (eXtra Fast Complementary Bipolar) which was introduced in 1992. This process yields 3 GHz PNPs and 5 GHz matching NPNs, and coupled with innovative circuit topologies allows 97 Chapter One op amps to achieve new levels of cost-effective performance at astonishing low quiescent currents. The approximate figure of merit for this process is typically 100 MHz/mA, although the AD8011 op amp is capable of 300 MHz bandwidth on 1 mA of supply current due to its unique two-stage current-feedback architecture described later in this section. Even faster CB processes have been developed at Analog Devices for low voltage supply products such as “XFCB 1.5” (5 GHz PNP, 9 GHz NPN), and “XFCB 2” (9 GHZ PNP, 16 GHz NPN). The AD8351 differential low distortion RF amplifier (shown on Figure 1-96) is fabricated on “XFCB 1.5” and has a bandwidth of 2 GHz for a gain of 12 dB. It is expected that newer complementary bipolar processes will be optimized for higher fts. In order to select intelligently the correct high speed op amp for a given application, an understanding of the various op amp topologies as well as the trade-offs between them is required. The two most widely used topologies are voltage feedback (VFB) and current feedback (CFB). An overview of these topologies has been presented in a previous section, but the following discussion treats the frequency-related aspects of the two topologies in considerably more detail. Voltage Feedback (VFB) Op Amps A voltage feedback (VFB) op amp is distinguished from a current feedback (CFB) op amp by circuit topology. The VFB op amp is certainly the most popular in low frequency applications, but the CFB op amp has some advantages at high frequencies. We will discuss CFB in detail later, but first the more traditional VFB architecture. Early IC voltage feedback op amps were made on “all NPN” processes. These processes were optimized for NPN transistors—the “lateral” PNP transistors had relatively poor performance. Some examples of these early VFB op amps using these poor quality PNPs include the 709, the LM101 and the 741 (see Chapter 8: “Op Amp History”). Lateral PNPs were generally used only as current sources, level shifters, or for other noncritical functions. A simplified diagram of a typical VFB op amp manufactur ed on such a process is shown in Figure 1-97. The input stage is a differential pair (sometimes called a long-tailed pair) consisting of either a bipolar pair (Q1, Q2) or a FET pair. This “gm” (transconductance) stage converts the small-signal differential input +VS I T “LATERAL” PNP I I T VBIAS 2 2 + i = v•gm T Q3 Q2 Q1 A “gm” STAGE v Q4 C − P I I T R v OUT T T 2 −VS gm = I c • q kT v OUT = i jωCP =v• gm jωCP @ HF Figure 1-97: Voltage feedback (VFB) op amp designed on an “all NPN” IC process 98 Op Amp Basics voltage, v, into a current, i, and its transfer function is measured in units of conductance, 1/Ω, (or mhos). The small-signal emitter resistance, re, is approximately equal to the reciprocal of the small-signal gm. The formula for the small-signal gm of a single bipolar transistor is given by the following equation: gm = 1 q q IT = IC ) = ,or ( re kT kT 2 Eq. 1-32 1 IT gm ≈ ⋅ 26mV 2 Eq. 1-33 where IT is the differential pair tail current, IC is the collector quiescent bias current (IC = IT/2), q is the electron charge, k is Boltzmann’s constant, and T is absolute temperature. At 25°C, VT = kT/q= 26 mV (often called the thermal voltage, VT). As we will see shortly, the amplifier unity gain-bandwidth product, fu, is equal to gm/2πCP, where the capacitance CP is used to set the dominant pole frequency. For this reason, the tail current, IT, is made proportional to absolute temperature (PTAT). This current tracks the variation in re with temperature thereby making gm independent of temperature. It is relatively easy to make CP reasonably constant over temperature. The Q2 collector output of the gm stage drives the emitter of a lateral PNP transistor (Q3). It is important to note that Q3 is not used to amplify the signal, only to level shift, i.e., the signal current variation in the collector of Q2 appears at the collector of Q3. The collector current of Q3 develops a voltage across high impedance node A, and CP sets the dominant pole of the amplifier. Emitter follower Q4 provides a low impedance output. The effective load at the high impedance node A can be represented by a resistance, RT, in parallel with the dominant pole capacitance, CP. The small-signal output voltage, vout, is equal to the small-signal current, i, multiplied by the impedance of the parallel combination of RT and CP. Figure 1-98 shows a simple model for the single-stage amplifier and the corresponding Bode plot. The Bode plot is conveniently constructed on a log-log scale. i = v • gm + + v gm − v OUT X1 − RT CP vin NOISE GAIN = G = 1+ R1 R2 AO fO fO = fu = 6dB/OCTAVE f 1+ R2 R1 CL = 1 2πR TC P gm 2πC P fu 1 + R2 R1 = fu G f u = UNITY GAIN FREQUENCY f 1 f CL = CLOSED LOOP BANDWIDTH Figure 1-98: Model and Bode plot for a VFB op amp 99 R2 R1 Chapter One The low frequency breakpoint, fO, is given by: fo = 1 2 πR T C P Eq. 1-34 Note that the high frequency response is determined solely by gm and CP: v out = v ⋅ gm j ωC P Eq. 1-35 The unity gain bandwidth frequency, fu, occurs where |vout| = |v|. Letting ω = 2πfu and |vout| = |v|, Eq. 1-35 can be solved for fu, fu = gm 2 πCP Eq. 1-36 We can use feedback theory to derive the closed-loop relationship between the circuit’s signal input voltage, vin, and its output voltage, vout: v out = v in R2 R1 jωCP R2 1+ 1 + gm R1 1+ Eq. 1-37 At the op amp 3 dB closed-loop bandwidth frequency, fcl, the following is true: 2 πfcl CP gm R2 1 + = 1, and hence R1 gm 1 fcl = , or R2 2 πCP 1+ R1 fcl = fu R2 1+ R1 Eq. 1-38 Eq. 1-39 Eq. 1-40 This demonstrates the fundamental property of VFB op amps: The closed-loop bandwidth multiplied by the closed-loop gain is a constant, i.e., the VFB op amp exhibits a constant gain-bandwidth product over most of the usable frequency range. As noted previously, some VFB op amps (called decompensated) are not stable at unity gain, but designed to be operated at some minimum (higher) amount of closed-loop gain. However, even for these op amps, the gain bandwidth product is still relatively constant over the region of stability. Now, consider the following typical example: IT = 100 µA, CP = 2 pF. We find that: gm = I T / 2 50 µA 1 = = VT 26 mV 520 Ω 100 Eq. 1-41 Op Amp Basics fu = gm 1 = = 153 MHz 2 πCP 2 π (520 ) 2 ⋅ 10 −12 ( ) Eq. 1-42 Now, we must consider the large-signal response of the circuit. The slew-rate, SR, is simply the total available charging current, IT/2, divided by the dominant pole capacitance, CP. For the example under consideration, dv dv I , = SR, SR = dt dt C Eq. 1-43 I T / 2 50 µA = = 25V / µs CP 2 pF Eq. 1-44 I=C SR = The full-power bandwidth (FPBW) of the op amp can now be calculated from the formula: FPBW = SR 25V / µs = = 4 MHz 2 πA 2 π ⋅ 1V Eq. 1-45 where A is the peak amplitude of the output signal. If we assume a 2 V peak-to-peak output sinewave (certainly a reasonable assumption for high speed applications), then we obtain a FPBW of only 4 MHz, even though the small-signal unity gain bandwidth product is 153 MHz. For a 2 V p-p output sinewave, distortion will begin to occur much lower than the actual FPBW frequency. We must increase the SR by a factor of about 40 in order for the FPBW to equal 153 MHz. The only way to do this is to increase the tail current, IT, of the input differential pair by the same factor. This implies a bias current of 4 mA in order to achieve a FPBW of 160 MHz. We are assuming that CP is a fixed value of 2 pF and cannot be lowered by design. These calculations are summarized in Figure 1-99. • Assume that I T = 100µA, Cp = 2pF I 50µ A 1 gm = c = = VT 26mV 520Ω fu = gm = 153MHz 2π Cp • Slew Rate = SR = But for 2V peak-peak output (A = 1V) SR FPBW = = 4MHz 2π A • Must increase I T to 4mA to get FPBW = 160MHz • Reduce g m by adding emitter degeneration resistors Figure 1-99: VFB op amp bandwidth and slew rate calculations In practice, the FPBW of the op amp should be approximately 5 to 10 times the maximum output frequency in order to achieve acceptable distortion performance (typically 55 dBc–80 dBc @ 5 MHz to 20 MHz, but actual system requirements vary widely). Notice, however, that increasing the tail current causes a proportional increase in gm and hence fu. In order to prevent possible instability due to the large increase in fu, gm can be reduced by inserting resistors in 101 Chapter One series with the emitters of Q1 and Q2 (this technique, called emitter degeneration, also serves to linearize the gm transfer function and thus also lowers distortion). This analysis points out that a major inefficiency of conventional bipolar voltage feedback op amps is their inability to achieve high slew rates without proportional increases in quiescent current (assuming that CP is fixed, and has a reasonable minimum value of 2 pF or 3 pF). This of course is not meant to say that high speed op amps designed using this architecture are deficient, just that circuit design techniques are available that allow equivalent performance at much lower quiescent currents. This is extremely important in portable battery-operated equipment where every milliwatt of power dissipation is critical. VFB Op Amps Designed on Complementary Bipolar Processes With the advent of complementary bipolar (CB) processes having high quality PNP transistors as well as NPNs, VFB op amp configurations such as the one shown in the simplified diagram in Figure 1-100 became popular. +VS D1 Q3 Q4 + Q1 Q2 OUTPUT BUFFER X1 CP − I T −VS Figure 1-100: VFB op amp using two gain stages Notice that the input differential pair (Q1, Q2) is loaded by a current mirror (Q3 and D1). We show D1 as a diode for simplicity, but it is actually a diode-connected PNP transistor (matched to Q3) with the base and collector connected to each other. This simplification will be used in many of the circuit diagrams to follow in this section. The common emitter transistor, Q4, provides a second voltage gain stage. Since the PNP transistors are fabricated on a complementary bipolar process, they are high quality and matched to the NPNs, and therefore suitable for voltage gain. The dominant pole of the Figure 1-100 amplifier is set by CP, and the combination of the gain stage, Q4, and local feedback capacitor CP is often referred to as a Miller Integrator. The unity gain output buffer is usually a complementary emitter follower. A model for this two-stage VFB op amp is shown in Figure 1-101. Notice that the unity gain bandwidth frequency, fu, is still determined by the input stage gm and the dominant pole capacitance, CP. The second gain stage increases the dc open-loop gain, but maximum slew rate is still limited by the input stage tail current as: SR = IT/CP. A two-stage amplifier topology such as this is widely used throughout the IC industry in VFB op amps, both precision and high speed. It can be recalled that a similar topology with a dual FET input stage was used in the early high speed, fast settling FET modular op amps (see Chapter 8: “Op Amp History”). 102 Op Amp Basics CP i = v•gm − + v − gm − + IT v in v out a X1 + VREF R1 R2 fu = fu gm f CL = 2πCP SR = 1+ R2 R1 IT CP Figure 1-101: Model for two stage VFB op amp Another popular VFB op amp architecture is the folded cascode as shown in Figure 1-102. An industrystandard video amplifier family (the AD847) is based on this architecture. This circuit also takes advantage of the fast PNPs available on a CB process. The differential signal currents in the collectors of Q1 and Q2 are fed to the emitters of a PNP cascode transistor pair (hence the term folded cascode). The collectors of Q3 and Q4 are loaded with the current mirror, D1 and Q5, and voltage gain is developed at the Q4–Q5 node. This single-stage architecture uses the junction capacitance at the high impedance node for compensation (CSTRAY). Some variations of the design bring this node to an external pin so that additional external capacitance can be added if desired. +VS 2IT 2IT CCOMP IT IT Q4 Q3 + Q2 Q1 VBIAS X1 CSTRAY − Q5 2IT AC GROUND D1 −VS Figure 1-102: AD847 family folded cascode simplified circuit With no emitter degeneration resistors in Q1 and Q2, and no additional external compensating capacitance, this circuit is only stable for high closed-loop gains. However, unity gain compensated versions of this family are available with the appropriate amount of emitter degeneration. 103 Chapter One The availability of JFETs on a CB process allows not only low input bias current but also improvements in the slew rate trade-off, which must be made between gm and IT found in bipolar input stages. Figure 1-103 shows a simplified diagram of the AD845 16 MHz op amp. JFETs have a much lower gm per mA of tail current than a bipolar transistor. This lower gm of the FET allows the input tail current (hence the slew rate) to be increased, without having to increase CP to maintain stability. +VS D1 Q5 Q6 Q3 Q4 VBIAS Q1 + CP X1 Q2 − −VS Figure 1-103: AD845 BiFET 16 MHz op amp simplified circuit The unusual thing about this seemingly poor performance of the JFET is that it is exactly what is needed for a fast, high SR input stage. For a typical JFET, the value of gm is approximately Is/1 V (Is is the source current), rather than Ic/26 mV for a bipolar transistor, i.e., the FET gm is about 40 times lower. This allows much higher tail currents (and higher slew rates) for a given gm when JFETs are used as the input stage. A New VFB Op Amp Architecture for “Current-on-Demand” Performance, Lower Power, and Improved Slew Rate Until recently, op amp designers had to make the above trade-offs between the input gm stage quiescent current and the slew rate and distortion performance. ADI has patented a circuit core that supplies current-ondemand, to charge and discharge the dominant pole capacitor, CP, while allowing the quiescent current to be small. The additional current is proportional to the fast slewing input signal and adds to the quiescent current. A simplified diagram of the basic core cell is shown in Figure 1-104. The quad-core (gm stage) consists of transistors Q1, Q2, Q3, and Q4 with their emitters connected together as shown. Consider a positive step voltage on the inverting input. This voltage produces a proportional current in Q1 that is mirrored into CP1 by Q5. The current through Q1 also flows through Q4 and CP2. At the dynamic range limit, Q2 and Q3 are correspondingly turned off. Notice that the charging and discharging current for CP1 and CP2 is not limited by the quad core bias current. In practice, however, small current-limiting resistors are required forming an “H” resistor network as shown. Q7 and Q8 form the second gain stage (driven differentially from the collectors of Q5 and Q6), and the output is buffered by a unity-gain complementary emitter follower (X1). 104 Op Amp Basics +VS Q5 Q7 Q1 Q2 CP1 − + X1 CP2 Q3 Q4 Q8 Q6 −VS Figure 1-104: “Quad-Core” VFB gm stage for current-on-demand The quad core configuration is patented (see Reference 1), as well as the circuits that establish the quiescent bias currents (not shown in Figure 1-104). A number of new VFB op amps using this proprietary configuration have been released and have unsurpassed high frequency low distortion performance, bandwidth, and slew rate at the indicated quiescent current levels as shown in Figure 1-105. LISTED IN ORDER OF DECREASING SUPPLY CURRENT PART # ISY / AMP AD9631/32 (1) 17mA 320MHz 1300V/µs –[email protected] AD8074/75 (3) 8mA 600MHz 1600V/µs –[email protected] BANDWIDTH SLEWRATE DISTORTION AD8047/48 (1) 5.8mA 250MHz 750V/µs –[email protected] AD8041 (1) 5.2mA 160MHz 160V/µs –[email protected] AD8042 (2) 5.2mA 160MHz 200V/µs –[email protected] AD8044 (3) 2.8mA 150MHz 150V/µs –[email protected] AD8039 (2) 1.5mA 300MHz 425V/µs –[email protected] AD8031 (1) 0.75mA 80MHz 30V/µs –[email protected] AD8032 (2) 0.75mA 80MHz 30V/µs –[email protected] Number in ( ) indicates single, dual, triple, or quad Figure 1-105: High speed VFB op amps The AD9631, AD8074, and AD8047 are optimized for a gain of +1, while the AD9632, AD8075, and AD8048 for a gain of +2. The same quad-core architecture is used as the second stage of the AD8041 rail-to-rail output, zero-volt input single-supply op amp. The input stage is a differential PNP pair which allows the input common-mode signal to go about 200 mV below the negative supply rail. The AD8042 and AD8044 are dual and quad versions of the AD8041. 105 Chapter One Current Feedback (CFB) Op Amps We will now examine in more detail the current feedback (CFB) op amp topology which is very popular in high speed op amps. As mentioned previously, the circuit concepts were introduced decades ago; however, modern high speed complementary bipolar processes are required to take full advantage of the architecture. It has long been known that in bipolar transistor circuits, currents can be switched faster than voltages, other things being equal. This forms the basis of nonsaturating emitter-coupled logic (ECL) and devices such as current-output DACs. Maintaining low impedances at the current switching nodes helps to minimize the effects of stray capacitance, one of the largest detriments to high speed operation. The current mirror is a good example of how currents can be switched with a minimum amount of delay. The current feedback op amp topology is simply an application of these fundamental principles of current steering. A simplified CFB op amp is shown in Figure 1-106. The noninverting input is high impedance and is buffered directly to the inverting input through the complementary emitter follower buffers Q1 and Q2. Note that the inverting input impedance is very low (typically 10 Ω to 100 Ω), because of the low emitter resistance (ideally, would be zero). This is a fundamental difference between a CFB and a VFB op amp, and also a feature that gives the CFB op amp some unique advantages. +VS Q3 Q1 i i X1 − + Q2 CP RT i Q4 −V S R2 R1 Figure 1-106: Simplified current feedback (CFB) op amp The collector outputs of Q1 and Q2 drive current mirrors, which mirror the inverting input current to the high impedance node, modeled by RT and CP. The high impedance node is buffered by a complementary unity gain emitter follower. Feedback from the output to the inverting input acts to force the inverting input current to zero, hence the term Current Feedback. Note that in a ideal case, for zero inverting input impedance, no small-signal voltage can exist at this node, only small-signal current. Now, consider a positive step voltage applied to the noninverting input of the CFB op amp. Q1 immediately sources a proportional current into the external feedback resistors creating an error current, which is mirrored to the high impedance node by Q3. The voltage developed at the high impedance node is equal to this current multiplied by the equivalent impedance. This is where the term transimpedance op amp originated, since the transfer function is an impedance, rather than a unitless voltage ratio as in a traditional VFB op amp. 106 Op Amp Basics Note also that the error current delivered to the high impedance node is not limited by the input stage tail current. In other words, unlike a conventional VFB op amp, there is no slew rate limitation in an ideal CFB op amp. The current mirrors supply current-on-demand from the power supplies. The negative feedback loop then forces the output voltage to a value that reduces the inverting input error current to zero. The model for a CFB op amp is shown in Figure 1-107, along with the corresponding Bode plot. The Bode plot is plotted on a log-log scale, and the open-loop gain is expressed as a transimpedance, T(s), with units of ohms. VIN VOUT X1 RT CP i X1 RO R1 R2 fO 1 RT f CL = 2πR2CP 6dB/OCTAVE |T(s)| (Ω ) ≈ f CL R ( 1 + R2O 1 2πR2CP + RO R1 ) FOR RO << R1 RO << R2 R2 12dB/OCTAVE RO Figure 1-107: CFB op amp model and Bode plot The finite output impedance of the input buffer is modeled by RO. The input error current is i. By applying the principles of negative feedback, we can derive the expression for the op amp transfer function: Vout = Vin 1+ R2 R1 Ro Ro + 1 + jωC P R2 1 + R2 R1 Eq. 1-46 At the op amp 3 dB closed-loop bandwidth frequency, fcl, the following is true: Ro Ro 2 πfcl CP R2 1 + + =1 R2 R1 fcl = Eq. 1-47 1 Ro Ro + 2 πCP R2 1 + R2 R1 Eq. 1-48 For the condition RO << R2 and R1, the equation simply reduces to: fcl = 1 2 πCP R2 107 Eq. 1-49 Chapter One Examination of this equation quickly reveals that the closed-loop bandwidth of a CFB op amp is determined by the internal dominant pole capacitor, CP, and the external feedback resistor, R2, and is independent of the gain-setting resistor, R1. This ability to maintain constant bandwidth independent of gain makes CFB op amps ideally suited for wideband programmable gain amplifiers. Because the closed-loop bandwidth is inversely proportional to the external feedback resistor, R2, a CFB op amp is usually optimized for a specific R2. Increasing R2 from its optimum value lowers the bandwidth, and decreasing it may lead to oscillation and instability because of high frequency parasitic poles. The frequency response of the AD8011 CFB op amp is shown in Figure 1-108 for various closed-loop values of gain (+1, +2, and +10). Note that even at a gain of +10, the closed-loop bandwidth is still greater than 100 MHz. The peaking that occurs at a gain of +1 is typical of wideband CFB op amps used in the noninverting mode, and is due primarily to stray capacitance at the inverting input. This peaking can be reduced by sacrificing bandwidth, by using a slightly larger feedback resistor. Figure 1-108: AD8011 frequency response, G = +1, +2, +10 The AD8011 CFB op amp (introduced in 1995) still represents state-of-the-art performance, and key specifications are shown in Figure 1-109. • • • • • 1mA Power Supply Current (+5V or ±5V) 300MHz Bandwidth (G = +1) 2000 V/µs Slew Rate 29ns Settling Time to 0.1% Video Specifications (G = +2) Differential Gain Error 0.02% Differential Phase Error 0.06° 25MHz 0.1dB Bandwidth • Distortion –70dBc @ 5MHz –62dBc @ 20MHz • Fully Specified for ±5V or +5V Operation Figure 1-109: AD8011 key specifications 108 Op Amp Basics Traditional current feedback op amps have been limited to a single gain stage, using current-mirrors. The AD8011 (and also others in this family) unlike traditional CFB op amps, use a two-stage gain configuration, as shown in Figure 1-110. +VS I1 Q3 Q1 CC/2 + X1 − CC/2 CP Q2 Q4 I2 −VS Figure 1-110: Simplified twostage current feedback op amp Until the advent of the AD8011, fully complementary two-gain stage CFB op amps had been impractical because of their high power dissipation. The AD8011 employs a patented (see Reference 2) second gain stage consisting of a pair of complementary amplifiers (Q3 and Q4). Note that they are not connected as current mirrors but as grounded-emitter gain stages. The detailed design of current sources (I1 and I2), and their respective bias circuits are the key to the success of the two-stage CFB circuit; they keep the amplifier’s quiescent power low, yet are capable of supplying current-on-demand for wide current excursions required during fast slewing. A further advantage of the two-stage amplifier is the higher overall bandwidth (for the same power), which means lower signal distortion and the ability to drive heavier external loads. Thus far, we have learned several key features of CFB op amps. The most important is that for a given complementary bipolar IC process, CFB generally yields higher FPBW (hence lower distortion) than VFB for the same amount of quiescent supply current. This is because there is practically no slew-rate limiting in CFB. Because of this, the full power bandwidth and the small signal bandwidth are approximately the same. The second important feature is that the inverting input impedance of a CFB op amp is very low. This is advantageous when using the op amp in the inverting mode as an I/V converter, because there is less sensitivity to inverting input capacitance than with VFB. The third feature is that the closed-loop bandwidth of a CFB op amp is determined by the value of the internal Cp capacitor and the external feedback resistor R2 and is relatively independent of the gain-setting resistor R1. 109 Chapter One The performance for a selected group of current feedback op amps is shown in Figure 1-111. Note that the op amps are listed in order of decreasing power supply current. LISTED IN ORDER OF DECREASING SUPPLY CURRENT DISTORTION PART # ISY /AMP BANDWIDTH SLEW RATE AD8009 (1) 14mA 1000MHz 5500V/µs –[email protected] AD8023 (3) 10mA 250MHz 1200V/µs ∆G = 0.06%, ∆φ = 0.02° AD8001 (1) 5.0mA 600MHz 1200V/µs –[email protected] AD8002 (2) 5.0mA 600MHz 1200V/µs –[email protected] AD8004 (4) 3.5mA 250MHz 3000V/µs –[email protected] AD8013 (3) 4.0mA 140MHz 1000V/µs ∆G = 0.02%, ∆φ = 0.06° AD8072 (2) 3.5mA 100MHz 500V/µs ∆G = 0.05%, ∆φ = 0.1° AD8073 (3) 3.5mA 100MHz 500V/µs ∆G = 0.05%, ∆φ = 0.1° AD8012 (2) 1.7mA 350MHz 2250V/µs –[email protected] AD8014 (1) 1.2mA 400MHz 4000V/µs –[email protected] AD8011 (1) 1.0mA 300MHz 5500V/µs –[email protected] AD8005 (1) 0.4mA 270MHz 1500/µs –[email protected] Number in ( ) Indicates Single, Dual, Triple, or Quad Figure 1-111: Performance of selected CFB op amps Figure 1-112 summarizes the general characteristics of CFB op amps. • CFB yields higher FPBW and lower distortion than VFB for the same process and power dissipation • Inverting input impedance of a CFB op amp is low, noninverting input impedance is high • Closed-loop bandwidth of a CFB op amp is determined by the internal dominant-pole capacitance and the external feedback resistor, independent of the gainsetting resistor Figure 1-112: Summary: CFB op amps Effects of Feedback Capacitance in Op Amps It is quite common to use a capacitor in the feedback loop of a VFB op amp, to shape the frequency response as in a simple single-pole lowpass filter shown in Figure 1-113A. The resulting noise gain is plotted on a Bode plot to analyze stability and phase margin. Stability of the system is determined by the net slope of the noise gain and the open-loop gain where they intersect. For unconditional stability, the noise gain plot must intersect the open-loop response with a net slope of less than 12 dB/octave. In this case, the net slope where they intersect is 6 dB/octave, indicating a stable condition. Notice for the case drawn in Figure 1-113A, the second pole in the frequency response occurs at a considerably higher frequency than fu. 110 Op Amp Basics C2 R1 A B R2 − VFB OP AMP |A(s)| + CFB OP AMP |T(s)| (Ω ) R2 1 + R1 1 f p = 2πR2C2 1 f p = 2πR2C2 R2 f CL fu RO f 1 f UNSTABLE Figure 1-113: Noise gain stability analysis for VFB and CFB op amps with feedback capacitor In the case of the CFB op amp (Figure 1-113B), the same analysis is used, except that the open-loop transimpedance gain, T(s), is used to construct the Bode plot. The definition of noise gain (for the purposes of stability analysis) for a CFB op amp, however, must be redefined in terms of a current noise source attached to the inverting input as shown in Figure 1-114. This current is reflected to the output by an impedance, which we define to be the “current noise gain” of a CFB op amp: R “CURRENT NOISE GAIN” ≡ R O + Z2 1 + O Z1 T(s) X1 Eq. 1-50 VOUT X1 i RO Z1 Z2 VOUT CURRENT “NOISE GAIN” Z2 i RO = VOUT i R = RO +Z2 1+ O Z1 ( Z1 Figure 1-114: Current “noise gain” definition for CFB op amp for use in stability analysis 111 ) Chapter One Now, return to Figure 1-113B, and observe the CFB current noise gain plot. At low frequencies, the CFB current noise gain is simply R2 (making the assumption that RO is much less than Z1 or Z2. The first pole is determined by R2 and C2. As the frequency continues to increase, C2 becomes a short circuit, and all the inverting input current flows through RO (again refer to Figure 1-114). A CFB op amp is normally optimized for best performance for a fixed feedback resistor, R2. Additional poles in the transimpedance gain, T(s), occur at frequencies above the closed-loop bandwidth, fcl, (set by R2). Note that the intersection of the CFB current noise gain with the open-loop T(s) occurs where the slope of the T(s) function is 12 dB/octave. This indicates instability and possible oscillation. It is for this reason that CFB op amps are not suitable in configurations that require capacitance in the feedback loop, such as simple active integrators or low-pass filters. They can, however, be used in certain active filters, such as the Sallen-Key configuration shown in Figure 1-115, which do not require capacitance in the feedback network. VIN VOUT R2 R1 R2 FIXED FOR CFB OP AMP Figure 1-115: The Sallen-Key filter configuration On the other hand, VFB op amps do make very flexible active filters. A multiple feedback 20 MHz low-pass filter example using an AD8048 op amp is shown in Figure 1-116. Figure 1-116: Multiple feedback 20 MHz low-pass filter using the AD8048 VFB op amp In general, an active filter amplifier should have a bandwidth that is at least 10 times the bandwidth of the filter, if problems due to phase shift of the amplifier are to be avoided. (The AD8048 has a bandwidth of over 200 MHz in this configuration.) Design details of the filter design can be found on the AD8048 data sheet. Further discussions on active filter design are included in Chapter 5 of this book. 112 Op Amp Basics High Speed Current-to-Voltage Converters, and the Effects of Inverting Input Capacitance Fast op amps are useful as current-to-voltage converters in such applications as high speed photodiode preamplifiers and current-output DAC buffers. A typical application using a VFB op amp as an I/V converter is shown in Figure 1-117. C2 R2 − i C1 VFB + fp = 1 2πR2C1 UNCOMPENSATED fx = 2πR2C2 COMPENSATED fx = fp • fu |A(s)| NOISE GAIN fx C1 f 1 fp 1 C2 = 2πR2 • f u FOR 45º PHASE MARGIN fu Figure 1-117: Compensating for input capacitance in a current-to-voltage converter using VFB op amp The net input capacitance, C1, forms a pole at a frequency fP in the noise gain transfer function as shown in the Bode plot, and is given by: fP = 1 2 πR2C1 Eq. 1-51 If left uncompensated, the phase shift at the frequency of intersection, fx, will cause instability and oscillation. Introducing a zero at fx by adding feedback capacitor C2 stabilizes the circuit and yields a phase margin of about 45°. The location of the zero is given by: fX = 1 2 πR2C2 Eq. 1-52 Although the addition of C2 actually decreases the pole frequency slightly, this effect is negligible if C2 << C1. The frequency fx is the geometric mean of fp and the unity-gain bandwidth frequency of the op amp, fu, fX = fP ⋅ fu Eq. 1-53 Combining Eq. 1-52 and Eq. 1-53 and solving for C2 yields: C2 = C1 2 πR2 ⋅ fu 113 Eq. 1-54 Chapter One This value of C2 will yield a phase margin of about 45°. Increasing the capacitor by a factor of 2 increases the phase margin to about 65° (see Reference 3). In practice, the optimum value of C2 may be optimized experimentally by varying it slightly, to optimize the output pulse response. A similar analysis can be applied to a CFB op amp as shown in Figure 1-118. In this case, however, the low inverting input impedance, RO, greatly reduces the sensitivity to input capacitance. In fact, an ideal CFB with zero input impedance would be totally insensitive to any amount of input capacitance. C2 R2 − i C1 RO + fp = 1 2πRO ||R2•C1 |T(s)| fx = UNCOMPENSATED ≈ 1 2πRO C1 1 2πR2C2 fx = f p • f CL C2 = RO R2 COMPENSATED fx f R2 • C1 2πR2•f CL FOR 45º PHASE MARGIN f CL fp Figure 1-118: Current-to-voltage converter using a CFB op amp The pole caused by C1 occurs at a frequency fP: fP = 1 1 ≈ 2 π (R O R2 )C1 2 πR O C1 Eq. 1-55 This pole frequency will generally be much higher than the case for a VFB op amp, and the pole can be ignored completely if it occurs at a frequency greater than the closed-loop bandwidth of the op amp. We next introduce a compensating zero at the frequency fx by inserting the capacitor C2: fx = 1 2 πR2C2 Eq. 1-56 As in the case for VFB, fx is the geometric mean of fp and fcl: fx = fP ⋅ fu Eq. 1-57 Combining Eq. 1-56 and Eq. 1-57 and solving for C2 yields: C2 = RO C1 ⋅ R2 2 πR2 ⋅ fcl Eq. 1-58 There is a significant advantage in using a CFB op amp in this configuration as can be seen by comparing Eq. 1-58 with the similar equation for C2 required for a VFB op amp, Eq. 1-54. If the unity-gain bandwidth 114 Op Amp Basics product of the VFB is equal to the closed-loop bandwidth of the CFB (at the optimum R2), then the size of the CFB compensation capacitor, C2, is reduced by a factor of . A comparison in an actual application is shown in Figure 1-119. The full scale output current of the DAC is 4 mA, the net capacitance at the inverting input of the op amp is 20 pF, and the feedback resistor is 500 Ω. In the case of the VFB op amp, the pole due to C1 occurs at 16 MHz. A compensating capacitor of 5.6 pF is required for 45° of phase margin, and the signal bandwidth is 57 MHz. C2 C2 R2 R2 500Ω 500Ω − 4mA C1 20pF + fp = 1 − 4mA C1 20pF VFB CFB + f u = 200MHz 1 fp = = 16MHz C2 = 5.6pF 2πR C1 O C2 = 1.8pF f x = 57MHz f x = 176MHz 2πR2C1 = 160MHz Figure 1-119: CFB op amp is relatively insensitive to input capacitance when used as an I/V converter For the CFB op amp, however, because of the low inverting input impedance (RO = 50 Ω), the pole occurs at 160 MHz, the required compensation capacitor is about 1.8 pF, and the corresponding signal bandwidth is 176 MHz. In practice, the pole frequency is so close to the closed-loop bandwidth of the op amp that it could probably be left uncompensated. It should be noted that a CFB op amp’s relative insensitivity to inverting input capacitance is when it is used in the inverting mode. In the noninverting mode, however, even a few picofarads of stray capacitance on the inverting input can cause significant gain peaking and potential instability. Another advantage of the low inverting input impedance of the CFB op amp is when it is used as an I/V converter to buffer the output of a high speed current output DAC. When a step function current (or DAC switching glitch) is applied to the inverting input of a VFB op amp, it can produce a large voltage transient until the signal can propagate through the op amp to its output and negative feedback is regained. Back-toback Schottky diodes are often used to limit this voltage swing as shown in Figure 1-120. These diodes must be low capacitance, small geometry devices because their capacitance adds to the total input capacitance. R2 CURRENT OUTPUT DAC − I VFB + *SCHOTTKY CATCH DIODES * NOT REQUIRED FOR CFB OP AMP BECAUSE OF LOW INVERTING INPUT IMPEDANCE Figure 1-120: Low inverting input impedance of CFB op amp helps reduce effects of fast DAC transients 115 Chapter One A CFB op amp, on the other hand, presents a low impedance (RO) to fast switching currents even before the feedback loop is closed, thereby limiting the voltage excursion without the requirement of the external diodes. This greatly improves the settling time of the I/V converter. Noise Comparisons between VFB and CFB Op Amps In most applications of high speed op amps, it is generally the total output RMS noise that is of interest. Because of the high bandwidths involved, the chief contributor to the output RMS noise is therefore the white noise, and the 1/f noise is negligible. Typical high speed op amps with bandwidths greater than 150 MHz or so, and bipolar VFB input stages, have input voltage noises ranging from about 2 nV to 20 nV Hz . For a VFB op amp, the inverting and noninverting input current noise are typically equal, and almost always uncorrelated. Typical values for wideband VFB op amps range from 0.5 pA Hz to 5 pA Hz. The input current noise of a bipolar input stage is increased when input bias-current compensation generators are added, because their current noise is not correlated, and therefore adds (in an RSS manner) to the intrinsic current noise of the bipolar stage. However, bias current compensation is rarely used in high speed op amps. The input voltage noise in CFB op amps tends to be lower than for VFB op amps having the same approximate bandwidth. This is because the input stage in a CFB op amp is usually operated at a higher current, thereby reducing the emitter resistance and hence the voltage noise. Typical values for CFB op amps range from about 1 nV to 5 nV Hz . The input current noise of CFB op amps tends to be larger than for VFB op amps because of the generally higher bias current levels. The inverting and noninverting current noise of a CFB op amp is usually different because of the unique input architecture, and are specified separately. In most cases, the inverting input current noise is the larger of the two. Typical input current noise for CFB op amps ranges from 5 pA to 40 pA Hz . This can often be dominant, except in cases of very high gain, when R1 is small. The noise sources that dominate the output noise are highly dependent on the closed-loop gain of the op amp and the values of the feedback and feedforward resistors. For high values of closed-loop gain, the op amp voltage noise will tend be the chief contributor to the output noise. At low gains, the effects of the input current noise must also be considered, and may dominate, especially in the case of a CFB op amp. Feedforward/feedback resistors in high speed op amp circuits may range from less than 100 Ω to more than 1 kΩ, so it is difficult to generalize about their contribution to the total output noise without knowing the specific values and the closed-loop gain. The best way to make the noise calculations is to write a simple computer program that automatically performs the calculations, and include all the noise sources. The equation previously discussed can be used for this purpose (see Figure 1-74). In most high speed op amp applications, the source impedance noise can often be neglected for source impedances of 100 Ω or less. Figure 1-121 summarizes the noise characteristics of high speed op amps. 116 Op Amp Basics • Voltage Feedback Op Amps: − Voltage noise: 2nV to 20nV/√Hz − Current noise: 0.5pA to 5pA/√Hz • Current Feedback Op Amps: − Voltage noise: 1nV to 5nV/√Hz − Current noise: 5nV to 40pA/√Hz • Noise Contribution from Source Negligible if < 100Ω • Voltage Noise Usually Dominates at High Gains • Reflect Noise Sources to Output and Combine (RSS) • Errors Will Result if there is Significant High Frequency Peaking Figure 1-121: High speed op amp noise summary DC Characteristics of High Speed Op Amps High speed op amps are optimized for bandwidth and settling time, not for precision dc characteristics as found in lower frequency precision op amps. In spite of this, however, high speed op amps do have reasonably good dc performance. Input offset voltages of high speed bipolar input op amps are rarely trimmed, since offset voltage matching of the input stage is excellent, typically ranging from 1 mV to 3 mV, with offset temperature coefficients of 5 µV to 15 µV/°C. Input bias currents on VFB op amps (with no input bias current compensation circuits) are approximately equal for (+) and (–) inputs, and can range from 1 µA to 5 µA. The output offset voltage due to the input bias currents can be nulled by making the effective source resistance, R3, equal to the parallel combination of R1 and R2. As previously discussed, this scheme will not work with bias-current compensated VFB op amps that have additional current generators on their inputs. In this case, the net input bias currents are not necessarily equal or of the same polarity. CFB op amps generally have unequal and uncorrelated input bias currents because the (+) and (–) inputs have completely different architectures. For this reason, external bias current cancellation schemes are also ineffective. CFB input bias currents range from 5 µA to 15 µA, being generally higher at the inverting input. 117 Chapter One Figure 1-122 summarizes the offset considerations for high speed op amps. • High Speed Bipolar Op Amp Input Offset Voltage: − Ranges from 1mV to 3mV for VFB and CFB − Offset TC ranges from 5µV to 15µV/°C • High Speed Bipolar Op Amp Input Bias Current: − For VFB ranges from 1µA to 5µA − For CFB ranges from 5µA to 15µA • Bias Current Cancellation Doesn’t Work for: − Bias current compensated op amps − Current feedback op amps Figure 1-122: High speed op amp offset voltage summary References: High Speed Op Amps 1. Roy Gosser, “Wide-Band Transconductance Generator,” US Patent 5,150,074, filed May 3, 1991, issued September 22, 1992. 2. Roy Gosser, DC-Coupled Transimpedance Amplifier, US Patent 4,970,470, filed October 10, 1989, issued November 13, 1990. 3. James L. Melsa and Donald G. Schultz, Linear Control Systems, McGraw-Hill, 1969, pp. 196–220, ISBN: 0-07-041481-5. 4. Thomas M. Frederiksen, Intuitive Operational Amplifiers, McGraw-Hill, 1988., ISBN: 0-07-021966-4. 5. Sergio Franco, Design With Operational Amplifiers and Analog Integrated Circuits, 2nd Ed., McGraw-Hill, 1998, ISBN: 0-07-021857-9. 6. Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0-916550-17-6, (available for download at www.analog.com). 7. Data sheet for AD8011 300 MHz, 1 mA Current Feedback Amplifier, www.analog.com. 118 CHAPTER 2 Specialty Amplifiers ■ Section 2-1: Instrumentation Amplifiers ■ Section 2-2: Programmable Gain Amplifiers ■ Section 2-3: Isolation Amplifiers This page intentionally left blank CHAPTER 2 Specialty Amplifiers Walt Kester, Walt Jung, James Bryant This chapter of the book discusses several popular types of specialty amplifiers, or amplifiers that are based in some way on op amp techniques. However, in an overall applications sense, they are not generally used as universally as op amps. Examples of specialty amplifiers include instrumentation amplifiers of various configurations, programmable gain amplifiers (PGAs), isolation amplifiers, and difference amplifiers. Other types of amplifiers, for example such types as audio and video amplifiers, cable drivers, high-speed variable gain amplifiers (VGAs), and various communications-related amplifiers might also be viewed as specialty amplifiers. However, these applications are more suitably covered in Chapter 6, within the various signal amplification sections. 121 This page intentionally left blank SECTION 2-1 Instrumentation Amplifiers Walt Kester, Walt Jung Probably the most popular among all of the specialty amplifiers is the instrumentation amplifier (hereafter called simply an in amp). The in amp is widely used in many industrial and measurement applications where dc precision and gain accuracy must be maintained within a noisy environment, and where large common-mode signals (usually at the ac power line frequency) are present. Op Amp/In Amp Functionality Differences An in amp is unlike an op amp in a number of very important ways. As already discussed, an op amp is a general-purpose gain block—user-configurable in myriad ways using external feedback components of R, C, and, (sometimes) L. The final configuration and circuit function using an op amp is truly whatever the user makes of it. In contrast to this, an in amp is a more constrained device in terms of functioning, and also the allowable range(s) of operating gain. In many ways, it is better suited to its task than would be an op amp—even though, ironically, an in amp may actually comprise of a number of op amps within it. People also often confuse in amps as to their function, calling them “op amps.” But the reverse is seldom (if ever) true. It should be understood that an in amp is not just a special type op amp; the function of the two devices is fundamentally different. Perhaps a good way to differentiate the two devices is to remember that an op amp can be programmed to do almost anything, by virtue of its feedback flexibility. In contrast to this, an in amp cannot be programmed to do just anything. It can only be programmed for gain, and then over a specific range. An op amp is configured via a number of external components, while an in amp is configured either by one resistor, or by pin-selectable taps for its working gain. In Amp Definitions An in amp is a precision closed-loop gain block. It has a pair of differential input terminals, and a singleended output that works with respect to a reference or common terminal, as shown in Figure 2-1. The input impedances are balanced and high in value, typically ≥109 Ω. Again, unlike an op amp, an in amp uses an RS/2 ∆RS RG COMMONMODE VOLTAGE VCM + ~ _ VSIG 2 + VSIG 2 _ IN AMP GAIN = G + ~ ~ _ RS/2 VOUT VREF ~ COMMON MODE-ERROR (RTI) = VCM CMRR Figure 2-1: The generic instrumentation amplifier (in amp) 123 Chapter Two internal feedback resistor network, plus one (usually) gain set resistance, RG. Also unlike an op amp is the fact that the internal resistance network and RG are isolated from the signal input terminals. In amp gain can also be preset via an internal RG by pin selection, (again isolated from the signal inputs). Typical in amp gains range from 1 to 1,000. The in amp develops an output voltage that is referenced to a pin usually designated REFERENCE, or VREF. In many applications, this pin is connected to circuit ground, but it can be connected to other voltages, as long as they lie within a rated compliance range. This feature is especially useful in single-supply applications, where the output voltage is usually referenced to mid-supply (i.e., 2.5 V in the case of a +5 V supply). In order to be effective, an in amp needs to be able to amplify microvolt-level signals, while simultaneously rejecting volts of common-mode (CM) signal at its inputs. This requires that in amps have very high common-mode rejection (CMR). Typical values of in amp CMR are from 70 dB to over 100 dB, with CMR usually improving at higher gains. It is important to note that a CMR specification for dc inputs alone isn’t sufficient in most practical applications. In industrial applications, the most common cause of external interference is 50 Hz/60 Hz ac power-related noise (including harmonics). In differential measurements, this type of interference tends to be induced equally onto both in amp inputs, so the interference appears as a CM input signal. Therefore, specifying CMR over frequency is just as important as specifying its dc value. Note that imbalance in the two source impedances can degrade the CMR of some in amps. Analog Devices fully specifies in amp CMR at 50 Hz/60 Hz, with a source impedance imbalance of 1 kΩ. Subtractor or Difference Amplifiers A simple subtractor or difference amplifier can be constructed with four resistors and an op amp, as shown in Figure 2-2. It should be noted that this is not a true in amp (based on the previously discussed criteria), but it is often used in applications where a simple differential-to-single-ended conversion is required. Because of its popularity, this circuit will be examined in more detail, in order to understand its fundamental limitations before discussing true in amp architectures. R1 R2 V1 _ VOUT 1+ CMR = 20 log 10 + R1' R2' V2 R2 R1 Kr REF Where Kr = Total Fractional Mismatch of R1/ R2 TO • • • R1'/R2' R2 VOUT = (V2 – V1) R1 R2' R2 CRITICAL FOR HIGH CMR = R1' R1 EXTREMELY SENSITIVE TO SOURCE IMPEDANCE IMBALANCE • 0.1% TOTAL MISMATCH YIELDS ≈ 66dB CMR FOR R1 = R2 Figure 2-2: Op amp subtractor or difference amplifier There are several fundamental problems with this simple circuit. First, the input impedance seen by V1 and V2 isn’t balanced. The input impedance seen by V1 is R1, but the input impedance seen by V2 is R1' + R2'. The configuration can also be quite problematic in terms of CMR, since even a small source impedance imbalance will degrade the workable CMR. This problem can be solved with well-matched open-loop 124 Specialty Amplifiers buffers in series with each input (for example, using a precision dual op amp). But, this adds complexity to a simple circuit, and may introduce offset drift and nonlinearity. The second problem with this circuit is that the CMR is primarily determined by the resistor ratio matching, not the op amp. The resistor ratios R1/R2 and R1'/R2' must match extremely well to reject common mode noise—at least as well as a typical op amp CMR of ≥100 dB. Note also that the absolute resistor values are relatively unimportant. Picking four 1% resistors from a single batch may yield a net ratio matching of 0.1%, which will achieve a CMR of 66 dB (assuming R1 = R2). But if one resistor differs from the rest by 1%, the CMR will drop to only 46 dB. Clearly, very limited performance is possible using ordinary discrete resistors in this circuit (without resorting to hand matching). This is because the best standard off-the-shelf RNC/RNR style resistor tolerances are on the order of 0.1% (see Reference 1). In general, the worst-case CMR for a circuit of this type is given by the following equation (see References 2 and 3): 1 + R 2 R1 CMR (dB) = 20 log , 4Kr Eq. 2-1 where Kr is the individual resistor tolerance in fractional form, for the case where four discrete resistors are used. This equation shows that the worst-case CMR for a tolerance build-up for four unselected samenominal-value 1% resistors to be no better than 34 dB. A single resistor network with a net matching tolerance of Kr would probably be used for this circuit, in which case the expression would be as noted in the figure, or: 1 + R 2 R1 CMR (dB) = 20 log Kr Eq. 2-2 A net matching tolerance of 0.1% in the resistor ratios therefore yields a worst-case dc CMR of 66 dB using Eq. 2-2, and assuming R1 = R2. Note that either case assumes a significantly higher amplifier CMR (i.e., >100 dB). Clearly for high CMR, such circuits need four single-substrate resistors, with very high absolute and TC matching. Such networks using thick/thin-film technology are available from companies such as Caddock and Vishay, in ratio matches of 0.01% or better. In implementing the simple difference amplifier, rather than incurring the higher costs and PCB real estate limitations of a precision op amp plus a separate resistor network, it is usually better to seek out a completely monolithic solution. The AMP03 is just such a precision difference amplifier, which includes an on-chip laser trimmed precision thin film resistor network. It is shown in Figure 2-3. The typical CMR of the AMP03F is 100 dB, and the small-signal bandwidth is 3 MHz. Figure 2-3: AMP03 precision difference amplifier 125 Chapter Two There are several devices related to the AMP03 in function. These are namely the SSM2141 and SSM2143 difference amplifiers. These sister parts are designed for audio line receivers (see Figure 2-4). They have low distortion, and high (pretrimmed) CMR. The net gains of the SSM2141 and SSM2143 are unity and 0.5, respectively. They are designed to be used with balanced 600 Ω audio sources (see the related discussions on these devices in the Audio Amplifiers section of Chapter 6). SSM2141 SSM2143 Figure 2-4: SSM2141 and SSM2143 difference amplifiers (audio line receivers) Another interesting variation on the simple difference amplifier is found in the AD629 difference amplifier, optimized for high common-mode input voltages. A typical current-sensing application is shown in Figure 2-5. The AD629 is a differential-to-single-ended amplifier with a gain of unity. It can handle a commonmode voltage of ±270 V with supply voltages of ±15 V, with a small signal bandwidth of 500 kHz. VCM = ± 270V for V S = ±15V Figure 2-5: High common-mode current sensing using the AD629 difference amplifier The high common-mode voltage range is obtained by attenuating the noninverting input (Pin 3) by a factor of 20 times, using the R1–R2 divider network. On the inverting input, resistor R5 is chosen such that R5||R3 equals resistor R2. The noise gain of the circuit is equal to 20 [1 + R4/(R3||R5)], thereby providing unity gain for differential input voltages. Laser wafer trimming of the R1–R5 thin film resistors yields a minimum CMR of 86 dB @ 500 Hz for the AD629B. Within an application, it is good practice to maintain 126 Specialty Amplifiers balanced source impedances on both inputs, so dummy resistor RCOMP is chosen to equal to the value of the shunt sensing resistor RSHUNT. David Birt (see Reference 4) of the BBC has analyzed the simple line receiver topology in terms of loading presented to the source, and presented a modified and balanced form, shown as Figure 2-6. Here stage U1 uses a 4 resistor network identical to that of Figure 2-2, while feedback from the added unity gain inverter U2 drives the previously grounded R2’ reference terminal. This has two overall effects; the input currents in the ± input legs become equal in magnitude, and the gain of the stage is halved. –VOUT R1 R2 _ 25kΩ +VOUT CF 25kΩ _ R3 10kΩ VIN U1 10kΩ _ + R1' R2' 25kΩ 25kΩ U2 + –VOUT + FOR R2 R2' = R1 R1' AND R3 = R4, G = VOUT VIN = R2 2R1 R3||R4 5kΩ Figure 2-6: Balanced difference amplifier using push-pull feedback path Compared to Figure 2-2, and for like resistor ratios, the Figure 2-6 gain from VIN to VOUT is one-half, or a gain of –6 dB (0.5) as shown. However the new circuit form also offers a complementary output from U2, –VOUT. The common-mode range of this circuit is the same as for Figure 2-2, but the CMR is about doubled with all resistors nominally equal (as measured to a single output). The inverter resistor ratio R3/R4 affects output balance, but not CMR. Like Figure 2-2, the gain of this circuit is not easily changed, as it involves precise resistor ratios. Because of the two feedback paths, this circuit holds the inputs of U1 at a null for differential input signals. However CM signals are seen by U1, and the CM range of the circuit is [1 + (R2'/R1')] × VCM(U1). Differential input resistance is R1 + R1'. As can be noted from Figure 2-6, this circuit can be broken into a simple line receiver (left), plus an inverter (right). Thus existing line receivers like Figure 2-2 can be converted to the fully balanced topology, by simply adding an appropriate inverter, U2. This of course not only balances the input currents, but it also provides a balanced output signal. For example, the SSM2141 line receiver and the OP275 are a good combination for implementing this approach. (See Reference 5, and the further discussions on these circuits in the Audio Amplifiers section of Chapter 6.) 127 Chapter Two In Amp Configurations The simple difference amplifier circuits described above are quite useful (especially at higher frequencies) but lack the performance required for most precision applications. In many cases, true in amps are more suitable, because of their balanced and high input impedance, as well as their high common-mode rejection. Two-Op-Amp In Amps As noted initially, in amps are based on op amps, and there are two basic configurations that are extremely popular. The first is based on two op amps, and the second on three op amps. The circuit shown in Figure 2-7 is referred to as the two-op-amp in amp. Dual IC op amps are used in most cases for good matching, such as the OP297 or the OP284. The resistors are usually a thin film laser trimmed array on the same chip. The in amp gain can be easily set with an external resistor, RG. Without RG, the gain is simply 1 + R2/R1. In a practical application, the R2/R1 ratio is chosen for the desired minimum in amp gain. V2 + V1 A _ A1 V1 VOUT A2 + R1' _ V2 R1 R2' C RG R2 VREF R2 2R2 G = 1 + R1 + R G 2R2 R2 VOUT = ( V2 – V1) 1 + R1 + R G + VREF R2 = R2' R1' R1 CMR ≤ 20log GAIN × 100 % MISMATCH Figure 2-7: The two-op-amp instrumentation amplifier The input impedance of the two-op-amp in amp is inherently high, permitting the impedance of the signal sources to be high and unbalanced. The dc common mode rejection is limited by the matching of R1/R2 to R1'/R2'. If there is a mismatch in any of the four resistors, the dc common mode rejection is limited to: GAIN × 100 CMR ≤ 20 log ⋅ %MISMATCH Eq. 2-3 Notice that the net CMR of the circuit increases proportionally with the working gain of the in amp, an effective aid to high performance at higher gains. IC in amps are particularly well suited to meeting the combined needs of ratio matching and temperature tracking of the gain-setting resistors. While thin film resistors fabricated on silicon have an initial tolerance of up to ±20%, laser trimming during production allows the ratio error between the resistors to be reduced to 0.01% (100 ppm). Furthermore, the tracking between the temperature coefficients of the thin film resistors is inherently low and is typically less than 3 ppm/ºC (0.0003%/ºC). 128 Specialty Amplifiers When dual supplies are used, VREF is normally connected directly to ground. In single supply applications, VREF is usually connected to a low impedance voltage source equal to one-half the supply voltage. The gain from VREF to node “A” is R1/R2, and the gain from node “A” to the output is R2'/R1'. This makes the gain from VREF to the output equal to unity, assuming perfect ratio matching. Note that it is critical that the source impedance seen by VREF be low, otherwise CMR will be degraded. One major disadvantage of the two-op-amp in amp design is that common mode voltage input range must be traded off against gain. The amplifier A1 must amplify the signal at V1 by 1 + R1/R2. If R1 >> R2 (a low gain example in Figure 2-7), A1 will saturate if the V1 common-mode signal is too high, leaving no A1 headroom to amplify the wanted differential signal. For high gains (R1<< R2), there is correspondingly more headroom at node “A,” allowing larger common-mode input voltages. The ac common-mode rejection of this configuration is generally poor because the signal path from V1 to VOUT has the additional phase shift of A1. In addition, the two amplifiers are operating at different closedloop gains (and thus at different bandwidths). The use of a small trim capacitor “C” as shown in Figure 2-7 can improve the ac CMR somewhat. A low gain (G = 2) single-supply two-op-amp in amp configuration results when RG is not used, and is shown in Figure 2-8. The input common mode and differential signals must be limited to values that prevent saturation of either A1 or A2. In the example, the op amps remain linear to within 0.1 V of the supply rails, and their upper and lower output limits are designated VOH and VOL, respectively. These saturation voltage limits would be typical for a single-supply, rail-rail output op amp (such as the AD822, for example). V2 + V1 + A1 A _ R1 R2 VREF VREF = VOH = 4.9V VOL = 0.1V _ R1 R2 10kΩ 10kΩ 10kΩ VOUT A2 VOH = 4.9V VOL = 0.1V 10kΩ V1,MIN ≥ 1 (G – 1)V + V OL REF G ≥ 1.3V 2.5V VOH + VOL = 2.5V 2 V1,MAX ≤ 1 (G – 1)VOH + VREF ≤ 3.7V G V2 – V1 MAX ≤ VOH – VOL G Figure 2-8: Two-op-amp in amp single-supply restrictions for Vs = +5 V, G = 2 129 ≤ 2.4V Chapter Two Using the Figure 2-8 equations, the voltage at V1 must fall between 1.3 V and 2.4 V to prevent A1 from saturating. Notice that VREF is connected to the average of VOH and VOL (2.5 V). This allows for bipolar differential input signals with VOUT referenced to 2.5 V. A high gain (G = 100) single-supply two-op-amp in amp configuration is shown in Figure 2-9. Using the same equations, note that voltage at V1 can now swing between 0.124 V and 4.876 V. VREF is again 2.5 V, to allow for bipolar input and output signals. V2 + V1 + A1 VOH = 4.9V VOL = 0.1V A _ R1 VOUT A2 VOH = 4.9V VOL = 0.1V _ R1 R2 10kΩ 10kΩ 990kΩ R2 990kΩ VREF V1,MIN ≥ 1 (G – 1)V + V OL REF G ≥ 0.124V 2.5V V1,MAX ≤ 1 (G – 1)VOH + VREF ≤ 4.876V G V + VOL VREF = OH = 2.5V 2 V2 – V1 MAX ≤ VOH – VOL G ≤ 0.048V Figure 2-9: Two-op-amp in amp single-supply restrictions for Vs = +5 V, G = 100 All of these discussions show that the conventional two-op-amp in amp architecture is fundamentally limited, when operating from a single power supply. These limitations can be viewed in one sense as a restraint on the allowable input CM range for a given gain. Or, alternately, it can be viewed as limitation on the allowable gain range, for a given CM input voltage. Nevertheless, there are ample cases where a combination of gain and CM voltage cannot be supported by the basic two-op-amp structures of Figures 2-7 through 2-9, even with perfect amplifiers (i.e., zero output saturation voltage to both rails). In summary, regardless of gain, the basic structure of the common two-op-amp in amp does not allow for CM input voltages of zero when operated on a single supply. The only route to removing these restrictions for single supply operation is to modify the in amp architecture. The AD627 Single-Supply Two-Op-Amp In Amp The above-mentioned CM limitations can be overcome with some key modifications to the basic two-opamp in amp architecture. These modifications are implemented in the circuit shown in Figure 2-10, which represents the AD627 in amp architecture. In this circuit, each of the two op amps is composed of a PNP common emitter input stage and a gain stage, designated Q1/A1, and Q2/A2, respectively. The PNP transistors not only provide gain but also level-shift the input signal positive by about 0.5 V, thereby allowing the common-mode input voltage to go to 0.1 V below the negative supply rail. The maximum positive input voltage allowed is 1 V less than the positive supply rail. The AD627 in amp delivers rail-to-rail output swing, and operates over a wide supply voltage range (+2.7 V to ±18 V). Without the external gain setting resistor RG, the in amp gain is a minimum of 5. Gains 130 Specialty Amplifiers RG 25kΩ V1 (–) Q1 25kΩ V2 (+) +VS _ 100kΩ Q2 +VS _ VOUT A1 100kΩ A2 + + –VS –VS G = 5+ + 200kΩ RG VB – VOUT = G(V2 – V1) + VREF VREF –VS Figure 2-10: The AD627 in amp architecture up to 1000 can be set with the addition of this external resistor. Common-mode rejection of the AD627B at 60 Hz with a 1 kΩ source imbalance is 85 dB when operating on a single 3 V supply and G = 5. Even though the AD627 is a two-op-amp in amp, it is worthwhile noting that it is not subject to the same CM frequency response limitations as the basic circuit of Figure 2-7. A patented circuit keeps the AD627 CMR flat out to a much higher frequency than would otherwise be achievable with a conventional discrete two-op-amp in amp. The AD627 data sheet has a detailed discussion of allowable input/output voltage ranges as a function of gain and power supply voltages (see Reference 7). In addition, interactive design tools that perform calculations relating these parameters for a number of in amps, including the AD627 are available on the ADI Web site. Key specifications for the AD627 are summarized in Figure 2-11. Although it has been designed as a low power, single-supply device, the AD627 is capable of operating on traditional higher voltage supplies such as ±15 V, with excellent performance. • Wide Supply Range: +2.7V to ±18V • Input Voltage Range: –VS – 0.1V to +V S – 1V • 85µA Supply Current • Gain Range: 5 to 1000 • 75µV Maximum Input Offset Volage (AD627B) • 10ppm/°C Maximum Offset Voltage TC (AD627B) • 10ppm Gain Nonlinearity • 85dB CMR @ 60Hz, 1kΩ Source Imbalance (G = 5) • 3µV p-p 0.1Hz to 10Hz Input Voltage Noise (G = 5) Figure 2-11: AD627 in amp key specifications 131 Chapter Two Three-Op-Amp In Amps A second popular in amp architecture is based on three op amps, and is shown in Figure 2-12. This circuit is typically referred to as the three-op-amp in amp. + R2' + R3' A1 VSIG ~ 2 _ _ _ R1' VCM VOUT RG A3 R1 + ~ _ + VSIG ~ 2 _ + CMR ≤ 20log R3 R2 A2 GAIN × 100 % MISMATCH 2R1 VOUT = VSIG • R3 1 + RG R2 IF R2 = R3, G = 1 + VREF + VREF 2R1 RG Figure 2-12: The three-op-amp in amp Resistor RG sets the overall gain of this amplifier. It may be internal, external, or (software or pin-strap) programmable, depending upon the in amp. In this configuration, CMR depends upon the ratio-matching of R3/R2 to R3'/R2'. Furthermore, common-mode signals are only amplified by a factor of 1, regardless of gain. (No common-mode voltage will appear across RG, hence, no common-mode current will flow in it because the input terminals of an op amp will have no significant potential difference between them.) As a result of the high ratio of differential-to-CM gain in A1–A2, CMR of this in amp theoretically increases in proportion to gain. Large common-mode signals (within the A1–A2 op amp headroom limits) may be handled at all gains. Finally, because of the symmetry of this configuration, common mode errors in the input amplifiers, if they track, tend to be canceled out by the subtractor output stage. These features explain the popularity of this three-op-amp in amp configuration—it is capable of delivering the highest performance. The classic three-op-amp configuration has been used in a number of monolithic IC in amps (see References 8 and 9). Besides offering excellent matching between the three internal op amps, thin film laser trimmed resistors provide excellent ratio matching and gain accuracy at much lower cost than using discrete precision op amps and resistor networks. The AD620 (see Reference 10) is an excellent example of monolithic IC in amp technology. A simplified device schematic is shown in Figure 2-13. The AD620 is a highly popular in amp and is specified for power supply voltages from ±2.3 V to ±18 V. @ 1 kHz. Maximum input bias current is only 1 nA, due to the use Input voltage noise is only of superbeta transistors for Q1–Q2. Overvoltage protection is provided by the internal 400 Ω thin-film current-limit resistors in conjunction with the diodes connected from the emitter-to-base of Q1 and Q2. The gain G is set with a single external RG resistor, as noted by Eq. 2-4. G = (49.4 kΩ R G ) + 1 Eq. 2-4 As can be noted from this expression and Figure 2-13, the AD620 internal resistors are trimmed so that standard 1% or 0.1% resistors can be used to set gain to popular values. 132 Specialty Amplifiers +VS 49.4kΩ RG = G – 1 VB _ + _ + A1 A2 10kΩ 10kΩ _ A3 + 10kΩ VO 10kΩ 24.7kΩ Q1 400Ω 24.7kΩ Q2 VREF 400Ω RG –IN +IN –VS Figure 2-13: The AD620 in amp simplified schematic As is true in the case of the two-op-amp in amp configuration, single supply operation of the three-op-amp in amp requires an understanding of the internal node voltages. Figure 2-14 shows a generalized diagram of the in amp operating on a single 5 V supply. The maximum and minimum allowable output voltages of the individual op amps are designated VOH (maximum high output) and VOL (minimum low output), respectively. VCM + + R2' + _ VOH = 4.9V VOL = 0.1V R1' _ VOUT RG A3 VOH = 4.9V VOL = 0.1V R1 ~ + VSIG ~ 2 _ R2' A1 VSIG ~ 2 _ VCM GVSIG 2 + _ VOH = 4.9V VOL = 0.1V VOUT = GVSIG + VREF R2 R2 A2 VREF = 2.5V + G = 1+ VCM – 2R1 RG GVSIG 2 Figure 2-14: Three-op-amp in amp single 5 V supply restrictions Note that the gain from the common-mode voltage to the outputs of A1 and A2 is unity. It can be stated that the sum of the common-mode voltage and the signal voltage at these outputs must fall within the amplifier output voltage range. Obviously this configuration cannot handle input common-mode voltages of either zero volts or 5 V, because of saturation of A1 and A2. As in the case of the two-op-amp in amp, the output reference is positioned halfway between VOH and VOL to allow for bipolar differential input signals. While there are a number of good single-supply in amps, such as the AD627 discussed above, the highest performance devices are still among those specified for traditional dual-supply operation, i.e., the 133 Chapter Two just-discussed AD620. For certain applications, even such devices as the AD620, which has been designed for dual supply operation, can be used with full precision on a single-supply power system. Precision Single-Supply Composite In Amp One way to achieve both high precision and single-supply operation takes advantage of the fact that many popular sensors (e.g. strain gauges) provide an output signal that is inherently centered around an approximate mid-point of the supply voltage (and/or the reference voltage). Taking advantage of this basic point allows the inputs of a signal conditioning in amp to be biased at “mid-supply.” As a consequence of this step, the inputs needn’t operate near ground or the positive supply voltage, and the in amp can still be used with all its precision. Under these conditions, an AD620 dual-supply in amp referenced to the supply mid-point followed by an rail-to-rail op amp output gain stage provides very high dc precision. Figure 2-15 illustrates one such high performance in amp, which operates on a single 5 V supply. +5V VSIG _ 2 ~ VCM = 2.5V ~ VSIG 2 + + 10µF + _ P1 5kΩ 0.22µF 47kΩ R3 24.9k AD620 _ RG + ~ 10Hz NOISE FILTER 0.1µF R1 REF _ 75.0kΩ R2 A2 + + A1, A2 = 1/2 AD822 A1 49.9kΩ R4 _ VOUT 10mV TO 4.98V VREF +2.5V 1µF Figure 2-15: A precision single-supply composite in amp with rail-to-rail output This circuit uses the AD620 as a low-cost precision in amp for the input stage, along with an AD822 JFET-input dual rail-to-rail output op amp for the output stage, comprised of A1 and A2. The output stage operates at a fixed gain of 3, with overall gain set by RG. In this circuit, R3 and R4 form a voltage divider which splits the supply voltage nominally in half to 2.5 V, with fine adjustment provided by a trimming potentiometer, P1. This voltage is applied to the input of A1, an AD822 voltage follower, which buffers it and provides a low impedance source needed to drive the AD620’s reference pin as well as providing the output reference voltage VREF. Note that this feature allows a bipolar VOUT to be measured with respect to this 2.5 V reference (not to GND). This is despite the fact that the entire circuit operates from a single (unipolar) supply. The other half of the AD822 is connected as a gain-of-3 inverter, so that it can output ±2.5 V, “rail-torail,” with only ±0.83 V required of the AD620. This output voltage level of the AD620 is well within the AD620’s capability, thus ensuring high linearity for the front end. 134 Specialty Amplifiers The general gain expression for this composite in amp is the product of the gain of the AD620 stage, and the gain of inverting amplifier: 49.4 kΩ R2 + 1 GAIN = ⋅ RG R1 Eq. 2-5 For this example, an overall gain of 10 is realized with RG = 21.5 kΩ (closest standard value). The table shown in Figure 2-16 summarizes various RG gain values, and the resulting performance for gains ranging from 10 to 1000. CIRCUIT GAIN RG (Ω) VOS, RTI (µV) TC VOS, RTI (µV/°C) NONLINEARITY (ppm) * BANDWIDTH (kHz)** 10 21.5k 1000 1000 < 50 600 30 5.49k 430 430 < 50 600 100 1.53k 215 215 < 50 300 300 499 150 150 < 50 120 1000 149 150 150 < 50 30 *Nonlinearity Measured Over Output Range: 0.1V < V OUT < 4.90V **Without 10Hz Noise Filter Figure 2-16: Performance summary of the 5 V single-supply AD620/AD822 composite in amp In this application, the allowable input voltage on either input to the AD620 must lie between 2 V and 3.5 V in order to maintain linearity. For example, at an overall circuit gain of 10, the common-mode input voltage range spans 2.25 V to 3.25 V, allowing room for the ±0.25 V full-scale differential input voltage required to drive the output ±2.5 V about VREF. The inverting configuration was chosen for the output buffer to facilitate system output offset voltage adjustment by summing currents into the A2 stage buffer’s feedback summing node. These offset currents can be provided by an external DAC, or from a resistor connected to a reference voltage. The AD822 rail-to-rail output stage exhibits a very clean transient response (not shown) and a small-signal bandwidth over 100 kHz for gain configurations up to 300. Note that excellent linearity is maintained over 0.1 V to 4.9 V VOUT. To reduce the effects of unwanted noise pickup, a filter capacitor is recommended across A2’s feedback resistance to limit the circuit bandwidth to the frequencies of interest. This capacitor forms a first order lowpass filter with R2. The corner frequency is 10 Hz as shown, but this may be easily modified. The capacitor should be a high quality film type, such as polypropylene. 135 Chapter Two The AD623 In Amp Like the two-op-amp in amp counterparts discussed previously, three-op-amp in amps require special design attention for wide CM range inputs on single power supplies. The AD623 single supply in amp configuration (see Reference 11), shown below in Figure 2-17 offers an attractive solution. In this device PNP emitter follower level shifters Q1 and Q2 allow the input signal to go 150 mV below the negative supply, and to within 1.5 V of the positive supply. The AD623 is fully specified for both single power supplies between 3 V and +12 V, and dual supplies between ±2.5 V and ±6 V. +VS + 50kΩ 50kΩ A1 –IN Q1 _ 50kΩ _ –VS A3 RG VOUT 50kΩ +VS + _ 50kΩ 50kΩ A2 +IN VREF + Q2 –VS Figure 2-17: AD623 single-supply in amp architecture The AD623 data sheet (Reference 11, again) contains excellent discussions and data on allowable input/output voltage ranges as a function of gain and power supply voltages. In addition, interactive design tools that perform calculations relating these parameters for a number of in amps, including the AD623, are available on the ADI Web site. The key specifications of the AD623 are summarized in Figure 2-18. • Wide Supply Range: +3V to ±6V • Input Voltage Range: –VS – 0.15V to +VS – 1.5V • 575µA Maximum Supply Current • Gain Range: 1 to 1000 • 100µV Maximum Input Offset Voltage (AD623B) • 1µV/°C Maximum Offset Voltage TC (AD623B) • 50ppm Gain Nonlinearity • 105dB CMR @ 60Hz, 1kΩ Source Imbalance, G≥100 • 3µV p-p 0.1Hz to 10Hz Input Voltage Noise (G = 1) Figure 2-18: AD623 in amp key specifications 136 Specialty Amplifiers In Amp DC Error Sources The dc and noise specifications for in amps differ slightly from conventional op amps, so some discussion is required in order to fully understand the error sources. The gain of an in amp is usually set by a single resistor. If the resistor is external to the in amp, its value is either calculated from a formula or chosen from a table on the data sheet, depending on the desired gain. Absolute value laser wafer trimming allows the user to program gain accurately with this single resistor. The absolute accuracy and temperature coefficient of this resistor directly affects the in amp gain accuracy and drift. Since the external resistor will never exactly match the internal thin film resistor tempcos, a low TC (<25 ppm/°C) metal film resistor should be chosen, preferably with a 0.1% or better accuracy. Often specified as having a gain range of 1 to 1000, or 1 to 10,000, many in amps will work at higher gains, but the manufacturer will not guarantee a specific level of performance at these high gains. In practice, as the gain-setting resistor becomes smaller, any errors due to the resistance of the metal runs and bond wires become significant. These errors, along with an increase in noise and drift, may make higher single-stage gains impractical. In addition, input offset voltages can become quite sizable when reflected to output at high gains. For instance, a 0.5 mV input offset voltage becomes 5 V at the output for a gain of 10,000. For high gains, the best practice is to use an in amp as a preamplifier, then use a post amplifier for further amplification. In a pin-programmable-gain in amp such as the AD621, the gain-set resistors are internal, well matched, and the device gain accuracy and gain drift specifications include their effects. The AD621 is otherwise generally similar to the externally gain-programmed AD620. The gain error specification is the maximum deviation from the gain equation. Monolithic in amps such as the AD624C have very low factory trimmed gain errors, with its maximum error of 0.02% at G = 1 and 0.25% at G = 500 being typical for this high quality in amp. Notice that the gain error increases with increasing gain. Although externally connected gain networks allow the user to set the gain exactly, the temperature coefficients of the external resistors and the temperature differences between individual resistors within the network all contribute to the overall gain error. If the data is eventually digitized and presented to a digital processor, it may be possible to correct for gain errors by measuring a known reference voltage and then multiplying by a constant. Nonlinearity is defined as the maximum deviation from a straight line on the plot of output versus input. The straight line is drawn between the end points of the actual transfer function. Gain nonlinearity in a high quality in amp is usually 0.01% (100 ppm) or less, and is relatively insensitive to gain over the recommended gain range. 137 Chapter Two The total input offset voltage of an in amp consists of two components (see Figure 2-19). Input offset voltage, VOSI, is the input offset component that is reflected to the output of the in amp by the gain G. Output offset voltage, VOSO, is independent of gain. RS/2 ∆RS VOSI RG ~ ~ ~ VSIG 2 VOSO IB+ VSIG 2 IN AMP GAIN = G VOUT ~ IB– VCM VREF RS/2 IOS = IB+ – IB– OFFSET (RTI) = VOSO G + VOSI + IB ∆RS + IOS(RS + ∆RS) OFFSET (RTO) = VOSO + G VOSI + IB ∆RS + IOS(RS + ∆RS) Figure 2-19: In amp offset voltage model At low gains, output offset voltage is dominant, while at high gains input offset dominates. The output offset voltage drift is normally specified as drift at G = 1 (where input effects are insignificant), while input offset voltage drift is given by a drift specification at a high gain (where output offset effects are negligible). The total output offset error, referred to the input (RTI), is equal to VOSI + VOSO/G. In amp data sheets may specify VOSI and VOSO separately, or give the total RTI input offset voltage for different values of gain. Input bias currents may also produce offset errors in in amp circuits (Figure 2-19). If the source resistance, RS, is unbalanced by an amount, ∆RS, (often the case in bridge circuits), there is an additional input offset voltage error due to the bias current, equal to IB∆RS (assuming that IB+ ≈ IB– = IB). This error is reflected to the output, scaled by the gain G. The input offset current, IOS, creates an input offset voltage error across the source resistance, RS + ∆RS, equal to IOS(RS + ∆RS), which is also reflected to the output by the gain, G. In amp common-mode error is a function of both gain and frequency. Analog Devices specifies in amp CMR for a 1 kΩ source impedance unbalance at a frequency of 60 Hz. The RTI common-mode error is obtained by dividing the common-mode voltage, VCM, by the common-mode rejection ratio, CMRR. Figure 2-20 shows the CMR for the AD620 in amp as a function of frequency, with a 1 kΩ source impedance imbalance. Power supply rejection (PSR) is also a function of gain and frequency. For in amps, it is customary to specify the sensitivity to each power supply separately, as shown in Figure 2-21 for the AD620. The RTI power supply rejection error is obtained by dividing the power supply deviation from nominal by the power supply rejection ratio, PSRR. 138 Specialty Amplifiers Figure 2-20: AD620 In amp common-mode rejection (CMR) versus frequency for 1 kΩ source imbalance POSITIVE SUPPLY NEGATIVE SUPPLY Figure 2-21: AD620 in amp power supply rejection (PSR) versus frequency Because of the relatively poor PSR at high frequencies, decoupling capacitors are required on both power pins to an in amp. Low inductance ceramic capacitors (0.01 µF to 0.1 µF) are appropriate for high frequencies. Low ESR electrolytic capacitors should also be located at several points on the PC board for low frequency decoupling. Note that these decoupling requirements apply to all linear devices, including op amps and data converters. Further details on power supply decoupling are found in Chapter 7. 139 Chapter Two Now that all dc error sources have been accounted for, a worst case dc error budget can be calculated by reflecting all the sources to the in amp input, as is illustrated by the table of Figure 2-22. It should be noted that the dc errors can be referred to the in amp output (RTO), by simply multiplying the RTI error by the in amp gain. ERROR SOURCE RTI VALUE Gain Accuracy (ppm) Gain Accuracy × FS Input Gain Nonlinearity (ppm) Gain Nonlinearity × FS Input Input Offset Voltage, V OSI VOSI Output Offset Voltage, VOSO VOSO ÷ G Input Bias Current, I B , Flowing in ∆RS Input Offset Current, I OS , Flowing in R S IB ∆RS Common Mode Input Voltage, VCM VCM ÷ CMRR Power Supply Variation, ∆VS ∆VS ÷ PSRR IOS(RS + ∆RS) Figure 2-22: In amp dc errors referred to the input (RTI) In Amp Noise Sources Since in amps are primarily used to amplify small precision signals, it is important to understand the effects of all the associated noise sources. The in amp noise model is shown in Figure 2-23. RS/2 VNI RG ~ ~ ~ VSIG 2 VSIG 2 + VNO IN+ IN AMP GAIN = G IN– VOUT ~ REF _ VCM VREF RS/2 IF IN+ = IN– NOISE (RTI) = NOISE (RTO) = BW • BW • VNO2 G2 + VNI2 + VNO2 + G 2 VNI2 + IN2RS2 2 IN2RS2 2 BW = 1.57 × IN AMP Bandwidth @ Gain = G Figure 2-23: In amp noise model There are two sources of input voltage noise. The first is represented as a noise source, VNI, in series with the input, as in a conventional op amp circuit. This noise is reflected to the output by the in amp gain, G. The second noise source is the output noise, VNO, represented as a noise voltage in series with the in amp output. The output noise, shown here referred to VOUT, can be referred to the input by dividing by the gain, G. There are also two noise sources associated with the input noise currents IN+ and IN–. Even though IN+ and IN– are usually equal (IN+ ≈ IN– = IN), they are uncorrelated, and therefore, the noise they each create must be 140 Specialty Amplifiers summed in a root-sum-squares (RSS) fashion. IN+ flows through one-half of RS, and IN– the other half. This generates two noise voltages, each having an amplitude, INRS/2. Each of these two noise sources is reflected to the output by the in amp gain, G. The total output noise is calculated by combining all four noise sources in an RSS manner: I 2R 2 I 2R 2 NOISE (RTO ) = BW VNO 2 + G 2 VNI 2 + N + S + N − S 4 4 Eq. 2-6 If IN+ = IN− = IN, I 2R 2 NOISE (RTO ) = BW VNO 2 + G 2 VNI 2 + N S 2 Eq. 2-7 The total noise, referred to the input (RTI) is simply the above expression divided by the in amp gain, G: NOISE (RTI ) = BW VNO 2 2 I N 2 R S2 + VNI + 2 G 2 Eq. 2-8 In amp data sheets often present the total voltage noise RTI as a function of gain. This noise spectral density includes both the input (VNI) and output (VNO) noise contributions. The input current noise spectral density is specified separately. As in the case of op amps, the total in amp noise RTI must be integrated over the applicable in amp closedloop bandwidth to compute an RMS value. The bandwidth may be determined from data sheet curves that show frequency response as a function of gain. Regarding this bandwidth, some care must be taken in computing it, as it is often not constant bandwidth product relationship, as is true with VFB op amps. In the case of the AD620 in amp family for example, the gain-bandwidth pattern is more like that of a CFB op amp. In such cases, the safest way to predict the bandwidth at a given gain is to use the curves supplied within the data sheet. 141 Chapter Two In Amp Bridge Amplifier Error Budget Analysis It is important to understand in amp error sources in a typical application. Figure 2-24 shows a 350 Ω load cell with a full-scale output of 100 mV when excited with a 10 V source. The AD620 is configured for a gain of 100 using the external 499 Ω gain-setting resistor. The table shows how each error source contributes to a total unadjusted error of 2145 ppm. Note, however, that the gain, offset, and CMR errors can all be removed with a system calibration. The remaining errors—gain nonlinearity and 0.1 Hz to 10 Hz noise— cannot be removed with calibration and ultimately limit the system resolution to 42.8 ppm (approximately 14-bit accuracy). This example is of course just an illustration, but should be useful towards the importance of addressing performance-limiting errors such as gain nonlinearity and LF noise. +10V VCM = 5V 499Ω RG + AD620B – REF G = 100 350Ω, 100mV FS LOAD CELL AD620B SPECS @ 25°C, ±15V VOSI + VOSO/G = 55µV max IOS = 0.5nA max Gain Error = 0.15% Gain Nonlinearity = 40ppm 0.1Hz to 10Hz Noise = 280nVp-p CMR = 120dB @ 60Hz MAXIMUM ERROR CONTRIBUTION, +25 °C FULLSCALE: V IN = 100mV, V OUT = 10V VOS 55µV ÷ 100mV 550ppm IOS 350Ω × 0.5nA ÷ 100mV 1.8ppm Gain Error 0.15% 1500ppm Gain Nonlinearity 40ppm 40ppm CMR Error 120dB 1ppm × 5V ÷ 100mV 50ppm 0.1Hz to 10Hz 1/f Noise 280nV ÷ 100mV 2.8ppm Total Unadjusted Error ≈ 9 Bits Accurate 2145ppm Resolution Error ≈ 14 Bits Accurate 42.8ppm Figure 2-24: AD620B bridge amplifier dc error budget In Amp Performance Tables Figure 2-25 shows a selection of precision in amps designed primarily for operation on dual supplies. It should be noted that the AD620 is capable of single 5 V supply operation (see Figure 2-15), but neither its input nor its output are capable of rail-to-rail swings. These tables allow at-a-glance inspection of key errors, which can be critical in getting the most performance from a system. From Figure 2-25 for example, it can be noted that the use of an AD621 in lieu of the AD620B in the gain-of-100 bridge circuit of Figure 2-24 allows reduction of the gain nonlinearity component of error by a factor of four times. It is also important to separate out errors that can be calibrated out as mentioned above, and those that can only be minimized by device specification improvements. Comparison of the AD620B and the AD622 specifications, for example, shows a higher VOS for the latter. But, since VOS can be calibrated out, the fact that it is higher for the AD622 isn’t material to this particular application. The gain nonlinearity between the AD620 and AD622 is the same, so in an auto-cal system, they would likely perform comparably. On the other hand, the AD621B would be preferable for its lower gain nonlinearity, as noted. 142 Specialty Amplifiers VOS Max VOS TC CMR Min 0.1Hz to 10Hz p-p Noise 100ppm 50µV 0.5µV/°C 120dB 0.3µV 0.5% / R 40ppm 50µV 0.6µV/°C 120dB 0.28µV AD621B 1 0.05% / P 10ppm 50µV 1.6µV/°C 100dB 0.28µV AD622 0.5% / R 40ppm 125µV 1µV/°C 103dB 0.3µV AD624C 2 0.25% / R 50ppm 25µV 0.25µV/°C 130dB 0.2µV AD625C 0.02% / R 50ppm 25µV 0.25µV/°C 125dB 0.2µV AMP01A 0.6% / R 50ppm 50µV 0.3µV/°C 125dB 0.12µV AMP02E 0.5% / R 60ppm 100µV 2µV/°C 115dB 0.4µV Gain Nonlinearity AD524C Gain Accuracy * 0.5% / P AD620B */P = Pin Programmable */R = Resistor Programmable 1 2 G = 100 G = 500 Figure 2-25: Precision in amps: data for Vs = ±15 V, G = 1000 In amps specifically designed for single supply operation are also shown, in Figure 2-26. It should be noted that although the specifications in this figure are given for a single 5 V supply, all of the amplifiers are also capable of dual supply operation and are specified for both dual and single supply operation on their data sheets. In addition, the AD623 and AD627 will operate on a single 3 V supply Gain Accuracy * 0.5% / R 0.1Hz to 10Hz Supply Current p-p Noise Gain Nonlinearity VOS Max VOS TC CMR Min 50ppm 100µV 1µV/°C 105dB 1.5µV 575µA AD627B 0.35% / R 10ppm 75µV 1µV/°C 85dB 1.5µV 85µA AMP04E 0.4% / R 250ppm 150µV 3µV/°C 90dB 0.7µV 290µA AD626B 1 200ppm 2.5mV 6µV/°C 80dB 2µV 700µA AD623B 0.6% / P 1 */P = Pin Programmable */R = Resistor Programmable Differential Amplifier, G = 100 Figure 2-26: Single-supply in amps: data for Vs = 5 V, G = 1000 Note that the AD626 is not a true in amp, but is in fact a differential amplifier with a thin-film input attenuator that allows the common-mode voltage to exceed the supply voltages. This device is designed primarily for high- and low-side current-sensing applications. It will also operate on a single 3 V supply. In Amp Input Overvoltage Protection As interface amplifiers for data acquisition systems, in amps are often subjected to input overloads, i.e., voltage levels in excess of the full scale for the selected gain range. The manufacturer’s “absolute maximum” input ratings for the device should be closely observed. As with op amps, many in amps have absolute maximum input voltage specifications equal to ±VS. 143 Chapter Two In some cases, external series resistors (for current limiting) and diode clamps may be used to prevent overload if necessary (see Figure 2-27). Some in amps have built-in overload protection circuits in the form of series resistors. For example, the AD620 series have thin film resistors, and the substrate isolation they provide allows input voltages that can exceed the supplies. Other devices use series-protection FETs; for example, the AMP02 and the AD524, because they act as a low impedance during normal operation, and a high impedance during overvoltage fault conditions. In any instance however, there are always finite safe limits to applied overvoltage (Figure 2-27). +VS RLIMIT + INPUTS RLIMIT IN-AMP OUTPUT – –VS • Always Observe Absolute Maximum Data Sheet Specs • Schottky Diode Clamps to the Supply Rails Will Limit Input to Approximately ±VS ±0.3V, TVSs Limit Differential Voltage • External Resistors (or Internal Thin-Film Resistors) Can Limit Input Current, but will Increase Noise • Some In-Amps Have Series-Protection Input FETs for Lower Noise and Higher Input Overvoltages (up to ±60V, Depending on Device) Figure 2-27: In amp input overvoltage considerations In some instances, an additional Transient Voltage Suppressor (TVS) may be required across the input pins to limit the maximum differential input voltage. This is especially applicable to three-op-amp in amps operating at high gain with low values of RG. A more detailed discussion of input overvoltage and EMI/RFI protection can be found in Chapter 7 of this book. In Amp Applications Some representative in amp applications round out this section, illustrating how the characteristics lend utility and efficiency to a range of circuits. In Amp Bridge Amplifier In amps are widely used as precision signal conditioning elements. A popular application is a bridge amplifier, shown in Figure 2-28. The in amp is ideally suited for this application because the bridge output is fundamentally balanced, and the in amp presents it with a truly balanced high impedance load. The nominal resistor values in the bridge can range from 100 Ω to several kΩ, but 350 Ω is popular for most precision load cells. Full-scale output voltages from a typical bridge circuit can range from approximately 10 mV to several hundred mV. Typical in amp gains in the order of 100 to 1000 are therefore ideally suited for amplifying these small voltages to levels compatible with popular analog-to-digital converter (ADC) input voltage ranges (usually 1 V to 10 V full scale). 144 Specialty Amplifiers VB R+∆R R–∆R +VS VOUT = VB − RG ∆R R GAIN IN AMP + REF VOUT R–∆R R+∆R −VS Figure 2-28: Generalized bridge amplifier using an in amp In addition, the in amp’s high CMR at power line frequencies allows common-mode noise to be rejected, when the bridge must be located remotely from the in amp. Note that a much more thorough discussion of bridge applications can be found in Chapter 4 of this book. In Amp A/D Interface Interfacing bipolar signals to single-supply ADCs presents a challenge. The bipolar signal must be amplified and level-shifted into the input range of the ADC. Figure 2-29 shows how this translation can be achieved using the AD623 in amp, when interfacing a bridge circuit to the AD7776 10-bit, 2.5 µs ADC. Figure 2-29: Single-supply data acquisition system The bridge circuit is excited by a 5 V supply. The full-scale output from the bridge (±10 mV) therefore has a common-mode voltage of 2.5 V. The AD623 removes the common-mode component, and amplifies the bridge output by a factor of 100 (RG = 1.02 kΩ). This results in an output signal swing of ±1 V. This signal is level-shifted by connecting the REF pin of the AD623 to the 2 V REFOUT of the AD7776 ADC. This sets the common-mode output voltage of the AD623 to 2 V, and the resulting signal into the ADC is +2 V ±1 V, corresponding to the input range of the AD7776. 145 Chapter Two In Amp Driven Current Source Figure 2-30 shows a precision voltage-controlled current source using an in amp. The input voltage VIN develops an output voltage, VOUT, equal to GVIN between the output pin of the AD620 and the REF pin. With the connections shown, VOUT is also applied across sense resistor RSENSE, thus developing a load current of VOUT/RSENSE. The OP97 acts as a unity gain buffer to isolate the load from the 20 kΩ impedance of the REF pin of the AD620. In this circuit the input voltage can be floating with respect to the load ground (as long as there exists a path for the in amp bias currents). The high CMR of the in amp allows high accuracy to be achieved for the load current, despite CM voltages. +VS (+15V) (0.5V FS) + VOUT RSENSE AD620 VIN ILOAD (10mA FS) (50Ω) RG REF +VS VOUT – Voltage Compliance = ±10V + –VS (–15V) OP97 LOAD – –VS ILOAD = VOUT RSENSE = G VIN RSENSE Figure 2-30: Precision voltage-controlled current source using an in amp The circuit will work for both large and small values of G in the AD620. The most simple form would be to let G = 1 with RG open. In this case, VOUT = VIN, and ILOAD is proportional to VIN. But the gain factor of the in amp can readily be used to scale almost any input voltage to a desired current level. The output load voltage compliance is typically ±10 V when operating on ±15 V power supplies, and load currents up to ±15 mA are allowable, limited by the AD620’s drive. A typical operating condition might be a full scale load current of 10 mA, a full-scale VOUT = 0.5 V, and RSENSE = 50 Ω. For small values of RSENSE, the OP97 buffer could possibly be eliminated provided the resulting error incurred by the loading effect of the AD620 REF pin is acceptable. In this case the load and bottom RSENSE node would be connected directly to the in amp REF pin. Many other useful variations of the basic circuit exist, and can easily be added. For currents of up to 50 mA, a unity gain, low offset buffer can be added between the AD620 output and the top of RSENSE. This will remove all load current from the AD620, allowing it to operate with greatest linearity. The circuit is also very useful at very small currents. It will work well with the OP97 down to around 1 µA, before bias current of the op amp becomes a performance limitation. For even lower currents, a precision JFET op amp such as the AD8610 can easily be substituted. This step will allow precise low level currents, down to below 1 nA. Note that the AD8610 must be operated on supplies of ±13 V or less, but this isn’t necessarily a problem (the AD620 will still operate well on supplies as low as ±2.5 V). 146 Specialty Amplifiers A factor that may not be obvious is that the output current capability of this current source is bilateral, as it is shown. This makes this form of current source a great advantage over a Howland type current source, which are always problematic with the numerous resistors required, which must be well-matched and stable for good performance. In contrast, the current source of Figure 2-30 is clean and efficient, requires no matched resistors, and is precise over very wide current ranges. In Amp Remote Load Driver Often remote loads present a problem in driving, when high accuracy must be maintained at the load end. For this type of requirement, an in amp (or simple differential amplifier) with separate SENSE/FORCE terminals can serve very well, providing a complete solution in one IC. Most of the more popular in amps available today have removed the separate SENSE/FORCE connections, due to the pin limitations of an 8-pin package (AD620, etc.). However, many classic in amps such as the AMP01 do have access to the SENSE/FORCE pins, and can perform remote sensing, as shown in Figure 2-31. Figure 2-31: Precision in amp remote load driver using FORCE/SENSE connections In this circuit a quad cable composed of two twisted pairs is used. One pair is dedicated to the load HIGH side, the other to the LO side. At the remote end, the load is connected as shown, with each twisted pair terminated at one end of the load. Although the full load current still flows in the FORCE (AMP01 Pin 9) and OUTPUT GROUND connections, the resulting drop does not create an error, since the remote sensing of the second lead of each pair is returned back to the driver, and carries comparatively very little current. The reverse-parallel connected diodes are optional, and perform a “safety-valve” function, in case a sense line becomes open-circuit (100 Ω resistors might also be used). The AMP01 is valuable to this function not simply because of the SENSE/FORCE capability, but because it also is capable of 50 mA output currents and is stable with the capacitive loading presented by a cable. Alternately, a precision differential amplifier like the AMP03 can also be used, at lower current levels. For additional in amp background and reference material, see References 12 through 15. 147 Chapter Two References: Instrumentation Amplifiers 1. MIL-PRF-55182G, “Resistors, Fixed, Film, Nonestablished Reliability, Established Reliability, And Space Level, General Specification For,” June 9, 1997. 2. Robert Demrow, “Narrowing the Margin of Error,” Electronics, April 15, 1968, pp. 108–117. 3. Robert Demrow, “Evolution from Operational Amplifier to Data Amplifier,” Analog Devices Application Note, September, 1968. 4. David Birt, “Electronically Balanced Analogue-Line Interfaces,” Proceedings of Institute of Acoustics Conference, Windermere, U.K., Nov. 1990. 5. Walt Jung, “Op Amps in Line-Driver and Receiver Circuits, Part 1,” Analog Dialogue, Vol. 26 No. 2, 1992. 6. W. Jung, A. Garcia, “Op Amps in Line-Driver and Receiver Circuits, Part 2,” Analog Dialogue, Vol. 27, No. 1, 1993. 7. Data sheet for AD627 Micropower, Single and Dual Supply Rail-to-Rail Instrumentation Amplifier, www.analog.com. 8. S. Wurcer, L. Counts, “A Programmable Instrumentation Amplifier for 12-Bit Resolution Systems,” IEEE Journal of Solid-State Circuits, Vol. SC-17 #6, Dec. 1982, pp. 1102–1111. 9. L. Counts, S. Wurcer, “Instrumentation Amplifier Nears Input Noise Floor,” Electronic Design, June 10, 1982, p. 177. 10. Data sheet for AD620 Low Cost, Low Power Instrumentation Amplifier, www.analog.com 11. Data sheet for AD623 Single Supply, Rail-to-Rail, Low Cost Instrumentation Amplifier, www.analog.com. 12. Charles Kitchen and Lew Counts, A Designer’s Guide to Instrumentation Amplifiers, Analog Devices, 2000. 13. Sections 2, 3, 4, of Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, Inc., 1999, ISBN: 0-916550-20-6. 14. Walter Borlase, “Application/Analysis of the AD520 Monolithic Data Amplifier,” Analog Devices Application Note, 1972. 15. Jeff Riskin, A User’s Guide to IC Instrumentation Amplifiers, Analog Devices AN244, January, 1978. 148 Specialty Amplifiers Classic Cameo Robert Demrow’s “Evolution from Operational Amplifier to Data Amplifier” As applications engineering manager in the early years of ADI, Robert Demrow published numerous articles and application notes. It is a testament to the quality of these articles that most of them are still germane today—due in no small part to their lucid outlining of fundamental principles. Demrow’s 1968 application note, “Evolution from Operational Amplifier to Data Amplifier” outlined the relevant amplifier operating principles for retrieving analog signals from a noisy environment. It also introduced the ADI Model 601 data amplifier (above). Of course, a data amplifier is what we know today as an instrumentation amplifier. Within his Figure 16 can be seen several key operating principles: 1) dual high impedance inputs, as necessary for high CMR, 2) the use of a precision bipolar transistor differential pair front end, for low offset and drift (the µA726),1 3) a balanced, three amplifier stage topology. It is interesting to note that some more popular IC in amps of 2004 utilize many of the same principles—for example, the AD620 family. Back in 1968, Robert Demrow outlined a host of sound design concepts, leading the way to later solid-state developments and the completely monolithic in amp ICs of today. 1 James N. Giles, Editor, “The µA726 Temperature-Stabilized Transistor Pair,” Chapter 8, Fairchild Semiconductor Linear Integrated Circuits Handbook, Fairchild Semiconductor, 1967. 149 This page intentionally left blank SECTION 2-2 Programmable Gain Amplifiers Walt Kester, James Bryant Most data acquisition systems with wide dynamic range need some method of adjusting the input signal level to the analog-to-digital-converter (ADC). Typical ADC full-scale input voltage ranges lie between 2 V and 10 V. To achieve the rated precision of the converter, the maximum input signal should be fairly near its full-scale voltage. Transducers, however, have a very wide range of output voltages. High gain is needed for a small sensor voltage, but with a large output, a high gain will cause the amplifier or ADC to saturate. So, some type of predictably controllable gain device is needed. Amplifiers with programmable gain have a variety of applications, and Figure 2-32 lists some of them. • Instrumentation • Photodiode circuits • Ultrasound preamplifiers • Sonar • Wide dynamic range sensors • Driving ADCs (some ADCs have on-chip PGAs) • Automatic gain control (AGC) loops Figure 2-32: Programmable gain amplifier (PGA) applications Such a device has a gain that is controlled by a dc voltage or, more commonly, a digital input. This device is known as a programmable gain amplifier, or PGA. Typical PGAs may be configured either for selectable decade gains such as 10, 100, 100, etc., or they might also be configured for binary gains such as 1, 2, 4, 8, etc. It is a function of the end system of course, which type might be the more desirable. It should be noted that a factor common to the above application examples is that the different types of signals being handled is diverse. Some may require wide bandwidth, others very low noise, from either high or low impedance sources. The inputs may be single-ended, or they may be differential, crossing over into the realm of the just-discussed in amps. The output from the PGA may be required to drive some defined input range of an ADC, or it may be part of a smaller subsystem, such as an AGC or gain-ranging loop. The circuits following fall into a range of categories addressing some of these requirements. 151 Chapter Two A PGA is usually located between a sensor and its ADC, as shown in Figure 2-33. Additional signal conditioning may take place before or after the PGA, depending on the application. For example, a photodiode needs a current-to-voltage converter between it and the PGA. In most other systems, it is better to place the gain first, and condition a larger signal. This reduces errors introduced by the signal conditioning circuitry. GAIN CONTROL SENSOR PGA ADC DIGITAL OUTPUT Used to increase the dynamic range of the system A PGA with a gain of 1 to 2 theoretically increases the dynamic range by 6dB. A gain of 1 to 4 gives a 12dB increase, etc. Figure 2-33: PGAs in data acquisition systems To understand the benefits of variable gain, assume an ideal PGA with two settings, gains of one and two. The dynamic range of the system is increased by 6 dB. Increasing the gain to a maximum four results in a 12 dB increase in dynamic range. If the LSB of an ADC is equivalent to 10 mV of input voltage, the ADC cannot resolve smaller signals, but when the gain of the PGA is increased to two, input signals of 5 mV may be resolved. Thus, a central processor can combine PGA gain information with the digital output of the ADC to increase its resolution by one bit. Essentially, this is the same as adding additional resolution to the ADC. In fact, a number of ADCs now have on-chip PGAs for increased dynamic range (AD77xx-series, for example, covered later). PGA Design Issues In practice, PGAs aren’t ideal, and their error sources must be studied and dealt with. A number of the various PGA design issues are summarized in Figure 2-34. A fundamental PGA design problem is programming gain accurately. Electromechanical relays have minimal on resistance (RON), but are unsuitable for gain switching—slow, large, and expensive. CMOS switches are small, but they have voltage-/temperature-dependent RON, as well as stray capacitance, which may affect PGA ac parameters. • • • • • • • • How to switch the gain Effects of the switch on-resistance (R ON ) Gain accuracy Gain linearity Bandwidth versus frequency versus gain Dc offset Gain and offset drift over temperature Settling time after switching gain Figure 2-34: PGA design issues 152 Specialty Amplifiers To understand RON’s effect on performance, consider Figure 2-35, a poor PGA design. A noninverting op amp has four different gain-set resistors, each grounded by a switch, with an RON of 100 Ω–500 Ω. Even with RON as low as 25 Ω, the gain of 16 error would be 2.4%, worse than 8-bits. RON also changes over temperature and switch-switch. RF = 10kΩ – 625Ω 1.43kΩ 3.33kΩ VOUT 10kΩ + G = 16 G=8 G=4 G=2 VIN Gain accuracy limited by switch’s on-resistance R ON and R ON modulation R ON typically 100 − 500Ω for CMOS or JFET switch Even for R ON = 25Ω, there is a 2.4% gain error for G = 16 R ON drift over temperature limits accuracy Must use very low R ON switches (relays) Figure 2-35: A poorly designed PGA To attempt “fixing” this design, the resistors might be increased, but noise and offset could then be a problem. The only way to accuracy with this circuit is to use relays, with virtually no RON. Only then will the few mΩ of relay RON be a small error vis-à-vis 625 Ω. It is much better to use a circuit insensitive to RON. In Figure 2-36, the switch is placed in series with the inverting input of an op amp. Since the op amp input impedance is very large, the switch RON is now irrelevant, and gain is now determined solely by the external resistors. Note: RON may add a small offset error if op amp bias current is high (if this is the case, it can readily be compensated with an equivalent resistance at VIN). VIN + VOUT – G=1 500Ω G=2 1kΩ 1kΩ • R ON is not in series with gain setting resistors • R ON is small compared to input impedance • Only slight offset errors occur due to bias current flowing through the switches Figure 2-36: Alternate PGA configuration minimizes the effects of RON 153 Chapter Two PGA Applications The following section illustrates several PGA circuits using the above and other concepts. AD526 Software Programmable PGA The AD526 amplifier uses the just-described PGA architecture, integrating it onto a single chip, as diagrammed in Figure 2-37 (see References 1 and 2). The AD526 has five binary gain settings from 1 to 16, and its internal JFET switches are connected to the inverting input of the amplifier as in Figure 2-37. The gain resistors are laser trimmed, providing a maximum gain error of only 0.02%, and a linearity of 0.001%. The use of the FORCE/SENSE terminals connected at the load ensures highest accuracy (it also allows the use of an optional unity-gain buffer, for low impedance loads). Figure 2-37: AD526 software programmable PGA simplified schematic Functionally speaking, the AD526 is a programmable, precision, noninverting op amp gain stage, logic programmable over a range of 1 to 16 times VIN. It typically operates from a ±15 V power supply, and has ±10 V output range (like a conventional op amp). The key specifications for the AD526 are summarized in Figure 2-38. • Software programmable binary gains from 1 to 16 • Low bias current JFET input stage • Worst-case gain error: 0.02% (12-bit performance) • Maximum gain nonlinearity: 0.001% • Gain change settling time: 5.6µs (G = 16) • Small signal bandwidth: 4MHz (G = 1), 0.35MHz (G = 16) • Latched TTL-compatible control inputs Figure 2-38: AD526 PGA key specifications 154 Specialty Amplifiers Low Noise PGA This same design concepts can be used to build a low noise PGA as shown in Figure 2-39. It uses a single op amp, a quad switch, and precision resistors. The lower noise AD797 replaces the JFET input op amp of the AD526, but almost any voltage feedback op amp could be used in this circuit. The ADG412 was picked for its RON of 35 Ω. VIN 100Ω +15V + AD797 – –15V VOUT 20pF +5V 1kΩ G=1 TTL GAIN CONTROL +15V 10kΩ G = 10 –15V 1kΩ G = 100 100Ω G = 1000 ADG412 11Ω Figure 2-39: A very low noise PGA using the AD797 and the ADG412 The resistors were chosen to give decade gains of 1, 10, 100, and 1000, but if other gains are required, the resistor values may easily be altered. Ideally, a single trimmed resistor network should be used both for initial gain accuracy and for low drift over temperature. The 20 pF feedback capacitor ensures stability and holds the output voltage when the gain is switched. The control signal to the switches turns one switch off a few nanoseconds before the second switch turns on. During this break, the op amp is open-loop. Without the capacitor the output would start slewing. Instead, the capacitor holds the output voltage during switching. Since the time that both switches are open is very short, only 20 pF is needed. For slower switches, a larger capacitor may be necessary. at 1 kHz, only The PGA’s input voltage noise spectral density at a gain of 1000 is only slightly higher than the noise performance of the AD797 alone. The increase is due to the ADG412 noise, and the current noise of the AD797 flowing through RON. The accuracy of the PGA is important in determining the overall accuracy of a system. The AD797 has a bias current of 0.9 µA, which, flowing in a 35 Ω RON, results in an additional offset error of 31.5 µV. Combined with the AD797 offset, the total VOS becomes 71.5 µV (max). Offset temperature drift is affected by the change in bias current and RON. Calculations show that the total temperature coefficient increases from 0.6 µV/ºC to 1.6 µV/ºC. Note that while these errors are small (and may not matter in the end) it is still important to be aware of them. 155 Chapter Two In practice, circuit accuracy and gain TC will be determined by the external resistors. Input characteristics such as common mode range and input bias current are determined solely by the AD797. A performance summary is shown below in Figure 2-40. • R ON adds additional input offset and drift: − ∆VOS = Ib RON = (0.9µA)(35Ω) = 31.5µV (max) − Total VOS = 40µV + 31.5µV = 71.5µV (max) • Temperature drift due to RON: − At +85°°C, ∆VOS = (2µA)(45Ω) = 90µV (max) • Temperature coefficient total: − ∆VOS /∆T = 0.6µV/°°C + 1.0µV/°°C = 1.6µV/°°C (max) − Note: 0.6µV/°°C is due to the AD797B • RTI Noise : 1.65nV/√Hz @ 1kHz, G = 1000 • Gain switching time < 1µs, G = 10 Figure 2-40: AD797/ADG412 PGA performance summary DAC Programmed PGA Another PGA configuration uses a DAC in the feedback loop of an op amp to adjust the gain under digital control, as shown in Figure 2-41. The digital code of the DAC controls its attenuation with respect to its reference input VREF, acting functionally similar to a potentiometer. Attenuating the feedback signal increases the closed-loop gain. DB0 DB15 RIN CS R / W LDAC CLR VREF+ VOUT AD7846 VREF– VSS VDD –15V +15V VCC DGND +5V 1000pF 1kΩ +15V – VOUT OP113 0V TO 5V VIN + –15V G= 216 Decimal Value of Digital Code Figure 2-41: Binary gain PGA using a DAC in the feedback path of an op amp A noninverting PGA of this type requires a multiplying DAC with a voltage mode output. Note that a multiplying DAC is a DAC with a wide reference voltage range, which includes zero. For most applications of the PGA, the reference input must be capable of handling bipolar signals. The AD7846 is a 16-bit converter that meets these requirements. In this application, it is used in the standard 2-quadrant multiplying mode. 156 Specialty Amplifiers The OP113 is a low drift, low noise amplifier, but the choice of the amplifier is flexible, and depends on the intended application. The input voltage range depends on the output swing of the AD7846, which is 3 V less than the positive supply, and 4 V above the negative supply. A 1000 pF capacitor is used in the feedback loop for stability. The gain of the circuit is set by adjusting the digital inputs of the DAC, according to the equation given in Figure 2-41. D0-15 represents the decimal value of the digital code. For example, if all the bits were set high, the gain would be 65,536/65,535 = 1.000015. If the eight least significant bits are set high and the rest low, the gain would be 65,536/255 = 257. The bandwidth of the circuit is a fairly high 4 MHz for a gain of +1. However, this does reduce with gain, and for a gain of 256, the bandwidth is only 600 Hz. If the gain-bandwidth product were constant, the bandwidth in a gain of 256 should be 15.6 kHz; but the internal capacitance of the DAC reduces the bandwidth to 600 Hz. Performance characteristics of this binary PGA are summarized in Figure 2-42. • Gain Accuracy: − 0.003% (G = +1) − 0.1% (G = +256) • Nonlinearity: 0.001% (G = 1) • Offset: 100µV • Noise: 50nV/√Hz • Bandwidth: − 4MHz (G = +1) − 600Hz (G = +256) Figure 2-42: Binary gain PGA performance The gain accuracy of the circuit is determined by the resolution of the DAC and the gain setting. At a gain of 1, all bits are on, and the accuracy is determined by the DNL specification of the DAC, which is ±1 LSB maximum. Thus, the gain accuracy is equivalent to 1 LSB in a 16-bit system, or 0.003%. However, as the gain is increased, fewer of the bits are on. For a gain of 256, only bit 8 is turned on. The gain accuracy is still dependent on the ±1 LSB of DNL, but now that is compared to only the lowest eight bits. Thus, the gain accuracy is reduced to 1 LSB in an 8-bit system, or 0.4%. If the gain is increased above 256, the gain accuracy is reduced further. The designer must determine an acceptable level of accuracy. In this particular circuit, the gain was limited to 256. Differential Input PGAs There are often applications where a PGA with differential inputs is needed, instead of the single-ended types discussed so far. The AD625 combines an instrumentation amplifier topology similar to the AD620 with external gain switching capabilities to accomplish 12-bit gain accuracy (see Reference 3). An external switch is needed to switch between different gain settings, but its on resistance does not significantly affect the gain accuracy due to the unique design of the AD625. 157 Chapter Two The circuit in Figure 2-43 uses an ADG409 CMOS switch to switch the connections to an external gainsetting resistor network. In the example shown, resistors were chosen for gains of 1, 4, 16, and 64. Other features of the AD625 are 0.001% nonlinearity, wide bandwidth, and very low input noise. ADG409 Figure 2-43: A software-programmable gain amplifier The AD625 is uniquely designed so that the on resistance of the switches does not introduce significant error in the circuit. This can be understood by considering the simplified AD625 circuit shown Figure 2-44. The voltages shown are for an input of +1 mV on +IN and 0 V on –IN. The gain is set to 64 with RG = 635 Ω and the two resistors, RF = 20 kΩ. +VS 50µA _ + +1 = 64 RG _ + A1 2RF G= 50µA VB A2 10kΩ SENSE 10kΩ _ VO –32mV +32mV GAIN DRIVE –IN GAIN DRIVE GAIN SENSE RF RG 20kΩ GAIN SENSE 50Ω +IN = +1mV 635Ω 50µA = +64mV REF Q2 RF 20kΩ A3 + 10kΩ Q1 50Ω 10kΩ 1mV 50µA –VS Figure 2-44: AD625 details showing external switches and gain-setting resistors for RG = 635 Ω, +IN = 1 mV, –IN = 0 V 158 Specialty Amplifiers Since transistors Q1 and Q2 have 50 µA current sources in both their emitters and their collectors, negative feedback around A1 and A2, respectively, will ensure that no net current flows through either gain sense pin into either emitter. Since no current flows in the gain sense pins, no current flows in the gain setting switches, and their RON does not affect either gain or offset. In real life there will be minor mismatches, but the errors are well under the 12-bit level. The differential gain between the inputs and the A1-A2 outputs is 2RF/RG + 1. The unity-gain difference amplifier and matched resistors removes CM voltage, and drives the output. Noninverting PGA circuits using an op amp are easily adaptable to single supply operation, but when differential inputs are desired, a single-supply in amp such as the AD623, AD627, or the AMP04 should be used. The AMP04 is used with an external CMOS switch in the single supply in amp PGA shown in Figure 2-45. V+ ADG511 G = 100kΩ / RG V+ Figure 2-45: Single supply instrumentation PGA using the AMP04 in amp and the ADG511 switch This circuit has selectable gains of 1, 10, 100, and 500, which are controlled by an ADG511. The ADG511 was chosen as a single supply switch with a low RON of 45 Ω. A disadvantage of this circuit is that the gain of this circuit is dependent on the RON of the switches. Trimming is required at the higher gains to achieve accuracy. At a gain of 500, two switches are used in parallel, but their resistance causes a 10% gain error in the absence of adjustment. ADC with Onboard PGA Certain ADCs (such as the AD77ss measurement series) have built-in PGAs and other conditioning circuitry. Circuit design with these devices is much easier, because an external PGA and its control logic are not needed. Furthermore, all the errors of the PGA are included in the specifications of the ADC, making error calculations simple. The PGA gain is controlled over the common ADC serial interface, and the gain setting is factored into the conversion, saving additional calculations to determine input voltage. 159 Chapter Two This combination of ADC and PGA is very powerful and enables the realization of a highly accurate system, with a minimum of circuit design. As an example, Figure 2-46 shows a simplified diagram of the AD7730 sigma-delta measurement ADC which is optimized for digitizing low voltage bridge outputs directly (as low as 10 mV full scale) to greater than 16 bits noise free code resolution, without the need for external signal conditioning circuits. Additional information and background reading on PGAs can be found in References 4 and 5. AVDD DVDD REFIN(–) REFIN(+) REFERENCE DETECT 100nA AIN1(+) AIN1(–) STANDBY SIGMA-DELTA ADC BUFFER + MUX + _ ∑ SIGMADELTA MODULATOR PGA +/– AIN2(+)/D1 AIN2(–)/D0 AD7730 100nA SERIAL INTERFACE AND CONTROL LOGIC 6-BIT DAC PROGRAMMABLE DIGITAL FILTER CLOCK GENERATION SYNC MCLK IN MCLK OUT REGISTER BANK SCLK VBIAS CS CALIBRATION MICROCONTROLLER ACX ACX DIN DOUT AC EXCITATION CLOCK AGND DGND POL RDY RESET Figure 2-46: AD7730 sigma-delta measurement ADC with on-chip PGA References: Programmable Gain Amplifiers 1. John Krehbiel, “Monolithic Software Programmable-Gain Amplifier,” Analog Dialogue, Vol. 21, No. 2, 1987, pp. 12–13. 2. Data sheet for AD526 Software Programmable Gain Amplifier, www.analog.com. 3. Data sheet for AD625 Programmable Gain Instrumentation Amplifier, www.analog.com. 4. Chapters 2, 3, 8, Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 5. Chapter 2, Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 160 SECTION 2-3 Isolation Amplifiers Walt Kester, James Bryant Analog Isolation Techniques There are many applications where it is desirable, or even essential, for a sensor to have no direct (“galvanic”) electrical connection with the system to which it is supplying data. This might be in order to avoid the possibility of dangerous voltages or currents from one half of the system doing damage in the other, or to break an intractable ground loop. Such a system is said to be “isolated,” and the arrangement that passes a signal without galvanic connections is known as an isolation barrier. The protection of an isolation barrier works in both directions, and may be needed in either, or even in both. The obvious application is where a sensor may accidentally encounter high voltages, and the system it is driving must be protected. Or a sensor may need to be isolated from accidental high voltages arising downstream in order to protect its environment. Examples include the need to prevent the ignition of explosive gases by sparks at sensors and the protection from electric shock of patients whose ECG, EEG, or EMG is being monitored. The ECG case is interesting, as protection may be required in both directions: the patient must be protected from accidental electric shock, but if the patient’s heart should stop, the ECG machine must be protected from the very high voltages (>7.5 kV) applied to the patient by the defibrillator that will be used to attempt to restart it. A summary of applications for isolation amplifiers (both analog and digital) is shown in Figure 2-47. • Sensor is at a High Potential Relative to Other Circuitry (or may become so under Fault Conditions) • Sensor May Not Carry Dangerous Voltages, Irrespective of Faults in Other Circuitry (e.g. Patient Monitoring and Intrinsically Safe Equipment for use with Explosive Gases) • To Break Ground Loops Figure 2-47: Applications for isolation amplifiers Just as interference, or unwanted information, may be coupled by electric or magnetic fields, or by electromagnetic radiation, these phenomena may be used for the transmission of wanted information in the design of isolated systems. The most common isolation amplifiers use transformers, which exploit magnetic fields, and another common type uses small high voltage capacitors, exploiting electric fields. Optoisolators, which consist of an LED and a photocell, provide isolation by using light, a form of electromagnetic radiation. Different isolators have differing performance: some are sufficiently linear to pass high accuracy analog signals across an isolation barrier. With others, the signal may need to be converted to digital form before transmission for accuracy is to be maintained (note this is a common V/F converter application). 161 Chapter Two Transformers are capable of analog accuracy of 12 to 16 bits and bandwidths up to several hundred kHz; their maximum voltage rating rarely exceeds 10 kV, and is often much lower. Capacitively-coupled isolation amplifiers have lower accuracy, perhaps 12 bits maximum, lower bandwidth, and lower voltage ratings—but they are low cost. Optical isolators are fast and cheap, and can be made with very high voltage ratings (4 kV – 7 kV is one of the more common ratings), but they have poor analog domain linearity and are not usually suitable for direct coupling of precision analog signals. Linearity and isolation voltage are not the only issues to be considered in the choice of isolation systems. Operating power is of course, essential. Both the input and the output circuitry must be powered and, unless there is a battery on the isolated side of the isolation barrier (which is possible, but rarely convenient), some form of isolated power must be provided. Systems using transformer isolation can easily use a transformer (either the signal transformer or another one) to provide isolated power. It is, however, impractical to transmit useful amounts of power by capacitive or optical means. Systems using these forms of isolation must make other arrangements to obtain isolated power supplies—this is a powerful consideration in favor of choosing transformer-isolated isolation amplifiers: they almost invariably include an isolated power supply. The isolation amplifier has an input circuit that is galvanically isolated from the power supply and the output circuit. In addition, there is minimal capacitance between the input and the rest of the device. Therefore, there is no possibility for dc current flow and minimum ac coupling. Isolation amplifiers are intended for applications requiring safe, accurate measurement of low frequency voltage or current (up to about 100 kHz) in the presence of high common-mode voltage (to thousands of volts) with high common-mode rejection. They are also useful for line-receiving of signals transmitted at high impedance in noisy environments, and for safety in general-purpose measurements, where dc and line-frequency leakage must be maintained at levels well below certain mandated minimums. Principal applications are in electrical environments of the kind associated with medical equipment, conventional and nuclear power plants, automatic test equipment, and industrial process control systems. AD210 Three-Port Isolator In a basic two-port form of isolator, the output and power circuits are not isolated from one another. A three-port isolator (input, power, output) is shown in Figure 2-48. Note that in this diagram, the input circuits, output circuits, and power source are all isolated from one another. This figure represents the circuit architecture of a self-contained isolator, the AD210 (see References 1 and 2). FB INPUT –IN _ +IN + T1 OUTPUT _ DEMOD FILTER MOD + ICOM +VISS –VISS VO OCOM T2 POWER INPUT POWER SUPPLY T3 OUTPUT POWER SUPPLY POWER OSCILLATOR PWR PWR COM Figure 2-48: AD210 three-port isolation amplifier 162 +VOSS –VOSS Specialty Amplifiers An isolator of this type requires power from a two-terminal dc power supply (PWR, PWR COM). An internal oscillator (50 kHz) converts the dc power to ac, which is transformer-coupled to the shielded input section, then converted to dc for the input stage and the auxiliary power output. The ac carrier is also modulated by the input stage amplifier output, transformer-coupled to the output stage, demodulated by a phase-sensitive demodulator (using the carrier as the reference), filtered, and buffered using isolated dc power derived from the carrier. The AD210 allows the user to select gains from 1 to 100, using external resistors with the input section op amp. Bandwidth is 20 kHz, and voltage isolation is 2500 V rms (continuous) and ±3500 V peak (continuous). The AD210 is a three-port isolation amplifier, thus the power circuitry is isolated from both the input and the output stages and may therefore be connected to either (or to neither), without change in functionality. It uses transformer isolation to achieve 3500 V isolation with 12-bit accuracy. Key specifications for the AD210 are summarized in Figure 2-49. • Transformer Coupled • High Common-Mode Voltage Isolation: − 2500V RMS Continuous − ±3500V Peak Continuous • Wide Bandwidth: 20kHz (Full Power) • 0.012% Maximum Linearity Error • Input Amplifier: Gain 1 to 100 • Isolated Input and Output Power Supplies, ±15V, ±5mA Figure 2-49: AD210 isolation amplifier key specifications 163 Chapter Two Motor Control Isolation Amplifier A typical isolation amplifier application using the AD210 is shown in Figure 2-50. The AD210 is used with an AD620 instrumentation amplifier in a current-sensing system for motor control. The input of the AD210, being isolated, can be directly connected to a 110 V or 230 V power line without protection being necessary. The input section’s isolated ±15 V powers the AD620, which senses the voltage drop in a small value current sensing resistor. The AD210 input stage op amp is simply connected as a unity-gain follower, which minimizes its error contribution. The 110 V or 230 V rms common-mode voltage is ignored by this isolated system. HIGH VOLAGE AC INPUT < 2500V RMS +15V RG 0.01Ω AD620 REF _ INPUT FB + –IN _ +IN + T1 OUTPUT _ DEMOD FILTER MOD + OUTPUT VO OCOM ICOM –15V +VISS –VISS M RG = 499Ω FOR G = 100 POWER T2 T3 OUTPUT POWER SUPPLY INPUT POWER SUPPLY AD210 +VOSS –VOSS POWER OSCILLATOR PWR PWR COM +15V Figure 2-50: Motor control current sensing Within this system the AD620 preamp is used as the system scaling control point, and will produce and output voltage proportional to motor current, as scaled by the sensing resistor value and gain as set by the AD620’s RG. The AD620 also improves overall system accuracy, as the AD210 VOS is 15 mV, versus the AD620’s 30 µV (with less drift also). Note that if higher dc offset and drift are acceptable, the AD620 may be omitted and the AD210 connected at a gain of 100. Optional Noise Reduction Post Filter Due to the nature of this type of carrier-operated isolation system, there will be certain operating situations where some residual ac carrier component will be superimposed upon the recovered output dc signal. When this occurs, a low impedance passive RC filter section following the output stage may be used (if the following stage has a high input impedance, i.e., nonloading to this filter). Note that will be the case for many high input impedance sampling ADCs, which appear essentially as a small capacitor. A 150 Ω resistance and 1 nF capacitor will provide a corner frequency of about 1 kHz. Note also that the capacitor should be a film type for low errors, such as polypropylene. AD215 Two-Port Isolator The AD215 is a high speed, two-port isolation amplifier, designed to isolate and amplify wide bandwidth analog signals (see Reference 3). The innovative circuit and transformer design of the AD215 ensures wideband dynamic characteristics, while preserving dc performance specifications. An AD215 block diagram is shown in Figure 2-51. The AD215 provides complete galvanic isolation between the input and output of the device, which also includes the user-available front-end isolated bipolar power supply. The functionally complete design, 164 Specialty Amplifiers Figure 2-51: AD215 120kHz low distortion two-port isolation amplifier powered by a ±15 V dc supply on the output side, eliminates the need for a user supplied isolated dc/dc converter. This permits the designer to minimize circuit overhead and reduce overall system design complexity and component costs. The design of the AD215 emphasizes maximum flexibility and ease of use in a broad range of applications where fast analog signals must be measured under high common-mode voltage (CMV) conditions. The AD215 has a ±10 V input/output range, a specified gain range of 1 V/V to 10 V/V, a buffered output with offset trim and a user-available isolated front end power supply which produces ±15 V dc at ±10 mA. The key specifications of the AD215 are summarized in Figure 2-52. • Isolation voltage: 1500V rms • Full power bandwidth: 120kHz • Slew rate: 6V/µs • Harmonic distortion: –80dB @ 1kHz • 0.005% maximum linearity error • Gain range: 1 to 10 • Isolated input power supply: ±15V @ ±10mA Figure 2-52: AD215 isolation amplifier key specifications 165 Chapter Two Digital Isolation Techniques Analog isolation amplifiers find many applications where a high isolation is required, such as in medical instrumentation. Digital isolation techniques provide similar galvanic isolation, and are a reliable method of transmitting digital signals without ground noise. Optocouplers (also called optoisolators) are useful and available in a wide variety of styles and packages. A typical optocoupler based on an LED and a phototransitor is shown in Figure 2-53. A current of approximately 10 mA drives an LED transmitter, with light output is received by a phototransistor. The light produced by the LED saturates the phototransistor. Input/output isolation of 5000 V rms to 7000 V rms is common. Although fine for digital signals, optocouplers are too nonlinear for most analog applications. Also, since the phototransistor is being saturated, response times can range from 10 µs to 20 µs in slower devices, limiting high speed applications. 10k Ω VDD1 (5V) 425Ω CMOS GATE VIN GND1 VDD2 (5V) IOUT IIN HIGH VOLTAGE ISOLATION BARRIER VOUT GND2 • Uses Light for Transmission over a High Voltage Barrier • The LED is the Transmitter, and the Phototransistor is the Receiver • High Voltage Isolation: 5000V to 7000V rms • Nonlinear — Best for Digital or Frequency Information • Rise and Fall times can be 10µs to 20µs in Slower Devices • Example: Siemens ILQ-1 Quad (www.siemens.com) Figure 2-53: Digital isolation using LED/phototransistor optocouplers A much faster optocoupler architecture is shown in Figure 2-54, and is based on an LED and a photodiode. The LED is again driven with a current of approximately 10 mA. VDD1 VDD2 (Data In) VIN VOUT (Data Out) GND1 GND2 • 5V Supply Voltage • 2500V rms I/O Withstand Voltage • Logic Signal Frequency: 12.5MHz Maximum • 25MBd Maximum Data Rate • 40ns Maximum Propagation Delay • 9ns Typical Rise/Fall Time • Example: Agilent HCPL-7720 • (www.semiconductor.agilent.com) Figure 2-54: Digital isolation using LED/photodiode optocouplers 166 Specialty Amplifiers This produces a light output sufficient to generate enough current in the receiving photodiode to develop a valid high logic level at the output of the transimpedance amplifier. Speed can vary widely between optocouplers, and the fastest ones have propagation delays of 20 ns typical, and 40 ns maximum, and can handle data rates up to 25 MBd for NRZ data. This corresponds to a maximum square wave operating frequency of 12.5 MHz, and a minimum allowable passable pulse width of 40 ns. AD260/AD261 High Speed Logic Isolators The AD260/AD261 family of digital isolators operates on a principle of transformer-coupled isolation (see Reference 4). They provide isolation for five digital control signals to/from high speed DSPs, microcontrollers, or microprocessors. The AD260 also has a 1.5 W transformer for a 3.5 kV rms isolated external dc/dc power supply circuit. Each line of the AD260 can handle digital signals up to 20 MHz (40 MBd) with a propagation delay of only 14 ns which allows for extremely fast data transmission. Output waveform symmetry is maintained to within ±1ns of the input so the AD260 can be used to accurately isolate time-based pulsewidth modulator (PWM) signals. A simplified schematic of one channel of the AD260/AD261 is shown in Figure 2-55. The data input is passed through a Schmitt trigger circuit, through a latch, and a special transmitter circuit which differentiates the edges of the digital input signal and drives the primary winding of a proprietary transformer with a “set-high/set-low” signal. The secondary of the isolation transformer drives a receiver with the same “set-hi/set-low” data, which regenerates the original logic waveform. An internal circuit operating in the background interrogates all inputs about every 5 µs, and in the absence of logic transitions, sends appropriate “set-hi/set-low” data across the interface. Recovery time from a fault condition or at power-up is thus between 5 µs and 10 µs. DATA IN SCHMITT TRIGGER TRI-STATE BUFFER LATCH D DATA OUT XMTR RCVR E ENABLE ENABLE CONTINUOUS UPDATE CIRCUIT ISOLATED POWER XFMR (AD260) 37V p-p, 1.5W NOTE: SINGLE DATA CHANNEL SHOWN 3500V RMS ISOLATION BARRIER (AD260B/AD261B) Figure 2-55: AD260/AD261 digital isolators The power transformer (available on the AD260) is designed to operate between 150 kHz and 250 kHz and will easily deliver more than 1 W of isolated power when driven push-pull (5 V) on the transmitter side. Different transformer taps, rectifier and regulator schemes will provide combinations of ±5 V, 15 V, 24 V, or even 30 V or higher. 167 Chapter Two The transformer output voltage when driven with a low voltage-drop drive will be 37 V p-p across the entire secondary with a 5 V push-pull drive. Figure 2-56 summarizes the key specifications of the AD260/261 series. • Isolation Test Voltage to 3500V rms (AD260B/AD261B) • Five Isolated Digital Lines Available in six Input/Output Configurations • Logic Signal Frequency: 20MHz Max. • Data Rate: 40MBd Max. • Isolated Power Transformer: 37V p-p, 1.5W (AD260) • Waveform Edge Transmission Symmetry: ±1ns • Propagation Delay: 14ns • Rise and Fall Times < 5ns Figure 2-56: AD260/AD261 digital isolator key specifications The availability of low cost digital isolators such as those previously discussed solves most system isolation problems in data acquisition systems as shown in Figure 2-57. In the upper example, digitizing the signal first, then using digital isolation eliminates the problem of analog isolation amplifiers. While digital isolation can be used with parallel output ADCs provided the bandwidth of the isolator is sufficient, it is more practical with ADCs that have serial outputs. This minimizes cost and component count. A 3-wire interface (data, serial clock, framing clock) is all that is required in these cases. An alternative (lower example) is to use a voltage-to-frequency converter (VFC) as a transmitter and a frequency-to-voltage converter (FVC) as a receiver. In this case, only one digital isolator is required. ISOLATION BARRIER SENSOR ADC DIGITAL ISOLATORS DAC SENSOR V/F CONVERTER DIGITAL ISOLATOR F/V CONVERTER GROUND REFERENCE A GROUND REFERENCE B Figure 2-57: Practical application of digital isolation in data acquisition systems 168 Specialty Amplifiers References: Isolation Amplifiers 1. James Conant, “Precision Wideband Three-Port Isolation Amplifier,” Analog Dialogue, Vol. 20, No. 2, 1986, p. 14. 2. Data sheet for AD210 Precision, Wide Bandwidth 3-Port Isolation Amplifier, www.analog.com. 3. Data sheet for AD215 120 kHz Bandwidth, Low Distortion, Isolation Amplifier, www.analog.com. 4. Data sheets for AD260 and AD261 High Speed Logic Isolators, www.analog.com. 5. Chapters 2, 3, 8, Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 6. Chapter 2, Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 7. Chapter 10, Walt Kester, Editor, Mixed-Signal and DSP Design Techniques, Analog Devices, 2000, ISBN: 0-916550-23-0. 169 This page intentionally left blank CHAPTER 3 Using Op Amps with Data Converters ■ Section 3-1: Introduction ■ Section 3-2: ADC/DAC Specifications ■ Section 3-3: Driving ADC Inputs ■ Section 3-4: Driving ADC/DAC Reference Outputs ■ Section 3-5: Buffering DAC Outputs This page intentionally left blank CHAPTER 3 Using Op Amps with Data Converters Walt Kester, James Bryant, Paul Hendriks SECTION 3-1 Introduction Walt Kester This chapter of the book deals with data conversion and associated signal conditioning circuitry involving the use of op amps. Data conversion is a very broad topic, and this chapter will provide only enough background material for the reader to make intelligent decisions regarding op amp selection. Much more material on the subject is available in the references (see References 1-5). Figure 3-1 shows a generalized sampled data system and some possible applications of op amps. The analog input signal is first buffered and filtered before it is applied to the analog-to-digital converter (ADC). The buffer may or may not be required, depending upon the input structure of the ADC. For example, some ADCs (such as switched capacitor) generate transient currents at their inputs due to the internal conversion architecture, and these currents must be isolated from the signal source. A suitable buffer amplifier provides a low impedance drive and absorbs these currents. In some cases, an op amp is required to provide the appropriate gain and offset to match the signal to the input range of the ADC. VREF ANALOG INPUT LPF OR BPF ADC SAMPLED AND QUANTIZED WAVEFORM VREF DSP DAC fS LPF OR BPF ANALOG OUTPUT RECONSTRUCTED WAVEFORM 1 fS 1 fS Figure 3-1: Typical sampled data system showing potential amplifier applications 173 Chapter Three Another key component in a sampled data system is the antialiasing filter which removes signals that fall outside the Nyquist bandwidth, fs/2. Normally this filter is a low-pass filter, but it can be a band-pass filter in certain undersampling applications. If the op amp buffer is required, it may be located before or after the filter, depending on system considerations. In fact, the filter itself may be an active one, in which case the buffering function can be performed by the actual output amplifier of the filter. More discussions regarding active filters can be found in Chapter 5 of this book. After the signal is buffered and filtered, it is applied to the ADC. The full-scale input voltage range of the ADC is generally determined by a voltage reference, VREF. Some ADCs have this function on chip, while others require an external reference. If an external reference is required, its output may require buffering using an appropriate op amp. The reference input to the ADC may be connected to an internal switched capacitor network, causing transient currents to be generated at that node (similar to the analog input of such converters). Some references may therefore require a buffer to isolate these transient currents from the actual reference output. Other references may have internal buffers that are sufficient, and no additional buffering is needed in those cases. The output of the ADC is then processed digitally by an appropriate processor, shown in the diagram as a digital signal processor (DSP). DSPs are processors that are optimized to perform fast repetitive arithmetic, as required in digital filters or fast Fourier transform (FFT) algorithms. The DSP output then drives a digital-to-analog converter (DAC) which converts the digital signal back into an analog signal. • • • • • • • Gain setting Level-shifting Buffering ADC transients from signal source Buffering voltage reference outputs Buffering DAC outputs Active antialiasing filter before ADC Active anti-imaging filter after DAC Figure 3-2: Data converter amplifier applications The DAC analog output must be filtered to remove the unwanted image frequencies caused by the sampling process, and further buffering may be required to provide the proper signal amplitude and offset. The output filter is generally placed between the DAC and the buffer amplifier, but their positions can be reversed in certain applications. It is also possible to combine the filtering and buffering function if an active filter is used to condition the DAC output. Trends in Data Converters It is useful to examine a few general trends in data converters, to better understand any associated op amp requirements. Converter performance is first and foremost; maintaining that performance in a system application is extremely important. In low frequency measurement applications (10 Hz bandwidth signals or lower), sigma-delta ADCs with resolutions up to 24 bits are now quite common. These converters generally have automatic or factory calibration features to maintain required gain and offset accuracy. In higher frequency signal processing, ADCs must have wide dynamic range (low distortion and noise), high sampling frequencies, and generally excellent ac specifications. In addition to sheer performance, other characteristics such as low power, single-supply operation, low cost, and small surface-mount packages also drive the data conversion market. These requirements result in 174 Using Op Amps with Data Converters application problems because of reduced signal swings, increased sensitivity to noise, and so forth. In addition, many data converters are now produced on low-cost foundry CMOS processes which generally make on-chip amplifier design more difficult and therefore less likely to be incorporated on-chip. As has been mentioned previously, the analog input to a CMOS ADC is usually connected directly to a switched-capacitor sample-and-hold (SHA), which generates transient currents that must be buffered from the signal source. On the other hand, data converters fabricated on Bi-CMOS or bipolar processes are more likely to have internal buffering, but generally have higher cost and power than their CMOS counterparts. It should be clear by now that selecting an appropriate op amp for a data converter application is highly dependent on the particular converter under consideration. Generalizations are difficult, but some meaningful guidelines can be followed. • • • • • • • Higher sampling rates, higher resolution, higher ac performance Single supply operation (e.g., 5V, 3V) Lower power Smaller input/output signal swings Maximize usage of low cost foundry CMOS processes Smaller packages Surface-mount technology Figure 3-3: Some general trends in data converters The most obvious requirement for a data converter buffer amplifier is that it not degrade the dc or ac performance of the converter. One might assume that a careful reading of the op amp datasheets would assist in the selection process: simply lay the data converter and the op amp datasheets side by side, and compare each critical performance specification. It is true that this method will provide some degree of success; however, in order to perform an accurate comparison, the op amp must be specified under the exact operating conditions required by the data converter application. Such factors as gain, gain setting resistor values, source impedance, output load, input and output signal amplitude, input and output common-mode (CM) level, power supply voltage, and so forth, all affect op amp performance. It is highly unlikely that even a well written op amp data sheet will provide an exact match to the operating conditions required in the data converter application. Extrapolation of specified performance to fit the exact operating conditions can give erroneous results. Also, the op amp may be subjected to transient currents from the data converter, and the corresponding effects on op amp performance are rarely found on datasheets. Converter datasheets themselves can be a good source for recommended op amps and other application circuits. However this information can become obsolete as newer op amps are introduced after the converter’s initial release. 175 Chapter Three Analog Devices and other op amp manufacturers today have on-line websites featuring parametric search engines, which facilitate part selection (see Reference 1). For instance, the first search might be for minimum power supply voltage, e.g., 3 V. The next search might be for bandwidth, and further searches on relevant specifications will narrow the selection of op amps even further. Figure 3-4 summarizes the selection process. • The amplifier should not degrade the performance of the ADC/DAC • Ac specifications are usually the most important − Noise − Bandwidth − Distortion • Selection based on op amp data sheet specifications difficult due to varying conditions in actual application circuit with ADC/DAC: − Power supply voltage − Signal range (differential and common-mode) − Loading (static and dynamic) − Gain • Parametric search engines may be useful • ADC/DAC data sheets often recommend op amps (but may not include newly released products) Figure 3-4: General amplifier selection criteria While not necessarily suitable for the final selection, this process can narrow the search to a manageable number of op amps whose individual datasheets can be retrieved, then reviewed in detail before final selection. From the discussion thus far, it should be obvious that in order to design a proper interface, an understanding of both op amps and data converters is required. References 2-6 provide background material on data converters. The next section of this chapter addresses key data converter performance specifications without going into the detailed operation of converters themselves. The remainder of the chapter shows a number of specific applications of op amps with various data converters. 176 Using Op Amps with Data Converters References: Introduction 1. ADI Web site, at www.analog.com. 2. Walt Kester, Editor, Practical Analog Design Techniques, Analog Devices, 1995, ISBN: 0-916550-16-8. 3. Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0-916550-17-6. 4. Chapters 3, 8, Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 5. Chapters 2, 3, 4, Walt Kester, Editor, Mixed-Signal and DSP Design Techniques, Analog Devices, 2000, ISBN: 0-916550-23-0. 6. Chapters 4, 5, Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 177 This page intentionally left blank SECTION 3-2 ADC/DAC Specifications Walt Kester ADC and DAC Static Transfer Functions and DC Errors The most important thing to remember about both DACs and ADCs is that either the input or output is digital, and therefore the signal is quantized. That is, an N-bit word represents one of 2N possible states, and therefore an N-bit DAC (with a fixed reference) can have only 2N possible analog outputs, and an N-bit ADC can have only 2N possible digital outputs. The analog signals will generally be voltages or currents. The resolution of data converters may be expressed in several different ways: the weight of the Least Significant Bit (LSB), parts per million of full scale (ppm FS), millivolts (mV), and so forth. It is common that different devices (even from the same manufacturer) will be specified differently, so converter users must learn to translate between the different types of specifications if they are to successfully compare devices. The size of the least significant bit for various resolutions is shown in Figure 3-5. RESOLUTION N 2-bit 2N 4 VOLTAGE (10V FS) 2.5 V ppm FS 250,000 % FS 25 dB FS −12 4-bit 16 625 mV 62,500 6.25 −24 6-bit 64 156 mV 15,625 1.56 −36 8-bit 256 39.1 mV 3,906 0.39 −48 10-bit 1,024 9.77 mV (10 mV) 977 0.098 −60 12-bit 4,096 2.44 mV 244 0.024 −72 14-bit 16,384 610 µV 61 0.0061 −84 16-bit 65,536 153 µV 15 0.0015 −96 18-bit 262,144 38 µV 4 0.0004 −108 20-bit 1,048,576 9.54 µV (10 µV) 1 0.0001 −120 22-bit 4,194,304 2.38 µV 0.24 0.000024 −132 24-bit 16,777,216 596 nV* 0.06 0.000006 −144 *600nV is the Johnson Noise in a 10kHz BW of a 2.2kΩ Resistor @ 25°C Note: 10 bits and 10V FS yields an LSB of 10mV, 1000ppm, or 0.1%. All other values may be calculated by powers of 2. Figure 3-5: Quantization: the size of a least significant bit (LSB) As noted above (and obvious from this table), the LSB scaling for a given converter resolution can be expressed in various ways. While it is convenient to relate this to a full scale of 10 V, as in Figure 3-5, other full scale levels can be easily extrapolated. Before we can consider op amp applications with data converters, it is necessary to consider the performance to be expected, and the specifications that are important when operating with data converters. The following sections will consider the definition of errors and specifications used for data converters. 179 Chapter Three The first applications of data converters were in measurement and control, where the exact timing of the conversion was usually unimportant, and the data rate was slow. In such applications, the dc specifications of converters are important, but timing and ac specifications are not. Today many, if not most, converters are used in sampling and reconstruction systems where ac specifications are critical (and dc ones may not be). Figure 3-6 shows the transfer characteristics for a 3-bit unipolar ideal and nonideal DAC. In a DAC, both the input and output are quantized, and the graph consists of eight points—while it is reasonable to discuss a line through these points, it is critical to remember that the actual transfer characteristic is not a line, but a series of discrete points. IDEAL NONIDEAL FS FS ANALOG OUTPUT NONMONOTONIC 000 001 010 011 100 101 110 000 111 001 010 011 100 101 110 111 DIGITAL INPUT DIGITAL INPUT Figure 3-6: DAC transfer functions Similarly, Figure 3-7 shows the transfer characteristics for a 3-bit unipolar ideal and nonideal ADC. Note that the input to an ADC is analog and is therefore not quantized, but its output is quantized. The ADC transfer characteristic therefore consists of eight horizontal steps (when considering the offset, gain and linearity of an ADC we consider the line joining the midpoints of these steps). IDEAL DIGITAL OUTPUT NONIDEAL 111 111 110 110 101 101 100 100 011 011 010 MISSING CODE 010 QUANTIZATION UNCERTAINTY 001 001 000 000 ANALOG INPUT FS ANALOG INPUT Figure 3-7: ADC transfer functions 180 FS Using Op Amps with Data Converters The (ideal) ADC transitions take place at ½ LSB above zero, and thereafter every LSB, until 1½ LSB below analog full scale. Since the analog input to an ADC can take any value, but the digital output is quantized, there may be a difference of up to ½ LSB between the actual analog input and the exact value of the digital output. This is known as the quantization error or quantization uncertainty as shown in Figure 3-7. In ac (sampling) applications this quantization error gives rise to quantization noise which will be discussed shortly. The integral linearity error of a converter is analogous to the linearity error of an amplifier, and is defined as the maximum deviation of the actual transfer characteristic of the converter from a straight line. It is generally expressed as a percentage of full scale (but may be given in LSBs). There are two common ways of choosing the straight line: end point and best straight line. In the end point system, the deviation is measured from the straight line through the origin and the full scale point (after gain adjustment). This is the most useful integral linearity measurement for measurement and control applications of data converters (since error budgets depend on deviation from the ideal transfer characteristic, not from some arbitrary “best fit”), and is the one normally adopted by Analog Devices, Inc. The best straight line, however, does give a better prediction of distortion in ac applications, and also gives a lower value of “linearity error” on a data sheet. The best fit straight line is drawn through the transfer characteristic of the device using standard curve fitting techniques, and the maximum deviation is measured from this line. In general, the integral linearity error measured in this way is only 50% of the value measured by end point methods. This makes the method good for producing impressive datasheets, but it is less useful for error budget analysis. For ac applications, it is even better to specify distortion than dc linearity, so it is rarely necessary to use the best straight line method to define converter linearity. The other type of converter nonlinearity is differential nonlinearity (DNL). This relates to the linearity of the code transitions of the converter. In the ideal case, a change of 1 LSB in digital code corresponds to a change of exactly 1 LSB of analog signal. In a DAC, a change of 1 LSB in digital code produces exactly 1 LSB change of analog output, while in an ADC there should be exactly 1 LSB change of analog input to move from one digital transition to the next. Where the change in analog signal corresponding to 1 LSB digital change is more or less than 1 LSB, there is said to be a DNL error. The DNL error of a converter is normally defined as the maximum value of DNL to be found at any transition. If the DNL of a DAC is less than –1 LSB at any transition (Figure 3-6), the DAC is nonmonotonic; i.e., its transfer characteristic contains one or more localized maxima or minima. A DNL greater than +1 LSB does not cause nonmonotonicity, but is still undesirable. In many DAC applications (especially closed-loop systems where nonmonotonicity can change negative feedback to positive feedback), it is critically important that DACs are monotonic. DAC monotonicity is often explicitly specified on datasheets, but if the DNL is guaranteed to be less than 1 LSB (i.e., |DNL| ≤ 1LSB) then the device must be monotonic, even without an explicit guarantee. ADCs can be nonmonotonic, but a more common result of excess DNL in ADCs is missing codes (Figure 3-7). Missing codes (or nonmonotonicity) in an ADC are as objectionable as nonmonotonicity in a DAC. Again, they result from DNL > 1 LSB. Quantization Noise in Data Converters The only errors (dc or ac) associated with an ideal N-bit ADC are those related to the sampling and quantization processes. The maximum error an ideal ADC makes when digitizing a dc input signal is ±½ LSB. Any ac signal applied to an ideal N-bit ADC will produce quantization noise whose rms value (measured over the Nyquist bandwidth, dc to fs/2) is approximately equal to the weight of the least significant bit (LSB), q, 181 Chapter Three divided by . This assumes that the signal is at least a few LSBs in amplitude so that the ADC output always changes state. The quantization error signal from a linear ramp input is approximated as a sawtooth waveform with a peak-to-peak amplitude equal to q, and its rms value is therefore (see Figure 3-8). DIGITAL CODE OUTPUT ANALOG INPUT q = 1LSB ERROR RMS ERROR = q/√12 SNR = 6.02N + 1.76dB + 10log fs FOR FS SINEWAVE 2•BW Figure 3-8: Ideal N-bit ADC quantization noise It can be shown that the ratio of the rms value of a full scale sinewave to the rms value of the quantization noise (expressed in dB) is: SNR = 6.02 N + 1.76 dB, Eq. 3-1 where N is the number of bits in the ideal ADC. Note—this equation is only valid if the noise is measured over the entire Nyquist bandwidth from dc to fs/2. If the signal bandwidth, BW, is less than fs/2, the SNR within the signal bandwidth BW is increased because the amount of quantization noise within the signal bandwidth is less. The correct expression for this condition is given by: f SNR = 6.02 N + 1.76 dB + 10 log S ⋅ 2 ⋅ BW Eq. 3-2 The above equation reflects the condition called oversampling, where the sampling frequency is higher than twice the signal bandwidth. The correction term is often called processing gain. Notice that for a given signal bandwidth, doubling the sampling frequency increases the SNR by 3 dB. 182 Using Op Amps with Data Converters ADC Input-Referred Noise The internal circuits of an ADC produce a certain amount of wideband rms noise due to thermal and kT/C effects. This noise is present even for dc input signals, and accounts for the fact that the output of most wideband (or high resolution) ADCs is a distribution of codes, centered around the nominal dc input value, as is shown in Figure 3-9. To measure its value, the input of the ADC is grounded, and a large number of output samples are collected and plotted as a histogram (sometimes referred to as a grounded-input histogram). Since the noise is approximately Gaussian, the standard deviation (σ) of the histogram is easily calculated, corresponding to the effective input rms noise. It is common practice to express this rms noise in terms of LSBs, although it can be expressed as an rms voltage. NUMBER OF OCCURRENCES P-P INPUT NOISE ≈ 6.6 × RMS NOISE RMS NOISE (σ) n–4 n–3 n–2 n–1 n n+1 n+2 n+3 n+4 OUTPUT CODE Figure 3-9: Effect of ADC input-referred noise on “grounded input” histogram 183 Chapter Three Calculating Op Amp Output Noise and Comparing it with ADC Input-Referred Noise In precision measurement applications utilizing 16- to 24-bit sigma-delta ADCs operating on low frequency (<20 Hz, e.g.) signals, it is generally undesirable to use a drive amplifier in front of the ADC because of the increased noise due to the amplifier itself. If an op amp is required, however, the op amp output 1/f noise should be compared to the input-referred ADC noise. The 1/f noise is usually specified as a peak-to-peak value measured over the 0.1 Hz to 10 Hz bandwidth and referred to the op amp input (see Chapter 1 of this book). Op amps such as the OP177 and the AD707 (input voltage noise 350 nV p-p) or the AD797 (input voltage noise 50 nV p-p) are appropriate for high resolution measurement applications if required. The general model for calculating the referred-to-input (RTI) or referred-to-output (RTO) noise of an op amp is shown in Figure 3-10. This model shows all possible noise sources. The results using this model are relatively accurate, provided there is less than 1 dB gain peaking in the closed loop frequency response. For higher frequency applications, 1/f noise can be neglected, because the dominant contributor is white noise. VN,R2 B VN,R1 R1 ∼ VN,R3 GAIN FROM = "A" TO OUTPUT VN R3 ∼ – CLOSED LOOP BW = f CL IN+ ∼ NOISE GAIN = R2 NG = 1 + R1 4kTR2 IN– 4kTR1 A R2 ∼ + VOUT R2 GAIN FROM = – "B" TO OUTPUT R1 4kTR3 V N2 RTI NOISE = BW • + 4kTR3 R1•R2 + IN+2R32 + IN–2 R1+R2 RTO NOISE = NG • RTI NOISE + 4kTR1 + 4kTR2 2 R2 R1+R2 R1 R1+R2 2 2 BW = 1.57 f CL Figure 3-10: Op amp noise model for a first-order circuit with resistive feedback An example of a practical noise calculation is shown in Figure 3-11. In this circuit, a wideband, low distortion amplifier (AD9632) drives a 12-bit, 25 MSPS ADC (AD9225). The input voltage noise spectral density of the AD9632 dominates the op amp noise because of the low gain and the low values of the external feedback resistors. The noise at the output of the AD9632 is obtained by multiplying the input voltage noise spectral density by the noise gain of 2. To obtain the rms noise, the noise spectral density is multiplied by the equivalent noise bandwidth of 50 MHz which is set by the single-pole low-pass filter placed between the op amp and the ADC input. Note that the closed-loop bandwidth of the AD9632 is 250 MHz, and the input bandwidth of the AD9225 is 105 MHz. With no filter, the output noise of the AD9632 would be integrated over the full 105 MHz ADC input bandwidth. However, the sampling frequency of the ADC is 25 MSPS, thereby implying that signals above 12.5 MHz are not of interest, assuming Nyquist operation (as opposed to undersampling applications where the input signal can be greater than the Nyquist frequency, fs/2). The addition of this simple filter significantly reduces noise effects. 184 Using Op Amps with Data Converters Vni 274Ω 274Ω R= − 75 Ω VREF 1.0kΩ AD9632 103Ω VINA 0.1uF + C= 100pF Noise Bandwidth = 1.57 • AD9225 12-bit ADC 50Ω fs = 25MSPS 1 = 50MHz 2π RC AD9632 OP AMP SPECIFICATIONS AD9225 ADC SPECIFICATIONS Effective Input Noise = 166µV rms Small Signal Input BW = 105MHz Input Voltage Noise = 4.3nV/√Hz Closed-Loop Bandwidth = 250MHz AD9632 Output Noise Spectral Density = 2 • 4.3nV/√ Hz = 8.6nV/√Hz Vni = 8.6nV/ 8.6nV/√Hz • 50MHz = 61µV rms Figure 3-11: Noise calculations for the AD9632 op amp driving the AD9225 12-bit, 25 MSPS ADC The noise at the output of the low-pass filter is calculated as approximately 61 µV rms which is less than half the effective input noise of the AD9225, 166 µV rms. Without the filter, the noise from the op amp would be about 110 µV rms (integrating over the full equivalent ADC input noise bandwidth of 1.57 × 105 MHz = 165 MHz). This serves to illustrate the general concept shown in Figure 3-12. In most high speed system applications a passive antialiasing filter (either low-pass for baseband sampling, or band-pass for undersampling) is required, and placing this filter between the op amp and the ADC will serve to reduce the noise due to the op amp. fFILTER LPF OR BPF f CL AMP fs f CL AMP ADC f ADC fs fFILTER LPF OR BPF AMP NOISE INTEGRATED OVER f CL OR f ADC, WHICHEVER IS LESS ADC f ADC AMP NOISE INTEGRATED OVER FILTER BW, f FILTER f IN GENERAL, f FILTER < s << f ADC < f CL 2 Figure 3-12: Proper positioning of the antialiasing filter will reduce the effects of op amp noise 185 Chapter Three Quantifying and Measuring Converter Dynamic Performance There are various ways to characterize the ac performance of ADCs. In the early years of ADC technology (over 30 years ago) there was little standardization with respect to ac specifications, and measurement equipment and techniques were not well understood or available. Over nearly a 30-year period, manufacturers and customers have learned more about measuring the dynamic performance of converters, and the specifications shown in Figure 3-13 represent the most popular ones used today. • Signal-to-Noise-and-Distortion Ratio (SINAD, or S/N +D) • Effective Number of Bits (ENOB) • Signal-to-Noise Ratio (SNR) • Analog Bandwidth (Full-Power, Small-Signal) • Harmonic Distortion • Worst Harmonic • Total Harmonic Distortion (THD) • Total Harmonic Distortion Plus Noise (THD + N) • Spurious Free Dynamic Range (SFDR) • Two-Tone Intermodulation Distortion • Multitone Intermodulation Distortion Figure 3-13: Quantifying ADC dynamic performance Practically all the specifications represent the converter’s performance in the frequency domain, and all are related to noise and distortion in one manner or another. ADC outputs are analyzed using fast Fourier transform (FFT) techniques, and DAC outputs are analyzed using conventional analog spectrum analyzers, as shown in Figure 3-14. In the case of an ADC, the input signal is an analog sinewave, and in the case of a DAC, the input is a digital sinewave generated by a direct digital synthesis (DDS) system. SIGNAL GEN. ADC BUFFER MEMORY M SAMPLES DSP M-POINT FFT Resolution = f s /M fs 2 DDS DAC ANALOG SPECTRUM ANALYZER f Figure 3-14: Measuring ADC/DAC dynamic performance 186 Using Op Amps with Data Converters Signal-to-Noise-and-Distortion Ratio (SINAD), Signal-to-Noise Ratio (SNR), and Effective Number of Bits (ENOB) SINAD and SNR deserve careful attention (see Figure 3-15), because there is still some variation between ADC manufacturers as to their precise meaning. Signal-to-noise-and-Distortion (SINAD, or S/N+D) is the ratio of the rms signal amplitude to the mean value of the root-sum-square (RSS) of all other spectral components, including harmonics, but excluding dc. SINAD is a good indication of the overall dynamic performance of an ADC as a function of input frequency, because it includes all components that make up noise (including thermal noise) and distortion. It is often plotted for various input amplitudes. SINAD is equal to THD+N if the bandwidth for the noise measurement is the same. • SINAD (Signal-to-Noise-and-Distortion Ratio): − The ratio of the rms signal amplitude to the mean value of the root-sum-squares (RSS) of all other spectral components, including harmonics, but excluding dc. • ENOB (Effective Number of Bits): ENOB = SINAD – 1.76 dB 6.02 • SNR (Signal-to-Noise Ratio, or Signal-to-Noise Ratio without Harmonics: − The ratio of the rms signal amplitude to the mean value of the root-sum-squares (RSS) of all other spectral components, excluding the first five harmonics and dc. Figure 3-15: SINAD, ENOB, and SNR The SINAD plot shows where the ac performance of the ADC degrades due to high-frequency distortion, and is usually plotted for frequencies well above the Nyquist frequency so that performance in undersampling applications can be evaluated. SINAD is often converted to effective-number-of-bits (ENOB) using the relationship for the theoretical SNR of an ideal N-bit ADC: SNR = 6.02N + 1.76dB. The equation is solved for N, and the value of SINAD is substituted for SNR: ENOB = SINAD − 1.76 dB 6.02 Eq. 3-3 Signal-to-noise ratio (SNR, or SNR-without-harmonics) is calculated the same as SINAD except that the signal harmonics are excluded from the calculation, leaving only the noise terms. In practice, it is only necessary to exclude the first five harmonics since they dominate. The SNR plot will degrade at high frequencies, but not as rapidly as SINAD because of the exclusion of the harmonic terms. Many current ADC datasheets somewhat loosely refer to SINAD as SNR, so the design engineer must be careful when interpreting these specifications. 187 Chapter Three A SINAD/ENOB plot for the AD9220 12-bit, 10MSPS ADC is shown in Figure 3-16. 13.0 12.2 11.3 SINAD (dB) ENOB 10.5 9.7 8.8 8.0 7.2 6.3 ANALOG INPUT FREQUENCY (MHz) Figure 3-16: AD9220 12-bit, 10 MSPS ADC SINAD and ENOB for various input signal levels Analog Bandwidth The analog bandwidth of an ADC is that frequency at which the spectral output of the fundamental swept frequency (as determined by the FFT analysis) is reduced by 3 dB. It may be specified for either a small signal bandwidth (SSBW), or a full-scale signal (FPBW – full power bandwidth), so there can be a wide variation in specifications between manufacturers. Like an amplifier, the analog bandwidth specification of a converter does not imply that the ADC maintains good distortion performance up to its bandwidth frequency. In fact, the SINAD (or ENOB) of most ADCs will begin to degrade considerably before the input frequency approaches the actual 3 dB bandwidth frequency. Figure 3-17 shows ENOB and full-scale frequency response of an ADC with a FPBW of 1 MHz; however, the ENOB begins to drop rapidly above 100 kHz. FPBW = 1MHz GAIN (FS INPUT) GAIN ENOB (FS INPUT) ENOB ENOB (-20dB INPUT) 10 100 1k 10k 100k 1M 10M ADC INPUT FREQUENCY (Hz) Figure 3-17: ADC Gain (bandwidth) and ENOB versus frequency shows importance of ENOB specification 188 Using Op Amps with Data Converters Harmonic Distortion, Worst Harmonic, Total Harmonic Distortion (THD), Total Harmonic Distortion Plus Noise (THD + N) There are a number of ways to quantify the distortion of an ADC. An FFT analysis can be used to measure the amplitude of the various harmonics of a signal. The harmonics of the input signal can be distinguished from other distortion products by their location in the frequency spectrum. Figure 3-18 shows a 7 MHz input signal sampled at 20 MSPS and the location of the first nine harmonics. RELATIVE AMPLITUDE f a = 7MHz f s = 20MSPS HARMONICS AT: |±Kf s ±nf a| n = ORDER OF HARMONIC, K = 0, 1, 2, 3, . . . 3 2 6 9 1 2 3 8 5 4 5 4 7 6 7 8 9 10 FREQUENCY (MHz) Figure 3-18: Location of harmonic distortion products: Input signal = 7 MHz, sampling rate = 20 MSPS Aliased harmonics of fa fall at frequencies equal to |±Kfs±nfa|, where n is the order of the harmonic, and K = 0, 1, 2, 3,... . The second and third harmonics are generally the only ones specified on a data sheet because they tend to be the largest, although some datasheets may specify the value of the worst harmonic. Harmonic distortion is normally specified in dBc (decibels below carrier), although in audio applications it may be specified as a percentage. Harmonic distortion is generally specified with an input signal near full scale (generally 0.5 dB to 1 dB below full scale to avoid clipping), but it can be specified at any level. For signals much lower than full scale, other distortion products due to the DNL of the converter (not direct harmonics) may limit performance. Total harmonic distortion (THD) is the ratio of the rms value of the fundamental signal to the mean value of the root-sum-square of its harmonics (generally, only the first five are significant). THD of an ADC is also generally specified with the input signal close to full scale, although it can be specified at any level. Total harmonic distortion plus noise (THD + N) is the ratio of the rms value of the fundamental signal to the mean value of the root-sum-square of its harmonics plus all noise components (excluding dc). The bandwidth over which the noise is measured must be specified. In the case of an FFT, the bandwidth is dc to fs/2. (If the bandwidth of the measurement is dc to fs/2, THD + N is equal to SINAD.) Spurious Free Dynamic Range (SFDR) Probably the most significant specification for an ADC used in a communications application is its spurious free dynamic range (SFDR). The SFDR specification is to ADCs what the third order intercept specification is to mixers and LNAs. 189 Chapter Three SFDR of an ADC is defined as the ratio of the rms signal amplitude to the rms value of the peak spurious spectral content (measured over the entire first Nyquist zone, dc to fs/2). SFDR is generally plotted as a function of signal amplitude and may be expressed relative to the signal amplitude (dBc) or the ADC full scale (dBFS) as shown in Figure 3-19. FULL SCALE (FS) INPUT SIGNAL LEVEL (CARRIER) SFDR (dBFS) SFDR (dBc) dB WORST SPUR LEVEL fs 2 FREQUENCY Figure 3-19: Spurious free dynamic range (SFDR) For a signal near full scale, the peak spectral spur is generally determined by one of the first few harmonics of the fundamental. However, as the signal falls several dB below full scale, other spurs generally occur which are not direct harmonics of the input signal. This is because of the differential nonlinearity of the ADC transfer function as discussed earlier. Therefore, SFDR considers all sources of distortion, regardless of their origin. Two-Tone Intermodulation Distortion (IMD) Two-tone IMD is measured by applying two spectrally pure sinewaves to the ADC at frequencies f1 and f2, usually relatively close together. The amplitude of each tone is set slightly more than 6 dB below full scale so that the ADC does not clip when the two tones add in-phase. Second- and third-order product locations are shown in Figure 3-20. 2 = SECOND-ORDER IMD PRODUCTS f1 3 f2 = THIRD-ORDER IMD PRODUCTS NOTE: f 1 = 5MHz, f 2 = 6MHz 2 2 f 2 − f1 3 3 2f 1 − f2 1 4 5 f2 + f1 2f 2 2f 1 3 2f 2 + f 1 2f 1 + f 2 2f 2 − f1 6 7 3 3f 1 10 11 12 3f 2 15 16 17 18 FREQUENCY: MHz Figure 3-20: Second and third-order intermodulation products for f1 = 5 MHz, f2 = 6 MHz 190 Using Op Amps with Data Converters Notice that the second-order products fall at frequencies which can be removed by digital filters. However, the third-order products 2f2–f1 and 2f1–f2 are close to the original signals, and are almost impossible to filter. Unless otherwise specified, two-tone IMD refers to these third-order products. The value of the IMD product is expressed in dBc relative to the value of either of the two original tones, and not to their sum. Note, however, that if the two tones are close to fs/4, the aliased third harmonics of the fundamentals can make the identification of the actual 2f2–f1 and 2f1–f2 products difficult. This is because the third harmonic of fs/4 is 3fs/4, and the alias occurs at fs – 3fs/4 = fs/4. Similarly, if the two tones are close to fs/3, the aliased second harmonics may interfere with the measurement. The same reasoning applies here; the second harmonic of fs/3 is 2 fs/3, and its alias occurs at fs – 2 fs/3 = fs/3. The concept of second- and third-order intercept points is not valid for an ADC, because the distortion products don’t vary predictably (as a function of signal amplitude). The ADC doesn’t gradually begin to compress signals approaching full scale (there is no 1 dB compression point); it acts as a hard limiter as soon as the signal exceeds the input range, producing extreme distortion due to clipping. Conversely, for signals much below full scale, the distortion floor remains relatively constant and is independent of signal level. Multitone SFDR is often measured in communications applications. The larger number of tones more closely simulates the wideband frequency spectrum of cellular telephone systems such as AMPS or GSM. High SFDR increases the receiver’s ability to capture small signals in the presence of large ones, and prevent the small signals from being masked by the intermodulation products of the larger ones. 191 Chapter Three References: ADC/DAC Specifications 1. Walt Kester, Editor, Practical Analog Design Techniques, Analog Devices, 1995, ISBN: 0-916550-16-8. 2. Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0-916550-17-6. 3. Chapters 3, 8, Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 4. Chapters 2, 3, 4, Walt Kester, Editor, Mixed-Signal and DSP Design Techniques, Analog Devices, 2000, ISBN: 0-916550-23-0. 5. Chapters 4, 5, Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 192 SECTION 3-3 Driving ADC Inputs Walt Kester, Paul Hendriks Introduction Op amps are often used as drivers for ADCs to provide the gain and level-shifting required for the input signal to match the input range of the ADC. An op amp may be required because of the antialiasing filter impedance matching requirements. In some cases, the antialiasing filter may be an active filter and include op amps as part of the filter itself. Some ADCs also generate transient currents on their inputs due to the conversion process, and these must be isolated from the signal source with an op amp. This section examines these and other issues involved in driving high performance ADCs. To begin with, one shouldn’t necessarily assume that a driver op amp is always required. Some converters have relatively benign inputs and are designed to interface directly to the signal source. There is practically no industry standardization regarding ADC input structures, and therefore each ADC must be carefully examined on its own merits before designing the input interface circuitry. In some applications, transformer drive may be preferable. Assuming an op amp is required for one reason or another, the task of its selection is a critical one and not at all straightforward. Figure 3-21 lists a few of the constraints and variables. The most important requirement is that the op amp should not significantly degrade the overall dc or ac performance of the ADC. At first glance, it would appear that a careful comparison of an op amp data sheet with the ADC data sheet would allow an appropriate choice. However, this is rarely the case. • • • • • • Minimize degradation of ADC/DAC performance specifications Fast settling to ADC/DAC transient High bandwidth Low noise Low distortion Low power • Note: Op amp performance must be measured under identical conditions as encountered in ADC/DAC application − − − − − − − Gain setting resistors Input source impedance, output load impedance Input / output signal voltage range Input signal frequency Input / output common-mode level Power supply voltage (single or dual supply) Transient loading Figure 3-21: General op amp requirements in ADC driver applications The problem is that the op amp performance specifications must be known for the exact circuit configuration used in the ADC driver circuit. Even a very complete data sheet is unlikely to provide all information required, due to the wide range of possible variables. 193 Chapter Three Although the op amp and ADC datasheets should definitely be used as a guide in the selection process, it is unlikely that the overall performance of the op amp/ADC combination can be predicted accurately without actually prototyping the circuit, especially in high performance applications. Various tested application circuits are often recommended on either the op amp or the ADC data sheet, but these can become obsolete quickly as new op amps are released. In most cases, however, the ADC data sheet application section should be used as the primary source for tested interfaces. Op Amp Specifications Key to ADC Applications The two most popular applications for ADCs today are in either precision high-resolution measurements or in low distortion high speed systems. Precision measurement applications require ADCs of at least 16 bits of resolution, and sometimes up to 24 bits. Op amps used with these ADCs must be low noise and have excellent dc characteristics. In fact, high resolution measurement ADCs are often designed to interface directly with the transducer, eliminating the need for an op amp entirely. If op amps are required, it is generally relatively straightforward to select one based on well understood dc specifications, as listed in Figure 3-22. • Dc − − − − − Offset, offset drift Input bias current Open loop gain Integral linearity 1/f noise (voltage and current) • Ac (Highly Application-Dependent) − Wideband noise (voltage and current) − Small and Large Signal Bandwidth − Harmonic Distortion − Total Harmonic Distortion (THD) − Total Harmonic Distortion + Noise (THD + N) − Spurious Free Dynamic Range (SFDR) − Third-Order Intermodulation Distortion − Third-Order Intercept Point Figure 3-22: Key op amp specifications It is much more difficult to provide a complete set of op amp ac specifications because they are highly dependent upon the application circuit. For example, Figure 3-23 shows some key specifications taken from the table of specifications on the data sheet for the AD8057/AD8058 high speed, low distortion op amp (see Reference 1). Note that the specifications depend on the supply voltage, the signal level, output loading, and so forth. It should also be emphasized that it is customary to provide only typical ac specifications (as opposed to maximum and minimum values) for most op amps. In addition, there are restrictions on the input and output CM signal ranges, which are especially important when operating on low voltage dual (or single) supplies. Most op amp datasheets contain a section that provides supplemental performance data for various other conditions not explicitly specified in the primary specification tables. For instance, Figure 3-24 shows the 194 Using Op Amps with Data Converters VS = ±5V VS = +5V Input Common-Mode Voltage Range Output Common-Mode Voltage Range –4.0V to +4.0V –4.0V to +4.0V 0.9V to 3.4V 0.9V to 4.1V Input Voltage Noise Small Signal Bandwidth 7nV/√Hz 325MHz 7nV/√Hz 300MHz THD @ 5MHz, VO = 2V p-p, R L = 1kΩ THD @ 20MHz, VO = 2V p-p, R L = 1kΩ – 85dBc – 62dBc – 75dBc – 54dBc Figure 3-23: AD8057/AD8058 op amp key ac specifications, G = +1 AD8057/AD8058 distortion as a function of frequency for G = +1 and VS = ±5 V. Unless it is otherwise specified, the data represented by these curves should be considered typical (it is usually marked as such). Note however that the data in both Figure 3-24 (and Figure 3-25) is given for a dc load of 150 Ω. This is a load presented to the op amp in the popular application of driving a source and load-terminated 75 Ω cable. Distortion performance is generally better with lighter dc loads, such as 500 Ω – 1000 Ω (more typical of many ADC inputs), and this data may or may not be found on the data sheet. Figure 3-24: AD8057/AD8058 op amp distortion versus frequency G = +1, RL = 150 Ω, VS = ±5 V Figure 3-25: AD8057/AD8058 op amp distortion versus output voltage G = +1, RL = 150 Ω, VS = ±5 V THD @ THD @ 195 Chapter Three On the other hand, Figure 3-25 shows distortion as a function of output signal level for a frequencies of 5 MHz and 20 MHz. Whether or not specifications such as those just described are complete enough to select an op amp for an ADC driver application depends upon the ability to match op amp specifications to the actually required ADC operating conditions. In many cases, these comparisons will at least narrow the op amp selection process. The following sections will examine a number of specific driver circuit examples using various types of ADCs, ranging from high resolution measurement to high speed, low distortion applications. Driving High Resolution Sigma-Delta Measurement ADCs The AD77XX family of ADCs is optimized for high resolution (16–24 bits) low frequency transducer measurement applications. Details of operation can be found in Reference 2, and general characteristics of the family are listed in Figure 3-26. • • • • • Resolution: 16 − 24 bits Input signal bandwidth: <60Hz Effective sampling rate: <100Hz Generally Sigma-Delta architecture Designed to interface directly to sensors (< 1 kΩ) such as bridges with no external buffer amplifier (e.g., AD77xx series) − On-chip PGA and high resolution ADC eliminates the need for external amplifier • If buffer is used, it should be precision low noise (especially 1/f noise) − OP177 − AD707 − AD797 Figure 3-26: High resolution low frequency measurement ADCs Some members of this family, such as the AD7730, have a high impedance input buffer which isolates the analog inputs from switching transients generated in the front end programmable gain amplifier (PGA) and the sigma-delta modulator. Therefore, no special precautions are required in driving the analog inputs. Other members of the AD77xx family, however, either do not have the input buffer or, if one is included on-chip, it can be switched either in or out under program control. Bypassing the buffer offers a slight improvement in noise performance. The equivalent input circuit of the AD77xx family without an input buffer is shown in Figure 3-27. The input switch alternates between the 10 pF sampling capacitor and ground. The 7 kΩ internal resistance, RINT, is the on resistance of the input multiplexer. The switching frequency is dependent on the frequency of the input clock and also the internal PGA gain. If the converter is working to an accuracy of 20-bits, the 10 pF internal capacitor, CINT, must charge to 20-bit accuracy during the time the switch connects the capacitor to the input. This interval is one-half the period of the switching signal (it has a 50% duty cycle). The input RC time constant due to the 7 kΩ resistor and the 10 pF sampling capacitor is 70 ns. If the charge is to achieve 20-bit accuracy, the capacitor must charge for at least 14 time constants, or 980 ns. Any external resistance in series with the input will increase this time constant. There are tables on the datasheets for the various AD77xx ADCs, which give the maximum allowable values of REXT in order to maintain a given level of accuracy. These tables should be consulted if the external source resistance is more than a few kΩ. 196 Using Op Amps with Data Converters REXT ~ RINT SWITCHING FREQ DEPENDS ON f CLKIN AND GAIN 7kΩ HIGH IMPEDANCE > 1GΩ VSOURCE CINT 10pF TYP AD77xx-Series (WITHOUT BUFFER) • R EXT Increases C INT Charge Time and May Result in Gain Error • Charge Time Dependent on the Input Sampling Rate and Internal PGA Gain Setting • Refer to Specific Data Sheet for Allowable Values of R EXT to Maintain Desired Accuracy • Some AD77xx-Series ADCs Have Internal Buffering which Isolates Input from Switching Circuits Figure 3-27: Driving unbuffered AD77xx-series Σ-∆ ADC inputs Note that for instances where an external op amp buffer is found to be required with this type of converter, guidelines exist for best overall performance. This amplifier should be a precision low noise bipolar input type, such as the OP177, AD707, or the AD797. Op Amp Considerations for Multiplexed Data Acquisition Applications Multiplexing is a fundamental part of many data acquisition systems. Switches used in multiplexed data acquisition systems are generally CMOS-types shown in Figure 3-28. Utilizing P-Channel and N-Channel MOSFET switches in parallel minimizes the change of on resistance (RON) as a function of signal voltage. On resistance can vary from less than five to several hundred ohms, depending upon the device. Variation in on resistance as a function of signal level (often called RON-modulation) causes distortion if the multiplexer drives a load, therefore RON flatness is also an important specification. +VS +VS ON P-CH –VS OFF VIN VOUT P-CH N-CH N-CH –VS RON PMOS NMOS CMOS – SIGNAL VOLTAGE Figure 3-28: Basic CMOS analog switch 197 + Chapter Three Because of the effects of nonzero RON and RON-modulation, multiplexer outputs should be isolated from the load with a suitable buffer op amp. A separate buffer is not required if the multiplexer drives a high input impedance, such as a PGA, SHA or ADC—but beware. Some SHAs and ADCs draw high frequency pulse current at their sampling rate and cannot tolerate being driven by an unbuffered multiplexer. Key multiplexer specifications are switching time, on resistance, on resistance flatness, and off-channel isolation, and crosstalk. Multiplexer switching time ranges from less than 20 ns to over 1 µs, RON from less than 5 Ω to several hundred ohms, and off-channel isolation from 50 dB to 90 dB. A number of CMOS switches can be connected to form an analog multiplexer, as shown in Figure 3-29. The number of input channels typically ranges from 4 to 16, and some multiplexers have internal channel-address decoding logic and registers, while with others, these functions must be performed externally. Unused multiplexer inputs must be grounded or severe loss of system accuracy may result. In applications requiring an op amp buffer, it should be noted that when the multiplexer changes channels it is possible to have a full-scale step function into the op amp and the ADC that follows it. CHANNEL ADDRESS ADDRESS REGISTER CLOCK fS ADDRESS DECODER SETTLING TIME TO 1 LSB < 1/f S fS RON OP AMP BUFFER CHANNEL 1 CMOS SWITCHES ADC N-BITS RON CHANNEL M CH 2 CH 1 Figure 3-29: Typical multiplexed data acquisition system requires fast settling op amp buffer Op amp settling time must be fast enough so that conversion errors do not result. It is customary to specify the op amp settling time to 1 LSB, and the allowed time for this settling is generally the reciprocal of the sampling frequency. Driving Single-Supply Data Acquisition ADCs with Scaled Inputs The AD789x and AD76xx family of single supply SAR ADCs (as well as the AD974, AD976, and AD977) includes a thin film resistive attenuator and level shifter on the analog input to allow a variety of input range options, both bipolar and unipolar. A simplified diagram of the input circuit of the AD7890-10 12-bit, 8-channel ADC is shown in Figure 3-30. This arrangement allows the converter to digitize a ±10 V input while operating on a single +5 V supply. Within the ADC, the R1/R2/R3 thin film network provides attenuation and level shifting to convert the ±10 V input to a 0 V to +2.5 V signal that is digitized. This type of input requires no special drive circuitry, because R1 isolates the input from the actual converter circuitry that may generate transient currents due to 198 Using Op Amps with Data Converters 5V 2.5V REFERENCE AD7890-10 12-BIT, 8-CHANNEL 2kΩ REFOUT/ REFIN + +2.5V TO ADC REF CIRCUITS _ RS ~ VINX R1 ±10V 30kΩ R2 7.5kΩ TO MUX, SHA, ETC. 0V TO 2.5V R3 10kΩ VS AGND R1, R2, R3 ARE RATIO-TRIMMED THIN FILM RESISTORS Figure 3-30: Driving single-supply data acquisition ADCs with scaled inputs the conversion process. Nevertheless, the external source resistance RS should be kept reasonably low, to prevent gain errors caused by the RS/R1 divider. Driving ADCs with Buffered Inputs Some ADCs have on-chip buffer amplifiers on their analog input to simplify the interface. This feature is most often found on ADCs designed on either bipolar or BiCMOS processes. Conversely, input amplifiers are rarely found on CMOS ADCs because of the inherent difficulty associated with amplifier design in CMOS. A typical input structure for an ADC with an input buffer is shown in Figure 3-31 for the AD9042 12-bit, 41 MSPS ADC. The effective input impedance is 250 Ω, and an external 61.9 Ω resistor in parallel with this internal 250 Ω provides an effective input termination of 50 Ω to the signal source. The circuit shows an accoupled input. An internal reference voltage of 2.4 V sets the input CM voltage of the AD9042. AD9042 250Ω INPUT = 1V p-p FROM 50Ω SOURCE 250Ω − RT TO SHA 61.9Ω VOFFSET + 50Ω +2.4V REF. Figure 3-31: AD9042 ADC is designed to be driven directly from 50 Ω source for best SFDR 199 Chapter Three The input amplifier precedes the ADC sample-and-hold (SHA), and therefore isolates the input from any transients produced by the conversion process. The gain of the amplifier is set such that the input range of the ADC is 1 V p-p. In the case of a single-ended input structure, the input amplifier serves to convert the single-ended signal to a differential one, which allows fully differential circuit design techniques to be used throughout the remainder of the ADC. Driving Buffered Differential Input ADCs Figure 3-32 below shows two possible input structures for an ADC with buffered differential inputs. The input CM voltage is set with an internal resistor divider network in Figure 3-32A (left), and by a voltage reference in Figure 3-32B (right). (A) AVDD VINA R1 R1 VINA INPUT BUFFER (B) INPUT BUFFER SHA SHA VINB VINB R2 R2 VREF GND • • • • Input buffers typical on BiMOS and bipolar processes Difficult on CMOS Simplified input interface − no transient currents Fixed common-mode level may limit flexibility Figure 3-32: Simplified input circuit of typical buffered ADC with differential inputs In single supply ADCs, the CM voltage is usually equal to one-half the power supply voltage, but some ADCs may use other values. Although the input buffers provide for a simplified interface, the fixed CM voltage may limit flexibility in some dc coupled applications. It is worth noting that differential ADC inputs offer several advantages over single-ended ones. First, many signal sources in communications applications are differential (such as the output of a balanced mixer or an RF transformer). Thus, an ADC that accepts differential inputs interfaces easily in such systems. Second, maintaining balanced differential transmission in the signal path and within the ADC itself often minimizes even-order distortion products as well as improving CM noise rejection. Third, (and somewhat more subtly), a differential ADC input swing of say, 2 V p-p requires only 1 V p-p from twin driving sources. On low voltage and single-supply systems, this lower absolute level of drive can often make a real difference in the dual amplifier driver distortion, due to practical headroom limitations. Given all of these points, it behooves the system engineer to operate a differential-capable ADC in the differential mode for best overall performance. This may be true even if a second amplifier must be added for the complementary drive signal, since dual op amps are only slightly more expensive than singles. 200 Using Op Amps with Data Converters Driving CMOS ADCs with Switched Capacitor Inputs CMOS ADCs are quite popular because of their low power and low cost. The equivalent input circuit of a typical CMOS ADC using a differential sample-and-hold is shown in Figure 3-33. While the switches are shown in the track mode, note that they open/ close at the sampling frequency. The 16 pF capacitors represent the effective capacitance of switches S1 and S2, plus the stray input capacitance. The CS capacitors (4pF) are the sampling capacitors, and the CH capacitors are the hold capacitors. Although the input circuit is completely differential, this ADC structure can be driven either single-ended or differentially. Optimum performance, however, is generally obtained using a differential transformer or differential op amp drive. CH S6 4pF 16pF CP S4 CS S1 VINA 4pF + S3 S2 A CS VINB − S5 4pF CP 16pF CH S7 4pF SWITCHES SHOWN IN TRACK MODE Figure 3-33: Simplified input circuit for a typical switched capacitor CMOS sample-and-hold In the track mode, the differential input voltage is applied to the CS capacitors. When the circuit enters the hold mode, the voltage across the sampling capacitors is transferred to the CH hold capacitors and buffered by the amplifier A (the switches are controlled by the appropriate sampling clock phases). When the SHA returns to the track mode, the input source must charge or discharge the voltage stored on CS to a new input voltage. This action of charging and discharging CS, averaged over a period of time and for a given sampling frequency, fs, makes the input impedance appear to have a benign resistive component. However, if this action is analyzed within a sampling period (1/fs), the input impedance is dynamic, and certain input drive source precautions should be observed. The resistive component to the input impedance can be computed by calculating the average charge that is drawn by CH from the input drive source. It can be shown that if CS is allowed to fully charge to the input voltage before switches S1 and S2 are opened, the average current into the input is the same as if there were a resistor equal to 1/(CSfS) connected between the inputs. Since CS is only a few picofarads, this resistive component is typically greater than several kΩ for an fS = 10 MSPS. Over a sampling period, the SHA’s input impedance appears as a dynamic load. When the SHA returns to the track mode, the input source should ideally provide the charging current through the RON of switches S1 and S2 in an exponential manner. The requirement of exponential charging means that the source impedance should be both low and resistive up to and beyond the sampling frequency. The output impedance of an op amp can be modeled as a series inductor and resistor. When a capacitive load is switched onto the output of the op amp, the output will momentarily change due to its effective 201 Chapter Three high frequency output impedance. As the output recovers, ringing may occur. To remedy this situation, a series resistor can be inserted between the op amp and the SHA input. The optimum value of this resistor is dependent on several factors including the sampling frequency and the op amp selected, but in most applications, a 25 Ω to 100 Ω resistor is optimum. Single-Ended ADC Drive Circuits Although most CMOS ADC inputs are differential, they can be driven single-ended with some ac performance degradation. An important consideration in CMOS ADC applications are the input switching transients previously discussed. For instance, the input switching transient on one of the inputs of the AD9225 12-bit, 25 MSPS ADC is shown in Figure 3-34. This data was taken driving the ADC with an equivalent 50 Ω source impedance. During the sample-to-hold transition, the input signal is sampled when CS is disconnected from the source. Notice that during the hold-to-sample transition, CS is reconnected to the source for recharging. The transients consist of linear, nonlinear, and CM components at the sample rate. In addition to selecting an op amp with sufficient bandwidth and distortion performance, the output should settle to these transients during the sampling interval, 1/fs. The general circuit shown in Figure 3-35 is typical for this type of singleended op amp ADC driver application. • Hold-to-Sample Mode Transition − C S Returned to Source for “recharging.” Transient Consists of Linear, Nonlinear, and CommonMode Components at Sample Rate. • Sample-to-Hold Mode Transition − Input Signal Sampled when C S is disconnected from Source. Hold-to-Sample Mode Transition Sample-to-Hold Mode Transition Figure 3-34: Single-ended input transient response of CMOS switched capacitor SHA (AD9225) In this circuit, series resistor RS has a dual purpose. Typically chosen in the range of 25 Ω–100 Ω, it limits the peak transient current from the driving op amp. Importantly, it also decouples the driver from the ADC input capacitance (and possible phase margin loss). Another feature of the circuit are the dual networks of RS and CF. Matching both the dc and ac the source impedance for the ADC’s VINA and VINB inputs ensures symmetrical settling of CM transients, for optimum noise and distortion performance. At both inputs, the CF shunt capacitor acts as a charge reservoir and steers the CM transients to ground. In addition to the buffering of transients, RS and CF also form a low-pass filter for VIN, which limits the output noise of the drive amplifier into the ADC input VINA. The exact values for RS and CF are generally 202 Using Op Amps with Data Converters VIN AD922X RS + VINA – CF RS VINB CF VREF 10µF 0.1µF Figure 3-35: Optimizing single-ended switched capacitor ADC input drive circuit optimized within the circuit, and the recommended values given on the ADC data sheet. The ADC data sheet information should also be consulted for the recommended drive op amp for best performance. To enable best correlation of performance between environments, an ADC evaluation board should used (if available). This will ensure confidence when the ADC data sheet circuit performance is duplicated. Analog Devices makes evaluation boards available for many of their ADC and DAC devices (plus, of course, op amps), and general information on them is contained in Chapter 7 of this book. Op Amp Gain Setting and Level Shifting in DC-Coupled Applications In dc-coupled applications, the drive amplifier must provide the required gain and offset voltage, to match the signal to the input voltage range of the ADC. Figure 3-36 summarizes various op amp gain and levelshifting options. The circuit of Figure 3-36A operates in the noninverting mode, and uses a low impedance reference voltage, VREF, to offset the output. Gain and offset interact according to the equation: VOUT = 1 + (R2 R1) • VIN − (R2 R1) • VREF Figure 3-36: Op amp gain and level shifting circuits VIN + A − VREF R1 VREF − + VIN R2 C + VREF R3 R4 203 R2 R4 R2 • VIN + • VREF 1 + R3 + R4 R1 R1 R2 NOISE GAIN = 1 + R1 VOUT = − − R1 R2 R2 • VIN − • VREF R1 R3 R2 NOISE GAIN = 1 + R1 || R3 VOUT = − R2 B R3 R2 R2 VOUT = 1 + • VIN − • VREF R1 R1 R2 NOISE GAIN = 1 + R1 R2 VIN R1 Eq. 3-4 Chapter Three The circuit in Figure 3-36B operates in the inverting mode, and the signal gain is independen\t of the offset. The disadvantage of this circuit is that the addition of R3 increases the noise gain, and hence the sensitivity to the op amp input offset voltage and noise. The input/output equation is given by: VOUT = − (R2 R1) • VIN − (R2 R3) • VREF Eq. 3-5 The circuit in Figure 3-36C also operates in the inverting mode, and the offset voltage VREF is applied to the noninverting input without noise gain penalty. This circuit is also attractive for single-supply applications (VREF > 0). The input/output equation is given by: VOUT = − (R2 R1) • VIN + (R4 (R3 + R4 ))(1 + (R2 R1)) • VREF Eq. 3-6 Note that the circuit of Figure 3-36A is sensitive to the impedance of VREF, unlike the counterparts in B and C. This is due to the fact that the signal current flows into/from VREF, due to VIN operating the op amp over its CM range. In the other two circuits the CM voltages are fixed, and no signal current flows in VREF. A dc-coupled single-ended op amp driver for the AD9225 12-bit, 25 MSPS ADC is shown in Figure 3-37. This circuit interfaces a ±2 V input signal to the single-supply ADC, and provides transient current isolation. The ADC input voltage range is 0 V to 4 V, and a dual supply op amp is required, since the ADC minimum input is 0 V. 1kΩ +2.0V ±2V 5V +5V 1kΩ INPUT − 33Ω AD8057 ±2V 52.3Ω VINA + 1k 1kΩ AD9225 100pF 1.0V −5V 1k Ω 0.1µF +2.0V VREF + 10µF 0.1µF 33Ω VINB 100pF Figure 3-37: Dc-coupled single-ended level shifter and driver for the AD9225 12-bit, 25 MSPS CMOS ADC The noninverting input of the AD8057 is biased at 1 V, which sets the output CM voltage at VINA to 2 V for a bipolar input signal source. Note that the VINA and VINB source impedances are matched for better CM transient cancellation. The 100 pF capacitors act as small charge reservoirs for the input transient currents, and also form low-pass noise filters with the 33 Ω series resistors. A similar level shifter and drive circuit is shown in Figure 3-38, operating on a single 5 V supply. In this circuit the bipolar ±1 V input signal is interfaced to the input of the ADC whose span is set for 2 V about a +2.5 V CM voltage. The AD8041 rail-to-rail output op amp is used. The 1.25 V input CM voltage for the AD8041 is developed by a voltage divider from the external AD780 2.5 V reference. Note that single-supply circuits of this type must observe op amp input and output CM voltage restrictions, to prevent clipping and excess distortion. 204 Using Op Amps with Data Converters 1k Ω 5V +2.5V ± 1V 5V 1k Ω INPUT − VINA 52.3Ω + 5V AD780 2.5V REF. AD922x 33 Ω AD8041 ± 1V 100pF +1.25V 1k Ω + 10µF 1k Ω 0.1µF 2.5V + 33Ω VINB 100pF 0.1µ 10µF Figure 3-38: Dc-coupled single-ended, single-supply ADC driver/level shifter using external reference Drivers for Differential Input ADCs Most high performance ADCs are now being designed with differential inputs. A fully differential ADC design offers the advantages of good CM rejection, reduction in second-order distortion products, and simplified dc trim algorithms. Although they can be driven single-ended as previously described, a fully differential driver usually optimizes overall performance. • High common-mode noise rejection • Flexible input common-mode voltage levels • Reduced input signal swings helps in low voltage, singlesupply applications • Reduced second-order distortion products • Simplified dc trim algorithms because of internal matching • Requires high performance differential driver Figure 3-39: Differential input ADCs offer performance advantages 205 Chapter Three Waveforms at the two inputs of the AD9225 12-bit, 25 MSPS CMOS ADC are shown in Figure 3-40A, designated as VINA and VINB. The balanced source impedance is 50 Ω, and the sampling frequency is set for 25 MSPS. The diagram clearly shows the switching transients due to the internal ADC switched capacitor sample-and-hold. Figure 3-40B shows the difference between the two waveforms, VINA−VINB. VINA VINA -VINB (A) (B) VINB • Differential charge transient is symmetrical around midscale and dominated by linear component • Common-mode transients cancel with equal source impedance Figure 3-40: Differential input transient response of CMOS switched capacitor SHA (AD9225) Note that the resulting differential charge transients are symmetrical about midscale, and that there is a distinct linear component to them. This shows the reduction in the CM transients, and also leads to better distortion performance than would be achievable with a single-ended input. Transformer coupling into a differential input ADC provides excellent CM rejection and low distortion if performance to dc is not required. Figure 3-41 shows a typical circuit. The transformer is a Mini-Circuits RF transformer, model #T4-6T which has an impedance ratio of 4 (turns ratio of 2). The schematic assumes that the signal source has a 50 Ω source impedance. The 1:4 impedance ratio requires the 200 Ω secondary termination for optimum power transfer and low VSWR. The Mini-Circuits T4-6T has a 1 dB bandwidth 5V RF TRANSFORMER: MINI-CIRCUITS T4-6T 33Ω 1:2 Turns Ratio AD922s VINA 49.9Ω 200Ω 2V p-p 33Ω VINB 2.5V CML 0.1µF Figure 3-41: Transformer coupling into AD922x ADC 206 Using Op Amps with Data Converters from 100 kHz to 100 MHz. The center tap of the transformer provides a convenient means of level shifting the input signal to the optimum CM voltage of the ADC. The AD922x CML (common-mode level) pin is used to provide the +2.5 CM voltage. Transformers with other turns ratios may also be selected to optimize the performance for a given application. For example, a given input signal source or amplifier may realize an improvement in distortion performance at reduced output power levels and signal swings. Hence, selecting a transformer with a higher impedance ratio (i.e. Mini-Circuits #T16-6T with a 1:16 impedance ratio, turns ratio 1:4) effectively “steps up” the signal level thus reducing the driving requirements of the signal source. Note the 33 Ω series resistors inserted between the transformer secondary and the ADC input. These values were specifically selected to optimize both the SFDR and the SNR performance of the ADC. They also provide isolation from transients at the ADC inputs. Transients currents are approximately equal on the VINA and VINB inputs, so they are isolated from the primary winding of the transformer by the transformer’s CM rejection. Transformer coupling using a CM voltage of +2.5 V provides the maximum SFDR when driving the AD922x series. By driving the ADC differentially, even-order harmonics are reduced compared with the single-ended circuit. Driving ADCs with Differential Amplifiers There are many applications where differential input ADCs cannot be driven with transformers because the frequency response must extend to dc. In these cases, op amps can be used to implement the differential drivers. Figure 3-42 shows how the dual AD8058 op amp can be connected to convert a single-ended bipolar signal to a differential one suitable for driving the AD922X family of ADCs. The input range of the ADC is set for a 2 V p-p signal on each input (4 V span), and a CM voltage of +2 V. The A1 amplifier is configured as a noninverting op amp. The 1 kΩ divider resistors level shift the ±1 V input signal to +1 V ±0.5 V at the noninverting input of A1. The output of A1 is therefore +2 V ±1 V. 1 1k kΩ +2.0V±1V +1V±0.5V INPUT +5V +5V 1 1k kΩ + 1/2 AD8058 ±1V +1.0V 1 1k kΩ − 33 33Ω AD922x V INA A1 Set for 4V p-p Differential Input Span 100pF 1 1k kΩ 33 33Ω V IN B 1kΩ 1k +2.0V±1V 100pF − 1/2 AD8058 + A2 VREF −5V 1 1k kΩ 1k 1kΩ +2.0V 10 µF + 0.1µF Figure 3-42: Op amp single-ended to differential dc-coupled driver with level shifting. 207 Chapter Three The A2 op amp inverts the input signal, and the 1 kΩ divider resistors establish a +1 V CM voltage on its noninverting input. The output of A2 is therefore +2 V ±1 V. This circuit provides good matching between the two op amps because they are duals on the same die and are both operated at the same noise gain of 2. However, the input voltage noise of the AD8058 is , and this appears as at the output of both A1 and A2 thereby introducing possible SNR degradation in some applications. In the circuit of Figure 3-42, this is mitigated somewhat by the 100 pF input capacitors which not only reduce the input noise but absorb some of the transient currents. It should be noted that because the input CM voltage of A1 can go as low as 0.5 V, dual supplies must be used for the op amps. A block diagram of the AD813x family of fully differential amplifiers optimized for ADC driving is shown in Figure 3-43 (see References 3-5). Figure 3-43A shows the details of the internal circuit, and Figure 3-43B shows the equivalent circuit. The gain is set by the external RF and RG resistors, and the CM voltage is set by the voltage on the VOCM pin. The internal CM feedback forces the VOUT+ and VOUT– outputs to be balanced, i.e., the signals at the two outputs are always equal in amplitude but 180° out of phase per the equation, VOCM = (VOUT + + VOUT − )/ 2 Eq. 3-7 The circuit can be used with either a differential or a single-ended input, and the voltage gain is equal to the ratio of RF to RG. The AD8138 has a 3 dB small-signal bandwidth of 320 MHz (G = +1) and is designed to give low harmonic distortion as an ADC driver. The circuit provides excellent output gain and phase matching, and the balanced structure suppresses even-order harmonics. RF (A) V+ + VOUT– VIN+ RG VIN– RG – + + – VOCM – – VOUT+ + V– RF (B) RF EQUIVALENT CIRCUIT: RG VIN+ GAIN = RF RG RG VIN– VOUT– + ~ VOCM – VOUT+ RF Figure 3-43: AD813x differential ADC driver functional diagram and equivalent circuit 208 Chapter Three At the same time however, a degradation occurs in the high frequency SINAD because of the larger distortion due to the larger signal swings. Overvoltage Considerations The input structures of most high performance ADCs are sensitive to overvoltage conditions because of the small geometry devices used in the designs. Although ADC inputs generally have ESD protection diodes connected from the analog input to each supply rail, these diodes are not designed to handle the large currents that can be generated from typical op amp drivers. Two good rules of thumb are to (1) limit the analog input voltage to no more than 0.3 V above or below the positive and negative supply voltages, respectively, and (2) limit the analog input current to 5 mA maximum in overvoltage conditions. Several typical configurations for the drive amp/ADC interface are shown in Figure 3-46. In Figure 3-46A, the ADC requires no additional input protection because both the op amp and the ADC are driven directly from the same supply voltages. While the RS resistor is not required for overvoltage protection, it does serve to isolate the capacitive input of the ADC from the output of the op amp. (A) Single or Dual, Same Supplies +5V RS ADC AMP (Or –5V) (B) Same +5V Supply (C) Separate Supplies +5V RS/2 AMP +5V RS/2 +5V RS/2 RS/2 AMP ADC −5V ADC −5V Figure 3-46: ADC input overvoltage protection circuits Figure 3-46B shows a dual supply op amp driving a single supply ADC, with the 5 V supply is shared between the two devices. The diode protects the input of the ADC in case the output of the op amp is driven below ground. A Schottky diode is used because of its low forward voltage drop and its low capacitance. The RS resistor is split into two equal resistors, and they are chosen to limit the ADC input fault current to 5 mA maximum. Note that the RS resistor in conjunction with the ADC input capacitance forms a low-pass filter. If RS is made too large, the input bandwidth may be restricted. Figure 3-46C shows the condition where the op amp and the ADC are driven from separate supplies. Two Schottky diodes are required to protect the ADC under all power supply and signal conditions. As in 3-46A, the RS/2 resistors limit ADC fault current. 210 Using Op Amps with Data Converters References: Driving ADC Inputs 1. Data sheet for AD8057/AD8058 Low Cost, High Performance Voltage Feedback, 325 MHz Amplifiers, www.analog.com. 2. Chapter 8 of Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 3. Data sheet for AD8131 Low-Cost, High-Speed Differential Driver, www.analog.com. 4. Data sheet for AD8132 Low-Cost, High-Speed Differential Amplifier, www.analog.com. 5. Data sheet for AD8138 Low Distortion Differential ADC Driver, www.analog.com. 6. Data Sheet for AD9203 10-Bit, 40 MSPS, 3 V, 74mW A/D Converter, www.analog.com. 7. Chapters 3–6, Walt Kester, Editor, Practical Analog Design Techniques, Analog Devices, 1995, ISBN: 0-916550-16-8. 8. Chapters 4, 5, Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0- 916550-17-6. 9. Chapters 3, 4, Walt Kester, Editor, Mixed-Signal and DSP Design Techniques, Analog Devices, 2000, ISBN: 0-916550-23-0. 10. Chapters 4, 5, Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 211 This page intentionally left blank SECTION 3-4 Driving ADC/DAC Reference Inputs Walt Jung, Walt Kester It might seem odd to include a section on voltage references in a book devoted primarily to op amp applications, but the relevance will shortly become obvious. Unfortunately, there is little standardization with respect to ADC/DAC voltage references. Some ADCs and DACs have internal references, while others do not. In some cases, the dc accuracy of a converter with an internal reference can often be improved by overriding the internal reference with a more accurate and stable external one. Although the reference element itself can be either a bandgap, buried zener, or XFET™ (see Reference 1), practically all references have some type of output buffer op amp. The op amp isolates the reference element from the output and also provides drive capability. However, this op amp must obey the general laws relating to op amp stability, and that is what makes the topic of references relevant to the discussion. Figure 3-47 summarizes voltage reference considerations. • Data converter accuracy determined by the reference, whether internal or external • Bandgap, buried zener, XFET generally have on-chip output buffer op amp • Transient loading can cause instability and errors • External decoupling capacitors may cause oscillation • Output may require external buffer to source and sink current • Reference voltage noise may limit system resolution Figure 3-47: ADC/DAC voltage reference considerations Note that a reference input to an ADC or DAC is similar to the analog input of an ADC, in that the internal conversion process can inject transient currents at that pin. This requires adequate decoupling to stabilize the reference voltage. Adding such decoupling might introduce instability in some reference types, depending on the output op amp design. Of course, a reference data sheet may not show any details of the output op amp, which leaves the designer in somewhat of a dilemma concerning whether or not it will be stable and free from transient errors. Fortunately, some simple lab tests can exercise a reference circuit for transient errors, and also determine stability for capacitive loading. 213 Chapter Three Figure 3-48 shows the transients associated with the reference input of a typical successive approximation ADC. The ADC reference voltage input must be stabilized with a sufficiently large decoupling capacitor, in order to prevent conversion errors. The value of the capacitor required as CB may range from below 1 µF, to as high as 100 µF. This capacitor must of course have a voltage rating greater than the reference voltage. Physically, it will be of minimum size when purchased in a surface-mount style. VIN START CONVERT SCOPE VREF AD780 CB CB = 0.01µF SAR ADC CB = 0.22µF CB = 1µF START CONVERT SCOPE TOP TRACE VERTICAL SCALE: 5V/div. ALL OTHER VERTICAL SCALES: 5mV/div. HORIZONTAL SCALE: 1µs/div. Figure 3-48: Successive approximation ADCs can present a transient load to the reference Note that in this case, a 1 µF capacitor on the reference input is required to reduce the transients to an acceptable level. Note that the capacitor size can be electrically larger for further noise reduction—the tradeoff here is of course cost and PCB real estate. The AD780 will work with capacitors of up to 100 µF. A well-designed voltage reference is stable with heavy capacitive decoupling. Unfortunately, some are not, as shown in Figure 3-49, where the addition of CL to the reference output (a 0.01 µF capacitor) actually increases the amount of transient ringing. Such references are practically useless in data converter applications, because some amount of local decoupling is almost always required at the converter. TOP TRACE: NO LOAD (C L = 0) 50mV/div. VIN 1mA to 2mA STEP SCOPE REFERENCE UNDER TEST CL RL BOTTOM TRACE: C L = 0.01µF 200mV/div. PULSE GENERATOR BOTH TRACES: 5µs/div. Figure 3-49: Make sure reference is stable with large capacitive loads A suitable op amp buffer might be added between the reference and the data converter. Many good references are available (such as the AD780) which are stable with an output capacitor. This type of reference 214 Using Op Amps with Data Converters should be chosen for a data converter application, rather than incurring the further complication and expense of an op amp. If very low noise levels are required from a reference, an additional low-pass filter followed by a low noise op amp can be used to achieve the desired performance. The reference circuit of Figure 3-50 is one such example (see References 2 and 3). This circuit uses external filtering and a precision low-noise op-amp to provide both very low noise and high dc accuracy. Reference U1 is a 2.5 V, 3.0 V, 5 V, or 10 V reference with a low noise buffered output. The output of U1 is applied to the R1–C1/C2 noise filter to produce a corner frequency of about 1.7 Hz. 15V 15V 100Ω 3 2 VIN VO 6 1kΩ 0.1µF U1 + R1 + R2 10kΩ GND 4 + 6 U2 C1 100µF 25V 7 2 DIODES: 1N4148 − 4 100Ω 1.1kΩ C2 100µF 25V + 3.3Ω 100µF, 25V + U1: AD586, AD587, REF01 REF02, REF05, REF10 U2: OP113, OP27 OP176, AD797 10µF 25V Figure 3-50: Low-noise op amp with filtering yields reference noise performance (1.5V to 5 nV/√HZ @ 1 kHz Electrolytic capacitors usually imply dc leakage errors, but the bootstrap connection of C1 causes its applied bias voltage to be only the relatively small drop across R2. This lowers the leakage current through R1 to acceptable levels. Since the filter attenuation is modest below a few Hertz, the reference noise still affects overall performance at low frequencies (i.e., <10 Hz). A precision low noise unity-gain follower, such as the OP113, then buffers the output of the filter. With less than ±150 µV of offset error and under 1 µV/°C drift, the buffer amplifier’s dc performance will not seriously affect the accuracy/drift of most references. For example, an ADR292E for U1 will have a typical drift of 3 ppm/°C, equivalent to 7.5 µV/°C, higher than the buffer amplifier. Almost any op amp will have a current limit higher than a typical IC reference, so this circuit allows greater current output. It also removes any load-related thermal errors that might occur when the reference IC is loaded directly. Even lower noise op-amps are available, for 5–10 V use. The AD797 offers 1kHz noise performance less in this circuit, compared to about for the OP113. With any buffer amplifier, than Kelvin sensing can be used at the load point, a technique that eliminates I × R related output voltage errors. 215 Chapter Three References: Driving ADC/DAC Reference Inputs 1. Chapter 2, Walt Kester, Editor, Practical Design Techniques for Power and Thermal Management, Analog Devices, 1998, ISBN: 0-916550-19-2. 2. Walt Jung, “Build an Ultra-Low-Noise Voltage Reference,” Electronic Design Analog Applications Issue, June 24, 1993. 3. Walt Jung, “Getting the Most from IC Voltage References,” Analog Dialogue, Vol. 28, No., 1994, pp. 13–21. 216 SECTION 3-5 Buffering DAC Outputs Walt Kester, Paul Hendriks General Considerations Another important op amp application is buffering DAC outputs. Modern IC DACs provide either voltage or current outputs. Figure 3-51 shows three fundamental configurations, all with the objective of using an op amp for a buffered output voltage. (A) + + N VOUT 1 + R2 R1 – VOUT R1 (B) R2 (C) R2 IOUT•RL 1 + R2 R1 + N – N – IOUT RL IOUT + –IOUT•R2 R2 R1 Figure 3-51: Buffering DAC outputs with op amps Figure 3-51A shows a buffered voltage output DAC. In many cases, the DAC output can be used directly, without additional buffering. If an additional op amp buffer is needed, it is usually configured in a noninverting mode, with gain determined by R1 and R2. There are two basic methods for dealing with a current output DAC. In Figure 3-51B, a voltage is simply developed across external load resistor, RL. An external op amp can be used to buffer and/or amplify this voltage if required. Many DACs supply full-scale currents of 20 mA or more, thereby allowing reasonable voltages to be developed across fairly low value load resistors. For instance, fast settling video DACs typically supply nearly 30 mA full-scale current, allowing 1 V to be developed across a source and load terminated 75 Ω coaxial cable (representing a dc load of 37.5 Ω to the DAC output). A direct method to convert the output current into a voltage is shown in Figure 3-51C, This circuit is usually called a current-to-voltage converter, or I/V. In this circuit, the DAC output drives the inverting input of an op amp, with the output voltage developed across the R2 feedback resistor. In this approach the DAC output always operates at virtual ground (which may give a linearity improvement vis-à-vis Figure 3-51B). The general selection process for an op amp used as a DAC buffer is similar to that of an ADC buffer. The same basic specifications such as dc accuracy, noise, settling time, bandwidth, distortion, and so forth, apply to DACs as well as ADCs, and the discussion will not be repeated here. Rather, some specific application examples will be shown. 217 Chapter Three Differential to Single-Ended Conversion Techniques A general model of a modern current output DAC is shown in Figure 3-52. This model is typical of the AD976x and AD977x TxDAC™ series (see Reference 1). Current output is more popular than voltage output, especially at audio frequencies and above. If the DAC is fabricated on a bipolar or BiCMOS process, it is likely that the output will sink current, and that the output impedance will be less than 500 Ω (due to the internal R/2R resistive ladder network). On the other hand, a CMOS DAC is more likely to source output current and have a high output impedance, typically greater than 100 kΩ. IFS – I IOUT ROUT I ROUT IOUT RSET • • • • I FS 2 − 20mA typical Bipolar or BiCMOS DACs sink current, R OUT < 500Ω CMOS DACs source current, R OUT > 100kΩ Output compliance voltage < ±1V for best performance Figure 3-52: Model of high speed DAC output Another consideration is the output compliance voltage—the maximum voltage swing allowed at the output in order for the DAC to maintain its linearity. This voltage is typically 1 V to 1.5 V, but can vary depending upon the DAC. Best DAC linearity is generally achieved when driving a virtual ground, such as an op amp I/V converter. Modern current output DACs usually have differential outputs, to achieve high CM rejection and reduce the even-order distortion products. Full-scale output currents in the range of 2 mA to 20 mA are common. In most applications, it is desirable to convert the differential output of the DAC into a single-ended signal, suitable for driving a coax line. This can be readily achieved with an RF transformer, provided low frequency response is not required. Figure 3-53 shows a typical example of this approach. The high impedance current output of the DAC is terminated differentially with 50 Ω, which defines the source impedance to the transformer as 50 Ω. MINI-CIRCUITS T1-1T 1:1 0 TO 20mA IOUT LC FILTER VLOAD = ±0.5V RDIFF = 50Ω CMOS DAC ±10mA IOUT 20 TO 0mA Figure 3-53: Differential transformer coupling 218 RLOAD = 50Ω Using Op Amps with Data Converters The resulting differential voltage drives the primary of a 1:1 RF transformer, to develop a single-ended voltage at the output of the secondary winding. The output of the 50 Ω LC filter is matched with the 50 Ω load resistor RL, and a final output voltage of 1 V p-p is developed. The transformer not only serves to convert the differential output into a single-ended signal, but it also isolates the output of the DAC from the reactive load presented by the LC filter, thereby improving overall distortion performance. An op amp connected as a differential to single-ended converter can be used to obtain a single-ended output when frequency response to dc is required. In Figure 3-54 the AD8055 op amp is used to achieve high bandwidth and low distortion (see Reference 2). The current output DAC drives balanced 25 Ω resistive loads, thereby developing an out-of-phase voltage of 0 V to 0.5 V at each output. The AD8055 is configured for a gain of 2, to develop a final single-ended ground-referenced output voltage of 2 V p-p. Note that because the output signal swings above and below ground, a dual-supply op amp is required. 1kΩ 0 TO 20mA 0V TO +0.5V 500Ω +5V – IOUT 25Ω CMOS DAC ±1V AD8055 CFILTER + –5V 500Ω IOUT 20 TO 0mA +0.5V TO 0V f 3dB = 25Ω 1kΩ 1 2π • 50Ω • CFILTER Figure 3-54: Differential dc-coupled output using a dual supply op amp The CFILTER capacitor forms a differential filter with the equivalent 50 Ω differential output impedance. This filter reduces any slew induced distortion of the op amp, and the optimum cutoff frequency of the filter is determined empirically to give the best overall distortion performance. 219 Chapter Three A modified form of the Figure 3-54 circuit can also be operated on a single supply, provided the CM voltage of the op amp is set to mid-supply (2.5 V). This is shown in Figure 3-55 below. The output voltage is 2 V p-p centered around a CM voltage of 2.5 V. This CM voltage can be either developed from the 5 V supply using a resistor divider, or directly from a 2.5 V voltage reference. If the 5 V supply is used as the CM voltage, it must be heavily decoupled to prevent supply noise from being amplified. 1kΩ 0 TO 20mA 0V TO +0.5V 500Ω +5V +2.5V ± 1V – IOUT 25Ω AD8055 CMOS DAC CFILTER + 500Ω IOUT +5V 20 TO 0mA +0.5V TO 0V 2kΩ 25Ω 2kΩ +5V f 3dB = 1 2π • 50Ω • CFILTER 1kΩ +2.5V REF SEE TEXT Figure 3-55: Differential dc-coupled output using a single-supply op amp Single-Ended Current-to-Voltage Conversion Single-ended current-to-voltage conversion is easily performed using a single op amp as an I/V converter, as shown in Figure 3-56. The 10 mA full-scale DAC current from the AD768 (see Reference 3) develops a 0 V to 2 V output voltage across the 200 Ω RF. CF RF = 200Ω 0 TO 10mA +5V – IOUT 0V TO +2.0V RDAC ||C DAC AD768 16-BIT BiCMOS DAC CIN AD8055 + –5V fu = Op Amp Unity Gain-Bandwidth Product IOUT For R DAC ≈ RF, make C F ≈ RDAC (CDAC + CIN) RF For R DAC >> RF, make C F ≈ CDAC + CIN 2π RF fu Figure 3-56: Single-ended I/V op amp interface for precision 16-bit AD768 DAC 220 Using Op Amps with Data Converters Driving the virtual ground of the AD8055 op amp minimizes any distortion due to nonlinearity in the DAC output impedance. In fact, most high resolution DACs of this type are factory trimmed using an I/V converter. It should be recalled, however, that compared to a differential operating mode using the single-ended output of the DAC in this manner will cause degradation in the CM rejection and increased second-order distortion products. The CF feedback capacitor should be optimized for best pulse response in the circuit. The equations given in the diagram should only be used as guidelines. A more detailed analysis of this circuit is given in Reference 6. Differential Current-to-Differential Voltage Conversion If a buffered differential voltage output is required from a current output DAC, the AD813x-series of differential amplifiers can be used as shown in Figure 3-57. 2.49k Ω 0 TO 20mA 0 TO +0.5V 499 Ω + I OUT 25Ω CMOS DAC AD813X 5V p-p DIFFERENTIAL OUTPUT 499 Ω IOUT 20 TO 0mA 0.5 TO 0V – 2.49k Ω 25Ω V OCM Figure 3-57: Buffering high speed DACs using AD813x differential amplifier The DAC output current is first converted into a voltage that is developed across the 25 Ω resistors. The voltage is amplified by a factor of 5 using the AD813x. This technique is used in lieu of a direct I/V conversion to prevent fast slewing DAC currents from overloading the amplifier and introducing distortion. Care must be taken so that the DAC output voltage is within its compliance rating. The VOCM input on the AD813x can be used to set a final output CM voltage within the range of the AD813x. If transmission lines are to be driven at the output, adding a pair of 75Ω resistors will allow this. 221 Chapter Three An Active Low-Pass Filter for Audio DAC Figure 3-58 shows an active low-pass filter which also serves as a current-to-voltage converter for the AD1853 sigma-delta audio DAC (see Reference 4). The filter is a 4-pole filter with a 3 dB cutoff frequency of approximately 75 kHz. Because of the high oversampling frequency (24.576 MSPS when operating the DAC at a 48 KSPS throughput rate), a simple filter is all that is required to remove aliased components above 12 MHz). 330pF FROM AD1853 DAC NOTE: ONLY RIGHT CHANNEL SHOWN 4.12kΩ ROUT+ +15V 2.74kΩ – U1A 1/2 OP275 + 0mA TO +1.5mA 2.74kΩ 220pF 2.94kΩ +15V 680pF VREF +2.75V 402Ω 402Ω 680pF 220pF ROUT– 604Ω RIGHT CHANNEL OUTPUT 49.9kΩ + U1B 1/2 OP275 2.74kΩ – 2.74kΩ –15V +1.5mA TO 0mA – U2A 1/2 OP275 + –15V 2.94kΩ 2.2nF 220pF 4.12kΩ 330pF Figure 3-58: A 75 kHz 4-pole gaussian active filter for buffering the output of AD1853 stereo DAC The diagram shows a single channel for the dual channel DAC output. U1A and U1B I/V stages form a 1-pole differential filter, while U2 forms a 2-pole multiple-feedback filter that also performs a differentialto-single-ended conversion. A final fourth passive pole is formed by the 604 Ω resistor and the 2.2 nF capacitor across the output. The OP275 op amp was chosen for operation at U1 and U2, and for its quality audio characteristics (see Reference 5). For further details of active filter designs, see Chapter 5 of this book. 222 Using Op Amps with Data Converters References: Buffering DAC Outputs 1. Data sheet for AD9772A 14-Bit, 160 MSPS TxDAC+® with 2x Interpolation Filter, www.analog.com. 2. Data sheet for AD8055/AD8056 Low Cost, 300 MHz Voltage Feedback Amplifiers, www.analog.com. 3. Data sheet for AD768 16-Bit, 30 MSPS D/A Converter, www.analog.com. 4. Data sheet for AD1853 Stereo, 24-Bit, 192 kHz, Multibit Σ-∆ DAC, www.analog.com. 5. Data sheet for OP275 Dual Bipolar/JFET, Audio Operational Amplifier, www.analog.com. 6. Chapters 5, Walt Kester, Editor, Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, 1999, ISBN: 0-916550-20-6. 223 This page intentionally left blank CHAPTER 4 Sensor Signal Conditioning ■ Section 4-1: Introduction ■ Section 4-2: Bridge Circuits ■ Section 4-3: Strain, Force, Pressure and Flow Measurements ■ Section 4-4: High Impedance Sensors ■ Section 4-5: Temperature Sensors This page intentionally left blank CHAPTER 4 Sensor Signal Conditioning Walt Kester, James Bryant, Walt Jung Scott Wurcer, Chuck Kitchin SECTION 4-1 Introduction Walt Kester This chapter of the book deals with various sensors and associated signal-conditioning circuitry involving the use of op amps and in amps. While the topic is generally very broad, the focus is to concentrate on circuit and signal processing applications of sensors rather than the details of the actual sensors themselves. Strictly speaking, a sensor is a device that receives a signal or stimulus and responds with an electrical signal, while a transducer is a converter of one type of energy into another. In practice, however, the terms are often used interchangeably. Sensors and their associated circuits are used to measure various physical properties such as temperature, force, pressure, flow, position, light intensity, and so forth. These properties act as the stimulus to the sensor, and the sensor output is conditioned and processed to provide the corresponding measurement of the physical property. We will not cover all possible types of sensors, only the most popular ones, and specifically, those that lend themselves to process control and data acquisition systems. Sensors do not operate by themselves. They are generally part of a larger system consisting of signal conditioners and various analog or digital signal processing circuits. The system could be a measurement system, data acquisition system, or process control system, for example. Sensors may be classified in a number of ways. From a signal-conditioning viewpoint it is useful to classify sensors as either active or passive. An active sensor requires an external source of excitation. Resistorbased sensors such as thermistors, resistance temperature detectors (RTDs), and strain gages are examples of active sensors, because a current must be passed through them and the corresponding voltage measured in order to determine the resistance value. An alternative would be to place the devices in a bridge circuit; however in either case, an external current or voltage is required. On the other hand, passive (or self-generating) sensors generate their own electrical output signal without requiring external voltages or currents. Examples of passive sensors are thermocouples and photodiodes which generate thermoelectric voltages and photocurrents, respectively, which are independent of external circuits. It should be noted that these definitions (active versus passive) refer to the need (or lack thereof) of external active circuitry to produce a sensor electrical output signal. It would seem equally logical to consider a thermocouple active, in the sense that it produces an output voltage without external circuitry; however the convention in the industry is to classify the sensor with respect to the external circuit requirement as defined above. 227 Chapter Four A logical way to classify sensors is with respect to the physical property the sensor is designed to measure. Thus we have temperature sensors, force sensors, pressure sensors, motion sensors, and so forth. However, sensors that measure different properties may have the same type of electrical output. For instance, Resistance Temperature Detector (RTD) is a variable resistance, as is a resistive strain gage. Both RTDs and strain gages are often placed in bridge circuits, and the conditioning circuits are therefore quite similar. In fact, bridges and their conditioning circuits deserve a detailed discussion. Figure 4-1 is an overview of basic sensor characteristics. • Sensors: Convert a Signal or Stimulus (Representing a Physical Property) into an Electrical Output • Transducers: Convert One Type of Energy into Another • The Terms are often Interchanged • Active Sensors Require an External Source of Excitation: RTDs, Strain-Gages • Passive (Self-Generating) Sensors do not: Thermocouples, Photodiodes Figure 4-1: An overview of sensor characteristics The full-scale outputs of most sensors (passive or active) are relatively small voltages, currents, or resistance changes, and therefore their outputs must be properly conditioned before further analog or digital processing can occur. Because of this, an entire class of circuits has evolved, generally referred to as signal-conditioning circuits. Amplification, level translation, galvanic isolation, impedance transformation, linearization, and filtering are fundamental signal-conditioning functions that may be required. Figure 4-2 summarizes sensors and their outputs. SENSOR ACTIVE/ PASSIVE OUTPUT Temperature Thermocouple Silicon RTD Thermistor Passive Active Active Active Voltage Voltage/Current Resistance Resistance Force / Pressure Strain Gage Piezoelectric Active Passive Resistance Voltage Acceleration Accelerometer Active Capacitance Position LVDT Active AC Voltage Light Intensity Photodiode Active Current PROPERTY Figure 4-2: Typical sensors and their output formats 228 Sensor Signal Conditioning Whatever form the conditioning takes, the circuitry and performance will be governed by the electrical character of the sensor and its output. Accurate characterization of the sensor in terms of parameters appropriate to the application, e.g., sensitivity, voltage and current levels, linearity, impedances, gain, offset, drift, time constants, maximum electrical ratings, stray impedances, and other important considerations can spell the difference between substandard and successful application of the device, especially where high resolution, precision, or low level measurements are necessary. Higher levels of integration now allow ICs to play a significant role in both analog and digital signal conditioning. ADCs specifically designed for measurement applications often contain on-chip programmable-gain amplifiers (PGAs) and other useful circuits, such as current sources for driving RTDs, thereby minimizing the external conditioning circuit requirements. To some degree or another, most sensor outputs are nonlinear with respect to the applied stimulus and as a result, their outputs must often be linearized in order to yield correct measurements. In terms of the design approach choice towards linearization, the designer can take a route along either of two major paths. Analog is one viable route, and such techniques may be used to perform an “analog domain” linearization function. However, the recent introduction of high performance ADCs now allows linearization to be done much more efficiently and accurately in software. This “digital domain” approach to linearization eliminates the need for tedious manual calibration using multiple and sometimes interactive analog trim adjustments. A quite common application of sensors is within process control systems. One example would be control of a physical property, such as temperature. A sample block diagram of how this might be implemented is illustrated in Figure 4-3. REMOTE SIGNAL CONDITIONING CONTROL ROOM 4 TO 20mA TRANSMITTER 4 TO 20mA RECEIVER TEMP SENSOR ADC HOST COMPUTER PROCESS HEATER SIGNAL CONDITIONING SIGNAL CONDITIONING MICRO CONTROLLER DAC 4 TO 20mA RECEIVER 4 TO 20mA TRANSMITTER SIGNAL CONDITIONING Figure 4-3: A typical industrial process temperature control loop In this system, an output from a temperature sensor is conditioned, transmitted over some distance, received, and then digitized by an ADC. The microcontroller or host computer determines if the temperature is above or below the desired value, and outputs a digital word to the digital-to-analog converter (DAC). 229 Chapter Four The DAC output is conditioned and drives the remotely located actuator, in this case a heater. Notice that the interface between the control center and the remote process is via the industry-standard 4-20 mA loop. Digital techniques are becoming more and more popular in processing sensor outputs in data acquisition, process control, and measurement. 8-bit microcontrollers (8051-based, for example) generally have sufficient speed and processing capability for most applications. By including the A/D conversion and the microcontroller programmability on the sensor itself, a “smart sensor” can be implemented with self-contained calibration and linearization features among others. However, such digital techniques aren’t a major focus of this text, so the section references may be consulted for further information. The remaining sections of the chapter deal with analog signal conditioning methods for a variety of sensor types. References: Introduction 1. Walt Kester, Bill Chestnut, and Grayson King, Smart Sensors, Chapter 9 of Practical Design Techniques for Sensor Signal Conditioning, Analog Devices, Inc., 1999, ISBN: 0-916550-20-6. 2. Compatibility of Analog Signals for Electronic Industrial Process Instruments, ANSI/ISA-S50.1-1982 (Rev. 1992), www.isa.org. 3. Editors, “Fieldbuses: Look Before You Leap,” EDN, November 5, 1998, p. 197. 4. “MicroConverter Technology Backgrounder,” Whitepaper, Analog Devices, Inc., www.analog.com. 5. Scott MacKenzie, The 8051 Microcontroller, 3rd Ed., Prentice-Hall, 1999, ISBN: 0-13-780008-8. 230 SECTION 4-2 Bridge Circuits Walt Kester An Introduction to Bridges This section of the chapter, 4-2, discusses more fundamental bridge circuit concepts. To gain greatest appreciation of these ideas, it should be studied along with those sections discussing precision op amps within Chapters 1 and 2. The next section (4-3) focuses on the detailed application circuits relating to strain-gagebased sensors. These sections can be read sequentially if the reader already understands the design issues related to precision op amp applications. Resistive elements are some of the most common sensors. They are inexpensive, and relatively easy to interface with signal-conditioning circuits. Resistive elements can be made sensitive to temperature, strain (by pressure or by flex), and light. Using these basic elements, many complex physical phenomena can be measured, such as: fluid or mass flow (by sensing the temperature difference between two calibrated resistances), dew-point humidity (by measuring two different temperature points), and so forth. Sensor element resistance can range from less than 100 Ω to several hundred kΩ, depending on the sensor design and the physical environment to be measured. Figure 4-4 indicates the wide range of sensor resistance encountered. For example, RTDs are typically 100 Ω or 1000 Ω. Thermistors are typically 3500 Ω or higher. • Strain Gages 120Ω, 350Ω, 3500Ω • Weigh-Scale Load Cells 350Ω − 3500Ω • Pressure Sensors 350Ω − 3500Ω • Relative Humidity 100kΩ − 10MΩ • Resistance Temperature Devices (RTDs) 100Ω, 1000Ω • Thermistors 100Ω − 10MΩ Figure 4-4: Sensor resistances used in bridge circuits span a wide dynamic range Resistive sensors such as RTDs and strain gages produce relatively small percentage changes in resistance, in response to a change in a physical variable such as temperature or force. For example, platinum RTDs have a temperature coefficient of about 0.385%/°C. Thus, in order to accurately resolve temperature to 1ºC, the overall measurement accuracy must be much better than 0.385 Ω when using a 100 Ω RTD. Strain gages present a significant measurement challenge because the typical change in resistance over the entire operating range of a strain gage may be less than 1% of the nominal resistance value. Accurately measuring small resistance changes is therefore critical when applying resistive sensors. 231 Chapter Four A simple method for measuring resistance is to force a constant current through the resistive sensor, and measure the voltage output. This requires both an accurate current source and an accurate means of measuring the voltage. Any change in the current will be interpreted as a resistance change. In addition, the power dissipation in the resistive sensor must be small and in accordance with the manufacturer’s recommendations, so that self-heating does not produce errors. As a result, the drive current must be small, which tends to limit the resolution of this approach. A resistance bridge, shown in Figure 4-5, offers an attractive alternative for accurately measuring small resistance changes. This is a basic Wheatstone bridge (actually developed by S. H. Christie in 1833), and is a prime example. It consists of four resistors connected to form a quadrilateral, a source of excitation voltage VB (or, alternately, a current) connected across one of the diagonals, and a voltage detector connected across the other diagonal. The detector measures the difference between the outputs of the two voltage dividers connected across the excitation voltage, VB. The general form of the bridge output VO is noted in the figure. VB THE WHEATSTONE BRIDGE: R4 R3 VO = VB R1 R1 + R4 R2 R2 + R3 AT BALANCE, VO VO = 0 if R1 − R1 R2 = R4 R3 R2 Figure 4-5: The basic Wheatstone bridge produces an output null when the ratios of sidearm resistances match There are two principal ways of operating a bridge such as this. One is by operating it as a null detector, where the bridge measures resistance indirectly by comparison with a similar standard resistance. On the other hand, it can be used as a device that reads a resistance difference directly, as a proportional voltage output. When R1/R4 = R2/R3, the resistance bridge is said to be at a null, irrespective of the mode of excitation (current or voltage, ac or dc), the magnitude of excitation, the mode of readout (current or voltage), or the impedance of the detector. Therefore, if the ratio of R2/R3 is fixed at K, a null is achieved when R1 = K · R4. If R1 is unknown and R4 is an accurately determined variable resistance, the magnitude of R1 can be found by adjusting R4 until an output null is achieved. Conversely, in sensor-type measurements, R4 may be a fixed reference, and a null occurs when the magnitude of the external variable (strain, temperature, and so forth.) is such that R1 = K · R4. Null measurements are principally used in feedback systems involving electromechanical and/or human elements. Such systems seek to force the active element (strain gage, RTD, thermistor, and so forth.) to balance the bridge by influencing the parameter being measured. 232 Sensor Signal Conditioning For the majority of sensor applications employing bridges, however, the deviation of one or more resistors in a bridge from an initial value is measured as an indication of the magnitude (or a change) in the measured variable. In these cases, the output voltage change is an indication of the resistance change. Because very small resistance changes are common, the output voltage change may be as small as tens of millivolts, even with the excitation voltage VB = 10 V (typical for a load cell application). In many bridge applications, there may not just be a single variable element, but two, or even four elements, all of which may vary. Figure 4-6 shows a family of four voltage-driven bridges, those most commonly suited for sensor applications. In the four cases the corresponding equations for VO relate the bridge output voltage to the excitation voltage and the bridge resistance values. In all cases we assume a constant voltage drive, VB. Note that since the bridge output is always directly proportional to VB, the measurement accuracy can be no better than that of the accuracy of the excitation voltage. VB VB R R VO: Linearity Error: ∆R ∆R 2 R + 0.5%/% (A) Single-Element Varying R ∆R ∆R 2 R + R VO R+∆R VB 2 R− −∆R R+∆R VO R+∆R VB 2 VB R− −∆R R VO R+∆R VB 4 R R+∆R VO R VB −∆R R− ∆R R VB R+∆R ∆R R 0.5%/% 0 0 (B) Two-Element Varying (1) (C) Two-Element Varying (2) (D) All-Element Varying Figure 4-6: The output voltage sensitivity and linearity of constant voltage drive bridge configurations differs according to the number of active elements In each case, the value of the fixed bridge resistor “R” is chosen to be equal to the nominal value of the variable resistor(s). The deviation of the variable resistor(s) about the nominal value is assumed to be proportional to the quantity being measured, such as strain (in the case of a strain gage), or temperature (in the case of an RTD). The sensitivity of a bridge is the ratio of the maximum expected change in the output voltage to the excitation voltage. For instance, if VB = 10 V, and the full-scale bridge output is 10mV, then the sensitivity is 1mV/V. For the four cases of Figure 4-6, sensitivity can be said to increase going left-right, or as more elements are made variable. The single-element varying bridge of Figure 4-6A is most suited for temperature sensing using RTDs or thermistors. This configuration is also used with a single resistive strain gage. All the resistances are nominally equal, but one of them (the sensor) is variable by an amount ∆R. As the equation indicates, the relationship between the bridge output and ∆R is not linear. For example, if R = 100 Ω and ∆R = 0.1 Ω (0.1% change in resistance), the output of the bridge is 2.49875 mV for VB = 10 V. The error is 2.50000 mV – 2.49875 mV, or 0.00125 mV. Converting this to a % of full-scale by dividing by 2.5 mV yields an end-point linearity error in percent of approximately 0.05%. (Bridge end-point linearity error is 233 Chapter Four calculated as the worst error in % FS from a straight line which connects the origin and the end point at FS, i.e., the FS gain error is not included). If ∆R = 1 Ω, (1% change in resistance), the output of the bridge is 24.8756 mV, representing an end-point linearity error of approximately 0.5%. The end-point linearity error of the single-element bridge can be expressed in equation form: Single-Element Varying Bridge End-Point Linearity Error ≈ % Change in Resistance ÷ 2 It should be noted that the above nonlinearity refers to the nonlinearity of the bridge itself and not the sensor. In practice, most sensors themselves will exhibit a certain specified amount of nonlinearity, which must also be accounted for in the final measurement. In some applications, the bridge nonlinearity noted above may be acceptable. If not, there are various methods available to linearize bridges. Since there is a fixed relationship between the bridge resistance change and its output (shown in the equations), software can be used to remove the linearity error in digital systems. Circuit techniques can also be used to linearize the bridge output directly, and these will be discussed shortly. There are two cases to consider in the instance of a two-element varying bridge. In Case 1 (Figure 4-6B), both of the diagonally opposite elements change in the same direction. An example would be two identical strain gages mounted adjacent to each other, with their axes in parallel. The nonlinearity for this case, 0.5%/%, the same as that of the single-element varying bridge of Figure 4-6A. However, it is interesting to note the sensitivity is now improved by a factor of 2, vis-à-vis the singleelement varying setup. The two-element varying bridge is commonly found in pressure sensors and flow meter systems. A second case of the two-element varying bridge, Case 2, is shown in Figure 4-6C. This bridge requires two identical elements that vary in opposite directions. This could correspond to two identical strain gages: one mounted on top of a flexing surface, and one on the bottom. Note that this configuration is now linear, and like two-element varying Case 1, it has twice the sensitivity of the Figure 4-6A configuration. Another way to view this configuration is to consider the terms R + ∆R and R – ∆R as comprising two sections of a linear potentiometer. The all-element varying bridge of Figure 4-6D produces the most signal for a given resistance change, and is inherently linear. It is also an industry-standard configuration for load cells constructed from four identical strain gages. Understandably, it is also one of the most popular bridge configurations. Bridges may also be driven from constant current sources, as shown in Figure 4-7, for the corresponding cases of single, dual, dual, and four active element(s). As with the voltage-driven bridges, the analogous output expressions are noted, along with the sensitivities. Current drive, although not as popular as voltage drive, does have advantages when the bridge is located remotely from the source of excitation. One advantage is that the wiring resistance doesn’t introduce errors in the measurement; another is simpler, less expensive cabling. Note also that with constant current excitation, all bridge configurations are linear except the single-element varying case of Figure 4-7A. In summary, there are many design issues relating to bridge circuits, as denoted by Figure 4-8. After selecting the basic configuration, the excitation method must be determined. The value of the excitation voltage or current must first be determined, as this directly influences sensitivity. Recall that the full-scale bridge output is directly proportional to the excitation voltage (or current). Typical bridge sensitivities are 1mV/V to 10mV/V. 234 Sensor Signal Conditioning IB R IB R R R+∆R VO: IB R 4 ∆R ∆R R + 4 Linearity Error: R− −∆R R VO VO 0.25%/% (A) Single-Element Varying R R VO R+∆R IB 2 ∆R 0 (B) Two-Element Varying (1) R− −∆R R+∆R VO R+∆R IB 2 IB IB R R+∆R R− −∆R ∆R IB R+∆R ∆R 0 0 (C) Two-Element Varying (2) (D) All-Element Varying Figure 4-7: The output voltage sensitivity and linearity of constant current drive bridge configurations also differs according to the number of active elements • Selecting Configuration (1-, 2-, 4-Element Varying) • Selection of Voltage or Current Excitation • Ratiometric Operation • Stability of Excitation Voltage or Current • Bridge Sensitivity: FS Output / Excitation Voltage 1mV/V to 10mV/V Typical • Full-scale Bridge Outputs: 10mV − 100mV Typical • Precision, Low Noise Amplification/Conditioning Techniques Required • Linearization Techniques May Be Required • Remote Sensors Present Challenges Figure 4-8: A number of bridge considerations impact design choices Although large excitation voltages yield proportionally larger full-scale output voltages, they also result in higher bridge power dissipation, and thus raise the possibility of sensor resistor self-heating errors. On the other hand, low values of excitation voltage require more gain in the conditioning circuits, and also increase sensitivity to low level errors such as noise and offset voltages. Regardless of the absolute level, the stability of the excitation voltage or current directly affects the overall accuracy of the bridge output, as is evident from the VB and IB terms in the output expressions. Therefore stable references and/or ratiometric drive techniques are required, to maintain highest accuracy. Here, ratiometric simply refers to the use of the bridge drive voltage of a voltage-driven bridge (or a current-proportional voltage, for a current-driven bridge) as the reference input to the ADC that digitizes the 235 Chapter Four amplified bridge output voltage. In this manner the absolute accuracy and stability of the excitation voltage becomes a second-order error. Examples to follow further illustrate this point. Amplifying and Linearizing Bridge Outputs The output of a single-element varying bridge may be amplified by a single precision op amp connected as shown in Figure 4-9. Unfortunately this circuit, although attractive because of relative simplicity, has poor overall performance. Its gain predictability and accuracy are poor, and it unbalances the bridge due to loading from RF and the op amp bias current. The RF resistors must be carefully chosen and matched to maximize common mode rejection (CMR). Also, it is difficult to maximize the CMR while at the same time allowing different gain options. Gain is dependent upon the bridge resistances and RF. In addition, the output is nonlinear, as the configuration does nothing to address the intrinsic bridge nonlinearity. In summary, the circuit isn’t recommended for precision use. VB RF R R +VS − + R R+∆R RF VS 2 Figure 4-9: Using a single op amp as a bridge amplifier However, a redeeming feature of this circuit is that it is capable of single supply operation, with a solitary op amp. Note that the RF resistor connected to the noninverting input is returned to VS/2 (rather than ground) so that both positive and negative ∆R values can be accommodated, with the bipolar op amp output swing referenced to VS/2. A much better approach is to use an instrumentation amplifier (in amp) for the required gain, as shown in Figure 4-10. This efficient circuit provides better gain accuracy, with the in amp gain usually set with a single resistor, RG. Since the amplifier provides dual, high-impedance loading to the bridge nodes, it does not unbalance or load the bridge. Using modern in amp devices with gains ranging from 10–1000, excellent common mode rejection and gain accuracy can be achieved with this circuit. However, due to the intrinsic characteristics of the bridge, the output is still nonlinear (see expression). As noted earlier, this can be corrected in software (assuming that the in amp output is digitized using an analog-to-digital converter and followed by a microcontroller or microprocessor). The in amp can be operated on either dual supplies as shown, or alternately, on a single positive supply. In the figure, this corresponds to –VS = 0. This is a key advantage, due to the fact that all such bridge circuits bias the in amp inputs at VB/2, a voltage range typically compatible with amplifier bias requirements. In amps such as the AD620 family, the AD623, and AD627 can be used in single (or dual) supply bridge applications, provided their restrictions on the gain and input and output voltage swings are observed. 236 Sensor Signal Conditioning VB OPTIONAL RATIOMETRIC OUTPUT R VREF = VB +V S R − RG VOUT = VB 4 ∆R R + IN AMP + ∆R GAIN 2 VOUT REF R −VS* R+∆R *SEE TEXT REGARDING SINGLE-SUPPLY OPERATION Figure 4-10: A generally preferred method of bridge amplification employs an instrumentation amplifier for stable gain and high CMR The bridge in this example is voltage driven, by the voltage VB. This voltage can optionally be used for an ADC reference voltage, in which case it also is an additional output, VREF. Various techniques are available to linearize bridge outputs, but it is important to distinguish between the linearity of the bridge equation (discussed earlier), and the sensor response linearity to the phenomenon being sensed. For example, if the active sensor element is an RTD, the bridge used to implement the measurement might have perfectly adequate linearity; yet the output could still be nonlinear, due to the RTD device’s intrinsic nonlinearity. Manufacturers of sensors employing bridges address the nonlinearity issue in a variety of ways, including keeping the resistive swings in the bridge small, shaping complementary nonlinear response into the active elements of the bridge, using resistive trims for first-order corrections, and others. In the examples which follow, what is being addressed is the linearity error of the bridge configuration itself (as opposed to a sensor element within the bridge). Figure 4-11 shows a single-element varying active bridge circuit, in which an op amp produces a forced bridge null condition. For this single-element varying case, only the op amp feedback resistance varies, with the remaining three resistances fixed. As used here, the op amp output provides a buffered, ground referenced, low impedance output for the bridge measurement, effectively suppressing the VB/2 CM bridge component at the op amp inputs. VB R R + +VS − −VS R R+∆R ∆R VOUT = − VB 2R Figure 4-11: Linearizing a single-element varying bridge (Method 1) 237 Chapter Four The circuit works by adding a voltage in series with the variable resistance arm. This voltage is equal in magnitude and opposite in polarity to the incremental voltage across the varying element, and is linear with ∆R. As can be noted, the three constant “R” valued resistances and the op amp operate to drive a constant current in the variable resistance. This is the basic mechanism that produces the linearized output. This active bridge has a sensitivity gain of two over the standard single-element varying bridge (Figure 4-6A). The key point is that the bridge’s incremental resistance/voltage output becomes linear, even for large values of ∆R. However, because of a still relatively small output signal, a second amplifier must usually follow this bridge. Note also that the op amp used in this circuit requires dual supplies, because its output must go negative for conditions where ∆R is positive. Another circuit for linearizing a single-element varying bridge is shown in Figure 4-12. The top node of the bridge is excited by the voltage, VB. The bottom of the bridge is driven in complementary fashion by the left op amp, which maintains a constant current of VB/R in the varying resistance element, R + ∆R. VB R R V ∆R R2 VOUT = B 1+ R1 2 R +VS + −VS − + +VS VOUT − R2 −VS R+∆R R R1 Figure 4-12: Linearizing a single-element varying bridge (Method 2) Like the circuit of Figure 4-11, the constant current drive for the single-element variable resistance provides the mechanism for linearity improvement. Also, because of the fact that the bridge left-side center node is ground-referenced by the op amp, this configuration effectively suppresses CM voltages. This has the virtue of making the op amp selection somewhat less critical. Of course, performance parameters of high gain, low offset/noise, and high stability are all still needed. The output signal is taken from the right-hand leg of the bridge, and is amplified by a second op amp, connected as a noninverting gain stage. With the scaling freedom provided by the second op amp, the configuration is very flexible. The net output is linear, and has a bridge-output referred sensitivity comparable to the single-element varying circuit of Figure 4-11. The Figure 4-12 circuit requires two op amps operating on dual supplies. In addition, paired resistors R1-R2 must be ratio matched and stable types, for overall accurate and stable gain. The circuit can be a practical one using a dual precision op amp, such as an AD708, the OP2177 or the OP213. A closely related circuit for linearizing a voltage-driven, two-element varying bridge can be adapted directly from the basic circuit of Figure 4-11. This form of the circuit, shown in Figure 4-13, is identical to the previous single-element varying case, with the exception that the resistance between VB and the op amp (+) input is now also variable (i.e., both diagonal R + ∆R resistances vary, in a like manner). 238 Sensor Signal Conditioning VB R R+∆R − + +VS −VS R+∆R R ∆R R V OUT = −VB Figure 4-13: Linearizing a two-element varying voltage-driven bridge (Method 1) For the same applied voltage VB, this form of the circuit has twice the sensitivity, which is evident in the output expressions. A dual supply op amp is again required, and additional gain may also be necessary. The two-element varying bridge circuit shown in Figure 4-14 uses an op amp, a sense resistor, and a voltage reference, set up in a feedback loop containing the sensing bridge. The net effect of the loop is to maintain a constant current through the bridge of IB = VREF/RSENSE. The current through each leg of the bridge remains constant (IB/2) as the resistances change, therefore the output is a linear function of ∆R. An in amp provides the additional gain. +VS R R+∆R ∆R VOUT = IB GAIN 2 − RG IB IN AMP + R R+∆R +VS − RSENSE IB VOUT −VS* * SEE TEXT REGARDING SINGLE-SUPPLY OPERATION + −VS* REF VREF Figure 4-14: Linearizing a two-element varying current-driven bridge (Method 2) This circuit can be operated on a single supply with the proper choice of amplifiers and signal levels. If ratiometric operation of an ADC is desired, the VREF voltage can be used to drive the ADC. 239 Chapter Four Driving Remote Bridges Wiring resistance and noise pickup are the biggest problems associated with remotely located bridges. Figure 4-15 shows a 350 Ω strain gage, which is connected to the rest of the bridge circuit by 100 feet of 30-gage twisted-pair copper wire. The resistance of the wire at 25ºC is 0.105 Ω/ft, or 10.5 Ω for 100 ft. The total lead resistance in series with the 350 Ω strain gage is therefore 21 Ω. The temperature coefficient of the copper wire is 0.385%/ºC. Now we will calculate the gain and offset error in the bridge output due to a 10ºC temperature rise in the cable. These calculations are easy to make, because the bridge output voltage is simply the difference between the output of two voltage dividers, each driven from a 10 V source. +10V 100 FEET, 30 GAGE COPPER WIRE = 10.5Ω @ 25°C TC = 0.385%/°C ASSUME 10°C TEMPERATURE CHANGE NUMBERS IN ( ) ARE @ 35°C 350Ω 350Ω − VO + RLEAD 10.5Ω (10.904Ω) 0 → 23.45mV STRAIN GAGE (5.44mV → 28.83mV) 350Ω → 353.5Ω FS 350Ω RCOMP 21Ω RLEAD 10.5Ω (10.904Ω) OFFSET ERROR OVER TEMPERATURE = +23%FS GAIN ERROR OVER TEMPERATURE = –0.26%FS Figure 4-15: Wiring resistance related errors with remote bridge sensor The full-scale variation of the strain gage resistance (with flex) above its nominal 350 Ω value is +1% (+3.5 Ω), corresponding to a full-scale strain gage resistance of 353.5 Ω which causes a bridge output voltage of +23.45 mV. Notice that the addition of the 21 Ω RCOMP resistor compensates for the wiring resistance and balances the bridge when the strain gage resistance is 350 Ω. Without RCOMP, the bridge would have an output offset voltage of 145.63 mV for a nominal strain gage resistance of 350 Ω. This offset could be compensated for in software just as easily but, for this example, we chose to do it with RCOMP. Assume that the cable temperature increases 10ºC above nominal room temperature. This results in a total lead resistance increase of +0.404 Ω (10.5 Ω × 0.00385/ºC × 10ºC) in each lead. Note: The values in parentheses in the diagram indicate the values at 35ºC. The total additional lead resistance (of the two leads) is +0.808 Ω. With no strain, this additional lead resistance produces an offset of +5.44 mV in the bridge output. Full-scale strain produces a bridge output of +28.83 mV (a change of +23.39 mV from no strain). Thus the increase in temperature produces an offset voltage error of +5.44 mV (+23% full-scale) and a gain error of –0.06 mV (23.39 mV – 23.45 mV), or –0.26% full-scale. Note that these errors are produced solely by the 30-gage wire, and do not include any temperature coefficient errors in the strain gage itself. The effects of wiring resistance on the bridge output can be minimized by the 3-wire connection shown in Figure 4-16. We assume that the bridge output voltage is measured by a high impedance device, therefore there is no current in the sense lead. Note that the sense lead measures the voltage output of a divider: the top half is the bridge resistor plus the lead resistance, and the bottom half is strain gage resistance plus the lead resistance. The nominal sense voltage is therefore independent of the lead resistance. When the strain gage resistance increases to full-scale (353.5 Ω), the bridge output increases to +24.15 mV. Increasing the temperature to 35ºC increases the lead resistance by +0.404 Ω in each half of the divider. The full-scale bridge output voltage decreases to +24.13 mV because of the small loss in sensitivity, but 240 Sensor Signal Conditioning 10V 100 FEET, 30-GAGE COPPER WIRE = 10.5Ω @ 25°C TC = 0.385%/°C ASSUME 10°C TEMPERATURE CHANGE NUMBERS IN ( ) ARE @ 35°C 350Ω 350Ω − VO + RLEAD 10.5Ω (10.904Ω) 0 → 24.15mV 350Ω STRAIN GAGE I=0 350Ω → 353.5Ω FS (0 → 24.13mV) RLEAD 10.5Ω (10.904Ω) OFFSET ERROR OVER TEMPERATURE = 0%FS GAIN ERROR OVER TEMPERATURE = –0.08%FS Figure 4-16: Remote bridge wiring resistance errors are reduced with 3-wire sensor connection there is no offset error. The gain error due to the temperature increase of 10ºC is therefore only –0.02 mV, or –0.08% of full-scale. Compare this to the +23% full-scale offset error and the –0.26% gain error for the 2-wire connection shown in Figure 4-14. The 3-wire method works well for remotely located resistive elements which make up one leg of a singleelement varying bridge. However, all-element varying bridges are generally housed in a complete assembly, as in the case of a load cell. When these bridges are remotely located from the conditioning electronics, special techniques must be used to maintain accuracy. Of particular concern is maintaining the accuracy and stability of the bridge excitation voltage. The bridge output is directly proportional to the excitation voltage, and any drift in the excitation voltage produces a corresponding drift in the output voltage. For this reason, most all-element varying bridges (such as load cells) are six-lead assemblies: two leads for the bridge output, two leads for the bridge excitation, and two sense leads. To take full advantage of the additional accuracy that these extra leads allow, a method called Kelvin or 4-wire sensing is employed, as shown in Figure 4-17. + +VB +FORCE RLEAD +SENSE – VO – SENSE – FORCE RLEAD – + Figure 4-17: A Kelvin sensing system with a 6-wire voltage-driven bridge connection and precision op amps minimizes errors due to wire lead resistances 241 Chapter Four In this setup the drive voltage VB is not applied directly to the bridge, but goes instead to the input of the upper precision op amp, which is connected in a feedback loop around the bridge (+) terminal. Although there may be a substantial voltage drop in the +FORCE lead resistance of the remote cable, the op amp will automatically correct for it, since it has a feedback path through the +SENSE lead. The net effect is that the upper node of the remote bridge is maintained at a precise level of VB (within the capability of the op amp used, of course). A similar situation occurs with the bottom precision op amp, which drives the bridge (–) terminal to a ground level, as established by the op amp input ground reference. Again, the voltage drop in the –FORCE lead is relatively immaterial, because of the sensing at the –SENSE terminal. In both cases, the sense lines go to high impedance op amp inputs, thus there is minimal error due to the bias current induced voltage drop across their lead resistance. The op amps maintain the required excitation voltage at the remote bridge, to make the voltage measured between the (+) and (−) sense leads always equal to VB. Note—a subtle point is that the lower op amp will need to operate on dual supplies, since the drive to the –FORCE lead will cause the op amp output to go negative. Because of relatively high current in the bridge (~30 mA), current buffering stages at the op amp outputs are likely advisable for this circuit. Although Kelvin sensing eliminates errors due to voltage drops in the bridge wiring resistance, the basic drive voltage VB must still be highly stable since it directly affects the bridge output voltage. In addition, the op amps must have low offset, low drift, and low noise. Ratiometric operation can be optionally added, simply by using VB to drive the ADC reference input. The constant current excitation method shown in Figure 4-18 is another method for minimizing the effects of wiring resistance on the measurement accuracy. This system drives a precise current I through the bridge, proportioned as per the expression in the figure. An advantage of the circuit in Figure 4-18 is that it only uses one amplifier. VREF + I RLEAD – 4-LEAD BRIDGE VO I RLEAD I= VREF I RSENSE RSENSE Figure 4-18: A 4-wire current-driven bridge scheme also minimizes errors due to wire lead resistances, plus allows simpler cabling The accuracy of the reference, the sense resistor, and the op amp all influence the overall accuracy. While the precision required of the op amp should be obvious, one thing not necessarily obvious is that it may be required to deliver appreciable current, when I is more than a few mA (which it will be with standard 350 Ω bridges). In such cases, current buffering of the op amp is again in order. 242 Sensor Signal Conditioning Therefore for highest precision with this circuit, a buffer stage is recommended. This can be as simple as a small transistor, since the bridge drive is unidirectional. System Offset Minimization Maintaining an accuracy of 0.1% or better with a full-scale bridge output voltage of 20 mV requires that the sum of all offset errors be less than 20 µV. Parasitic thermocouples are cases in point and, if not given due attention, can cause serious temperature drift errors. All dissimilar metal-metal connections generate voltages between a few and tens of microvolts for a 1ºC temperature differential, are basic thermocouple facts of life. Fortunately, however, within a bridge measurement system the signal connections are differential; therefore this factor can be used to minimize the impact of parasitic thermocouples. Figure 4-19 shows some typical sources of offset error that are inevitable in a system. Within a differential signal path, only those thermocouple pairs whose junctions are actually at different temperatures will degrade the signal. The diagram shows a typical parasitic junction formed between the copper printed circuit board traces and the kovar pins of an IC amplifier. THERMOCOUPLE VOLTAGE ≈ 35µV/ °C × (T1 – T2) + VB IB + T1 VOS + VO + T2 AMP – – IB – COPPER TRACES KOVAR PINS Figure 4-19: Typical sources of offset voltage within bridge measurement systems This thermocouple voltage is about 35 µV/ºC temperature differential. Note that this package-PC trace thermocouple voltage is significantly less when using a plastic package with a copper lead frame (recommended). Regardless of what package is used, all metal-metal connections along the signal path should be designed so that minimal temperature differences occur between the sides. The amplifier offset voltage and bias currents are further sources of offset error. The amplifier bias current must flow through the source impedance. Any unbalance in either the source resistances or the bias currents produces offset errors. In addition, the offset voltage and bias currents are a function of temperature. 243 Chapter Four High performance low offset, low offset drift, low bias current, and low noise precision amplifiers such as the AD707, the OP177 or OP1177 are required. In some cases, chopper-stabilized amplifiers such as the AD8551/AD8552/AD8554 may be a solution. Ac bridge excitation such as that shown in Figure 4-20 can effectively remove offset voltage effects in series with a bridge output, VO. NORMAL DRIVE VOLTAGES + VB EOS = SUM OF ALL OFFSET ERRORS – + EOS + + VA = VO + EOS VO – - VA – VB = (VO + EOS) – (– VO + EOS) = 2 VO REVERSE DRIVE VOLTAGES EOS – VO + – + + VB = – VO + EOS – + VB Figure 4-20: Ac bridge excitation minimizes system offset voltages The concept is simple, and can be described as follows. The net bridge output voltage is measured under the two phased-sequence conditions, as shown. A first measurement (top) drives the bridge at the top node with excitation voltage VB. This yields a first-phase measurement output VA, where VA is the sum of the desired bridge output voltage VO and the net offset error voltage EOS. In the second measurement (bottom) the polarity of the bridge excitation is then reversed, and a second measurement, VB, is made. Subtracting VB from VA yields 2 VO, and the offset error term EOS cancels as noted from the mathematical expression in the figure. Obviously, a full implementation of this technique requires a highly accurate measurement ADC such as the AD7730 (see Reference 5) as well as a microcontroller to perform the subtraction. Note that if a ratiometric reference is desired, the ADC must also accommodate the changing polarity of the reference voltage, as well as sense the magnitude. Again, the AD7730 includes this capability. A very powerful combination of bridge circuit techniques is shown in Figure 4-21, an example of a high performance ADC. In Figure 4-21A is shown a basic dc operated ratiometric technique, combined with Kelvin sensing to minimize errors due to wiring resistance, which eliminates the need for an accurate excitation voltage. The AD7730 measurement ADC can be driven from a single supply voltage of 5 V, which in this case is also used to excite the remote bridge. Both the analog input and the reference input to the ADC are high impedance and fully differential. By using the + and – SENSE outputs from the bridge as the differential reference voltage to the ADC, there is no loss in measurement accuracy if the actual bridge excitation voltage varies. To implement ac bridge operation of the AD7730, an “H” bridge driver of P-Channel and N-Channel MOSFETs can be configured as shown in Figure 4-21B (note—dedicated bridge driver chips are available, 244 Sensor Signal Conditioning +5V +FORCE RLEAD 6-LEAD BRIDGE AV DD +5V/+3V + FORCE + SENSE +SENSE + VREF VO + A IN – A IN VO AD7730 ADC – SENSE 24 BITS – SENSE RLEAD Q4 Q2 – VREF – FORCE V3,4 Q3 Q1 DVDD V1,2 V1,2 GND V3,4 (A) DC excitation + FORCE Q1,Q2 ON Q1,Q2 ON Q3,Q4 ON Q3,Q4 ON (B) AC excitation (simplified) Figure 4-21: Ratiometric dc or ac operation with Kelvin sensing can be implemented using the AD7730 ADC such as the Micrel MIC4427). This scheme, added to the basic functionality of the AD7730 configuration of 4-21A greatly increases the utility of the offset canceling circuit, as generally outlined in the preceding discussion of Figure 4-20. Because of the on-resistance of the H-bridge MOSFETs, Kelvin sensing must also be used in these ac bridge applications. It is also important that the drive signals be nonoverlapping, as noted, to prevent excessive MOSFET switching currents. The AD7730 ADC has on-chip circuitry which generates the required nonoverlapping drive signals to implement this ac bridge excitation. All that needs adding is the switching bridge as noted in Figure 4-21B. The AD7730 is one of a family of sigma-delta ADCs with high resolution (24 bits) and internal programmable gain amplifiers (PGAs) and is ideally suited for bridge applications. These ADCs have self- and system calibration features, which allow offset and gain errors due to the ADC to be minimized. For instance, the AD7730 has an offset drift of 5 nV/ºC and a gain drift of 2 ppm/ºC. Offset and gain errors can be reduced to a few microvolts using the system calibration feature. 245 Chapter Four References: Bridge Circuits 1. Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New York, 1991. 2. Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980, ISBN: 0-916550-05-2. 3. Sections 2, 3, Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN: 0-916550-10-9. 4. Sections 1, 6, Walt Kester, Editor, System Applications Guide, Analog Devices, 1993, ISBN: 0-916550-13-3. 5. Data sheet for AD7730 Bridge Transducer ADC, www.analog.com. 246 SECTION 4-3 Strain, Force, Pressure and Flow Measurements Walt Kester Strain Gages The most popular electrical elements used in force measurements include the resistance strain gage, the semiconductor strain gage, and piezoelectric transducers. The strain gage measures force indirectly by measuring the deflection it produces in a calibrated carrier. Pressure can be converted into a force using an appropriate transducer, and strain gage techniques can then be used to measure pressure. Flow rates can be measured using differential pressure measurements, which also make use of strain gage technology. These principles are summarized in Figure 4-22. • • • • Strain: Force: Pressure: Flow: Strain Gage, Piezoelectric Transducers Load Cell Diaphragm to Force to Strain Gage Differential Pressure Techniques Figure 4.22 Strain gages are directly or indirectly the basis for a variety of physical measurements The resistance-based strain gage uses a resistive element that changes in length, hence resistance, as the force applied to the base on which it is mounted causes stretching or compression. It is perhaps the most well-known transducer for converting force into an electrical variable. An unbonded strain gage consists of a wire stretched between two points. Force acting upon the wire (area = A, length = L, resistivity = ρ) will cause the wire to elongate or shorten, which will cause the resistance to increase or decrease proportionally according to: R = ρL A Eq. 4-1 and, ∆R R = GF ⋅ ∆ L L Eq. 4-2 where GF = Gage factor (2.0 to 4.5 for metals, and more than 150 for semiconductors). In this expression, the dimensionless quantity ∆L/L is a measure of the force applied to the wire and is expressed in microstrains (1 µε = 10–6 cm/cm) which is the same as parts-per-million (ppm). 247 Chapter Four From Eq. 4-2, note that larger gage factors result in proportionally larger resistance changes, hence this implies greater strain gage sensitivity. These concepts are summarized in the drawing of Figure 4-23. FORCE R= ρL A ∆R = GF • ∆L R L STRAIN SENSING WIRE AREA = A LENGTH = L RESISTIVITY =ρ RESISTANCE = R ∆L L GF = GAGE FACTOR 2 TO 4.5 FOR METALS >150 FOR SEMICONDUCTORS = MICROSTRAINS ( µε ) 1 µε = 1×10–6 cm/cm = 1 ppm FORCE Figure 4-23: Operating principles of a basic unbonded strain gage A bonded strain gage consists of a thin wire or conducting film arranged in a coplanar pattern and cemented to a base or carrier. The basic form of this type of gage is shown in Figure 4-24. FORCE SMALL SURFACE AREA LOW LEAKAGE HIGH ISOLATION FORCE Figure 4-24: A bonded wire strain gage This strain gage is normally mounted so that as much as possible of the length of the conductor is aligned in the direction of the stress that is being measured, i.e., longitudinally. Lead wires are attached to the base and brought out for interconnection. Bonded devices are considerably more practical and are in much wider use than are the aforementioned unbonded devices. Perhaps the most popular version is the foil-type gage, produced by photo-etching techniques, and using similar metals to the wire types. Typical alloys are of copper-nickel (Constantan), nickel-chromium (Nichrome), nickel-iron, platinum-tungsten, and so forth. This strain gage type is shown in Figure 4-25. 248 Sensor Signal Conditioning FORCE PHOTO ETCHING TECHNIQUE LARGE AREA STABLE OVER TEMPERATURE THIN CROSS SECTION GOOD HEAT DISSIPATION FORCE Figure 4-25: A metal foil strain gage Gages having wire sensing elements present a small surface area to the specimen; this reduces leakage currents at high temperatures and permits higher isolation potentials between the sensing element and the specimen. Foil sensing elements, on the other hand, have a large ratio of surface area to cross-sectional area and are more stable under extremes of temperature and prolonged loading. The large surface area and thin cross section also permit the device to follow the specimen temperature and facilitate the dissipation of selfinduced heat. Semiconductor Strain Gages Semiconductor strain gages make use of the piezoresistive effect in certain semiconductor materials such as silicon and germanium in order to obtain greater sensitivity and higher level output. Semiconductor gages can be produced to have either positive or negative changes when strained. They can be made physically small while still maintaining a high nominal resistance. Semiconductor strain gage bridges may have 30 times the sensitivity of bridges employing metal films, but are temperature-sensitive and difficult to compensate. Their change in resistance with strain is also nonlinear. They are not in as widespread use as the more stable metal-film devices for precision work; however, where sensitivity is important and temperature variations are small, they may have some advantage. 249 Chapter Four Instrumentation is similar to that for metal-film bridges but is less critical because of the higher signal levels and decreased transducer accuracy. Figure 4-26 summarizes the relative performance of metal and semiconductor strain gages. SEMICONDUCTOR STRAIN GAGE METAL STRAIN GAGE PARAMETER Measurement Range 0.1 to 40,000 µε 0.001 to 3000 µε Gage Factor 2.0 to 4.5 50 to 200 Resistance, Ω 120, 350, 600, …, 5000 1000 to 5000 Resistance Tolerance 0.1% to 0.2% 1% to 2% Size, mm 0.4 to 150 Standard: 3 to 6 1 to 5 Figure 4-26: A comparison of metal and semiconductor type strain gages Piezoelectric force transducers are employed where the forces to be measured are dynamic (i.e., continually changing over the period of interest—usually of the order of milliseconds). These devices utilize the effect that changes in charge are produced in certain materials when they are subjected to physical stress. In fact, piezoelectric transducers are displacement transducers with quite large charge outputs for very small displacements, but they are invariably used as force transducers on the assumption that in an elastic material, displacement is proportional to force. Piezoelectric devices produce substantial output voltage in instruments such as accelerometers for vibration studies. Piezoelectric sensor output conditioning is discussed within Section 4-4 of this chapter. Strain gages can be used to measure force, as shown in Figure 4-27, where a cantilever beam is slightly deflected by the applied force. Four strain gages are used to measure the flex of the beam, two on the top, and two on the bottom. The gages are connected in a four-element bridge configuration. Recall from Section 4-2 that this configuration gives maximum sensitivity and is inherently linear. This configuration also offers first-order correction for temperature drift in the individual strain gages. VB RIGID BEAM FORCE R1 R1 R4 _ R3 + VO R2 R4 R2 R3 Figure 4-27: A beam force sensor using a strain gage bridge 250 Sensor Signal Conditioning Strain gages are low-impedance devices, consequently they require significant excitation power to obtain reasonable levels of output voltage. A typical strain-gage-based load cell bridge will have a 350 Ω impedance and is specified as having a sensitivity in a range 3 mV–10 mV full scale, per volt of excitation. The load cell is composed of four individual strain gages arranged as a bridge, as shown in Figure 4-28. For a 10 V bridge excitation voltage with a rating of 3 mV/V, 30 mV of signal will be available at full-scale loading. FORCE +VB +SENSE +VOUT –VOUT –SENSE –VB Figure 4-28: A load cell comprising four strain gages is shown in physical (top) and electrical (bottom) representations While increasing the drive to the bridge can increase the output, self-heating effects are a significant limitation to this approach—they can cause erroneous readings, or even device destruction. One technique for evading this limitation is to use a low duty cycle pulsed drive signal for the excitation. Many load cells have the ±”SENSE” connections as shown, to allow the signal-conditioning electronics to compensate for dc drops in the wires (Kelvin sensing as discussed in Section 4-2). This brings the wires to a total of six for the fully instrumented bridge. Some load cells may also have additional internal resistors for temperature compensation purposes. 251 Chapter Four Pressures in liquids and gases are measured electrically by a variety of pressure transducers. A number of mechanical converters (including diaphragms, capsules, bellows, manometer tubes, and Bourdon tubes) are used to measure pressure by measuring an associated length, distance, or displacement, and to measure pressure changes by the motion produced, as shown by Figure 4-29. PRESSURE SOURCE STRAIN GAGE MECHANICAL OUTPUT PRESSURE SENSOR (DIAPHRAGM) SIGNAL CONDITIONING ELECTRONICS Figure 4-29: Pressure sensors use strain gages for indirect pressure measurement The output of this mechanical interface is then applied to an electrical converter such as a strain gage, or piezoelectric transducer. Unlike strain gages, piezoelectric pressure transducers are typically used for high frequency pressure measurements (such as sonar applications, or crystal microphones). There are many ways of defining flow (mass flow, volume flow, laminar flow, turbulent flow). Usually the amount of a substance flowing (mass flow) is the most important, and if the fluid’s density is constant, a volume flow measurement is a useful substitute that is generally easier to perform. One commonly used class of transducers, which measures flow rate indirectly, involves the measurement of pressure. Flow can be derived by taking the differential pressure across two points in a flowing medium—one at a static point and one in the flow stream. Pitot tubes are one form of device used to perform this function, where flow rate is obtained by measuring the differential pressure with standard pressure transducers. Differential pressure can also be used to measure flow rate using the venturi effect by placing a restriction in the flow. Although there are a wide variety of physical parameters being sensed, the electronics interface is very often strain gage based. Bridge Signal Conditioning Circuits The remaining discussions of this section deal with applications that apply the bridge and strain gage concepts discussed thus far in general terms. An example of an all-element varying bridge circuit is a fatigue monitoring strain sensing circuit, as shown in Figure 4-30. The full bridge is an integrated unit, which can be attached to the surface on which the strain or flex is to be measured. In order to facilitate remote sensing, current mode bridge drive is used. The remotely located bridge is connected to the conditioning electronics through a 4-wire shielded cable. The OP177 precision op amp servos the bridge current to 10 mA, being driven from an AD589 reference voltage of 1.235 V. Current buffering of the op amp is employed in the form of the PNP transistor, for lowest op amp self-heating, and highest gain linearity. 252 Sensor Signal Conditioning +15V Figure 4-30: A precision strain gage sensor amplifier using a remote current-driven 1 kΩ bridge, a buffered precision op amp driver, and a precision in amp 100X gain stage 7 100Ω 1 2 – 10mA 499Ω 8 VOUT 6 AD620 0.1µF 1kΩ –15V –3.500V = –3500µε +5.000V = +5000µε 5 3 + 1kΩ 4 100Ω +15V 1.7kΩ 2N2907A 8.2kΩ 1kΩ 6 1kΩ 7 +15V STRAIN SENSOR: Columbia Research Labs 2682 Range: –3500µε to +5000µε Output: 10.25mV/1000µε 4 OP177 + +1.235V 30.1kΩ –15V – 3 27.4kΩ 2 124Ω +15V +1.235V AD589 The strain gage produces an output of 10.25 mV/1000 µε. The signal is amplified by the AD620 in amp, which is configured for a gain of 100 times, via an effective RG of 500 Ω. Full-scale voltage calibration is set by adjusting the 100Ω gain potentiometer such that, for a sensor strain of –3500 µε, the output reads –3.500 V; and for a strain of +5000 µε, the output registers +5.000 V. The measurement may then be digitized with an ADC which has a 10 V full-scale input range. The 0.1 µF capacitor across the AD620 input pins serves as an EMI/RFI filter in conjunction with the bridge resistance of 1 kΩ. The corner frequency of this filter is approximately 1.6 kHz. Another example is a load cell amplifier circuit, shown in Figure 4-31. This circuit is more typical of a bridge workhorse application. It interfaces with a typical 350Ω load cell, and can be configured to accommodate typical bridge sensitivities over a range of 3 mV–10 mV/V. +15V 2 +15V Figure 4-31: A precision 350 Ω load cell amplifier, using a buffered voltagedriven configuration with Kelvin sensing and a precision in amp +15V 2N2219A 7 1kΩ 6 350Ω 13 1 3 3 – 2 6 8 10 4 4 –15V 475Ω 100Ω +15 2 350Ω – 7 8 5 + 4 –15V 253 8 1 AD621B or AD620B (see text) 3 350Ω LOAD CELL 100mV FS 11 9 1 350Ω 12 AD588 OP177 +10.000V 350Ω +10.000V + –15V 16 6 Use with AD620 VOUT 0 TO +10.000V FS Chapter Four A 10.000 V bridge excitation excitation is derived from an AD588 10 V reference, with an OP177 and 2N2219A used as a buffer. The 2N2219A is within the OP177 feedback loop and supplies the necessary bridge drive current (28.57 mA). This ensures that the op amp performance will not be compromised. The Kelvin sensing scheme used at the bridge provides for low errors due to wiring resistances, and a precision zener diode reference, the AD588, provides lowest excitation drift and scaling with temperature changes. To ensure highest linearity is preserved, a low drift instrumentation amplifier is used as the gain stage. This design has a minimum number of critical resistors and amplifiers, making the entire implementation accurate, stable, and cost effective. In addition to low excitation voltage TC, another stability requirement is minimum in amp gain TC. Both factors are critical towards insuring stable circuit scaling over temperature. With the use of the AD621B in amp as shown, the scaling is for a precise gain of 100 (as set by the Pin 1–8 jumper), for lowest in amp gain TC. The AD621B is specified for a very low gain TC, only 5 ppm/°C. The gain of 100 translates a 100 mV full-scale bridge output to a nominal 10 V output. Alternately, an AD620B could also be used, with the optional gain network consisting of the fixed 475 Ω resistor, and 100 Ω potentiometer for gain adjustment. This will provide a 50 ppm/°C gain TC for the in amp, plus the TC of the external parts (which should have low temperature coefficients). While the lowest TC is provided by the fixed gain AD621 setup, it doesn’t allow direct control of overall scaling. To retain the very lowest TC, scaling could be accomplished via a software autocalibration routine. Alternately, the AD588 and OP177 reference/op amp stage could be configured for a variable excitation voltage (as opposed to a fixed 10.000 V as shown). Variable gain in the reference voltage driver will effectively alter the excitation voltage as seen by the bridge, and thus provide flexible overall system scaling. Of course, it is imperative that such a scheme be implemented with low TC resistances. As shown previously, a precision load cell is usually configured as a 350 Ω bridge. Figure 4-32 shows a precision load cell amplifier, within a circuit possessing the advantage of being powered from just a single power supply. +VS 2 6 (VREF) 10kΩ 196Ω 28.7Ω 1kΩ 1kΩ 10kΩ +5.000V REF195 1µF 2 4 350Ω 8 1/2 OP213 350Ω 3 350Ω – + 4 – 1 G = 100 6 1/2 OP213 5 + 7 VOUT 350Ω Figure 4-32: a single-supply load cell amplifier As noted previously, the bridge excitation voltage must be both precise and stable, otherwise it can introduce measurement errors. In this circuit, a precision REF195 5 V reference is used as the bridge drive, allowing a TC as low as 5 ppm/°C. The REF195 reference can also supply more than 30 mA to a load, so 254 Sensor Signal Conditioning it can drive a 350 Ω bridge (~14 mA) without need of a buffer. The dual OP213 is configured as a gain-of100, two-op-amp in amp. The resistor network sets the gain according to the formula: G = 1+ 10 kΩ 20 kΩ + = 100 1kΩ 196 Ω + 28.7 Ω Eq. 4-3 For optimum CMR, the 10 kΩ/1 kΩ resistor ratio matching should be precise. Close tolerance resistors (±0.5% or better) should be used, and all resistors should be of the same type. For a zero volt bridge output signal, the amplifier will swing to within 2.5 mV of 0 V. This is the minimum output limit of the OP213. Therefore, if an offset adjustment is required, the adjustment should start from a positive voltage at VREF and adjust VREF downward until the output (VOUT) stops changing. This is the point at which the amplifier limits the swing. Because of the single supply design, the amplifier cannot sense input signals that have negative polarity. If linearity around or at zero volts input is required, or if negative polarity signals must be processed, the VREF connection can be connected to a stable voltage that is mid-supply (i.e., 2.5 V) rather than ground. Note that when VREF is not at ground, the output must be referenced to VREF. An advantage of this type of referencing is that the output is now bipolar, with respect to VREF. The AD7730 24-bit sigma-delta ADC is ideal for direct conditioning of bridge outputs, and requires no interface circuitry (see Reference 10). A simplified connection diagram was shown in Figure 4.21A. The entire circuit operates on a single 5 V supply, which also serves as the bridge excitation voltage. Note that the measurement is ratiometric, because the sensed bridge excitation voltage is also used as the ADC reference. Variations in the 5 V supply do not affect the accuracy of the measurement. The AD7730 has an internal programmable gain amplifier that allows a full-scale bridge output of ±10 mV to be digitized to 16-bit accuracy. The AD7730 has self- and system calibration features that allow offset and gain errors to be minimized with periodic recalibrations. A “chop” or ac mode option minimizes the offset voltage and drift and operates similarly to a chopper-stabilized amplifier. The effective input voltage noise RTI is approximately 40nV rms, or 264 nV peak-to-peak. This corresponds to a resolution of 13 ppm, or approximately 16.5 bits. Gain linearity is also approximately 16 bits. 255 Chapter Four References: Strain, Force, Pressure And Flow Measurements 1. Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New York, 1991. 2. Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980, ISBN: 0-916550-05-2. 3. Sections 2, 3, Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN: 0-916550-10-9. 4. Sections 1, 6, Walt Kester, Editor, System Applications Guide, Analog Devices, 1993, ISBN: 0-916550-13-3. 5. Harry L. Trietley, Transducers in Mechanical and Electronic Design, Marcel Dekker, Inc., 1986. 6. Jacob Fraden, Handbook of Modern Sensors, 2nd Ed., Springer-Verlag, New York, NY, 1996. 7. The Pressure, Strain, and Force Handbook, Vol. 29, Omega Engineering, One Omega Drive, P.O. Box 4047, Stamford CT, 06907-0047, 1995. www.omega.com. 8. The Flow and Level Handbook, Vol. 29, Omega Engineering, One Omega Drive, P.O. Box 4047, Stamford CT, 06907-0047, 1995, www.omega.com. 9. Ernest O. Doebelin, Measurement Systems Applications and Design, 4th Ed., McGraw-Hill, 1990. 10. Data sheet for AD7730 Bridge Transducer ADC, www.analog.com. 256 SECTION 4-4 High Impedance Sensors Walt Kester, Scott Wurcer, Chuck Kitchin Many popular sensors have output impedances greater than several megohms, and thus the associated signal-conditioning circuitry must be carefully designed to meet the challenges of low bias current, low noise, and high gain. Figure 4-33 lists a few examples of high impedance sensors. A large portion of this section is devoted to a germane example, the analysis of a photodiode preamplifier. This application demonstrates many of the problems associated with high impedance sensor signal-conditioning circuits, and offers a host of practical solutions that can be applied to virtually all such sensors. • • • • • • Photodiode Preamplifiers Piezoelectric Sensors Humidity pH Monitors Chemical Sensors Smoke Detectors Figure 4-33: High impedance sensors Other examples of high impedance sensors to be discussed are piezoelectric sensors and charge-output sensors. Photodiode Preamplifier Design Photodiodes generate a small current that is proportional to the level of illumination. Their applications range from relatively low speed, wide dynamic range circuits to much higher speed circuits. Examples of the types of applications are precision light meters and high-speed fiber optic receivers. One of the standard methods for specifying photodiode sensitivity is to state its short-circuit photocurrent (Isc) for a given light level from a well-defined light source. The most commonly used source is an incandescent tungsten lamp running at a color temperature of 2850K. At 100 fc (foot candles) of illumination (approximately the light level on an overcast day), the short-circuit current usually falls in a range of picoamps to hundreds of microamps for small area (less than 1 mm2) diodes. 257 Chapter Four The equivalent circuit for a photodiode is shown in Figure 4-34. The short-circuit current is very linear over 6 to 9 decades of light intensity, and is therefore often used as a measure of absolute light levels. The opencircuit forward voltage drop across the photodiode varies logarithmically with light level but, because of its large temperature coefficient, the diode voltage is seldom used as an accurate measure of light intensity. The shunt resistance RSH is usually on the order of 1000 MΩ at room temperature, and decreases by a factor of 2 for every 10ºC rise in temperature. Diode capacitance CJ is a function of junction area and the diode bias voltage. A value of 50 pF at zero bias is typical for small-area diodes. INCIDENT LIGHT PHOTO CURRENT RSH(T) IDEAL DIODE CJ 100kΩ − 100GΩ NOTE: R SH HALVES EVERY 10°C TEMPERATURE RISE Figure 4-34: A photodiode equivalent circuit Photodiodes may be operated in either of two basic modes, as shown in Figure 4-35. These modes are with zero bias voltage (photovoltaic mode, left) or with a reverse-bias voltage (photoconductive mode, right). – – + + –VBIAS • • • • • PHOTOVOLTAIC Zero Bias No “Dark” Current Linear Low Noise (Johnson) Precision Applications • • • • • PHOTOCONDUCTIVE Reverse Bias Has “Dark” Current Nonlinear Higher Noise (Johnson + Shot) High Speed Applications Figure 4-35: Photodiode operating modes The most precise linear operation is obtained in the photovoltaic mode, while higher switching speeds can be realized when the diode is operated in the photoconductive mode at the expense of linearity. Under these reverse-bias conditions, a small amount of current called dark current will flow—even when there is no illumination. 258 Sensor Signal Conditioning There is no dark current in the photovoltaic mode. In the photovoltaic mode, the diode noise is basically the thermal noise generated by the shunt resistance. In the photoconductive mode, shot noise due to conduction is an additional source of noise. Photodiodes are usually optimized during the design process for use in either the photovoltaic mode or the photoconductive mode, but not both. Figure 4-36 shows the photosensitivity for a small photodiode (Silicon Detector Part Number SD-020-12-001). This diode has a basic sensitivity of 0.03 µA/fc, and was chosen for the design example to follow. As this chart indicates, this photodiode’s dynamic range covers six orders of magnitude. ENVIRONMENT ILLUMINATION (fc) SHORT CIRCUIT CURRENT Direct Sunlight 1000 30µA Overcast Day 100 3µA Twilight 1 0.03µA Full Moonlit Night 0.1 3000pA Clear Night / No Moon 0.001 30pA Figure 4-36: Short circuit current versus light intensity for SD-020-12-001 photodiode (photovoltaic operating mode) A convenient way to convert the photodiode current into a usable voltage is to use a low bias current op amp, configured as a current-to-voltage converter as shown in Figure 4-37. The diode bias is maintained at zero volts by the virtual ground of the op amp, and the short-circuit current is converted into a voltage. At maximum sensitivity the amplifier must be able to detect a diode current of 30 pA. This implies that the feedback resistor must be very large, and the amplifier bias current very small. R = 1000MΩ ISC = 30pA (0.001 fc) _ VOUT = 30mV + Sensitivity: 1mV/pA Figure 4-37: A simplified current-to-voltage converter uses a low bias current op amp and a high value feedback resistor For example, 1000 MΩ will yield a corresponding voltage of 30 mV for this amount of current. Larger resistor values are impractical, so we will use 1000 MΩ for the most sensitive range. This will give an output voltage range of 10 mV for 10 pA of diode current and 10 V for 10 nA of diode current. This yields a range of 60 dB. For higher values of light intensity, the gain of the circuit must be reduced by using a smaller feedback resistor. For this range of maximum sensitivity, we should be able to easily distinguish between the light intensity on a clear, moonless night (0.001 fc), and that of a full moon (0.1 fc). 259 Chapter Four Notice that we have chosen to get as much gain as possible from one stage, rather than cascading two stages. This is in order to maximize the signal-to-noise ratio (SNR). If we halve the feedback resistor value, the signal level decreases by a factor of 2, while the noise due to the feedback resistor decreases by only . This reduces the SNR by 3 dB, assuming the closed loop bandwidth remains constant. Later in the analysis, we will find the resistors one of the largest overall output noise contributors. To accurately measure photodiode currents in the tens of picoamps range, the bias current of the op amp should be no more than a few picoamps. This considerably narrows the choice. The industry-standard OP07 is an ultralow offset voltage (10 µV) bipolar op amp, but its bias current is 4 nA (4000 pA). Even superbeta bipolar op amps with bias current compensation (such as the OP97) have bias currents on the order of 100 pA at room temperature, but they might be suitable for very high temperature applications, as unlike FET amplifiers, the bias currents do not double for every 10ºC increase. A JFET input electrometer-grade op amp is chosen for our photodiode preamp, since it must operate only over a limited temperature range. Figure 4-38 summarizes the performance of several popular “electrometer grade” FET input op amps. PART # VOS, MAX* TC VOS, TYP IB , MAX* 0.1Hz TO 10Hz NOISE, TYP AD549K 250µV 5µV/°C 100fA 4µV p-p TO-99 AD795JR 500µV 3µV/°C 3pA 1µV p-p SOIC AD820B 1000µV 2µV/°C 10pA 2µV p-p SOIC, DIP PACKAGE *25°C SPECIFICATION Figure 4-38: Some JFET input electrometer grade op amps suitable for use in photodiode preamplifiers As can be noted from this figure, the 25°C maximum bias current specification ranges from a few pA down to as low as 100 fA, and there are a number of packages types from which to choose. As will be seen shortly, the package finally chosen can and will affect the performance of the circuit in terms of the bias current realized within an application. This is due to relative ability to control the inevitable leakage currents in a design’s production environment. Of these devices, the AD549 and AD795 are fabricated on a BiFET process and use P-Channel JFETs as the input stage, as is shown in Figure 4-39. The rest of the op amp circuit is designed using bipolar devices. These BiFET op amps are laser trimmed at the wafer level, to minimize offset voltage and offset voltage drift. The offset voltage drift is minimized, by first trimming the input stage for equal currents in the JFET differential pair (drift trim resistors). A further trim of the JFET source resistors minimizes the input offset voltage (offset voltage trim resistors). For these discussions, an AD795JR was selected for the photodiode preamplifier, with key specifications summarized in Figure 4-38. This allows high circuit performance in an SOIC packaged device. Alternately, for even greater performance, the AD549 could be used. The AD549 uses the glass sealed TO-99 package, which allows the very highest performance in terms of low leakage. More on this follows. Since the photodiode current is measured in terms of picoamperes, it should be understood that extremely close attention must be given to all potential leakage paths in the actual physical circuit. To put this in some 260 Sensor Signal Conditioning +VS _ 2 OFFSET VOLTAGE TRIM RESISTORS REST OF AMPLIFIER + 3 6 VBIAS 1 5 NULL DRIFT TRIM RESISTORS NULL Figure 4-39: JFET input stage op amp with separate trims for offset voltage and drift perspective, consider the a simple printed circuit card example with two parallel conductor traces on a high-quality, well-cleaned epoxy-glass PC board 0.05 inches apart and parallel for 1 inch. Such an insulator has a leakage resistance of approximately 1011 Ω at +125ºC. By simple application of Ohm’s law, 15 V of bias between these runs produces a 150 pA current—sufficient to mask all signal levels below this current. Obviously then, low-level photodiode circuitry needs to employ all possible means of minimizing such parasitic currents. Unfortunately, they can arise from numerous sources, some of which can be quite subtle in origin. Figure 4-40 illustrates the circuit elements subject to leakage for the photodiode circuit, as enclosed within the dotted lines. The feedback resistor is highly critical, and should be a close tolerance (1%), low TC (50 ppm/°C) unit. Typical units suitable for R2 will be manufactured with thin film or metal oxide construction on ceramic or glass, with glass insulation. It should be readily apparent that any shunt conductive paths C2 R2 +VS _ 2 7 6 3 + 4 –VS Figure 4-40: Critical leakage paths and components for a photodiode preamplifier circuit are those within the dotted line area 261 Chapter Four across this resistor’s body can (and will) degrade or lower the net effective resistance, producing scaling errors. It is for this reason that such high value resistors are often glass enclosed, and can require special handling. Some sources of suitable high value resistors are listed in the section references. If used, compensation capacitor C2 should use the lowest loss dielectric possible. Typically this will mean a film type capacitor of Teflon, polypropylene, or polystyrene construction. All connections to the op amp’s summing junction should be kept short, clean, and free from manufacturing process chemicals and residues. In cases where an input cable is used to connect the photodiode to the preamp, it should be kept as short as possible, and should use Teflon or similar low loss dielectric insulation. The above considerations deal mainly with the more obvious construction points towards optimizing accuracy and keeping leakage low. However, two of the more difficult leakage sources that can plague this circuit aren’t quite as obvious. These are the op amp package-related parasitic leakages, which can occur from all op amp package pins adjacent to the input pin. Consider leakage as a high value resistance to Pin 2. Although it doesn’t show in this particular figure (since Pin 1 isn’t actively used by the application), any leakage from package Pin 1 can be very relevant. Note also, that since Pin 3 is grounded, it prevents error from leakage between Pins 4 and 2. If however, Pin 1 has any significant voltage on it (which it does in the case of the offset null pin of the AD820BN DIP device) serious leakage will then occur between Pins 1 and 2. The AD795JR SOIC is immune to this leakage, as Pin 1 isn’t connected internally. These comments serve to illustrate some of the subtleties of these leakage sources. The situation just described for the AD820BN DIP packaged device is by no means unique, as Pin 1 is a standard offset trim pin on many op amps. This circumstance will always tend to leak current into any high impedance source seen at Pin 2. There are also cases for follower-connected stages where leakage is just as critical, if not more so. In such cases the leakage goes into Pin 3 as a high impedance, typically from Pin 4, which is –VS. Fortunately however, there is a highly effective answer to controlling both of these leakage problems, and that is the use of circuit guard techniques. Guarding is used to reduce parasitic leakage currents, by isolating a sensitive amplifier input from large voltage gradients across the PC board. It does this by interposing a conductive barrier or screen between a high voltage source and a sensitive input. The barrier intercepts the leakage which would otherwise flow into the sensitive node, and diverts it away. In physical terms, a guard is a low impedance conductor that completely surrounds an input line or node, and it is biased to a potential equal to the line’s voltage. Note that the low impedance nature of a guard conductor shunts leakage harmlessly away. The biasing of the guard to the same potential as the guarded pin reduces any possibility of leakage between the guard itself and the guarded node. The exact technique for guarding depends on the amplifier’s mode of operation, i.e., whether the connection is inverting (like Figure 4-40), or a noninverting stage. Figure 4-41 shows a PC board layout for guarding the inputs of the AD820 op amp, as operated within either an inverting (top) or a noninverting gain stage (bottom). This setup uses the DIP (“N”) package, and would also be applicable to other devices where relatively high voltages occur at Pin 1 or 4. Using a standard 8-pin DIP outline, it can be noted that this package’s 0.1" pin spacing allows a PC trace (the guard trace) to pass between adjacent pins. This is the key to implementing effective DIP package guarding—the complete surrounding of the guarded trace with a low impedance trace. In the inverting mode (top), note that Pin 3 connected and grounded guard traces surround the op amp inverting input (Pin 2), and run parallel to the input trace. This guard would be continued out to and around the source device and feedback connection in the case of a photodiode (or around the input pad, in the case of a cable). In the follower mode (bottom), the guard voltage is the feedback divider tap voltage to Pin 2, i.e., the inverting input node of the amplifier. Although the feedback divider impedance isn’t as low 262 Sensor Signal Conditioning INVERTER 8 1 2 GUARD INPUT 2 3 GUARD AD820BN “N” PACKAGE 7 _ AD820BN 6 6 3 + 5 4 FOLLOWER 1 GUARD 2 INPUT GUARD 3 AD820BN 8 “N” PACKAGE 7 4 3 + 6 AD820BN 2 _ 6 5 Figure 4-41: Guard techniques for inverting and noninverting op amp stages using DIP package devices in absolute terms as a direct ground, it is still quite effective. Even a 1 kΩ or so impedance here will still be many orders of magnitude lower than the Pin 3 impedance. In both the inverting and the noninverting modes, the guard traces should be located on both sides of the PC board, with top and bottom side traces connected with several vias. Things become slightly more complicated when using guarding techniques with the SOIC surface mount (“R”) package, because the 0.05" pin spacing doesn’t allow routing of PC board traces between the pins. But there still is an effective guarding answer, at least for the inverting case. Figure 4-42 shows the preferred method. INVERTER GUARD 1 8 2 AD795JR 7 2 INPUT 3 GUARD –VS 4 “R” PACKAGE _ 6 AD795JR 6 3 + 5 PINS 1, 5, 8 ARE OPEN ON "R" PACKAGE FOLLOWER 1 AD795JR 8 GUARD 2 “R” PACKAGE 7 INPUT 3 6 GUARD 4 –VS 5 3 + 6 AD795JR 2 _ Figure 4-42: Guard techniques for inverting and noninverting op amp stages using SOIC package devices 263 Chapter Four In the AD795 SOIC “R” package, Pins 1, 5, and 8 are “no-connect” pins and can be used to route signal traces as shown. Thus in the case of the inverting stage (top), guarding is still completely effective, with dummy Pin 1 and Pin 3 acting as a grounded guard trace. In the case of the follower stage (bottom), the guard trace must be routed around the –VS pin, and thus the Pin 4 to Pin 3 leakage is not fully guarded. For this reason, a very high impedance follower stage using an SOIC package op amp isn’t generally recommended, as adequate guarding simply isn’t possible. An exception to this caveat would apply the use of a single-supply op amp as a follower (for example, the AD820), in which case Pin 4 becomes grounded by default, and some degree of intrinsic guarding is established. For extremely low bias current applications, such as for example with the AD549 with input bias current of 100 fA, the high impedance input signal connection of the op amp should be made to a virgin Teflon standoff insulator, as shown in Figure 4-43. Note—“virgin” Teflon is a solid piece of new Teflon material that has been machined to shape (as opposed to one welded together from powder or grains). BENT INPUT PIN: PIN 2 FOR INVERTER PIN 3 FOR FOLLOWER INPUT SIGNAL LEAD TO-99 PACKAGE PC BOARD “VIRGIN” TEFLON INSULATED STANDOFF Figure 4-43: Input pin isolation technique using virgin Teflon standoff insulator If mechanical and manufacturing considerations allow, the sensitive op amp input pin should be soldered directly to the Teflon standoff, rather than going through a PCB hole. For TO-99 packaged devices, such as the AD549KH, two possible guarding choices present themselves. One method is to employ the device in a scheme like Figure 4-43, with the sensitive input pin going to the Teflon stand-off. Alternately, a round PCB layout scheme that is more amenable to the TO-99 package can be used, as shown in Figure 4-44. This scheme uses a guard ring, which completely surrounds the input and feedback nodes, with the ring tied to the device’s metal can through the Pin 8 connection. The guard ring is then also tied to either ground or the feedback divider, as suits the application. This setup can also be further modified, to use the more sensitive of the two inputs going to a Teflon stand-off within the guard ring, for the ultimate in performance. Note that in all cases where control of leakage is critical, the PC board itself must be carefully cleaned and then sealed against humidity and dirt using a high quality conformal coating material. In addition to minimizing leakage currents, the entire circuit should be well shielded with a grounded metal shield to prevent stray signal pickup. 264 Sensor Signal Conditioning −VS OP AMP INPUTS 3 4 2 5 6 OUTPUT GUARD RING (BOTH PCB SIDES) 7 1 8 +VS GUARD CIRCUIT CONNECTION Figure 4-44: TO-99 package devices can use guard rings surrounding input pins 2 and 3 (PCB bottom view shown) Preamplifier Offset Voltage and Drift Analysis A photodiode preamp offset voltage and bias current model is shown in Figure 4-45. There are two important considerations in this circuit. First, the diode shunt resistance (R1) is a function of temperature—it halves every time the temperature increases by 10ºC. At room temperature (25ºC), R1 = 1000 MΩ, but at 70ºC it decreases to 43 MΩ. This has a drastic impact on the circuit noise gain and hence the output offset voltage. In the example, at 25ºC the dc noise gain is 2, but at 70ºC it increases to 24. The second circuit difficulty is that the input bias current doubles with every 10ºC temperature rise. The bias current produces an output offset error equal to IBR2. At 70ºC bias current increases to 72 pA, compared to 3 pA at room temperature. Normally, the addition of a resistor (R3) between the noninverting input of the op amp and ground, with a value of R1||R2 would yield a first-order cancellation of this effect. However, because R1 changes with temperature, this method simply isn’t effective. In addition, if R3 is R2 1000MΩ IB ~ R1 _ VOS AD795JR IB R3 OFFSET RTO + DC NOISE GAIN = 1 + R2 R1 • I B DOUBLES EVERY 10°C TEMPERATURE RISE • R1 = 1000MΩ@ 25°C (DIODE SHUNT RESISTANCE) • R1 HALVES EVERY 10°C TEMPERATURE RISE • R3 CANCELLATION RESISTOR NOT EFFECTIVE Figure 4-45: AD795JR photodiode preamplifier offset error model 265 Chapter Four used, the bias current then develops a voltage across it, which in turn would be applied to the photodiode as a parasitic bias. Such a bias would cause the diode response to become nonlinear, thus the use of R3 is also undesirable from a linearity point-of-view. The total referred-to-output (RTO) offset voltage preamp errors are summarized in Figure 4-46. Notice that at 70ºC the total error is 87.2 mV. This error is acceptable for the design under consideration. The primary contributor to the error at high temperature is of course the bias current. 0°C 25°C 50°C 70°C VOS 0.575mV 0.500mV 0.575mV 0.635mV Noise Gain 1.1 2 7 24 VOS Error RTO 0.6mV 1.0mV 4.0mV 15.2mV IB 0.6pA 3.0pA 18.0pA 72.0pA IB Error RTO 0.6mV 3.0mV 18.0mV 72.0mV Total Error RTO 1.2mV 4.0mV 22.0mV 87.2mV Figure 4-46: AD795JR photodiode preamplifier offset error summary Several steps can be taken to minimize amplifier temperature rise, and thus offset drift. Operating the amplifier at reduced supply voltages, minimizing the output drive requirements, and heat sinking are some ways to reduce this error. The addition of an external offset nulling circuit would minimize the initial input offset voltage error. Thermoelectric Voltages as Sources of Input Offset Voltage As discussed earlier in this chapter, thermoelectric potentials are generated by electrical connections are made between different metals. For example, the copper PC board electrical contacts to the kovar input pins of a TO-99 IC package can create an offset voltage of up to 40 µV/°C, if the two bimetal junctions so formed are at different temperatures. Even ordinary solders, being composed of alloys different from PCB copper traces, can give rise to thermoelectric voltages. For example, common high tin content lead-tin solder alloys, when used with copper, create thermoelectric voltages on the order of 1 µV/°C to 3 µV/°C (see Reference 8). While some special cadmium-tin solders can reduce this voltage to 0.3 µV/°C, cadmium solders aren’t in general use for health reasons. Another possible low thermal EMF solder is a low tin alloy such as Sn10Pb90. The best general solution to minimizing this spurious thermocouple problem is to ensure that the connections to the inverting and noninverting input pins of the IC are made with the same material, and that the PC board thermal layout is such that these two pins remain at the same temperature. Everything should be balanced from a thermal standpoint. In the case where a Teflon standoff is used as an insulated connection point for the inverting input (as in the case of this preamp), prudence dictates that connections to the noninverting inputs also be made in a similar manner to minimize possible thermoelectric effects, and in keeping with the principle of thermal symmetry. 266 Sensor Signal Conditioning Preamplifier AC Design, Bandwidth, and Stability The key to the preamplifier ac design is an understanding of the circuit noise gain as a function of frequency. Plotting gain versus frequency on a log-log scale makes the analysis relatively simple (see Figure 4-47). This type of plot is also referred to as a Bode plot. The noise gain is the gain seen by a small voltage source in series with one of the op amp input terminals. It is also the same as the noninverting signal gain (the gain from “A” to the output). In the photodiode preamplifier, the signal current from the photodiode passes through the C2/R2 network. It is important to distinguish between the signal gain and the noise gain, because it is the noise gain characteristic that determines the net circuit stability, regardless of where the signal is actually applied. Open Loop Gain 100k NG = 1 + R2 ( R1 C1s + 1 ) R1 ( R2 C2s + 1 ) GAIN 10k = C1 C2 R1 _ R2 1 + R2 R1 τ 1s + 1 τ 2s + 1 B τ1= 1k C2 = 0 A 100 10 C1 + C2 τ 2 = R2 C2 + f1 = R1 R2 R1+R2 f CL = Closed Loop BW 1 + C1 C2 1 2π τ 1 1 + R2 R1 f2 = 1 2π τ2 fU 1 0.1 1 10 100 1k 10k 100k 1M 10M FREQUENCY (Hz) Figure 4-47: A generalized noise gain Bode plot Note that the net slope between the noise gain and the open loop gain curves, at the point where they intersect, determines system stability. For unconditional stability, the noise gain curve must intersect the open loop response with a net slope of less than 12 dB/octave (or 20 dB per decade). In the figure, the dotted (C2 = 0) line shows a noise gain that intersects the open loop gain at a net slope of 12 dB/octave, indicating an unstable condition. This is what would occur in the circuit, without a feedback capacitor. The general equations for determining the break points and gain values in the Bode plot are also given in Figure 4-47. It is useful to examine these gain characteristics with increasing frequency. At low frequencies, the circuit noise gain is 1 + R2/R1, as indicated by the lowest frequency shelf (below 10 Hz). There are two key time constants in this circuit, τ1 and τ2. The first comes into play as a zero in the noise gain transfer function, which occurs at a frequency of f1 = 1/2πτ1, where τ1 = R1||R2 (C1 + C2). Stated simply, this frequency falls where the noise gain begins to increase to a new (higher) value from the low frequency gain of 1 + R2/R1 plateau. In the Figure 4-47 example f1 occurs at 10 Hz. Above f1, gain increases towards a high frequency gain plateau where the gain is 1 + C1/C2, which is indicated as the highest frequency shelf (above 100 Hz). The second time constant, τ2, comes into play as a pole of the transfer function, which occurs at a corner frequency, f2 = 1/2πτ2, where τ2 = R2C2. It can also be noted that this is equal to the signal bandwidth, if the signal is applied at point “B.” 267 Chapter Four Plotting the composite noise gain curve on the log-log graph is a simple matter of connecting the f1 and f2 breakpoints with a line having a 45º slope, after first sketching the flat low and high frequency gain plateaus. The point at which the high frequency noise gain intersects the op amp open loop gain is called the closed loop bandwidth. Notice that the signal bandwidth for a signal applied at point “B” is much less, and is 1/2 πR2C2. Figure 4-48 shows the noise gain plot for the photodiode preamplifier using actual circuit values. The choice of C2 determines the actual signal bandwidth and also the phase margin. In the example, a signal bandwidth of 16 Hz was chosen. Notice that a smaller value of C2 would result in a higher signal bandwidth and a corresponding reduction in phase margin. It is also interesting to note that although the signal bandwidth is only 16 Hz, the closed loop bandwidth is 167 kHz. This will have important implications with respect to the output noise voltage analysis to follow. C1 C2 R1 _ R2 100k B GAIN 10k ID A Open Loop Gain + AD795JR R1 = 1000MΩ @ 25°C R2 = 1000MΩ C1 = 50pF C2 = 10pF f u = 1MHz Signal BW = 1k 1 2π R2 C2 100 167kHz = f cl Closed Loop BW 16Hz = Signal BW 10 5.3Hz f u = 1MHz NG = 6 NG = 2 1 0.1 1 10 100 1k 10k 100k 1M 10M FREQUENCY (Hz) Figure 4-48: Noise gain of the AD795 photodiode preamplifier at 25°C It is important to note that temperature changes do not significantly affect the stability of the circuit. Changes in R1 (the photodiode shunt resistance) affect only the low frequency noise gain and the frequency at which the zero in the noise gain response occurs. The high frequency noise gain is determined by the C1/C2 ratio. Photodiode Preamplifier Noise Analysis To begin a noise analysis, we first consider the AD795 input voltage and current noise spectral densities, as shown in Figure 4-49. The AD795 performance is truly impressive for a JFET input op amp: 1 µV p-p typical 0.1 Hz to 10 Hz noise, and a 1/f corner frequency of 12 Hz, comparing favorably with all but the best bipolar op amps. As shown in the (right) figure, the current noise is much lower than for bipolar op amps, a key factor making it an ideal choice for high impedance applications. 268 Sensor Signal Conditioning VOTAGE NOISE DENSITY CURRENT NOISE DENSITY 100 1k nV Hz fA Hz 10 100 8 nV/ √Hz 0.6 fA / √Hz 1.0 10 1 / f Corner = 12Hz 0 1 10 100 1k 10k 100k 1M 0.1 1 10 100 1k 10k 100k 1M FREQUENCY − Hz FREQUENCY − Hz Figure 4-49: AD795 Voltage and current noise density performance The complete noise model for an op amp is shown in Figure 4-50. This model includes the reactive elements C1 and C2. Each individual output noise contributor is calculated by integrating the square of its spectral density over the appropriate frequency bandwidth and then taking the square root, as: RMS OUTPUT NOISE DUE TO V1 = ∫ V (f ) df 2 1 Eq. 4-4 In most cases, this integration can be done by inspection of the graph of the individual spectral densities superimposed on a graph of the noise gain. The total output noise is then obtained by combining the individual components in a root-sum-squares manner. The table in the diagram shows how each individual source is reflected to the output, and the corresponding bandwidth for integration. The factor of 1.57 (π/2) is required to convert the single-pole bandwidth into its equivalent noise bandwidth. C2 VN,R2 C1 B VN,R1 R2 1kΩ @ 25°C has 4nV/√Hz Noise ∼ R1 ∼ IN– ∼ TOTAL NOISE RTO = – ∫ V1(f) 2df + ∫ V2(f) 2df + ... VN(f) A VN,R3 R3 ∼ VON IN+ + NOISE SOURCE RTO INTEGRATION BW 1.57•Closed Loop BW VN(f) VN(f)•Noise Gain IN+ IN+•R3• Noise Gain 1.57•Closed Loop BW IN– R1 IN–•R2 VN,R1•(R2/R1) 1.57 •Signal BW 1.57 •Signal BW R2 VN,R2 1.57 •Signal BW R3 VN,R3 •Noise Gain 1.57•Closed Loop BW Figure 4-50: A noise model of preamp 269 Chapter Four The resistor Johnson noise spectral density VR is given by: VR = 4kTR Eq. 4-5 where R is the resistance in ohms, k is Boltzmann’s constant (1.38 × 10−23 J/K), and T is the absolute temperature in Kelvins. A simple way to compute this is to remember that the noise spectral density of a 1 kΩ resistor is 4 nV Hz at +25ºC. The Johnson noise of another resistor value can be found by multiplying by the square root of the ratio of the resistor value to 1000Ω. For example, a 4 kΩ resistor produces a noise density times a 1 kΩ resistor, or (at +25ºC). Finally, note that Johnson noise is broadband, and its spectral density is constant with frequency. Input Voltage Noise In order to obtain the output voltage noise spectral density plot due to the input voltage noise, the input voltage noise spectral density plot is multiplied by the noise gain plot. This is easily accomplished using the Bode plot on a log-log scale. The total RMS output voltage noise due to the input voltage noise is then obtained by integrating the square of the output voltage noise spectral density plot, and then taking the square root. In most cases, this integration may be approximated. A lower frequency limit of 0.01 Hz in the 1/f region is normally used. If the bandwidth of integration for the input voltage noise is greater than a few hundred Hz, the input voltage noise spectral density may be assumed to be constant. Usually, the value of the input voltage noise spectral density at 1 kHz will provide sufficient accuracy. It is important to note that the input voltage noise contribution must be integrated over the entire closedloop bandwidth of the circuit (the closed loop bandwidth, fcl, is the frequency at which the noise gain intersects the op amp open loop response). This is also true of the other noise contributors that are reflected to the output by the noise gain (namely, the non inverting input current noise and the non inverting input resistor noise). The inverting input noise current flows through the feedback network to produce a noise voltage contribution at the output. The input noise current is approximately constant with frequency, therefore, the integration is accomplished by multiplying the noise current spectral density (measured at 1 kHz) by the noise bandwidth which is 1.57 times the signal bandwidth (1/2 πR2C2). The factor of 1.57 (π/2) arises when single-pole 3 dB bandwidth is converted to equivalent noise bandwidth. Johnson Noise Due to Feedforward Resistor R1 The noise current produced by the feedforward resistor R1 also flows through the feedback network to produce a contribution at the output. The noise bandwidth for integration is also 1.57 times the signal bandwidth. Noninverting Input Current Noise The noninverting input current noise, IN+, develops a voltage noise across R3 that is reflected to the output by the noise gain of the circuit. The bandwidth for integration is therefore the closed-loop bandwidth of the circuit. However, there is no contribution at the output if R3 = 0 (or, if R3 is used, but it is bypassed with a large capacitor). This will usually be desirable when operating the op amp in the inverting mode. 270 Sensor Signal Conditioning Johnson Noise Due to Resistor in Noninverting Input The Johnson voltage noise due to R3 is also reflected to the output by the noise gain of the circuit. Again, if R3 is bypassed sufficiently, it makes no significant contribution to the output noise. Summary of Photodiode Circuit Noise Performance Figure 4-51 shows the output noise spectral densities for each of the contributors at 25ºC. As can be noted, there is no contribution due to IN+ or R3, since the noninverting input of the op amp is grounded. 10k 1k nV Hz 16Hz = Signal BW 4000 TOTAL AREAS: R1 R2 IN– VN(f ) R1, R2 IN– 600 100 VN(f) 48 40 TOTAL = 37.6µV RMS f CL = 167kHz = Closed Loop BW 10 C1 B R1 C2 R1 = 1000MΩ @ +25°C R2 = 1000MΩ C1 = 50pF C2 = 10pF f u = 1MHz _ R2 1 ID A 1 20µV RMS 20µV RMS 3µV RMS 24.6µV RMS 16Hz 12Hz 5.3Hz 0.1 0.1 : : : : 10 + AD795JR 100 1k 10k 100k 1M 10M FREQUENCY − Hz Figure 4-51: Preamp output spectral noise densities (nV/√ √Hz) @25ºC 271 Chapter Four Noise Reduction Using Output Filtering From the above analysis, the largest contributor to the output noise voltage at 25°C is the input voltage noise of the op amp reflected to the output by the noise gain. This contributor is large primarily because the noise gain over which the integration is performed extends to a bandwidth of 167 kHz (the intersection of the noise gain curve with the open-loop response of the op amp). If the op amp output is filtered by a singlepole low-pass filter with a 20 Hz cutoff frequency (τ = 7.95 ms), this contribution is reduced to less than 1 µVrms. The diagram for the final, filtered, optimized photodiode circuit design is shown in Figure 4-52. 10pF GAIN: 1mV / pA 1000MΩ _ ID NOISE: 37.6µV RMS 20Hz LOWPASS FILTER AD795K + +15V 100kΩ 1MΩ 0.1µF NOISE: 28.5µV RMS 100Ω –15V INPUT OFFSET NULL RANGE: ±1.5mV Figure 4-52: AD795K preamp with output filter and offset null option Notice that the same results would not be achieved simply by increasing the feedback capacitor, C2. Increasing C2 lowers the high frequency noise gain, but the integration bandwidth becomes proportionally higher. Larger values of C2 may also decrease the signal bandwidth to unacceptable levels. The addition of the post-filter stage reduces output noise to 28.5 µVrms; approximately 75% of its former value, and the resistor noise and current noise are now the largest contributors to output noise. Practically, this filter can be either active or passive. Care will need to be taken, of course, that the filter circuit does not add any significant noise of its own to the signal. Filter design is discussed in greater detail in Chapter 5 of this book. The final circuit also includes an offset trim arrangement that is capable of nulling op amp offsets of up to ±1.5 mV. Summary of Circuit Performance Performance characteristics are summarized in Figure 4-53. The total output voltage drift over 0 to 70ºC is 87.2 mV, corresponding to 87.2 pA of diode current. The offset nulling circuit shown on the noninverting input can be used to null out the room temperature offset. Note that this method is better than using the offset null pins because using the offset null pins will increase the offset voltage TC by about 3 µV/ºC for each millivolt nulled. In addition, the AD795 SOIC package does not have offset nulling pins. The input sensitivity based on a total output voltage noise of 44 µV is obtained by dividing the output voltage noise by the value of the feedback resistor R2. This yields a minimum detectable diode current of 44 fA. If a 12-bit ADC is used to digitize the 10 V full-scale output, the weight of the least significant bit (LSB) is 2.5 mV. The output noise level is much less than this. 272 Sensor Signal Conditioning • Output Offset Error (0°C to 70°C) : 87.2mV • Output Sensitivity: 1mV/pA • Output Photosensitivity: 30V / foot-candle • Total Output Noise @ 25°C : 28.5µV RMS • Total Noise RTI @ 25°C : 44fA RMS, or 26.4pA p-p • Range with R2 = 1000MΩ: 0.001 to 0.33 foot-candles • Bandwidth: 16Hz Figure 4-53: AD795JR photodiode preamp performance summary Photodiode Circuit Trade-off Many trade-offs could be made in the basic photodiode circuit design we have described. More signal bandwidth can be achieved in exchange for a larger output noise level. Reducing the feedback capacitor C2 to 1 pF increases the signal bandwidth to approximately 160 Hz. Further reductions in C2 are not practical because the parasitic capacitance is probably in the order of 1 pF to 2 pF. Some small amount of feedback capacitance is also required to maintain stability. If the circuit is to be operated at higher levels of illumination (greater than approximately 0.3 fc), the value of the feedback resistor can be reduced, thereby resulting in further increases in circuit bandwidth and less resistor noise. If gain-ranging is to be used to measure higher light levels, extreme care must be taken in the design and layout of the additional switching networks to minimize leakage paths and other parasitic effects. Compensation of a High Speed Photodiode I/V Converter A classical I/V converter is shown in Figure 4-54. Note that it is the same as the previous photodiode preamplifier, if we assume that R1 >> R2. The total input capacitance, C1, is the sum of the diode capacitance and the op amp input capacitance. Dynamically, this is a classical second-order system, and the following guidelines can be applied in order to determine the proper compensation. C2 f 2 = SIGNAL BW R2 f u = OP AMP UNITY GAIN BW PRODUCT _ C1 I Total Input Capacitance fu f1 = + –VB OPEN LOOP GAIN GAIN 1 2π R2 C1 f2 = 1 2π R2 C2 f2 = f 1• f u UNCOMPENSATED NOISE GAIN C2 = COMPENSATED f2 1 f1 f C1 2π R2 f u FOR 45° PHASE MARGIN fu f2 = 2π R2 C1 fu Figure 4-54: Input capacitance compensation for an I/V converter 273 Chapter Four The net input capacitance, C1, forms a zero at a frequency f1 in the noise gain transfer function as shown in the Bode plot. 1 f1 = Eq. 4-6 2 πR2C1 Note that we are neglecting the effects of the compensation capacitor C2 and are assuming that it is small relative to C1 and will not significantly affect the zero frequency f1 when it is added to the circuit. In most cases, this approximation yields results that are close enough, considering the other variables in the circuit. If left uncompensated, the phase shift at the frequency of intersection, f2, will cause instability and oscillation. Introducing a pole at f2 by adding the feedback capacitor C2 stabilizes the circuit and yields a phase margin of about 45 degrees. 1 Eq. 4-7 2 πR2C2 Since f2 is the geometric mean of f1 and the unity-gain bandwidth frequency of the op amp, fu, f2 = f2 = f1 ⋅ fu Eq. 4-8 These equations can be combined and solved for C2: C2 = C1 2 πR2 ⋅ fu Eq. 4-9 This C2 value yields a phase margin of about 45 degrees; increasing it by a factor of 2 increases phase margin to about 65 degrees. In practice, an optimum C2 value should be determined experimentally, by varying it slightly to optimize the output pulse response. Op Amp Selection for Wideband Photodiode I/V Converters The op amp in the high speed photodiode I/V converter should be a wideband FET-input one in order to minimize the effects of input bias current and allow low values of photocurrents to be detected. In addition, if the equation for the 3 dB bandwidth, f2, is rearranged in terms of fu, R2, and C1, then f2 = fu 2 πR2C1 Eq. 4-10 where C1 is the sum of the diode capacitance, CD, and the op amp input capacitance, CIN. In a high speed application, the diode capacitance will be much smaller than that of the low frequency preamplifier design previously discussed—perhaps as low as a few pF. By inspection of this equation, it is clear that in order to maximize f2, the FET-input op amp should have both a high unity gain bandwidth product, fu, and a low input capacitance, CIN. In fact, the ratio of fu to CIN is a good figure-of-merit when evaluating different op amps for this application. Figure 4-55 compares a number of FET-input op amps suitable for photodiode preamps. By inspection, the AD823 op amp has the highest ratio of unity gain bandwidth product to input capacitance, in addition to relatively low input bias current. For these reasons, the AD823 op amp was chosen for the wideband design. 274 Sensor Signal Conditioning Input Bias Current IB (pA) Unity GBW Product fu (MHz) Input Capacitance CIN (pF) f u /CIN (MHz/pF) AD823 16 1.8 8.9 3 16 AD843 34 6 5.7 600 19 AD744 13 5.5 2.4 100 16 AD845 16 8 2 500 18 OP42 10 6 1.6 100 12 AD745* 20 20 1 250 2.9 AD795 1 1 1 3 8 AD820 1.9 2.8 0.7 10 13 AD743 4.5 20 0.2 250 2.9 Voltage Noise @ 10kHz (nV/√Hz) *Stable for Noise Gains ≥5, Usually the Case, Since High Frequency Noise Gain = 1 + C1/C2, and C1 Usually ≥ 4C2 Figure 4-55: FET input op amps suitable for high speed photodiode preamps High Speed Photodiode Preamp Design The HP 5082-4204 PIN Photodiode will be used as an example for our discussion. Its characteristics are listed in Figure 4-56. It is typical of many PIN photodiodes. • Sensitivity: 350µA @ 1mW, 900nm • Maximum Linear Output Current: 100µA • Area: 0.002cm 2 (0.2mm 2) • Capacitance: 4pF @ 10V Reverse Bias • Shunt Resistance: 1011Ω • Risetime: 10ns • Dark Current: 600pA @ 10V Reverse Bias Figure 4-56: HP 5082-4204 photodiode characteristics As in most high speed photodiode applications, the diode will be operated in the reverse-biased or photoconductive mode. This greatly lowers the diode junction capacitance, but causes a small amount of dark current to flow even when the diode is not illuminated (we will show a circuit that compensates for the dark current error later in the section). This photodiode is linear with illumination up to approximately 50 µA to 100 µA of output current. The available dynamic range is limited by the total circuit noise, and the diode dark current (assuming no dark current compensation). 275 Chapter Four Using the circuit shown in Figure 4-57, assume that we wish to have a full scale output of 10 V for a diode current of 100 µA. This determines the value of the feedback resistor R2 to be 10 V/100 µA = 100 kΩ. ≈ C2 CD = 4pF, C IN = 1.8pF C1 = CD + CIN = 5.8pF 33.2kΩ 33.2kΩ 33.2kΩ R2 = 100kΩ _ –10V D1 D2 0.8pF C1 5.8pF +15V AD823 + D1, D2: HP-5082-4204 –15V 0.1µF LOW LEAKAGE POLYPROPYLENE 100kΩ Figure 4-57: 2 MHz bandwidth photodiode preamp with dark current compensation Using the diode capacitance, CD = 4 pF, and the AD823 input capacitance, CIN = 1.8 pF, the value of C1 = CD + CIN = 5.8 pF. Solving the above equations using C1=5.8pF, R2 = 100 kΩ, and fu = 16 MHz, we find that: f1 = 274 kHz C2 = 0.76 pF f2 = 2.1 MHz. In the final circuit shown, notice at the 100 kΩ resistor is replaced with three 33.2 kΩ film resistors to minimize stray capacitance. The feedback capacitor, C2, is a variable 1.5 pF ceramic and is adjusted in the final circuit for best bandwidth/pulse response. The overall circuit bandwidth is approximately 2 MHz. The full-scale output voltage of the preamp for 100 µA diode current is 10 V, and therefore the (uncompensated) error (RTO) due to the photodiode dark current of 600 pA is 60 µV. This dark current error can be effectively canceled using a second photodiode, D2, of the same type. This diode is biased with a voltage identical to D1 and, with nominally matched characteristics, will tend to conduct a similar dark current. In the circuit, this “dummy” dark current drives the 100 kΩ resistance in the noninverting input of the op amp. This produces a dark current proportional bias voltage which, due to the CM rejection of the op amp, has an end result of suppressing the dark current effects. High Speed Photodiode Preamp Noise Analysis As in most noise analyses, only the key contributors need be identified. Because the noise sources combine in an RSS manner, any single noise source that is at least three or four times as large as any of the others will dominate. In the case of the wideband photodiode preamp, the dominant sources of output noise are the input voltage noise of the op amp, VN, and the resistor noise due to R2, VN,R2 (see Figure 4-58). The input current noise of the FET-input op amp is negligible. The shot noise of the photodiode (caused by the reverse bias) is negligible because of the filtering effect of the shunt capacitance C1. 276 Sensor Signal Conditioning C2 C1 = 5.8pF C2 = 0.76pF R2 = 100kΩ R2 VN = 16nV/√Hz C1 ~ ~ _ VN AD823 VN,R2 1+ + VBIAS = –10V 1 C1 C2 NOISE GAIN fu f1 f2 274kHz 2.1MHz 16MHz • VN RTO NOISE ≈ VN 1 + C1 • VN,R2 RTO NOISE ≈ • TOTAL RTO NOISE • C2 1.57 f 2 = 250µV RMS 4kTR2 • 1.57f 2 = 2502 + 732 DYNAMIC RANGE = 20 log 10V 260µV = 73µV RMS = 260µV RMS = 92dB Figure 4-58: Equivalent circuit of preamp for output noise analysis The resistor noise is easily calculated by knowing that a 1 kΩ resistor generates about 4 nV z , therefore, a 100 kΩ resistor generates 40 nV z . The bandwidth for integration is the signal bandwidth, 2.1 MHz, yielding a total output rms noise of: VN,R2 RTO NOISE = 40 1.57 ⋅ 2.1⋅ 106 = 73 µV rms The factor of 1.57 converts the amplifier approximate single-pole bandwidth of 2.1 MHz into the equivalent noise bandwidth. The output noise due to the input voltage noise is obtained by multiplying the noise gain by the voltage noise and integrating the entire function over frequency. This would be tedious if done rigorously, but a few reasonable approximations can be made which greatly simplify the math. Obviously, the low frequency 1/f noise can be neglected in the case of the wideband circuit. The primary source of output noise is due to the high frequency noise-gain peaking that occurs between f1 and fu. If we simply assume that the output noise is constant over the entire range of frequencies and use the maximum value for ac noise gain [1 + (C1/C2)], then C1 VN RTO NOISE ≈ VN 1 + 1.57f2 = 250 µV rms C2 The total rms noise referred to the output is then the RSS value of the two components: TOTAL RTO NOISE = (73)2 + (250)2 = 260 µV rms The total output dynamic range can be calculated by dividing the 10 V full-scale output by the total 260 µ Vrms noise, and, converting to dB, yielding approximately 92 dB. 277 Chapter Four High Impedance Charge Output Sensors High impedance transducers such as piezoelectric sensors, hydrophones, and some accelerometers require an amplifier that converts a transfer of charge into a voltage change. Due to the high dc output impedance of these devices, appropriate buffer amplifiers are required. The basic circuit for an inverting charge sensitive amplifier is shown in Figure 4-59. C2 ∆Q = ∆C VC R2 R1 _ VOUT ∆C C1 + + VC • • FOR CAPACITIVE SENSORS: ∆VOUT = FOR CHARGE-EMITTING SENSORS: ∆VOUT = –VC ∆C C2 –∆Q C2 Figure 4-59: Charge amplifier basic principles There are basically two types of charge transducers: capacitive and charge-emitting. In a capacitive transducer, the voltage across the capacitor (VC) is held constant. The change in capacitance, ∆C, produces a change in charge, ∆Q = ∆CVC. This charge is transferred to the op amp output as a voltage, ∆VOUT = –∆Q/C2 = –∆CVC/C2. Charge-emitting transducers produce an output charge, ∆Q, and their output capacitance remains constant. This charge would normally produce an open-circuit output voltage at the transducer output equal to ∆Q/C. However, since the voltage across the transducer is held constant by the virtual ground of the op amp (R1 is usually small), the charge is transferred to capacitor C2 producing an output voltage ∆VOUT = –∆Q/C2. In an actual application, this charge amplifier only responds to ac inputs. It should be noted that ac gain for this charge amplifier is determined by the capacitance ratio, not the resistances. This is unlike a conventional wideband amplifier, where the upper cutoff frequency is given by f2 = 1/2 πR2C2, and the lower by f1 = 1/2 πR1C1. In the Figure 4-59 charge amplifier, with nominal transducer capacitance fixed, gain is set by C2. Typically, bias return resistor R2 will be a high value (≥1 megΩ), and R1 a much lower value. The resulting frequency response will be relatively narrow and bandpass shaped, with gain and frequency manipulated by the relative values, as suitable to SPICE analysis. Low Noise Charge Amplifier Circuit Configurations Figure 4-60 shows two ways to buffer and amplify the output of a charge output transducer. Both require using an amplifier which has a very high input impedance, such as the AD745. The AD745 provides both low voltage noise and low current noise. This combination makes this device particularly suitable in applications requiring very high charge sensitivity, such as capacitive accelerometers and hydrophones. 278 Sensor Signal Conditioning CHARGE OUTPUT MODE VOLTAGE OUTPUT MODE CF SOURCE CS RS R2 CB RF _ _ AD745 RB R1 + AD745 SOURCE CB CB = CF || C S RB CS RS RB = RF || R S 30 + C B = CS RB = RS FOR RS >> R1, R2 UNBALANCED RTI 20 NOISE nV Hz BALANCED 2.9 nV/√ Hz 10 0 10 100 1000 INPUT CAPACITANCE (pF) Figure 4-60: Two basic charge amplifier configurations using the AD745 low noise FET op amp The first (left) circuit in Figure 4-60 uses the op amp in the inverting mode. Amplification depends on the principle of conservation of charge at the inverting input of the amplifier. The charge on capacitor CS is transferred to capacitor CF, thus yielding an output voltage of ∆Q/CF. The amplifier’s input voltage noise will appear at the output amplified by the ac noise gain of the circuit, 1 + CS/CF. The second (right) circuit shown in Figure 4-60 is simply a high impedance follower with gain. Here the noise gain (1 + R2/R1) is the same as the gain from the transducer to the output. Resistor RB, in both circuits, is required as a dc bias current return. To maximize dc performance over temperature, source resistances should be balanced at the amplifier inputs, as represented by the resistor RB shown in Figure 4-60. For best noise performance, the source capacitance should also be balanced with the capacitor CB. In general, it is good practice to balance the source impedances (both resistive and reactive) as seen by the inputs of precision low noise BiFET amplifiers such as the AD743/AD745. Balancing the resistive components will optimize dc performance over temperature, as balancing mitigates the effects of any bias current errors. Balancing the input capacitance will minimize ac response errors due to the amplifier’s nonlinear common-mode input capacitance and, as shown in Figure 4-60, noise performance will be optimized. In any FET input amplifier, the current noise of the internal bias circuitry can be coupled to the inputs via the gate-to-source capacitances (20 pF for the AD743 and AD745) and appears as excess input voltage noise. This noise component is correlated at the inputs, so source impedance matching will tend to cancel out its effect. Figure 4-60 shows the required external components for both inverting and noninverting configurations. For values of CB greater than 300 pF, there is a diminishing impact on noise, and CB can then be simply a polyester bypass capacitor of 0.01 µF or greater. 279 Chapter Four 40dB Gain Piezoelectric Transducer Amplifier Operates on Reduced Supply Voltages for Lower Bias Current Figure 4-61 shows a gain-of-100 piezoelectric transducer amplifier connected in the voltage-output mode. Reducing the op amp power supplies to ±5 V reduces the effects of bias current in two ways: first, by lowering the total power dissipation and, second, by reducing the basic gate-to-junction leakage current. The addition of a clip-on heat sink such as the Aavid #5801 will further limit the internal junction temperature rise. With ac coupling capacitor C1 shorted, the amplifier will operate over a range of 0°C to 85°C. If the optional ac coupling capacitor C1 is used, the circuit will operate over the entire –55°C to +125°C temperature range, but dc information is lost. R2, 10k Ω CB _ R1 100Ω +5V 8 R B ,10 Ω AD745 SOURCE C1* CS + RS 10 8 Ω –5V, IQ = 8mA C B = CS • ±5V Power Supplies Reduce I B for 0°C to +85°C Operation, PD = 80mW • C1 Allows −55°C to +125°C Operation Figure 4-61: A gain-of-100 piezoelectric transducer amplifier Hydrophones Interfacing the outputs of highly capacitive transducers such as hydrophones, some accelerometers, and condenser microphones to the outside world presents many design challenges. Previously designers had to use costly hybrid amplifiers consisting of discrete low-noise JFETs in front of conventional op amps to achieve the low levels of voltage and current noise required by these applications. Using AD743/AD745 monolithic ICs, designers can achieve almost the same level of performance of a hybrid approach. In sonar applications, a piezo-ceramic cylinder is commonly used as the active element in the hydrophone. A typical cylinder has a nominal capacitance of around 6,000 pF with a series resistance of 10 Ω. The output impedance is typically 108 Ω or 100 MΩ. Since the hydrophone signals of interest are inherently ac with wide dynamic range, noise is an overriding concern for sonar system designs. The noise floor of the hydrophone and its preamplifier together limit the system sensitivity, and thus the overall hydrophone usefulness. Typical hydrophone bandwidths are in the and 1 kHz to 10 kHz range. The AD743 and AD745 op amps, with their low noise voltages of high input impedance of 1010 Ω (or 10 GΩ) are ideal for use as hydrophone amplifiers. 280 Sensor Signal Conditioning Op Amp Performance: JFET versus Bipolar The AD743 and AD745 op amps are the first monolithic JFET devices to offer the low input voltage noise comparable to a bipolar op amp, without the high input bias currents typically associated with bipolar op amps. Figure 4-62 shows input voltage noise versus input source resistance of the OP27 (bipolar-input) and the JFET-input AD745 op amps. Note: the noise levels of the AD743 and the AD745 are identical. From this figure (left), it is clear that at high source impedances, the low current noise of the AD745 provides lower overall noise than a high performance bipolar op amp such as the OP27. It is also important to note that, with the AD745, this noise reduction extends down to low source impedances. At high source impedances, the lower dc current errors of the AD745 also reduce errors due to offset and drift, as shown in Figure 4-62 (right). + RS _ RS INPUT VOLTAGE NOISE 1k 100 OP27 nV Hz INPUT OFFSET VOLTAGE mV OP27 10 100 AD745 OP27 AD745 AD745 1 10 RS NOISE ONLY 1 100 1k 10k 100k 1M 10M SOURCE RESISTANCE − Ω 0.1 100 1k 10k 100k 1M 10M SOURCE RESISTANCE − Ω Figure 4-62: Total noise performance comparison, OP27 (bipolar) and AD745 (FET) op amps The AD743 and AD745 are related, companion amplifiers, which differ in their levels of internal compensation. The AD743 is internally compensated for unity gain stability. The AD745, stable for noise gains of 5 or higher, has a much higher bandwidth and slew rate. This makes the latter device especially useful as a high-gain preamplifier where it provides both high gain and wide bandwidth. The AD743 and AD745 also operate with very low levels of distortion; less than 0.0003% and 0.0002% (at 1 kHz), respectively. 281 Chapter Four A pH Probe Buffer Amplifier A typical pH probe requires a buffer amplifier to isolate its 106 to 109 Ω source resistance from external circuitry. Such an amplifier is shown in Figure 4-63. The low input current of the AD795JR minimizes the voltage error produced by the bias current and electrode resistance. The use of guarding, shielding, high insulation resistance standoffs, and other such standard picoamp methods previously discussed should be used to minimize leakage. Are all needed to maintain the accuracy of this circuit. –VS GUARD VOS ADJUST 100kΩ 4 1 3 + 5 AD795JR pH PROBE OUTPUT 6 1V/pH UNIT 50mV/pH TC = +3500ppm/°C Output Impedance: 1MΩ to 1GΩ 2 _ 8 7 19.6kΩ +VS RT 1kΩ +3500ppm/°C Precision Resistor Co, Inc. #PT146 Figure 4-63: A gain of 20x pH probe amplifier allows 1 V/pH output scaling The slope of the pH probe transfer function, 50 mV per pH unit at room temperature, has an approximate +3500 ppm/°C temperature coefficient. The buffer amplifier shown as Figure 4-63 provides a gain of 20, and yields a final output voltage equal to 1 V/pH unit. Temperature compensation is provided by resistor RT, which is a special temperature compensation resistor, 1 kΩ, 1%, +3500 ppm/°C, #PT146 available from Precision Resistor Co., Inc. (see Reference 15). 282 Sensor Signal Conditioning References: High Impedance Sensors 1. Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New York, 1991. 2. Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980, ISBN: 0-916550-05-2. 3. Section 3, Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN: 0-916550-10-9. 4. Walt Kester, Editor, System Applications Guide, Analog Devices, 1993, ISBN: 0-916550-13-3. 5. Walt Kester, Editor, Linear Design Seminar, Analog Devices, 1995, ISBN: 0-916550-15-X. 6. Walt Kester, Editor, Practical Analog Design Techniques, Analog Devices, 1995, ISBN: 0-916550-16-8. 7. Walt Kester, Editor, High Speed Design Techniques, Analog Devices, 1996, ISBN: 0-916550-17-6. 8. Jiri Dostal, Section 9.3.1, “Thermoelectric Voltages,” Operational Amplifiers 2nd Ed., ButterworthHeinemann, 1993, pp. 265–268. 9. Optoelectronics Data Book, EG&G Vactec, St. Louis, MO, 1990. 10. Silicon Detector Corporation, Camarillo, CA, Part Number SD-020-12-001 Data Sheet. 11. Photodiode 1991 Catalog, Hamamatsu Photonics, Bridgewater, NJ. 12. Lewis Smith and Dan Sheingold, “Noise and Operational Amplifier Circuits,” Analog Dialogue 25th Anniversary Issue, pp. 19–31, Analog Devices Inc., 1991. 13. James L. Melsa and Donald G. Schultz, Linear Control Systems, pp. 196–220, McGraw-Hill, 1969. 14. Jerald G. Graeme, Photodiode Amplifiers: Op Amp Solutions, McGraw-Hill, 1995. 15. Precision Resistor Co., Inc., 10601 75th St. N., Largo, FL, 33777-1427, 727 541-5771, www.precisionresistor.com. 16. Ohmite Victoreen MAXI-MOX Resistors, 3601 Howard Street, Skokie, IL 60076, 847 675-2600, www.ohmite.com/victoreen/. 17. Vishay/Dale RNX Resistors, 2300 Riverside Blvd., Norfolk, NE, 68701-2242, 402 371-0800, www.vishay.com. 283 This page intentionally left blank SECTION 4-5 Temperature Sensors Walt Kester, James Bryant, Walt Jung Temperature measurement is critical in many modern electronic devices, especially expensive laptop computers and other portable devices; their densely packed circuitry dissipates considerable power in the form of heat. Knowledge of system temperature can also be used to control battery charging, as well as to prevent damage to expensive microprocessors. Compact high power portable equipment often has fan cooling to maintain junction temperatures at proper levels. In order to conserve battery life, the fan should only operate when necessary. Accurate control of the fan requires, in turn, knowledge of critical temperatures from an appropriate temperature sensor. Accurate temperature measurements are required in many other measurement systems, for example within process control and instrumentation applications. Some popular types of temperature transducers and their characteristics are indicated in Figure 4-64. In most cases, because of low level and/or nonlinear outputs, the sensor output must be properly conditioned and amplified before further processing can occur. THERMOCOUPLE RTD THERMISTOR SEMICONDUCTOR Widest Range: –184°C to +2300°C Range: –200°C to +850°C Range: 0°C to +100°C Range: –55°C to +150°C High Accuracy and Repeatability Fair Linearity Poor Linearity Linearity: 1ºC Accuracy: 1ºC Needs Cold Junction Compensation Requires Excitation Requires Excitation Requires Excitation High Sensitivity 10mV/K, 20mV/K, or 1µA/K Typical Output Low-Voltage Output Low Cost Figure 4-64: Some common types of temperature transducers Except for the semiconductor sensors of the last column, all of the temperature sensors shown have nonlinear transfer functions. In the past, complex analog conditioning circuits were designed to correct for the sensor nonlinearity. These circuits often required manual calibration and precision resistors to achieve the desired accuracy. Today, however, sensor outputs may be digitized directly by high resolution ADCs. Linearization and calibration can then be performed digitally, substantially reducing cost and complexity. Resistance Temperature Devices (RTDs) are accurate, but require excitation current and are generally used within bridge circuits such as those described earlier. Thermistors have the most sensitivity, but are also the most nonlinear. Nevertheless, they are popular in portable applications for measurement of battery and other critical system temperatures. 285 Chapter Four Modern semiconductor temperature sensors offer both high accuracy and linearity over about a –55ºC to +150ºC operating range. Internal amplifiers can scale output to convenient values, such as 10 mV/ºC. They are also useful in cold-junction compensation circuits for wide temperature range thermocouples. Semiconductor temperature sensors are also integrated into ICs that perform other hardware monitoring functions—an example is the imbedded transistor sensors used within modern µP chips. Thermocouple Principles and Cold-Junction Compensation Thermocouples comprise a more common form of temperature measurement. In operation, thermocouples rely on the fact that two dissimilar metals joined together produce a voltage output roughly proportional to temperature. They are small, rugged, relatively inexpensive, and operate over the widest range of contact temperature sensors. Thermocouples are especially useful for making measurements at extremely high temperatures (up to +2300°C), and within hostile environments. Characteristics of some common types are shown in Figure 4-65. JUNCTION MATERIALS TYPICAL USEFUL RANGE (°C) NOMINAL SENSITIVITY (µV/°C) ANSI DESIGNATION Platinum (6%)/ RhodiumPlatinum (30%)/Rhodium 38 to 1800 7.7 B Tungsten (5%)/RheniumTungsten (26%)/Rhenium 0 to 2300 16 C Chromel-Constantan 0 to 982 76 E Iron-Constantan 0 to 760 55 E Chromel-Alumel −184 to 1260 39 K Platinum (13%)/RhodiumPlatinum 0 to 1593 11.7 R Platinum (10%)/RhodiumPlatinum 0 to 1538 10.4 S Copper-Constantan −184 to 400 45 T Figure 4-65: Some common thermocouples and their characteristics However, thermocouples produce only millivolts of output, and thus they typically require precision amplification for further processing. They also require cold-junction-compensation (CJC) techniques, to be discussed shortly. They are more linear than many other sensors, and their nonlinearity has been well characterized. The most common metals used for thermocouples are iron, platinum, rhodium, rhenium, tungsten, copper, alumel (composed of nickel and aluminum), chromel (composed of nickel and chromium) and constantan (composed of copper and nickel). Figure 4-66 shows the voltage-temperature curves for three commonly used thermocouples, Types J, K, and S, referred to a 0°C fixed-temperature reference junction. Of these, Type J thermocouples are the most sensitive, producing the highest output voltage for a given temperature change, but over a relatively narrow temperature span. On the other hand, Type S thermocouples are the least sensitive, but can operate over a much wider range. 286 Sensor Signal Conditioning Figure 4-66: Type J, K, and S thermocouple output voltage versus temperature THERMOCOUPL E OUTPUT VOL TAGE− m V 60 50 TYPE K 40 TYPE J 30 20 TYPE S 10 0 -10 -250 0 250 500 750 1000 1250 1500 1750 TEMPERATURE −°C These characteristics are very important considerations when designing thermocouple signal conditioning circuitry. A main consideration is the fact that virtually any thermocouple employed will have a relatively low output signal, thus they generally require the careful application of stable, high gain amplifiers. To understand thermocouple behavior more fully, it is also necessary to consider the nonlinearities in their response to temperature differences. As noted, Figure 4-66 shows the relationships between sensing junction temperature and voltage output for a number of thermocouple types (in all cases, the reference cold junction is maintained at 0°C). While close scrutiny of these data may reveal the fact that none of the responses are quite linear, the exact nature of the nonlinearity isn’t so obvious. What is needed is another perspective on the relationships displayed by these curves, to gain better insight into how the various devices can be best utilized. Figure 4-67 shows how the thermocouple Seebeck coefficient varies with sensor junction temperature. The Seebeck coefficient is the change of output voltage with change of sensor junction temperature (i.e., the first derivative of output with respect to temperature). Note that we are still considering the case where the reference junction is maintained at 0°C. 70 60 SEEB ECK COEFFICIENT −µV/ °C Figure 4-67: Type J, K and S thermocouple Seebeck coefficient versus temperature TYPE J 50 TYPE K 40 30 20 TYPE S 10 0 -250 0 250 500 750 1000 TEMPERATURE− °C 287 1250 1500 1750 Chapter Four An ideal linear thermocouple would have a constant Seebeck coefficient with varying temperature, but in practice all thermocouples are nonlinear to some degree. In selecting a measurement thermocouple for a particular temperature range, we should therefore choose one whose Seebeck coefficient varies as little as possible over that range. For example, a Type J thermocouple has a nominal Seebeck coefficient of 55 µV/°C, which varies by less than 1 µV/°C between 200°C and 500°C, making it ideal for measurements over this range (the flat region of the upper curve within Figure 4-67). Presenting these data on thermocouples serves two purposes. First, Figure 4-66 illustrates the range and sensitivity of the three thermocouple types so that the system designer can, at a glance, determine that a Type S thermocouple has the widest useful temperature range, but a Type J thermocouple is the more sensitive of the three. Second, the relative stability of the Seebeck coefficient over temperature provides a quick guide to a thermocouple’s linearity. Using Figure 4-67, a system designer can choose a Type K thermocouple for its relatively linear Seebeck coefficient over the range of 400°C to 800°C, or a Type S over the range of 900°C to 1700°C. The behavior of a thermocouple’s Seebeck coefficient is important in applications where variations of temperature rather than absolute magnitude are important. These data also indicate what performance is required of the associated signal-conditioning circuitry. To successfully apply thermocouples we must also understand their basic operating principles. Consider the diagrams shown in Figure 4-68. If we join two dissimilar metals, A and B, at any temperature above absolute zero, there will be a potential difference between them, i.e., their “thermoelectric EMF” or “contact potential,” V1. This voltage is a function of the temperature of the measurement junction, T1, as is noted in Figure 4-68A. If we join two wires of metal A with metal B at two places, two measurement junctions are formed, T1 and T2 (Figure 4-68B). If the two junctions are at different temperatures, there will be a net EMF in the circuit, and a current I will flow, as determined by the EMF V1 – V2, and the total resistance R in the circuit (Figure 4-68B). A. THERMOELECTRIC VOLTAGE C. THERMOCOUPLE MEASUREMENT Metal A Metal A V1 – V2 Metal A V1 Thermoelectric EMF Metal B T1 V1 T1 D. THERMOCOUPLE MEASUREMENT B. THERMOCOUPLE Copper Metal A R Metal A V Metal A T3 T1 T2 Copper Metal A I V1 V2 T2 Metal B V2 V1 Metal B T4 T1 T2 Metal B R = Total Circuit Resistance I = (V1 – V2) / R V = V1 – V2, If T3 = T4 Figure 4-68: Thermocouple basics 288 V2 Sensor Signal Conditioning If we open the circuit as in Figure 4-68C, the voltage across the break will be equal to the net thermoelectric EMF of the circuit; and if we measure this voltage, we can use it to calculate the temperature difference between the two junctions. We must remember that a thermocouple always measures the temperature difference between two junctions, not the absolute temperature at one junction. We can only measure the temperature at the measuring junction if we know the temperature of the other junction. This is the origin of the terms “reference” or “cold” junction. But of course, it is not so easy to just measure the voltage generated by a thermocouple. Any wire attached to a thermocouple is also a thermocouple itself, and if care is not taken, errors can be introduced. Suppose that we attach a voltmeter to the circuit of Figure 4-68C, as shown in Figure 4-68D. The wires of the voltmeter will form further thermocouple junctions where they are attached (T3, T4). If both these additional junctions are at the same temperature (it does not matter exactly what temperature), then the “Law of Intermediate Metals” states that they will make no net contribution to the total EMF of the system. If they are at different temperatures, they will introduce errors. Since every pair of dissimilar metals in contact generates a thermoelectric EMF (including copper/solder, kovar/copper [kovar is the alloy used for IC leadframes] and aluminum/kovar [at the bond inside the IC]), it is obvious that in practical circuits the problem is even more complex. In fact, it is necessary to take extreme care to ensure that both junctions of each junction pair in series with a thermocouple are at the same temperature, except for the measurement and reference junctions themselves. Thermocouples generate a voltage, albeit a very small one, and don’t require excitation for this most basic operation. As was shown in Figure 4-68D, however, two junctions are always involved (T1, the measurement junction temperature and T2, the reference junction temperature). If T2 = T1, then V2 = V1, and the output voltage V = 0. Thermocouple output voltages are often defined with respect to a reference junction temperature of 0ºC (hence the term cold or ice point junction). In such a system the thermocouple provides a convenient output voltage of 0 V at 0ºC. Obviously, to maintain system accuracy, the reference junction must remain at a well-defined temperature (but not necessarily 0ºC). A conceptually simple approach to this need is shown in Figure 4-69, the ice-point reference, where junction T2 is kept at 0°C by virtue of being immersed in an ice water slurry. Although this ice water bath is relatively easy to define conceptually, it is quite inconvenient to maintain. METAL A METAL A V1 – V(0°C) T1 V1 METAL B V(0°C) ICE BATH T2 0°C Figure 4-69: A thermocouple cold junction reference system using an ice-point (0°C) T2 reference 289 Chapter Four Today the inconvenient ice/water bath reference is replaced by an electronic equivalent. A temperature sensor of another sort (often a semiconductor sensor, sometimes a thermistor) measures the cold junction temperature and is used to inject a voltage into the thermocouple circuit which compensates for the difference between the actual cold junction temperature and its ideal value (usually 0°C) as shown in Figure 4-70. V(OUT) V(COMP) COPPER METAL A T1 TEMPERATURE COMPENSATION CIRCUIT COPPER METAL A SAME TEMP TEMP SENSOR V(T1) V(T2) T2 METAL B V(COMP) = f(T2) ISOTHERMAL BLOCK V(OUT) = V(T1) – V(T2) + V(COMP) IF V(COMP) = V(T2) – V(0°C), V(OUT) = V(T1) – V(0°C) Figure 4-70: A semiconductor temperature sensor can be used to provide cold junction compensation Ideally, the compensation voltage should be an exact match for the difference voltage required, which is why the diagram gives the voltage V(COMP) as f(T2) (a function of T2) rather than KT2, where K is a simple constant. In practice, since the cold junction is rarely more than a few tens of degrees from 0°C, and generally varies by little more than ±10°C, a linear approximation (V = KT2) to the more complex reality is usually sufficiently accurate and is often used. (Note—the expression for the output voltage of a thermocouple with its measuring junction at T°C and its reference at 0°C is a polynomial of the form V = K1T + K2T2 + K3T3 + ..., but the values of the coefficients K2, K3, and so forth. are very small for most common types of thermocouple). References 7 and 8 give the values of these coefficients for a wide range of thermocouples. When electronic cold-junction compensation is used, it is common practice to eliminate the additional thermocouple wire, and terminate the thermocouple leads in the isothermal block, as shown in the arrangement of Figure 4-71. COPPER Figure 4-71: Termination of thermocouple leads directly to an isothermal block V(OUT) = V1 – V(0°C) T2 METAL A COPPER T1 V1 METAL B TEMPERATURE COMPENSATION CIRCUIT TEMP SENSOR COPPER T2 ISOTHERMAL BLOCK 290 Sensor Signal Conditioning In Figure 4-71, the Metal A-Copper and the Metal B-Copper junctions, if at temperature T2, are equivalent to the Metal A-Metal B thermocouple junction in Figure 4-70. Type K Thermocouple Amplifier and Cold Junction Compensator The circuit in Figure 4-72 conditions the output of a Type K thermocouple, while providing cold-junction compensation, operating over temperatures between 0ºC and 250ºC. The circuit operates from single +3.3 V to +5.5 V supplies with the AD8551, and has been designed to produce a basic output voltage transfer characteristic of 10 mV/ºC. A Type K thermocouple exhibits a Seebeck coefficient of approximately 40 µV/ºC; therefore, at the cold junction, the TMP35 voltage output sensor with a temperature coefficient of 10 mV/ºC is used with divider R1 and R2, to introduce an opposing cold-junction temperature coefficient of –40 µV/ºC. This prevents the isothermal, cold-junction connection between the circuit’s printed circuit board traces and the thermocouple’s wires from introducing an error in the measured temperature. This compensation works extremely well for conditioning circuit ambient temperatures of 20ºC to 50ºC. 3.3V TO 5.5V 0.1µF TMP35 TYPE K THERMO COUPLE R5* 1.21MΩ 1.21M R4* 4.99kΩ R1* ? 24.9k? 24.9kΩ P1 50kΩ – 0°C < T < 250°°C VOUT 0.1 − 2.6V R3* 1.24MΩ 1.24M CHROMEL Cu + – COLD JUNCTION + R7* 4.99kΩ 4.99k Cu R2* 102Ω ALUMEL U1 AD8551 0.1µF FILM 10mV/°C R6 100kΩ *USE 1% RESISTORS ISOTHERMAL BLOCK Figure 4-72: Using a TMP35 temperature sensor for cold junction compensation within a Type K thermocouple amplifier-conditioner Over a 250ºC measurement temperature range, the thermocouple produces an output voltage change of ~10 mV. Since the circuit’s required full-scale output voltage change is 2.5 V, the required gain is ~250. Choosing R4 equal to 4.99 kΩ sets R5 ~1.24 MΩ. With a fixed 1% value for R5 of 1.21 MΩ, a 50 kΩ potentiometer is used with R5 for fine trim of the full-scale output voltage. The U1 amplifier should be a low drift, very high gain type. A chopper-stabilized AD8551 or an OP777 precision bipolar op amp is suitable for U1. Both the AD8551 and the OP777 have rail-rail output stages. To extend low range linearity, bias resistor R3 is added to the circuit, supplying an output offset voltage of about 0.1 V (for a nominal supply voltage of 5 V). Note that this 10°C offset must be subtracted, when making final measurements referenced to the U1 output. Note also that R3 provides a useful open thermocouple detection function, forcing the U1 output to greater than 3 V should the thermocouple open. Resistor R7 balances the dc input impedance at the U1 (+) input, and the 0.1 µF film capacitor reduces noise coupling. 291 Chapter Four Single-Chip Thermocouple Signal Conditioners While the construction of thermocouple signal conditioners with op amps and other discrete circuit elements offers great flexibility, this does come at the expense of component count. To achieve a greater level of integration in the thermocouple conditioning function, dedicated thermocouple signal conditioners can be used. One such solution lies with the AD594 and AD595 (see Reference 9), which are complete, single-chip instrumentation amplifiers and thermocouple cold junction compensators, as shown in Figure 4-73. Suitable for use with either Type J (AD594) or Type K (AD595) thermocouples, these two devices combine an ice point reference with a precalibrated scaling amplifier. They provide a high level (10 mV/°C) output working directly from a thermocouple input, without additional precision parts. Pin-strapping options allow the devices to be used as a linear amplifier-compensator, or as a switched output set-point controller with fixed or remote setpoint control. 5V 0.1µF BROKEN THERMOCOUPLE ALARM 4.7k 4.7kΩ OVERLOAD DETECT TYPE J: AD594 TYPE K: AD595 THERMOCOUPLE VOUT 10mV/°°C AD594/AD595 +A – – G + G + + ICE POINT COMP –TC +TC Figure 4-73: Functional diagram of AD594 and AD595 thermocouple signal-conditioning amplifiers The AD594 and AD595 can be used to amplify the cold-junction compensation voltage directly, thereby becoming a standalone, 10 mV/°C output Celsius transducer. In such applications it is very important that the IC chip be at the same temperature as the cold junction of the thermocouple; this is usually achieved by keeping the two in close proximity and isolated from any heat sources. The AD594/AD595 structure includes a flexible thermocouple failure alarm output, which provides broken thermocouple indication. The devices can be powered from either dual or single power supplies (as low as 5 V), but the use of a negative supply also allows temperatures below 0°C to be measured. To minimize self-heating, an unloaded AD594/AD595 operates with 160 µA of supply current, and can deliver ±5 mA to a load. Although the AD594 is precalibrated by laser wafer trimming to match the characteristics of Type J thermocouples, and the AD595 for Type K, the temperature transducer voltages and gain control resistors are also made available at the package pins. So, if desired, the circuit can be recalibrated for other thermocouple types with the addition of external resistors. These terminals also allow more precise calibration for both 292 Sensor Signal Conditioning thermocouple and thermometer applications. The AD594/AD595 are available in C and A performance grades, with calibration accuracies of ±1°C and ±3°C, respectively. Both are designed to be used with cold junctions between 0 to 50°C. The 5 V powered, single-supply circuit shown of Figure 4-73 provides a scaled 10 mV/°C output capable of measuring a range of 0°C to 300°C. This can be from either a Type J thermocouple using the AD594, or a Type K with the AD595. Resistance Temperature Detectors The Resistance Temperature Detector (RTD), is a sensor whose resistance changes with temperature. Typically built of a platinum (Pt) wire wrapped around a ceramic bobbin, the RTD exhibits behavior which is more accurate and more linear than a thermocouple over wide temperature ranges. Figure 4-74 illustrates the temperature coefficient of a 100 Ω RTD, and the Seebeck coefficient of a Type S thermocouple. Over the entire range (approximately –200°C to +850°C), the RTD is a more linear device. Hence, linearizing an RTD is less complex. • Platinum (Pt) the Most Common • 100Ω, 1000Ω Standard Values • Typical TC = 0.385%/°C = 0.385Ω/°C for 100Ω Pt RTD • Good Linearity − Better than Thermocouple, • Easily Compensated 11.5 0.400 RTD RESISTANCE TC, ∆Ω /°C 100Ω Pt RTD 100 10.5 TYPE S THERMOCOUPLE 0.375 9.50 0.350 TYPE S THERMOCOUPLE SEEBECK COEFFICIENT, µV/°C 8.50 0.325 7.50 0.300 0.275 6.50 0 400 800 5.50 TEMPERATURE °C Figure 4-74: Resistance temperature detectors Unlike a thermocouple, however, an RTD is a passive sensor, and a current excitation is required to produce an output voltage. The RTD’s low temperature coefficient of 0.385%/°C requires high performance signalconditioning circuitry similar to that used by a thermocouple. However, the typical voltage drop seen across an RTD is much larger than a thermocouple’s output voltage. A system designer may opt for large value RTDs with higher output, but large-valued RTDs exhibit slow response times. Furthermore, although the cost of RTDs is higher than that of thermocouples, they use copper leads, and thermoelectric effects from terminating junctions do not affect their accuracy. And finally, because their resistance is a function of the absolute temperature, RTDs do not require cold-junction compensation. Caution must be exercised with the level of current excitation applied to an RTD, because excessive current can cause self-heating. Any self-heating changes the RTD temperature, and therefore results in a measurement error. Hence, careful attention must be paid to the design of the signal-conditioning circuitry so that 293 Chapter Four self-heating errors are kept below 0.5°C. Manufacturers specify self-heating errors for various RTD values and sizes, in both still and moving air. To reduce the error due to self-heating, the minimum current should be used to achieve the required system resolution, and the largest RTD value chosen that results in acceptable response time. Another effect that can produce measurement error is voltage drop in RTD lead wires. This is especially critical with low value, 2-wire RTDs, because both the temperature coefficient and absolute value of the RTD resistance are small. If the RTD is located a long distance from the signal-conditioning circuitry, the connecting lead resistance can be ohms or tens of ohms. Even this small amount of lead resistance can contribute a significant error to the temperature measurement, as shown in Figure 4-75. 10.5Ω R = 10.5 COPPER 100Ω 100 Pt RTD 10.5Ω R = 10.5 COPPER RESISTANCE TC OF COPPER = 0.40%/°C @ 20°C RESISTANCE TC OF Pt RTD = 0.385%/°C @ 20°C Figure 4-75: A 100 Ω Pt RTD with 100-foot #30 AWG lead wires To illustrate this point, assume that a 100 Ω platinum RTD with 30-gage copper leads is located about 100 feet from a controller’s display console. The resistance of 30-gage copper wire is 0.105 Ω/ft, and the two leads of the RTD will contribute a total 21 Ω to the network. Uncorrected, this additional resistance will produce a 55°C measurement error. Obviously, the temperature coefficient of the connecting leads can contribute an additional, and possibly significant, error to the measurement. To eliminate the effect of the lead resistance, a 4-wire technique is used. In Figure 4-76, a 4-wire (Kelvin) connection is made to the RTD. A constant current, I, is applied though the FORCE leads of the RTD, and the voltage across the RTD itself is measured remotely, via the SENSE leads. The measuring device can be a DVM or an in amp, and high accuracy can be achieved provided that the measuring device exhibits high FORCE LEAD SENSE LEAD RLEAD 100Ω Pt RTD I FORCE LEAD TO HIGH − Z IN AMP OR ADC SENSE LEAD RLEAD Figure 4-76: Use of Kelvin or 4-wire Pt RTD connections provides high accuracy 294 Sensor Signal Conditioning input impedance and/or low input bias current. Since the SENSE leads don’t carry appreciable current, this technique is relatively insensitive to lead wire length. Some major sources of errors in this scheme are the stability of the constant current source, and the input impedance and/or bias currents in the amplifier or DVM, and the associated drift. RTDs are generally configured in a four-resistor bridge circuit. The bridge output is amplified by an in amp for further processing. However, high resolution measurement ADCs allow the RTD output to be digitized directly. In this manner, linearization can be performed digitally, thereby easing the analog circuit requirements considerably. For example, an RTD output can be digitized by one of the AD77xx series high resolution ADCs. Figure 4-77 shows a 100 Ω Pt RTD, driven with a 400 µA excitation current source. Note that the 400 µA RTD excitation current source also generates a 2.5 V reference voltage for the ADC, by virtue of flowing in a 6.25 kΩ resistor, RREF, with the drop across this resistance being metered by the ADC’s VREF (+) and (–) input terminals. 3V OR 5V (DEPENDING ON ADC) +VREF RREF 6.25kΩ –VREF + 400µA 100Ω Pt RTD CONTROL REGISTER AIN1+ MUX PGA – Σ−∆ ADC OUTPUT REGISTER AIN1– G = 1 TO 128 AD77xx SERIES (16−22 BITS) SERIAL INTERFACE TO MICROCONTROLLER Figure 4-77: A Pt RTD interfaced to the AD77xx series of high resolution ADCs It should be noted that this simple scheme has great benefits (beyond the obvious one of simplicity). Variations in the magnitude of the 400 µA excitation current do not affect circuit accuracy, since both the input voltage drop across the RTD as well as the reference voltage across RREF vary ratiometrically with the excitation current. However, it should be noted that the 6.25 kΩ resistor must be a stable type with a low temperature coefficient, to avoid errors in the measurement. Either a wirewound resistor, or a very low TC metal film type is most suitable for RREF within this application. In this application, the ADC’s high resolution and the gain of 1 to 128 input PGA eliminates the need for any additional conditioning. The high resolution ADC can in fact perform virtually all the conditioning necessary for an RTD, leaving any further processing such as linearization to be performed in the digital domain. Thermistors Similar in general function to RTDs, thermistors are low-cost temperature-sensitive resistors, constructed of solid semiconductor materials which exhibit a positive or negative temperature coefficient. Although positive temperature coefficient devices do exist, the most common thermistors are negative temperature coefficient (NTC) devices. 295 Chapter Four 40 ALPHA THERMISTOR, INCORPORATED RESISTANCE/TEMPERATURE CURVE ‘A’ 'A' ? THERMISTOR,#13A1002-C3 #13A1002-C3 10 k? 10kΩTHERMISTOR, 30 THERMISTOR RESISTANCE k kΩ 20 10 Nominal Value NOMINAL VALUE @ 25 @ 25°C °C 0 0 20 40 60 80 100 TEMPERATURE −°°C Figure 4-78: Resistance characteristics for a 10kΩ NTC thermistor Figure 4-78 shows the resistance-temperature characteristic of a commonly used NTC thermistor. Although the thermistor is the most nonlinear of the three temperature sensors discussed, it is also the most sensitive. The thermistor’s very high sensitivity (typically – 44,000 ppm/°C at 25°C) allows it to detect minute temperature variations not readily observable with an RTD or thermocouple. This high sensitivity is a distinct advantage over the RTD, in that 4-wire Kelvin connections to the thermistor aren’t needed for lead wire error compensation. To illustrate this point, suppose a 10 kΩ NTC thermistor with a typical 25°C temperature coefficient of –44,000 ppm/°C were substituted for the 100 Ω Pt RTD in the example given earlier. The total lead wire resistance of 21 Ω would generate less than 0.05°C error in the measurement, using the thermistor in lieu of the RTD. This is roughly a factor of 500 improvement in error sensitivity over an RTD. However, the thermistor’s high sensitivity to temperature does not come without a price. As previously shown in Figure 4-78, the temperature coefficient of thermistors does not decrease linearly with increasing temperature as with RTDs, and as a result linearization is required for all but the most narrow temperature ranges. Thermistor applications are limited to a few hundred degrees at best, because thermistors are also more susceptible to damage at high temperatures. Compared to thermocouples and RTDs, thermistors are fragile in construction and require careful mounting procedures to prevent crushing or bond separation. Although a thermistor’s response time is short due to its small size, its small thermal mass also makes it very sensitive to self-heating errors. Thermistors are very inexpensive, highly sensitive temperature sensors. However, we have noted that a thermistor’s temperature coefficient can vary, from –44,000 ppm/°C at 25°C, to –29,000 ppm/°C at 100°C. Not only is this nonlinearity the largest source of error in a temperature measurement, it also limits useful applications to very narrow temperature ranges without linearization. As shown in Figure 4-79, a parallel resistor combination exhibits a more linear variation with temperature compared to the thermistor itself. This approach to linearizing a thermistor simply shunts it with a fixed, temperature-stable resistor. Paralleling the thermistor with a fixed resistor increases the linearity significantly. Also, the sensitivity of the combination still is high compared to a thermocouple or RTD. The primary disadvantage of the technique is that linearization is only effective within a narrow range. However, it is possible to use a thermistor over a wide temperature range, if the system designer can tolerate a lower net sensitivity, in order to achieve improved linearity. 296 Sensor Signal Conditioning 40 RESISTANCE − kΩ 30 20 THERMISTOR PARALLEL COMBINATION 10 0 0 20 40 60 80 100 TEMPERATURE −°C Figure 4-79: Linearization of NTC thermistor using a fixed shunt resistance R, the value of the fixed shunt resistor, can be calculated from the following equation: R= RT2 ⋅ (RT1 + RT3) − 2 ⋅ RT1 ⋅ RT3 RT1 + RT3 − 2 ⋅ RT2 Eq. 4-11 where RT1 is the thermistor resistance at T1, the lowest temperature in the measurement range, RT3 is the thermistor resistance at T3, the highest temperature in the range, and RT2 is the thermistor resistance at T2, the midpoint, T2 = (T1 + T3)/2. For a typical 10 kΩ NTC thermistor, RT1 = 32,650 Ω at 0°C, RT2 = 6,532 Ω at 35°C, and RT3 = 1,752 Ω at 70°C. This results in a value of 5.17 kΩ for R. The accuracy needed in the associated signal-conditioning circuitry depends on the linearity of the network. For the example given above, the network shows a nonlinearity of –2.3°C/+2.0°C. The output of the network can be applied to an ADC for digital conversion (with optional linearization) as shown in Figure 4-80. Note that the output of the thermistor network has a slope of approximately –10 mV/°C, which implies that an 8- or 10-bit ADC easily has more than sufficient resolution with a full scale range of 1 V or less. The further linearization can be applied to the data in the digital domain, if desired. 226µA VOUT ≈ 0.994V @ T = 0°°C VOUT ≈ 0.294V @ T =70°°C ∆V VOUT//∆T T ≈ −10mV/°°C AMPLIFIER OR ADC 5.17kΩ 5.17k LINEARIZATION RESISTOR LINEARITY ≈ ±2°C, 0°C TO +70°C Figure 4-80: Linearized thermistor network with amplifier or ADC 297 Chapter Four Semiconductor Temperature Sensors Modern semiconductor temperature sensors offer high accuracy and high linearity over an operating range of about –55°C to +150°C. Internal amplifiers can scale the output to convenient values, such as 10 mV/°C. They are also useful in cold-junction-compensation circuits for wide temperature range thermocouples. All semiconductor temperature sensors make use of the relationship between a bipolar junction transistor’s (BJT) base-emitter voltage to its collector current: VBE = kT I C ln q I S Eq. 4-12 In this expression k is Boltzmann’s constant, T is the absolute temperature, q is the charge of an electron, and IS is a current related to the geometry and the temperature of the transistors. (The equation assumes a voltage of at least a few hundred mV on the collector, and ignores Early effects.) If we take ‘N’ transistors identical to the first (see Figure 4-81) and allow the total current IC to be shared equally among them, we find that the new base-emitter voltage applicable to this case is given by the equation VN = kT I C ln q N ⋅ I S IC IC ONE TRANSISTOR VBE VBE = Eq. 4-13 N TRANSISTORS VN kT IC ln q IS VN = ∆VBE = VBE − VN = kT I C ln q N ⋅ IS kT ln( N) q INDEPENDENT OF IC, IS Figure 4-81: The basic relationships for BJT-based semiconductor temperature sensors Neither of these circuits is of much use by itself, because of the strong temperature dependence of IS. However, if we have equal currents flowing in one BJT, as well as the N similar BJTs, then the expression for the difference between the respective base-emitter voltages (or ∆VBE) is proportional to absolute temperature, and it does not contain Is. This then leads to a far more useful relationship, developed as follows: ∆VBE = VBE − VN = kT I C kT I C ln ln − q I S q N ⋅ I S 298 Sensor Signal Conditioning ∆VBE = VBE − VN = ∆VBE I kT I C − ln C ln q I S N ⋅ I S I C kT I S = kT ln (N ) = VBE − VN = ln IC q q N ⋅ I S This end result of this algebra is expressed in a single key equation, one worthy of restatement: ∆VBE = kT ln (N ) q Eq. 4-14 As one can note, Eq. 4-14 contains only the transistor emitter area ratio N and T as variables. Since N is fixed within a given design, it can be the basis of a transducer for T measurement. The circuit as shown in Figure 4-82 implements the above equation, and is popularly known as the “Brokaw Cell,” after its inventor (see Reference 10). +VIN R − Q2 NA kT ln( N) q VBANDGAP = 1.205V + I2 ≅ I1 ∆VBE = VBE − VN = "BROKAW CELL" R Q1 A VN VBE (Q1) R2 VPTAT = 2 R1 kT ln(N) R2 q R1 Figure 4-82: The “Brokaw Cell” is both a silicon bandgap voltage-based reference as well as a temperature sensor The voltage ∆VBE = VBE – VN appears across resistor R2, as noted. The emitter current in Q2 is therefore ∆VBE/R2. The op amp’s servo loop and the two resistors ‘R’ force an identical current to flow through Q1. The Q1 and Q2 currents are equal, and they are summed, flowing in resistor R1. The corresponding voltage developed across R1 is VPTAT, a voltage proportional to absolute temperature (PTAT). This is given by: VPTAT = 2R1(VBE − VN ) R2 299 =2 R1 kT ln (N ) R2 q Chapter Four Within the circuit, a voltage labeled as VBANDGAP appears at the base of Q1, and, as can be noted, is the sum of VBE(Q1) and VPTAT. When this voltage is set by the design to be exactly equal to the bandgap voltage of silicon, it will then become independent of temperature. The voltage VBE(Q1) is complementary to absolute temperature (CTAT), and summing it with a properly proportioned VPTAT from across R1 gives the desired end result; the bandgap voltage becomes constant with respect to temperature. Note that this assumes the proper choice of R1/R2 ratio and N, to make the summed voltage equal to VBANDGAP, the silicon bandgap voltage (in this instance 1.205 V). This circuit has the virtues of dual application because of the above features. It is useful as a basic silicon bandgap temperature sensor, with either direct or scaled use of the voltage VPTAT. It is also widely used a temperature stable reference voltage source, by suitable scaling of VBANDGAP to standard outputs of 2.500 V, 5.000 V, and so forth. Current and Voltage Output Temperature Sensors The concepts used in the bandgap voltage temperature sensor discussion above can also be used as the basis for a variety of IC temperature sensors, with linear, proportional-to-temperature outputs, of either current or voltage. The AD592 device shown in Figure 4-83 is a two-terminal, current output sensor with a scale factor of 1 µA/K. This device does not require external calibration, and is available in several accuracy grades. The AD592 is a TO92 packaged version of the original AD590 TO52 metal packaged temperature transducer device (see Reference 11). V+ AD592: TO-92 PACKAGE V– • 1µA/K Scale Factor • Nominal Output Current @ 25°C: 298.2µA • Operation from 4V to 30V • ±0.5°C Max Error @ 25°C, ±1.0°C Error Over Temp, ±0.1°C Typical Nonlinearity (AD592CN) • AD592 Specified from –25°C to +105°C Figure 4-83: Current output absolute temperature sensor The simplest operating mode for current mode temperature sensors is to load them with a precision resistor of 1% or better tolerance, and read the output voltage developed with either an ADC or a scaling amplifier/buffer. Figure 4-84 shows this technique with an ADC, as applicable to the AD592. The resistor load R1 converts the basic scaling of the sensor (1 µA/K) into a proportional voltage. Choice of this resistor determines the overall sensitivity of the temperature sensor, in terms of V/K. For example, with a 1 kΩ precision resistor load as shown, the net circuit sensitivity becomes 1 mV/K. With a 5 V bias on the temperature sensor as shown, the AD592’s full dynamic range is allowed with a 1 KΩ load. If a higher value R1 is used, higher bias voltage may be required, as the AD592 requires 4 V of operating headroom. 300 Sensor Signal Conditioning +VS +5V AD592 1µA/K ∆VOUT/∆T ≈ 1mV/K R1 1k ∆VOUT = 0.248V to 0.378V ADC Figure 4-84: Current output temperature sensor driving a resistive load The function just described is a Kelvin-scaled temperature sensor, so the ADC will be required to read the full dynamic range of voltage across R1. With an AD592, this span is from the range corresponding to –25°C (248 K) to 105°C (378 K), which is 0.248 V to 0.378 V. A 10-bit, 0.5 V scaled ADC can read this range directly with ≈0.5°C resolution. If a centigrade-scaled reading is desired, two options present themselves. For a traditional analog approach, the common terminal of the ADC input can easily be biased with a reference voltage corresponding to 0°C, or 0.273 V. Alternately, the 0°C reference can be inserted in the digital domain, with the advantage of no additional hardware requirement. The AD592 is available in three accuracy grades. The highest grade version (AD592CN) has a maximum error @ 25ºC of ±0.5ºC and ±1.0ºC error from –25ºC to +105ºC, and a linearity error of ±0.35ºC. The AD592 is available in a TO-92 package. With regard to stand-alone digital output temperature sensors, it is worthy of note that such devices do exist, that is ADCs with built-in temperature sensing. The AD7816/AD7817/AD7818-series ADCs have on-board temperature sensors digitized by a 10-bit 9 µs conversion time switched capacitor SAR ADC. The device family offers a variety of input options for flexibility. The similar AD7416/AD7417/AD7418 have serial interfaces. For a great many temperature sensing applications, a voltage mode output sensor is most appropriate. For this, there are a variety of standalone sensors that can be directly applied. In such devices the basic mode of operation is as a three-terminal device, using power input, common, and voltage output pins. In addition, some devices offer an optional shutdown pin. 301 Chapter Four The TMP35/TMP36 are low voltage (2.7 V to 5.5 V), SO-8 or TO-92 packaged voltage output temperature sensors with a 10 mV/°C scale factor, as shown in Figure 4-85. Supply current is below 50 µA, providing very low self-heating (less than 0.1°C in still air). +VS = 2.7V TO 5.5V SHUTDOWN TMP35 TMP36 VOUT 0.1µF • V OUT : – TMP35, 250mV @ 25°C, 10mV/°C (10°C to 125°C) – TMP36, 750mV @ 25°C, 10mV/°C (–40°C to +125°C) • ±2°C Error Over Temp (Typical), ±0.5°C Nonlinearity (Typical) • Specified –40°C to +125°C • 50µA Quiescent Current, 0.5µA in Shutdown Mode Figure 4-85: TMP35/36 absolute scaled voltage mode output temperature sensors with shutdown capability Output scaling of this device family differs in range and 25°C offset. The TMP35 provides a 250 mV output at 25°C, and reads temperature from 10°C to 125°C. The TMP36 is specified from –40°C to +125°C. and provides a 750 mV output at 25°C. Both the TMP35 and TMP36 have an output scale factor of +10 mV/°C. An optional shutdown feature is provided for the SO8 package devices, which reduces the standby current to 0.5 µA. This pin, when taken to a logic LOW, turns the device OFF, and the output becomes a high impedance state. If shutdown isn’t used, the pin should be connected to +VS. The power supply pin of these voltage mode sensors should be bypassed to ground with a 0.1 µF ceramic capacitor having very short leads (preferably surface mount) and located as close to the power supply pin as possible. Since these temperature sensors operate on very little supply current and could be exposed to very hostile electrical environments, it is also important to minimize the effects of EMI/RFI on these devices. The effect of RFI on these temperature sensors is manifested as abnormal dc shifts in the output voltage due to rectification of the high frequency noise by the internal IC junctions. In those cases where the devices are operated in the presence of high frequency radiated or conducted noise, a large value tantalum electrolytic capacitor (>2.2 µF) placed across the 0.1 µF ceramic may offer additional noise immunity. Ratiometric Voltage Output Temperature Sensors In some cases, it is desirable for the output of a temperature sensor to be ratiometric with respect its supply voltage. A series of ADI temperature sensors have been designed to fulfill this need, in the form of the AD2210x series (see references 12–14). Of this series, the AD22103 illustrated in Figure 4-86 has an output that is ratiometric with regard its nominal 3.3 V supply voltage, according to the equation: VOUT = VS 28mV × 0.25V + × TA ⋅ 3.3V °C 302 Eq. 4-15 Sensor Signal Conditioning VS = 3.3V 0.1µF REFERENCE R14 R22 R32 R16 ADC + RT VOUT INPUT – R24 R18 GND AD22103 VOUT = 28mV VS × 0.25 V + × TA 3.3 V °C Figure 4-86: Ratiometric voltage output temperature sensors Note also that the Figure 4-86 circuit uses the 3.3 V AD22103 power supply voltage as the reference input to the ADC. This step eliminates the need for a separate precision voltage reference source. Within a system, this key point potentially can have a positive impact. Operation of the AD22103 is accomplished with an on-chip temperature sensing resistance RT, which operates similarly to the RTD types discussed earlier in this section. This resistance is fed from a resistance network comprised of R14, R16, and R32. R14 and R16 provide a current drive component for RT that is proportional to the supply voltage, a factor that gives the AD22103 a basic sensitivity that is proportional to the supply. RT, like a classic platinum RTD, exhibits a nonlinear resistance versus temperature behavior. This nonlinear characteristic of RT is corrected by a positive feedback loop, composed of R32 along with the Thevenin equivalent of resistances R14 and R16. Gain scaling for the changing RT output voltage is provided by the op amp negative feedback loop, R18, and the Thevenin equivalent of resistances R24 and R22. This references the gain network of the op amp to the supply voltage, instead of ground. The various resistance networks around the op amp are actively trimmed at temperature, to calibrate the sensor for its rated offset and scaling. The net combination of these factors allows the device to behave in accordance with the relationship of Eq. 4-15. The AD22103 is specified over a range of 0°C to 100°C, and has an accuracy better than ±2.5°C, along with a linearity better than ±0.5% of full scale, i.e., 0.5°C over 100°C. Since the AD22103 is a single-supply part, the sensing of low temperatures necessarily involves a positive output offset. For example, for 3.3 V operation of this example, the output offset is simply the 0.25 V term of Eq. 4-15. Accordingly, the 0 to 100°C temperature span translates to an output swing of 0.25 V to 3.05 V. Should it be desired, operation of the AD22103 device is also possible at higher supply voltages. Because of the ratiometric operation feature, this will necessarily involve a change to both the basic sensitivity and the offset. For example, in operating the AD22103 at 5 V, the output expression changes to: VOUT = VS 42.42mV × 0.378V + × TA °C 5V 303 Eq. 4-16 Chapter Four However, it should be noted that the fact that the AD22103 is ratiometric does not preclude operating the part from a fixed reference voltage. The nominal current drain of the AD22103 is 500 µA, allowing a number of these sensors to be operated from a common reference IC without danger of overload (as well as other analog parts). For example, one such reference family is the REF19x series, which can supply output currents of up to 30 mA. In addition to the above-described AD22103 3.3 V part, there is also a companion device, the AD22100. While basically quite similar to the AD22103, the AD22100 operates from a nominal 5 V power supply with reduced sensitivity, allowing operation over a range of –50 to +150°C. Over this range the rated accuracy of the AD22100 is 2% or better, and linearity error is 1% or less. References: Temperature Sensors 1. Ramon Pallas-Areny and John G. Webster, Sensors and Signal Conditioning, John Wiley, New York, 1991. 2. Dan Sheingold, Editor, Transducer Interfacing Handbook, Analog Devices, Inc., 1980, ISBN: 0-916550-05-2. 3. Sections 2, 3, Walt Kester, Editor, 1992 Amplifier Applications Guide, Analog Devices, 1992, ISBN: 0-916550-10-9. 4. Sections 1, 6, Walt Kester, Editor, System Applications Guide, Analog Devices, 1993, ISBN: 0-916550-13-3. 5. Dan Sheingold, Editor, Nonlinear Circuits Handbook, Analog Devices, Inc., 1974. 6. James Wong, “Temperature Measurements Gain from Advances in High-precision Op Amps,” Electronic Design, May 15, 1986. 7. OMEGA Temperature Measurement Handbook, Omega Instruments, Inc. 8. Handbook of Chemistry and Physics, Chemical Rubber Co. 9. Joe Marcin, “Thermocouple Signal Conditioning Using the AD594/AD595,” Analog Devices AN369. 10. Paul Brokaw, “A Simple Three-Terminal IC Bandgap Voltage Reference,” IEEE Journal of SolidState Circuits, Vol. SC-9, No. 6, December, 1974, pp. 388–393. 11. Mike Timko, “A Two-Terminal IC Temperature Transducer,” IEEE Journal of Solid-State Circuits, Vol. SC-11, No. 6, December, 1976, pp. 784–788. 12. Data sheet for AD22103 3.3 V Supply, Voltage Output Temperature Sensor with Signal Conditioning, www.analog.com. 13. Data sheet for AD22100 Voltage Output Temperature Sensor with Signal Conditioning, www analog.com. 14. Adrian P. Brokaw, “Monolithic Ratiometric Temperature Measurement Circuit,” US Patent No. 5,030,849, filed June 30, 1989, issued July 9, 1991. 304 Sensor Signal Conditioning Classic Cameo AD590 Two-Terminal IC Temperature Transducer AD590 basic (left), and complete schematics (right) Designed by Mike Timko, based on an original Paul Brokaw concept,1 the AD590 2,3,4 current mode IC temperature transducer was introduced in 1977. The AD590 established early an elegant method of accurate temperature measurement, based upon fundamental silicon transistor operating principles. It has been in ADI production since introduction, along with such related ICs as the AD592 discussed within this chapter. The references below discuss operation in great detail, but suffice it to say that in the basic structure (left) a voltage proportional to absolute temperature, VT, appears across resistor R. This makes the current IT drawn from an external source proportional to absolute temperature. In the full circuit (right), trimmed thin film resistors implement a calibrated scaling for IT of 1µA/K. Additional circuitry is added for startup and for increased accuracy, both with respect to applied voltage as well as against high temperature leakage. A current-operated transducer such as this is quite convenient to operate, the output being impervious to long lead lengths, and also virtually noise-immune. The low scaling factor also makes the AD590 easy to operate on low voltage supplies without self-heating, yet high output impedance also holds calibration with higher applied voltages. Readout is simply accomplished with a single resistance, making a simple, two-component Kelvin-scaled thermometer possible. 1 2 3 4 Adrian P. Brokaw, “Digital-to-Analog Converter with Current Source Transistors Operated Accurately at Different Current Densities,” US Patent No. 3,940,760, filed March 21, 1975, issued Feb. 24, 1976. Mike Timko, “A Two-Terminal IC Temperature Transducer,” IEEE Journal of Solid-State Circuits, Vol. SC-11, No. 6, December, 1976, pp. 784–788. Mike Timko, Goodloe Suttler, “1µA/K IC Temperature-to-Current Transducer,” Analog Dialogue, Vol. 12, No. 1, 1978, pp. 3–5. Michael P. Timko, Adrian P. Brokaw, “Integrated Circuit Two Terminal Temperature Transducer,” US Patent No. 4,123,698, filed July 6, 1976, issued October 31, 1978. 305 This page intentionally left blank CHAPTER 5 Analog Filters ■ Section 5-1: Introduction ■ Section 5-2: The Transfer Function ■ Section 5-3: Time Domain Response ■ Section 5-4: Standard Responses ■ Section 5-5: Frequency Transformations ■ Section 5-6: Filter Realizations ■ Section 5-7: Practical Problems in Filter Implementation ■ Section 5-8: Design Examples This page intentionally left blank CHAPTER 5 Analog Filters Hank Zumbahlen SECTION 5-1 Introduction Filters are networks that process signals in a frequency-dependent manner. The basic concept of a filter can be explained by examining the frequency-dependent nature of the impedance of capacitors and inductors. Consider a voltage divider where the shunt leg is a reactive impedance. As the frequency is changed, the value of the reactive impedance changes, and the voltage divider ratio changes. This mechanism yields the frequency dependent change in the input/output transfer function that is defined as the frequency-response. Filters have many practical applications. A simple, single pole, low-pass filter (the integrator) is often used to stabilize amplifiers by rolling off the gain at higher frequencies where excessive phase shift may cause oscillations. A simple, single pole, high pass filter can be used to block dc offset in high gain amplifiers or single supply circuits. Filters can be used to separate signals, passing those of interest, and attenuating the unwanted frequencies. An example of this is a radio receiver, where the signal to be processed is passed through, typically with gain, while attenuating the rest of the signals. In data conversion, filters are also used to eliminate the effects of aliases in A/D systems. They are used in reconstruction of the signal at the output of a D/A as well, eliminating the higher frequency components, such as the sampling frequency and its harmonics, thus smoothing the waveform. There are a large number of texts dedicated to filter theory. No attempt will be made to go heavily into much of the underlying math—Laplace transforms, complex conjugate poles and the like—although they will be mentioned. While they are appropriate for describing the effects of filters and examining stability, in most cases examination of the function in the frequency domain is more illuminating. An ideal filter will have an amplitude response that is unity (or at a fixed gain) for the frequencies of interest (called the pass band) and zero everywhere else (called the stop band). The frequency at which the response changes from pass band to stop band is referred to as the cutoff frequency. 309 Chapter Five Figure 5-1(A) shows an idealized low-pass filter. In this filter the low frequencies are in the pass band and the higher frequencies are in the stop band. The functional complement to the low-pass filter is the high-pass filter. Here, the low frequencies are in the stop band, and the high frequencies are in the pass band. Figure 5-1(B) shows the idealized high-pass filter. If a high-pass filter and a low-pass filter are cascaded, a band-pass filter is created. The band-pass filter passes a band of frequencies between a lower cutoff frequency, fl, and an upper cutoff frequency, fh. Frequencies below fl and above fh are in the stop band. An idealized band-pass filter is shown in Figure 5-1(C). MAGNITUDE M AGNITUDE A complement to the band-pass filter is the bandreject, or notch filter. Here, the pass bands include frequencies below fl and above fh. The band from fl to fh is in the stop band. Figure 5-1(D) shows a notch response. fc fc FREQUENCY FREQUENCY (B) High Pass MA GNITUDE MA GNITUDE (A) Low Pass f1 fh f1 FREQUENCY (C) Band Pass fh FREQUENCY (D) Notch (Bandreject) Figure 5-1: Idealized filter responses Unfortunately, the idealized filters defined above cannot be easily built. The transition from pass band to stop band will not be instantaneous, but instead there will be a transition region. Stop band attenuation will not be infinite. The five parameters of a practical filter are defined in Figure 5-2. Figure 5-2: Key filter parameters PASS BAND RIPPLE A MAX 3dB POINT OR CUTOFF FREQUENCY Fc STOP BAND ATTENUATION A MIN STOP BAND FREQUENCY Fs PASS BAND STOP BAND TRANSITION BAND 310 Analog Filters The cutoff frequency (Fc) is the frequency at which the filter response leaves the error band (or the −3 dB point for a Butterworth response filter). The stop band frequency (Fs) is the frequency at which the minimum attenuation in the stop band is reached. The pass band ripple (Amax) is the variation (error band) in the pass band response. The minimum pass band attenuation (Amin) defines the minimum signal attenuation within the stop band. The steepness of the filter is defined as the order (M) of the filter. M is also the number of poles in the transfer function. A pole is a root of the denominator of the transfer function. Conversely, a zero is a root of the numerator of the transfer function. Each pole gives a –6 dB/octave or –20 dB/decade response. Each zero gives a +6 dB/octave, or +20 dB/decade response. Note that not all filters will have all these features. For instance, all-pole configurations (i.e., no zeros in the transfer function) will not have ripple in the stop band. Butterworth and Bessel filters are examples of allpole filters with no ripple in the pass band. Typically, one or more of the above parameters will be variable. For instance, if you were to design an antialiasing filter for an ADC, you will know the cutoff frequency (the maximum frequency to be passed), the stop band frequency, (which will generally be the Nyquist frequency (= ½ the sample rate)) and the minimum attenuation required (which will be set by the resolution or dynamic range of the system). Go to a chart or computer program to determine the other parameters, such as filter order, F0, and Q, which determines the peaking of the section, for the various sections and/or component values. It should also be pointed out that the filter will affect the phase of a signal, as well as the amplitude. For example, a single pole section will have a 90° phase shift at the crossover frequency. A pole pair will have a 180° phase shift at the crossover frequency. The Q of the filter will determine the rate of change of the phase. This will be covered more in depth in the next section. 311 This page intentionally left blank SECTION 5-2 The Transfer Function The S-Plane Filters have a frequency dependent response because the impedance of a capacitor or an inductor changes with frequency. Therefore the complex impedances: Z L = sL Eq. 5-1 1 sC Eq. 5-2 and ZC = s = σ + jω Eq. 5-3 are used to describe the impedance of an inductor and a capacitor, respectively, where σ is the Neper frequency in nepers per second (NP/s) and ω is the angular frequency in radians per sec (rad/s). By using standard circuit analysis techniques, the transfer equation of the filter can be developed. These techniques include Ohm’s law, Kirchoff’s voltage and current laws, and superposition, remembering that the impedances are complex. The transfer equation is then: H (s) = a m s m + a m − 1 s m − 1 + … + a 1s + a 0 b n sn + b n −1sn −1 + … + b1s + b 0 Eq. 5-4 Therefore, H(s) is a rational function of s with real coefficients with the degree of m for the numerator and n for the denominator. The degree of the denominator is the order of the filter. Solving for the roots of the equation determines the poles (denominator) and zeros (numerator) of the circuit. Each pole will provide a –6 dB/octave or –20 dB/decade response. Each zero will provide a +6 dB/octave or +20 dB/decade response. These roots can be real or complex. When they are complex, they occur in conjugate pairs. These roots are plotted on the s plane (complex plane) where the horizontal axis is σ (real axis) and the vertical axis is ω (imaginary axis). How these roots are distributed on the s plane can tell us many things about the circuit. In order to have stability, all poles must be in the left side of the plane. If there is a zero at the origin, that is a zero in the numerator, the filter will have no response at dc (high pass or band pass). 313 Chapter Five Assume an RLC circuit, as in Figure 5-3. Using the voltage divider concept it can be shown that the voltage across the resistor is: H (s) = Vo RCs = 2 Vin LCs + RCs + 1 Eq. 5-5 Substituting the component values into the equation yields: H (s) = 103 × s s + 103 s + 10 7 2 Factoring the equation and normalizing gives: H (s) = 103 × s s − (−0.5 + j 3.122 )× 10 × s − (−0.5 − j 3.122 )× 103 3 10mH 10µF ~ VOUT 10Ω Figure 5-3: RLC circuit This gives a zero at the origin and a pole pair at: s = (−0.5 ± j 3.122 ) × 103 Next, plot these points on the s plane as shown in Figure 5-4: Im (krad/s) Figure 5-4: Pole and zero plotted on the s-plane X +3.122 Re (kNP/s) –0.5 X –3.122 The above discussion has a definite mathematical flavor. In most cases there is more interest in the circuit’s performance in real applications. While working in the s plane is completely valid, most of us don’t think in terms of Nepers and imaginary frequencies. 314 Analog Filters Fo and Q So if it is not convenient to work in the s plane, why go through the above discussion? The answer is that the groundwork has been set for two concepts that will be infinitely more useful in practice: Fo and Q. Fo is the cutoff frequency of the filter. This is defined, in general, as the frequency where the response is down 3 dB from the passband. It can sometimes be defined as the frequency at which it will fall out of the pass band. For example, a 0.1 dB Chebyshev filter can have its Fo at the frequency at which the response is down > 0.1 dB. The shape of the attenuation curve (as well as the phase and delay curves, which define the time domain response of the filter) will be the same if the ratio of the actual frequency to the cutoff frequency is examined, rather than just the actual frequency itself. Normalizing the filter to 1 rad/s, a simple system for designing and comparing filters can be developed. The filter is then scaled by the cutoff frequency to determine the component values for the actual filter. Q is the “quality factor” of the filter. It is also sometimes given as α where: 1 α= Q This is commonly known as the damping ratio. ξ is sometimes used where: Eq. 5-6 ξ = 2α Eq. 5-7 If Q is > 0.707, there will be some peaking in the filter response. If the Q is < 0.707, roll-off at F0 will be greater; it will have a more gentle slope and will begin sooner. The amount of peaking for a 2-pole low-pass filter versus Q is shown in Figure 5-5. 30 Q = 20 MAGNITUDE − dB 20 10 0 –10 –20 Q = 0.1 –30 –40 –50 0.1 1 10 FREQUENCY − Hz Figure 5-5: Low-pass filter peaking versus Q Rewriting the transfer function H(s) in terms of ω0 and Q: H (s) = H0 ω s2 + 0 s + ω 0 2 Q where H0 is the pass band gain and ω0 = 2π F0. This is now the low-pass prototype that will be used to design the filters. 315 Eq. 5-8 Chapter Five High-Pass Filter Changing the numerator of the transfer equation, H(s), of the low-pass prototype to H0s2 transforms the low-pass filter into a high-pass filter. The response of the high-pass filter is similar in shape to a low-pass, just inverted in frequency. The transfer function of a high-pass filter is then: H (s) = H 0 s2 ω s2 + 0 s + ω 0 2 Q Eq. 5-9 The response of a 2-pole high-pass filter is illustrated in Figure 5-6. 30 Q = 20 MAGNITUDE − dB 20 10 0 –10 Q = 0.1 –20 –30 –40 –50 0.1 1 10 FREQUENCY − Hz Figure 5-6: High-pass filter peaking versus Q Band-Pass Filter Changing the numerator of the low-pass prototype to H0ω02 will convert the filter to a band-pass function. The transfer function of a band-pass filter is then: H (s) = H0 ω02 ω s2 + 0 s + ω 0 2 Q Eq. 5-10 ω0 here is the frequency (F0 = 2 π ω0) at which the gain of the filter peaks. H0 is the circuit gain and is defined: H0 = H Q Eq. 5-11 Q has a particular meaning for the band-pass response. It is the selectivity of the filter. It is defined as: Q= F0 FH − FL where FL and FH are the frequencies where the response is –3 dB from the maximum. 316 Eq. 5-12 Analog Filters The bandwidth (BW) of the filter is described as: BW = FH − FL Eq. 5-13 It can be shown that the resonant frequency (F0) is the geometric mean of FL and FH, which means that F0 will appear halfway between FL and FH on a logarithmic scale. F0 = FH FL Eq. 5-14 Also, note that the skirts of the band-pass response will always be symmetrical around F0 on a logarithmic scale. The response of a band-pass filter to various values of Q are shown in Figure 5-7. 10 Q = 0.1 MA GNITUDE − dB 0 –10 –20 –30 –40 Q = 100 –50 –60 –70 0.1 1 10 FREQUENCY − Hz Figure 5-7: Band-pass filter peaking versus Q A word of caution is appropriate here. Band-pass filters can be defined two different ways. The narrowband case is the classic definition that we have shown above. In some cases, however, if the high and low cutoff frequencies are widely separated, the band-pass filter is constructed of separate high-pass and low-pass sections. Widely separated in this context means separated by at least two octaves (×4 in frequency). This is the wideband case. Bandreject (Notch) Filter By changing the numerator to s2 + ωz2, we convert the filter to a bandreject or notch filter. As in the bandpass case, if the corner frequencies of the bandreject filter are separated by more than an octave (the wideband case), it can be built out of separate low-pass and high-pass sections. The following convention will be adopted: A narrow band bandreject filter will be referred to as a notch filter and the wide band bandreject filter will be referred to as bandreject filter. A notch (or bandreject) transfer function is: H (s) = ( H 0 s2 + ω Z 2 ) ω s2 + 0 s + ω 0 2 Q 317 Eq. 5-15 Chapter Five There are three cases of the notch filter characteristics. These are illustrated in Figure 5-8. The relationship of the pole frequency, ω0, and the zero frequency, ωz, determines if the filter is a standard notch, a low-pass notch or a high-pass notch. LOW-PASS NOTCH A MPL ITUDE − dB Figure 5-8: Standard, low-pass, and high-pass notches STANDARD NOTCH HIGH-PASS NOTCH 0.1 0.3 3.0 1.0 10 FREQUENCY − kHz If the zero frequency is equal to the pole frequency a standard notch exists. In this instance the zero lies on the jω plane where the curve that defines the pole frequency intersects the axis. A low-pass notch occurs when the zero frequency is greater than the pole frequency. In this case, ωz lies outside the curve of the pole frequencies. What this means in a practical sense is that the filter’s response below ωz will be greater than the response above ωz. This results in an elliptical low-pass filter. A high-pass notch filter occurs when the zero frequency is less than the pole frequency. In this case, ωz lies inside the curve of the pole frequencies. What this means in a practical sense is that the filter’s response below ωz will be less than the response above ωz. This results in an elliptical high-pass filter. The variation of the notch width with Q is shown in Figure 5-9. 5 Q = 20 0 –5 MAGNITUDE − dB Figure 5-9: Notch filter width versus frequency for various Q values –10 Q = 0.1 –15 –20 –25 –30 –35 –40 –45 –50 0.1 1 10 FREQUENCY − Hz All-Pass Filter There is another type of filter that leaves the amplitude of the signal intact but introduces phase shift. This type of filter is called an all-pass. The purpose of this filter is to add phase shift (delay) to the response of 318 Analog Filters the circuit. The amplitude of an all-pass is unity for all frequencies. The phase response, however, changes from 0° to 360° as the frequency is swept from 0 to infinity. The purpose of an all-pass filter is to provide phase equalization, typically in pulse circuits. It also has application in single sideband, suppressed carrier (SSB-SC) modulation circuits. The transfer function of an all-pass filter is: ω0 s + ω02 Q H (s) = ω s2 + 0 s + ω 0 2 Q s2 − Eq. 5-16 Note that an allpass transfer function can be synthesized as: H AP = H LP − H BP + H HP = 1 − 2H BP Eq. 5-17 Figure 5-10 compares the various filter types. FILTER TYPE POLE LOCATION X LOW PASS X X BAND PASS X X X NOTCH (BANDREJECT) TRANSFER EQUATION ω02 ω s2 + 0 s + ω 0 2 Q ω02 s Q ω s2 + 0 s + ω 0 2 Q s2 + ω Z 2 ω s2 + 0 s + ω 0 2 Q X s2 X HIGH PASS X ALL PASS X Figure 5-10: Standard second-order filter responses MAGNITUDE 319 s2 + ω0 s + ω02 Q ω0 s + ω02 Q ω s2 + 0 s + ω 0 2 Q s2 − Chapter Five Phase Response As mentioned earlier, a filter will change the phase of the signal as well as the amplitude. The question is, does this make a difference? Fourier analysis indicates a square wave is made up of a fundamental frequency and odd order harmonics. The magnitude and phase responses of the various harmonics are precisely defined. If the magnitude or phase relationships are changed, the summation of the harmonics will not add back together properly to give a square wave. It will instead be distorted, typically showing overshoot and ringing or a slow rise time. This would also hold for any complex waveform. Each pole of a filter will add 45° of phase shift at the corner frequency. The phase will vary from 0° (well below the corner frequency) to 90° (well beyond the corner frequency). The start of the change can be more than a decade away. In multipole filters, each of the poles will add phase shift, so that the total phase shift will be multiplied by the number of poles (180° total shift for a two-pole system, 270° for a three-pole system, and so forth). The phase response of a single pole, low pass filter is: φ (ω ) = − arctan ω ω0 Eq. 5-18 The phase response of a low-pass pole pair is: 1 ω φ (ω ) = − arctan 2 + 4 − α2 α ω 0 1 ω − arctan 2 − 4 − α2 α ω 0 Eq. 5-19 For a single pole high-pass filter the phase response is: φ (ω ) = π ω − arctan 2 ω0 Eq. 5-20 The phase response of a high-pass pole pair is: 1 ω φ (ω ) = π − arctan 2 + 4 − α2 α ω 0 1 ω − arctan 2 − 4 − α2 α ω 0 Eq. 5-21 The phase response of a band-pass filter is: φ (ω ) = 2Qω π − arctan + 4Q 2 − 1 2 ω0 Eq. 5-22 2Qω − arctan − 4Q 2 − 1 ω0 The variation of the phase shift with frequency due to various values of Q is shown in Figure 5-11 (for lowpass, high-pass, band-pass, and all-pass) and in Figure 5-12 (for notch). 320 Analog Filters 0 180 90 0 Q = 20 –40 160 70 –20 –80 140 50 –40 PHA SE − DEGREES Q = 0.1 –120 120 30 –60 10 –80 –160 100 –200 80 –10 –100 Q = 0.1 –240 60 –30 –120 –280 40 –50 –140 Q = 20 –320 20 –70 –160 –360 0 –90 –180 1 L OW P A SS HIGH PASS B A ND PA SS A L L PA SS 0.1 10 FREQUENCY − Hz Figure 5-11: Phase response versus frequency 90 Q=0.1 PHA SE − DEGREES 70 50 30 10 Q=20 Q=20 –10 –30 –50 Q=0.1 –70 –90 0.1 10 1 FREQUENCY − Hz Figure 5-12: Notch filter phase response It is also useful to look at the change of phase with frequency. This is the group delay of the filter. A flat (constant) group delay gives best phase response, but, unfortunately, it also gives the least amplitude discrimination. The group delay of a single low-pass pole is: τ (ω ) = − dφ (ω ) dω = cos2 φ ω0 Eq. 5-23 For the low-pass pole pair it is: τ (ω ) = 2 sin 2 φ sin 2φ − 2ω αω 0 Eq. 5-24 For the single high-pass pole it is: τ (ω ) = − dφ (ω ) dω 321 = sin 2 φ ω0 Eq. 5-25 Chapter Five For the high-pass pole pair it is: 2 sin 2 φ sin 2φ − 2ω αω 0 Eq. 5-26 2Q2 cos2 φ sin 2φ + αω 0 2ω Eq. 5-27 τ (ω ) = And for the band-pass pole pair it is: τ (ω ) = The Effect of Nonlinear Phase A waveform can be represented by a series of frequencies of specific amplitude, frequency and phase relationships. For example, a square wave is: 2 2 2 1 2 F (t ) = A + sin ωt + sin 3ωt + sin 5ωt + sin 7ωt + … 2 π 3π 5π 7π Eq. 5-28 If this waveform were passed through a filter, the amplitude and phase response of the filter to the various frequency components of the waveform could be different. If the phase delays were identical, the waveform would pass through the filter undistorted. If, however, the different components of the waveform were changed due to different amplitude and phase response of the filter to those frequencies, they would no longer add up in the same manner. This would change the shape of the waveform. These distortions would manifest themselves in what we typically call overshoot and ringing of the output. Not all signals will be composed of harmonically related components. An amplitude modulated (AM) signal, for instance, will consist of a carrier and two sidebands at ± the modulation frequency. If the filter does not have the same delay for the various waveform components, then “envelope delay” will occur and the output wave will be distorted. Linear phase shift results in constant group delay since the derivative of a linear function is a constant. 322 SECTION 5-3 Time Domain Response Until now the discussion has been primarily focused on the frequency domain response of filters. The time domain response can also be of concern, particularly under transient conditions. Moving between the time domain and the frequency domain is accomplished by the use of the Fourier and Laplace transforms. This yields a method of evaluating performance of the filter to a nonsinusoidal excitation. The transfer function of a filter is the ratio of the output to input time functions. It can be shown that the impulse response of a filter defines its bandwidth. The time domain response is a practical consideration in many systems, particularly communications, where many modulation schemes use both amplitude and phase information. Impulse Response The impulse function is defined as an infinitely high, infinitely narrow pulse, with an area of unity. This is, of course, impossible to realize in a physical sense. If the impulse width is much less than the rise time of the filter, the resulting response of the filter will give a reasonable approximation actual impulse response of the filter response. The impulse response of a filter, in the time domain, is proportional to the bandwidth of the filter in the frequency domain. The narrower the impulse, the wider the bandwidth of the filter. The pulse amplitude is equal to ωc/π, which is also proportional to the filter bandwidth, the height being taller for wider bandwidths. The pulsewidth is equal to 2π/ωc, which is inversely proportional to bandwidth. It turns out that the product of the amplitude and the bandwidth is a constant. It would be a nontrivial task to calculate the response of a filter without the use of Laplace and Fourier transforms. The Laplace transform converts multiplication and division to addition and subtraction, respectively. This takes equations, which are typically loaded with integration and/or differentiation, and turns them into simple algebraic equations, which are much easier to deal with. The Fourier transform works in the opposite direction. The details of these transforms will not be discussed here. However, some general observations on the relationship of the impulse response to the filter characteristics will be made. It can be shown, as stated, that the impulse response is related to the bandwidth. Therefore, amplitude discrimination (the ability to distinguish between the desired signal from other, out-of-band signals and noise) and time response are inversely proportional. That is to say that the filters with the best amplitude response are the ones with the worst time response. For all-pole filters, the Chebyshev filter gives the best amplitude discrimination, followed by the Butterworth and then the Bessel. If the time domain response were ranked, the Bessel would be best, followed by the Butterworth and then the Chebyshev. Details of the different filter responses will be discussed in the next section. The impulse response also increases with increasing filter order. Higher filter order implies greater bandlimiting, therefore degraded time response. Each section of a multistage filter will have its own impulse response, and the total impulse response is the accumulation of the individual responses. The degradation in 323 Chapter Five the time response can also be related to the fact that as frequency discrimination is increased, the Q of the individual sections tends to increase. The increase in Q increases the overshoot and ringing of the individual sections, which implies longer time response. Step Response The step response of a filter is the integral of the impulse response. Many of the generalities that apply to the impulse response also apply to the step response. The slope of the rise time of the step response is equal to the peak response of the impulse. The product of the bandwidth of the filter and the rise time is a constant. Just as the impulse has a function equal to unity, the step response has a function equal to 1/s. Both of these expressions can be normalized, since they are dimensionless. The step response of a filter is useful in determining the envelope distortion of a modulated signal. The two most important parameters of a filter’s step response are the overshoot and ringing. Overshoot should be minimal for good pulse response. Ringing should decay as fast as possible, so as not to interfere with subsequent pulses. Real life signals typically aren’t made up of impulse pulses or steps, so the transient response curves don’t give a completely accurate estimation of the output. They are, however, a convenient figure of merit so that the transient responses of the various filter types can be compared on an equal footing. Since the calculations of the step and impulse response are mathematically intensive, they are most easily performed by computer. Many CAD (Computer Aided Design) software packages have the ability to calculate these responses. Several of these responses are also collected in the next section. 324 SECTION 5-4 Standard Responses There are many transfer functions to satisfy the attenuation and/or phase requirements of a particular filter. The one chosen will depend on the particular system. The importance of the frequency domain response versus the time domain response must be determined. Also, both of these considerations might be traded off against filter complexity, and thereby cost. Butterworth The Butterworth filter is the best compromise between attenuation and phase response. It has no ripple in the pass band or the stop band, and because of this is sometimes called a maximally flat filter. The Butterworth filter achieves its flatness at the expense of a relatively wide transition region from pass band to stop band, with average transient characteristics. The normalized poles of the Butterworth filter fall on the unit circle (in the s plane). The pole positions are given by: − sin (2K − 1)π + j cos (2K − 1)π 2n 2n K = 1,2....n Eq. 5-29 where K is the pole pair number, and n is the number of poles. The poles are spaced equidistant on the unit circle, which means the angles between the poles are equal. Given the pole locations, ω0, and α (or Q) can be determined. These values can then be used to determine the component values of the filter. The design tables for passive filters use frequency and impedance normalized filters. They are normalized to a frequency of 1 rad/sec and impedance of 1 Ω. These filters can be denormalized to determine actual component values. This allows the comparison of the frequency domain and/or time domain responses of the various filters on equal footing. The Butterworth filter is normalized for a –3 dB response at ωo = 1. The values of the elements of the Butterworth filter are more practical and less critical than many other filter types. The frequency response, group delay, impulse response and step response are shown in Figure 5-15. The pole locations and corresponding ωo and α terms are tabulated in Figure 5-26. Chebyshev The Chebyshev (or Chevyshev, Tschebychev, Tschebyscheff or Tchevysheff, depending on how you translate from Russian) filter has a smaller transition region than the same-order Butterworth filter, at the expense of ripples in its pass band. This filter gets its name because the Chebyshev filter minimizes the height of the maximum ripple, which is the Chebyshev criterion. Chebyshev filters have 0 dB relative attenuation at dc. Odd order filters have an attenuation band that extends from 0 dB to the ripple value. Even order filters have a gain equal to the pass band ripple. The number of cycles of ripple in the pass band is equal to the order of the filter. 325 Chapter Five The poles of the Chebyshev filter can be determined by moving the poles of the Butterworth filter to the right, forming an ellipse. This is accomplished by multiplying the real part of the pole by kr and the imaginary part by kI. The values kr and kI can be computed by: K r = sinh A Eq. 5-30 K I = cosh A Eq. 5-31 1 1 sinh −1 ε n Eq. 5-32 ε = 10 R − 1 Eq. 5-33 R dB 10 Eq. 5-34 R dB = pass band ripple in dB Eq. 5-35 where: A= where n is the filter order and: where: R= where: The Chebyshev filters are typically normalized so that the edge of the ripple band is at ω0 = 1. The 3 dB bandwidth is given by: 1 1 Eq. 5-36 A 3dB = cosh −1 ε n This is shown in Table 1. The frequency response, group delay, impulse response and step response are cataloged in Figures 5-16 to 5-20 on following pages, for various values of pass band ripple (0 .01 dB, 0.1 dB, 0.25 dB, 0.5 dB and 1 dB). The pole locations and corresponding ω0 and α terms for these values of ripple are tabulated in Figures 5-27 to 5-31 on following pages. ORDER 0.01dB 0.1dB 0.25dB 0.5dB 1dB 2 3.30362 1.93432 1.59814 1.38974 1.21763 3 1.87718 1.38899 1.25289 1.16749 1.09487 4 1.46690 1.21310 1.13977 1.09310 1.05300 5 1.29122 1.13472 1.08872 1.05926 1.03381 6 1.19941 1.09293 1.06134 1.04103 1.02344 7 1.14527 1.06800 1.04495 1.03009 1.01721 8 1.11061 1.05193 1.03435 1.02301 1.01316 9 1.08706 1.04095 1.02711 1.01817 1.01040 10 1.07033 1.03313 1.02194 1.01471 1.00842 Table 1: 3dB bandwidth to ripple bandwidth for Chebyshev filters 326 Analog Filters Bessel Butterworth filters have fairly good amplitude and transient behavior. The Chebyshev filters improve on the amplitude response at the expense of transient behavior. The Bessel filter is optimized to obtain better transient response due to a linear phase (i.e., constant delay) in the pass band. This means that there will be relatively poorer frequency response (less amplitude discrimination). The poles of the Bessel filter can be determined by locating all of the poles on a circle and separating their imaginary parts by: 2 Eq. 5-37 n where n is the number of poles. Note that the top and bottom poles are distanced by where the circle crosses the jω axis by: 1 n Eq. 5-38 or half the distance between the other poles. The frequency response, group delay, impulse response and step response for the Bessel filters are cataloged in Figure 5-21. The pole locations and corresponding ωo and α terms for the Bessel filter are tabulated in Figure 5-32. Linear Phase with Equiripple Error The linear phase filter offers linear phase response in the pass band, over a wider range than the Bessel, and superior attenuation far from cutoff. This is accomplished by letting the phase response have ripples, similar to the amplitude ripples of the Chebyshev. As the ripple is increased, the region of constant delay extends further into the stop band. This will also cause the group delay to develop ripples, since it is the derivative of the phase response. The step response will show slightly more overshoot than the Bessel and the impulse response will show a bit more ringing. It is difficult to compute the pole locations of a linear phase filter. Pole locations are taken from the Williams book (see Reference 2), which, in turn, comes from the Zverev book (see Reference 1). The frequency response, group delay, impulse response and step response for linear phase filters of 0.05° ripple and 0.5° ripple are given in Figures 5-22 and 5-23. The pole locations and corresponding ωo and α terms are tabulated in Figures 5-33 and 5-34. Transitional Filters A transitional filter is a compromise between a Gaussian filter, which is similar to a Bessel, and the Chebyshev. A transitional filter has nearly linear phase shift and smooth, monotonic rolloff in the pass band. Above the pass band there is a break point beyond which the attenuation increases dramatically compared to the Bessel, and especially at higher values of n. Two transition filters have been tabulated. These are the Gaussian to 6 dB and Gaussian to 12 dB. The Gaussian to 6 dB filter has better transient response than the Butterworth in the pass band. Beyond the breakpoint, which occurs at ω = 1.5, the roll-off is similar to the Butterworth. The Gaussian to 12 dB filter’s transient response is much better than Butterworth in the pass band. Beyond the 12 dB breakpoint, which occurs at ω = 2, the attenuation is less than the Butterworth. 327 Chapter Five As is the case with the linear phase filters, pole locations for transitional filters do not have a closed form method for computation. Again, pole locations are taken from Williams’s book (see Reference 2). These were derived from iterative techniques. The frequency response, group delay, impulse response and step response for Gaussian to 12 dB and 6 dB are shown in Figures 5-24 and 5-25. The pole locations and corresponding ωo and α terms are tabulated in Figures 5-35 and 5-36. Comparison of All-Pole Responses The responses of several all-pole filters, namely the Bessel, Butterworth and Chebyshev (in this case of 0.5 dB ripple) will now be compared. An 8-pole filter is used as the basis for the comparison. The responses have been normalized for a cutoff of 1 Hz. Comparing Figures 5-13 and 5-14, it is easy to see the trade-offs in the response types. Moving from Bessel through Butterworth to Chebyshev, notice that the amplitude discrimination improves as the transient behavior gets progressively poorer. Figure 5-13: Comparison of amplitude response of Bessel, Butterworth and Chebyshev filters Figure 5-14: Comparison of Step and Impulse Responses of Bessel, Butterworth and Chebyshev Elliptical The previously mentioned filters are all-pole designs, which mean that the zeros of the transfer function (roots of the numerator) are at one of the two extremes of the frequency range (0 or ∞). For a low-pass filter, the zeros are at f = ∞. If finite frequency transfer function zeros are added to poles an Elliptical filter (sometimes referred to as Cauer filters) is created. This filter has a shorter transition region than the Chebyshev filter because it allows ripple in both the stop band and pass band. It is the addition of zeros in the stop 328 Analog Filters band that causes ripple in the stop band but gives a much higher rate of attenuation, the most possible for a given number of poles. There will be some “bounceback” of the stop band response between the zeros. This is the stop band ripple. The Elliptical filter also has degraded time domain response. Since the poles of an elliptical filter are on an ellipse, the time response of the filter resembles that of the Chebyshev. An elliptical filter is defined by the parameters shown in Figure 5-2, those being Amax, the maximum ripple in the pass band, Amin, the minimum attenuation in the stop band, Fc, the cutoff frequency, which is where the frequency response leaves the pass band ripple and FS, the stop band frequency, where the value of Amax is reached. An alternate approach is to define a filter order n, the modulation angle, θ, which defines the rate of attenuation in the transition band, where: 1 θ = sin −1 Eq. 5-39 Fs and ρ which determines the pass band ripple, where: ρ= ε2 1 + ε2 Eq. 5-40 where ε is the ripple factor developed for the Chebyshev response, and the pass band ripple is: ( R dB = −10 log 1 − ρ2 ) Eq. 5-41 Some general observations can be made. For a given filter order n, and θ, Amin increases as the ripple is made larger. Also, as θ approaches 90°, FS approaches FC. This results in extremely short transition region, which means sharp roll-off. This comes at the expense of lower Amin. As a side note, ρ determines the input resistance of a passive elliptical filter, which can then be related to the VSWR (Voltage Standing Wave Ratio). Because of the number of variables in the design of an elliptic filter, it is difficult to provide the type of tables provided for the previous filter types. Several CAD (Computer Aided Design) packages can provide the design values. Alternatively several sources, such as Williams’s (see Reference 2), provide tabulated filter values. These tables classify the filter by C n ρ θ where the C denotes Cauer. Elliptical filters are sometime referred to as Cauer filters after the network theorist Wilhelm Cauer. Maximally Flat Delay With Chebyshev Stop band Bessel type (Bessel, linear phase with equiripple error and transitional) filters give excellent transient behavior, but less than ideal frequency discrimination. Elliptical filters give better frequency discrimination, but degraded transient response. A maximally flat delay with Chebyshev stop band filter takes a Bessel type function and adds transmission zeros. The constant delay properties of the Bessel type filter in the pass band are maintained, and the stop band attenuation is significantly improved. The step response exhibits no overshoot or ringing, and the impulse response is clean, with essentially no oscillatory behavior. Constant group delay properties extend well into the stop band for increasing n. As with the elliptical filter, numeric evaluation is difficult. Williams’s book (see Reference 2) tabulates passive prototypes normalized component values. 329 Chapter Five Inverse Chebyshev The Chebyshev response has ripple in the pass band and a monotonic stop band. The inverse Chebyshev response can be defined that has a monotonic pass band and ripple in the stop band. The inverse Chebyshev has better pass band performance than even the Butterworth. It is also better than the Chebyshev, except very near the cutoff frequency. In the transition band, the inverse Chebyshev has the steepest roll-off. Therefore, the inverse Chebyshev will meet the Amin specification at the lowest frequency of the three. In the stop band there will, however, be response lobes which have a magnitude of: ε2 (1 − ε ) Eq. 5-42 where ε is the ripple factor defined for the Chebyshev case. This means that deep into the stop band, both the Butterworth and Chebyshev will have better attenuation, since they are monotonic in the stop band. In terms of transient performance, the inverse Chebyshev lies midway between the Butterworth and the Chebyshev. The inverse Chebyshev response can be generated in three steps. First take a Chebyshev low-pass filter. Then subtract this response from 1. Finally, invert in frequency by replacing ω with 1/ω. These are by no means all the possible transfer functions, but they do represent the most common. Using the Prototype Response Curves In the following pages, the response curves and the design tables for several of the low-pass prototypes of the all-pole responses will be cataloged. All the curves are normalized to a −3 dB cutoff frequency of 1 Hz. This allows direct comparison of the various responses. In all cases the amplitude response for the 2- through 10-pole cases for the frequency range of 0.1 Hz. to 10 Hz. will be shown. Then a detail of the amplitude response in the 0.1 Hz to 2 Hz. pass band will be shown. The group delay from 0.1 Hz to 10 Hz and the impulse response and step response from 0 seconds to 5 seconds will also be shown. To use these curves to determine the response of real life filters, they must be denormalized. In the case of the amplitude responses, this is accomplished simply by multiplying the frequency axis by the desired cutoff frequency FC. To denormalize the group delay curves, divide the delay axis by 2π FC, and multiply the frequency axis by FC, as before. Denormalize the step response by dividing the time axis by 2π FC. Denormalize the impulse response by dividing the time axis by 2π FC and multiplying the amplitude axis by the same amount. For a high-pass filter, simply invert the frequency axis for the amplitude response. In transforming a low-pass filter into a high-pass (or bandreject) filter, the transient behavior is not preserved. Zverev (see Reference 1) provides a computational method for calculating these responses. In transforming a low-pass into a narrowband band-pass, the 0 Hz axis is moved to the center frequency F0. It stands to reason that the response of the band-pass case around the center frequency would then match the low-pass response around 0 Hz. The frequency response curve of a low-pass filter actually mirrors itself around 0 Hz, although negative frequency generally is not a concern. To denormalize the group delay curve for a band-pass filter, divide the delay axis by πBW, where BW is the 3 dB bandwidth in Hz. Then multiply the frequency axis by BW/2. In general, the delay of the band-pass filter at F0 will be twice the delay of the low-pass prototype with the same bandwidth at 0Hz. This is due to the fact that the low-pass to band-pass transformation results in a filter with order 2n, even though it is typically referred to it as having the same order as the low-pass filter from which it is derived. This approximation holds for narrowband filters. As the bandwidth of the filter is increased, some distortion of the curve occurs. The delay becomes less symmetrical, peaking below F0. 330 Analog Filters The envelope of the response of a band-pass filter resembles the step response of the low-pass prototype. More exactly, it is almost identical to the step response of a low-pass filter having half the bandwidth. To determine the envelope response of the band-pass filter, divide the time axis of the step response of the lowpass prototype by πBW, where BW is the 3 dB bandwidth. The previous discussions of overshoot, ringing, and so forth can now be applied to the carrier envelope. The envelope of the response of a narrowband band-pass filter to a short burst of carrier (that is where the burst width is much less than the rise time of the denormalized step response of the band-pass filter) can be determined by denormalizing the impulse response of the low pass prototype. To do this, multiply the amplitude axis and divide the time axis by πBW, where BW is the 3 dB bandwidth. It is assumed that the carrier frequency is high enough so that many cycles occur during the burst interval. While the group delay, step, and impulse curves cannot be used directly to predict the distortion to the waveform caused by the filter, they are a useful figure of merit when used to compare filters. 331 Chapter Five AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) GROUP DELAY 2.0 DEL AY − s 1.0 A MPL ITUDE 0 1.0 – 4.0 0.1 0.2 0.8 0.4 1.1 0 0.1 2.0 0.4 IMPULSE RESPONSE 4.0 10 STEP RESPONSE 1.2 A MPL ITUDE − V 8.0 4.0 A MPL ITUDE − V 1.1 FREQUENCY − Hz FREQUENCY − Hz 0 –4.0 0.8 0.4 0 0 1 2 TIME − s 3 4 5 0 1 Figure 5-15: Butterworth response 332 3 2 TIME − s 4 5 Analog Filters AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) GROUP DELAY 1.0 5.0 A MPL ITUDE DEL A Y − s 0 – 4.0 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 0.4 IMPULSE RESPONSE 8.0 1.1 4.0 FREQUENCY − Hz 10 STEP RESPONSE A MPL ITUDE − V 1.5 4.0 AMPL ITUDE − V 0 0.1 2.0 0 1.0 0.5 –4.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-16: 0.01 dB Chebyshev response 333 3 4 5 Chapter Five AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) 1.0 GROUP DELAY 5.0 A MPL ITUDE DEL A Y − s 0 – 4.0 0.1 0.2 0.8 1.1 0 2.0 0.4 0.1 IMPULSE RESPONSE 8.0 1.1 4.0 FREQUENCY − Hz 10 STEP RESPONSE 1.5 A MPL ITUDE − V A MPL ITUDE − V 0.4 FREQUENCY − Hz 4.0 1.0 0.5 0 –2.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-17: 0.1 dB Chebyshev response 334 3 4 5 Analog Filters AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) GROUP DELAY 7.0 1.0 0 DEL A Y − s AMPL ITUDE 5.0 – 4.0 0 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 2.0 IMPULSE RESPONSE 8.0 1.1 4.0 FREQUENCY − Hz 10 STEP RESPONSE A MPL ITUDE − V 1.5 4.0 A MPL ITUDE − V 0.4 0.1 1.0 0.5 0 –4.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-18: 0.25 dB Chebyshev response 335 3 4 5 Chapter Five AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) GROUP DELAY 6.0 1.0 5.0 A MPL ITUDE DEL A Y − s 0 – 4.0 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 0 2.0 0.4 0.1 IMPULSE RESPONSE 10 STEP RESPONSE 1.5 A MPL ITUDE − V 4.0 A MPL ITUDE − V 1.1 4.0 FREQUENCY − Hz 2.0 0 1.0 0.5 –2.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-19: 0.5 dB Chebyshev response 336 3 4 5 Analog Filters AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) 5.0 DEL A Y − s A MPL ITUDE 0 – 3.5 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 0 2.0 0.4 0.1 IMPULSE RESPONSE 8.0 1.1 4.0 FREQUENCY − Hz 10 STEP RESPONSE 1.5 A MPL ITUDE − V A MPL ITUDE − V GROUP DELAY 8.0 1.5 4.0 1.0 0.5 0 0 –4.0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-20: 1 dB Chebyshev response 337 3 4 5 Chapter Five AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz 1.0 AMPLITUDE (DETAIL) GROUP DELAY 0.6 –4.0 0.1 DEL A Y − s AMPL ITUDE 0 0.2 0.4 FREQUENCY − Hz 0.8 1.1 IMPULSE RESPONSE 0.4 4.0 0 1.1 FREQUENCY − Hz 4.0 10 4 5 STEP RESPONSE 1.2 A MPL ITUDE − V 8.0 A MPL ITUDE − V 0 0.1 2.0 0.8 0.4 –4.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-21: Bessel response 338 3 Analog Filters AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 8.0 4.0 2.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) 1.0 GROUP DELAY 1.0 DEL A Y − s A MPL ITUDE 0 0 –4.0 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 0.1 2.0 0.4 IMPULSE RESPONSE 10 A MPL ITUDE − V 1.2 4.0 A MPL ITUDE − V 4.0 STEP RESPONSE 8.0 0 –4.0 0 1.1 FREQUENCY − Hz 0.8 0.4 1 2 TIME (s) 3 4 5 0 0 1 2 TIME (s) Figure 5-22: Linear phase response with equiripple error of 0.05° 339 3 4 5 Chapter Five AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) 1.0 GROUP DELAY 1.0 AMPL ITUDE DEL A Y − s 0 –4.0 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 2.0 0 0.1 0.4 IMPULSE RESPONSE 4.0 10 STEP RESPONSE 8.0 A MPL ITUDE − V 1.2 4.0 A MPL ITUDE − V 1.1 FREQUENCY − Hz 0 0.8 0.4 –4.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-23: Linear phase response with equiripple error of 0.5° 340 3 4 5 Analog Filters AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz AMPLITUDE (DETAIL) GROUP DELAY 2.0 1.0 AMPL ITUDE DEL A Y − s 0 –4.0 0.1 0.2 0.8 1.1 0.4 FREQUENCY − Hz 2.0 1.0 0 3.0 0.1 10 3.0 FREQUENCY − Hz IMPULSE RESPONSE STEP RESPONSE 8.0 A MPL ITUDE − V 1.2 4.0 A MPL ITUDE − V 1.0 0.3 0 0.8 0.4 –4.0 0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-24: Gaussian to 12 dB response 341 3 4 5 Chapter Five AMPLITUDE A MPL ITUDE − dB 0 –50 –90 0.4 0.2 0.1 0.8 1.1 4.0 2.0 8.0 10 FREQUENCY − Hz GROUP DELAY AMPLITUDE (DETAIL) 4.0 1.0 DEL A Y − s A MPL ITUDE 0 0 –4.0 0.1 0.2 0.4 FREQUENCY − Hz 0.8 1.1 2.0 0.4 0.1 IMPULSE RESPONSE 4.0 0 1.1 FREQUENCY − Hz 4.0 10 STEP RESPONSE 1.2 A MPL ITUDE − V 8.0 A MPL ITUDE − V 2.0 0.8 0.4 0 –4.0 0 1 2 TIME − s 3 4 5 0 1 2 TIME − s Figure 5-25: Gaussian to 6 dB response 342 3 4 5 Analog Filters Figure 5-26: Butterworth design table Figure 5-27: 0.01dB Chebyshev design table 343 Chapter Five Figure 5-28: 0.1 dB Chebyshev design table Figure 5-29: 0.25 dB Chebyshev design table 344 Analog Filters Figure 5-30: 0.5 dB Chebyshev design table Figure 5-31: 1 dB Chebyshev design table 345 Chapter Five Figure 5-32: Bessel design table Figure 5-33: Linear phase with equiripple error of 0.05° design table 346 Analog Filters Figure 5-34: Linear phase with equiripple error of 0.5° design table Figure 5-35: Gaussian to 12 dB design table 347 Chapter Five Figure 5-36: Gaussian to 6 dB design table 348 SECTION 5-5 Frequency Transformations Until now, only filters using the low pass configuration have been examined. In this section, transforming the low-pass prototype into the other configurations: high pass, band pass, bandreject (notch) and all pass will be discussed. Low Pass to High Pass The low-pass prototype is converted to high-pass filter by scaling by 1/s in the transfer function. In practice, this amounts to capacitors becoming inductors with a value 1/C, and inductors becoming capacitors with a value of 1/L for passive designs. For active designs, resistors become capacitors with a value of 1/R, and capacitors become resistors with a value of 1/C. This applies only to frequency setting resistor, not those only used to set gain. Another way to look at the transformation is to investigate the transformation in the s plane. The complex pole pairs of the low-pass prototype are made up of a real part, α, and an imaginary part, β. The normalized high-pass poles are then given by: α HP = α α 2 + β2 Eq. 5-43 βHP = β α 2 + β2 Eq. 5-44 and: A simple pole, α0, is transformed to: 1 α0 Eq. 5-45 1 ω Z,LP Eq. 5-46 α ω ,HP = Low-pass zeros, ωz,lp, are transformed by: ω Z,HP = In addition, a number of zeros equal to the number of poles are added at the origin. After the normalized low pass prototype poles and zeros are converted to high pass, they are then denormalized in the same way as the low pass, that is, by frequency and impedance. As an example a 3-pole 1dB Chebyshev low-pass filter will be converted to a high-pass filter. 349 Chapter Five From the design tables of the last section: αLP1 = 0.2257 βLP1 = 0.8822 αLP2 = 0.4513 This will transform to: αHP1 = 0.2722 βHP1 = 1.0639 αHP2 = 2.2158 Which then becomes: F01 = 1.0982 α = 0.4958 Q = 2.0173 F02 = 2.2158 A worked out example of this transformation will appear in a later section. A high-pass filter can be considered to be a low-pass filter turned on its side. Instead of a flat response at dc, there is a rising response of n × (20 dB/decade), due to the zeros at the origin, where n is the number of poles. At the corner frequency a response of n × (–20 dB/decade) due to the poles is added to the above rising response. This results in a flat response beyond the corner frequency. Low Pass to Band Pass Transformation to the band pass response is a little more complicated. Band-pass filters can be classified as either wideband or narrowband, depending on the separation of the poles. If the corner frequencies of the band pass are widely separated (by more than two octaves), the filter is wideband and is made up of separate low pass and high pass sections, which will be cascaded. The assumption made is that with the widely separated poles, interaction between them is minimal. This condition does not hold in the case of a narrowband band-pass filter, where the separation is less than two octaves. We will be covering the narrowband case in this discussion. As in the high pass transformation, start with the complex pole pairs of the low-pass prototype, α and β. The pole pairs are known to be complex conjugates. This implies symmetry around dc (0 Hz.). The process of transformation to the band pass case is one of mirroring the response around dc of the low-pass prototype to the same response around the new center frequency F0. This clearly implies that the number of poles and zeros is doubled when the band pass transformation is done. As in the low pass case, the poles and zeros below the real axis are ignored. So an nth order low-pass prototype transforms into an nth order band pass, even though the filter order will be 2 n. An nth order bandpass filter will consist of n sections, versus n/2 sections for the low-pass prototype. It may be convenient to think of the response as n poles up and n poles down. The value of QBP is determined by: Q BP = F0 BW where BW is the bandwidth at some level, typically –3 dB. 350 Eq. 5-47 Analog Filters A transformation algorithm was defined by Geffe (Reference 16) for converting low-pass poles into equivalent band-pass poles. Given the pole locations of the low-pass prototype: −α ± jβ Eq. 5-48 and the values of F0 and QBP, the following calculations will result in two sets of values for Q and frequencies, FH and FL, which define a pair of band-pass filter sections. C = α 2 + β2 2α Q BP Eq. 5-50 C +4 Q BP 2 Eq. 5-51 D= E= Eq. 5-49 G = E 2 − 4 D2 Q= Eq. 5-52 E+G 2 D2 Eq. 5-53 αQ Q BP Eq. 5-54 Observe that the Q of each section will be the same. The pole frequencies are determined by: M= W = M + M2 − 1 FBP1 = F0 W FBP2 = W F0 Eq. 5-55 Eq. 5-56 Eq. 5-57 Each pole pair transformation will also result in two zeros that will be located at the origin. A normalized low-pass real pole with a magnitude of α0 is transformed into a band pass section where: Q= Q BP α0 and the frequency is F0. Each single pole transformation will also result in a zero at the origin. 351 Eq. 5-58 Chapter Five Elliptical function low-pass prototypes contain zeros as well as poles. In transforming the filter the zeros must be transformed as well. Given the low-pass zeros at ± jωZ, the band pass zeros are obtained as follows: αQ M= Eq. 5-59 Q BP W = M + M2 − 1 FBP1 = Eq. 5-60 F0 W Eq. 5-61 FBP2 = W F0 Eq. 5-62 Since the gain of a band-pass filter peaks at FBP instead of F0, an adjustment in the amplitude function is required to normalize the response of the aggregate filter. The gain of the individual filter section is given by: F F A R = A 0 1 + Q 2 0 − BP FBP F0 2 Where: A0 = AR = F0 = FBP = gain a filter center frequency filter section gain at resonance filter center frequency filter section resonant frequency. Again using a 3 pole 1dB Chebychev as an example: αLP1 = 0.2257 βLP1 = 0.8822 αLP2 = 0.4513 A 3 dB bandwidth of 0.5 Hz. with a center frequency of 1 Hz. is arbitrarily assigned. Then: QBP = 2 Going through the calculations for the pole pair the intermediate results are: C = 0.829217 E = 4.207034 M = 1.01894 D = 0.2257 G = 4.098611 W = 1.214489 FBP1 = 0.823391 FBP2 = 1.214489 and: QBP1 = QBP2 = 9.029157 And for the single pole: FBP3 = 1 QBP3 = 4.431642 Again a full example will be worked out in a later section. 352 Eq. 5-63 Analog Filters Low Pass to Bandreject (Notch) As in the band pass case, a bandreject filter can be either wideband or narrowband, depending on whether or not the poles are separated by two octaves or more. To avoid confusion, the following convention will be adopted. If the filter is wideband, it will be referred to as a bandreject filter. A narrowband filter will be referred to as a notch filter. One way to build a notch filter is to construct it as a band-pass filter whose output is subtracted from the input (1 – BP). Another way is with cascaded low pass and high pass sections, especially for the bandreject (wideband) case. In this case, the sections are in parallel, and the output is the difference. Just as the band pass case is a direct transformation of the low-pass prototype, where dc is transformed to F0, the notch filter can be first transformed to the high-pass case, and then dc, which is now a zero, is transformed to F0. A more general approach would be to convert the poles directly. A notch transformation results in two pairs of complex poles and a pair of second order imaginary zeros from each low-pass pole pair. First, the value of QBR is determined by: Q BR = F0 BW Eq. 5-64 where BW is the bandwidth at –3 dB. Given the pole locations of the low-pass prototype −α ± jβ Eq. 5-65 and the values of F0 and QBR, the following calculations will result in two sets of values for Q and frequencies, FH and FL, which define a pair of notch filter sections. C = α 2 + β2 D= E= α Q BR C β Q BR C F = E 2 − 4 D2 + 4 G= F F2 + + D2 E 2 2 4 H= K= 1 2 DE G (D + H )2 + (E + G )2 Q= K D+H 353 Eq. 5-66 Eq. 5-67 Eq. 5-68 Eq. 5-69 Eq. 5-70 Eq. 5-71 Eq. 5-72 Eq. 5-73 Chapter Five The pole frequencies are given by: FBRI = F0 K Eq. 5-74 FBR2 = K F0 Eq. 5-75 FZ = F0 Eq. 5-76 F0 = FBRI ∗ FBR2 Eq. 5-77 where F0 is the notch frequency and the geometric mean of FBR1 and FBR2. A simple real pole, α0, transforms to a single section having a Q given by: Q = Q BR α 0 Eq. 5-78 with a frequency FBR = F0. There will also be transmission zero at F0. In some instances, such as the elimination of the power line frequency (hum) from low level sensor measurements, a notch filter for a specific frequency may be designed. Assuming that an attenuation of A dB is required over a bandwidth of B, the required Q is determined by: ω0 Q= Eq. 5-79 B 10.1 A − 1 A 3-pole 1 dB Chebychev is again used as an example: αLP1 = 0.2257 βLP1 = 0.8822 αLP2 = 0.4513 A 3 dB bandwidth of 0.1 Hz with a center frequency of 1 Hz is arbitrarily assigned. Then: QBR = 10 Going through the calculations for the pole pair yields the intermediate results: C = 0.829217 D = 0.027218 E = 0.106389 F = 4.079171 G = 2.019696 H = 0.001434 K = 1.063139 and: FBR1 = 0.94061 FBR2 = 1.063139 QBR1 = QBR2 = 37.10499 And for the single pole: FBP3 = 1 QBP3 = 4.431642 Once again a full example will be worked out in a later section. Low Pass to All Pass The transformation from low pass to all pass involves adding a zero in the right-hand side of the s plane corresponding to each pole in the left-hand side. 354 Analog Filters In general, however, the all-pass filter is usually not designed in this manner. The main purpose of the allpass filter is to equalize the delay of another filter. Many modulation schemes in communications use some form or another of quadrature modulation, which processes both the amplitude and phase of the signal. All-pass filters add delay to flatten the delay curve without changing the amplitude. In most cases a closed form of the equalizer is not available. Instead the amplitude filter is designed and the delay calculated or measured. Then graphical means or computer programs are used to figure out the required sections of equalization. Each section of the equalizer gives twice the delay of the low-pass prototype due to the interaction of the zeros. A rough estimate of the required number of sections is given by: n = 2 ∆BW ∆T + 1 where ∆BW is the bandwidth of interest in hertz and ∆T is the delay distortion over ∆BW in seconds. 355 This page intentionally left blank SECTION 5-6 Filter Realizations Now that it has been decided what to build, it must be decided how to build it. That means it is necessary to decide which of the filter topologies to use. Filter design is a two-step process where it is determined what is to be built (the filter transfer function) and then how to build it (the topology used for the circuit). In general, filters are built from one-pole sections for real poles, and two-pole sections for pole pairs. While a filter can be built from three-pole, or higher order sections, the interaction between the sections increases, and therefore, component sensitivities go up. It is better to use buffers to isolate the various sections. In addition, it is assumed that all filter sections are driven from a low impedance source. Any source impedance can be modeled as being in series with the filter input. In all of the design equation figures the following convention will be used: H = circuit gain in the passband or at resonance F0 = cutoff or resonant frequency in Hertz ω0 = cutoff or resonant frequency in radians/sec Q = circuit “quality factor.” Indicates circuit peaking α = 1/Q = damping ratio It is unfortunate that the symbol α is used for damping ratio. It is not the same as the α that is used to denote pole locations (α ± jβ). The same issue occurs for Q. It is used for the circuit quality factor and also the component quality factor, which are not the same thing. The circuit Q is the amount of peaking in the circuit. This is a function of the angle of the pole to the origin in the s plane. The component Q is the amount of loss in what should be lossless reactances. These losses are the parasitics of the components; dissipation factor, leakage resistance, ESR (equivalent series resistance), and so forth, in capacitors and series resistance and parasitic capacitances in inductors. 357 Chapter Five Single-Pole RC The simplest filter building block is the passive RC section. The single pole can be either low pass or high pass. Odd order filters will have a single pole section. The basic form of the low pass RC section is shown in Figure 5-37(A). It is assumed that the load impedance is high (> ×10), so that there is no loading of the circuit. The load will be in parallel with the shunt arm of the filter. If this is not the case, the section will have to be buffered with an op amp. A low-pass filter can be transformed to a high-pass filter by exchanging the resistor and the capacitor. The basic form of the high-pass filter is shown in Figure 5-37(B). Again it is assumed that load impedance is high. (A) LOW PASS (B) HIGH PASS Figure 5-37: Single pole sections The pole can also be incorporated into an amplifier circuit. Figure 5-38(A) shows an amplifier circuit with a capacitor in the feedback loop. This forms a low-pass filter since as frequency is increased, the effective feedback impedance decreases, which causes the gain to decrease. Figure 5-38(B) shows a capacitor in series with the input resistor. This causes the signal to be blocked at dc. As the frequency is increased from dc, the impedance of the capacitor decreases and the gain of the circuit increases. This is a high-pass filter. The design equations for single pole filters appear in Figure 5-66. − − + + (A) LOW PASS (B) HIGH PASS Figure 5-38: Single pole active filter blocks 358 Analog Filters Passive LC Section While not strictly a function that uses op amps, passive filters form the basis of several active filters topologies and are included here for completeness. As in active filters, passive filters are built up of individual subsections. Figure 5-39 shows low-pass filter sections. The full section is the basic two-pole section. Odd order filters use one half section which is a single pole section. The m-derived sections, shown in Figure 5-40, are used in designs requiring transmission zeros as well as poles. (A) HALF SECTION (B) FULL SECTION Figure 5-39: Passive filter blocks (low pass) (A) HALF SECTION (B) FULL SECTION Figure 5-40: Passive filter blocks (low pass m-derived) 359 Chapter Five A low-pass filter can be transformed into a high-pass (see Figures 5-41 and 5-42) by simply replacing capacitors with inductors with reciprocal values and vise versa so: L HP = 1 CLP Eq. 5-80 CHP = 1 L LP Eq. 5-81 and (B) FULL SECTION (A) HALF SECTION Figure 5-41: Passive filter blocks (high pass) (A) HALF SECTION (B) FULL SECTION Figure 5-42: Passive filter blocks (high pass m-derived) Transmission zeros are also reciprocated in the transformation so: ω Z,HP = 1 ω Z,LP Eq. 5-82 The low-pass prototype is transformed to band pass and bandreject filters as well by using the table in Figure 5-43. For a passive filter to operate, the source and load impedances must be specified. One issue with designing passive filters is that in multipole filters each section is the load for the preceding sections and also the source impedance for subsequent sections, so component interaction is a major concern. Because of this, designers typically make use of tables, such as in Williams’s book (Reference 2). 360 Analog Filters LOW-PASS BRANCH CIRCUIT VALUES BAND-PASS CONFIGURATION L C C= 1 ω02 L L= 1 ω02 C C L L C La Ca = 1 ω02 La Lb = 1 ω02 Cb Ca La Lb Cb L1 Cb C2 L1 C2 C1 L2 HIGH-PASS BRANCH BANDREJECT CONFIGURATION C1 = 1 ω02 L1 L2 = 1 ω02 C2 CIRCUIT VALUES Figure 5-43: Low pass → band pass and high pass → bandreject transformation Integrator Any time a frequency-dependent impedance is put in a feedback network the inverse frequency response is obtained. For example, if a capacitor, which has a frequency dependent impedance that decreases with increasing frequency, is put in the feedback network of an op amp, an integrator is formed, as in Figure 5-44. The integrator has high gain (i.e., the open-loop gain of the op amp) at dc. An integrator can also be thought of as a low-pass filter with a cutoff frequency of 0 Hz. − + Figure 5-44: Integrator 361 Chapter Five General Impedance Converter Figure 5-45 is the block diagram of a general impedance converter. The impedance of this circuit is: Z= Z1 Z3 Z5 Z2 Z4 Eq. 5-83 By substituting one or two capacitors into appropriate locations (the other locations being resistors), several impedances can be synthesized (see Reference 25). One limitation of this configuration is that the lower end of the structure must be grounded. Active Inductor Substituting a capacitor for Z4 and resistors for Z1, Z2, Z3, and Z5 in the GIC results in an impedance given by: Z11 = sC R1 R3 R5 R2 Eq. 5-84 By inspection it can be shown that this is an inductor with a value of: L= C R1 R3 R5 R2 Eq. 5-85 This is just one way to simulate an inductor as shown in Figure 5-46. Z1 R1 Z2 R2 + + - - − − + + Z3 R3 L= C R1 R3 R5 R2 Z4 C Z5 R5 Figure 5-46: Active inductor Figure 5-45: General impedance converter 362 Analog Filters Frequency-Dependent Negative Resistor (FDNR) By substituting capacitors for two of the Z1, Z3, or Z5 elements, a structure known as a frequencydependant negative resistance (FDNR) is generated. The impedance of this structure is Z11 = sC2 R2 R4 R5 Eq. 5-86 This impedance, which is called a D element, has the value: D = C2 R4 Eq. 5-87 C1 = C2 and R2 = R5 Eq. 5-88 assuming The three possible versions of the FDNR are shown in Figure 5-47. + + − − − + − + + (A) + − − (B) (C) Figure 5-47: Frequency-dependent negative resistor blocks There is theoretically no difference in these three blocks, and so they should be interchangeable. In practice, though, there may be some differences. Circuit (a) is sometimes preferred because it is the only block to provide a return path for the amplifier bias currents. For the FDNR filter (see Reference 24), the passive realization of the filter is used as the basis of the design. As in the passive filter, the FDNR filter must then be denormalized for frequency and impedance. This is typically done before the conversion by 1/s. First take the denormalized passive prototype filter and transform the elements by 1/s. This means that inductors, whose impedance is equal to sL, transform into a resistor with an impedance of L. A resistor of value R becomes a capacitor with an impedance of R/s; and a capacitor of impedance 1/sC transforms into a frequency dependent resistor, D, with an impedance of 1/s2C. The transformations involved with the FDNR configuration and the GIC implementation of the D element 363 Chapter Five are shown in Figure 5-48. We can apply this transformation to low-pass, high-pass, band-pass, or notch filters, remembering that the FDNR block must be restricted to shunt arms. L 1 C R 1 R C 1 1 C 1 Figure 5-48: 1/s transformation A worked out example of the FDNR filter is included in the next section. A perceived advantage of the FDNR filter in some circles is that there are no op amps in the direct signal path, which can add noise and/or distortion, however small, to the signal. It is also relatively insensitive to component variation. These advantages of the FDNR come at the expense of an increase in the number of components required. Sallen-Key The Sallen-Key configuration, also known as a voltage control voltage source (VCVS), was first introduced in 1955 by R. P. Sallen and E. L. Key of MIT’s Lincoln Labs (see Reference 14). It is one of the most widely used filter topologies and is shown in Figure 5-49. One reason for this popularity is that this configuration shows the least dependence of filter performance on the performance of the op amp. This is R1 Figure 5-49: Sallen-Key low-pass filter C1 OUT IN R2 + − C2 R3 R4 364 Analog Filters due to the fact that the op amp is configured as an amplifier, as opposed to an integrator, which minimizes the gain-bandwidth requirements of the op amp. This infers that for a given op amp, it is possible to design a higher frequency filter than with other topologies since the op amp gain bandwidth product will not limit the performance of the filter as it would if it were configured as an integrator. The signal phase through the filter is maintained (noninverting configuration). Another advantage of this configuration is that the ratio of the largest resistor value to the smallest resistor value and the ratio of the largest capacitor value to the smallest capacitor value (component spread) are low, which is good for manufacturability. The frequency and Q terms are somewhat independent, but they are very sensitive to the gain parameter. The Sallen-Key is very Q-sensitive to element values, especially for high Q sections. The design equations for the Sallen-Key low pass are shown in Figure 5-67. There is a special case of the Sallen-Key low-pass filter. If the gain is set to 2, the capacitor values, as well as the resistor values, will be the same. While the Sallen-Key filter is widely used, a serious drawback is that the filter is not easily tuned, due to interaction of the component values on F0 and Q. To transform the low pass into the high pass we simply exchange the capacitors and the resistors in the frequency determining network (i.e., not the op amp gain resistors). This is shown in Figure 5-50. The comments regarding sensitivity of the filter given above for the low pass case apply to the high pass case as well. The design equations for the Sallen-Key high pass are shown in Figure 5-68. The band-pass case of the Sallen–Key filter has a limitation (see Figure 5-51). The value of Q will determine the gain of the filter, i.e., it can not be set independently, as in the low pass or high pass cases. The design equations for the Sallen-Key band-pass are shown in Figure 5-69. A Sallen-Key notch filter may also be constructed, but it has a large number of undesirable characteristics. The resonant frequency, or the notch frequency, cannot be adjusted easily due to component interaction. As in the band pass case, the section gain is fixed by the other design parameters, and there is a wide spread in component values, especially capacitors. Because of this, and the availability of easier to use circuits, it is not covered here. C1 R1 IN OUT OUT R2 IN C2 R1 + + − C1 − C2 R3 R2 R4 R3 R4 R5 Figure 5-50: Sallen-Key high-pass filter Figure 5-51: Sallen-Key band-pass filter 365 Chapter Five Multiple Feedback The multiple feedback filter uses an op amp as an integrator as shown in Figure 5-52. Therefore, the dependence of the transfer function on the op amp parameters is greater than in the Sallen-Key realization. It is hard to generate high Q, high frequency sections due to the limitations of the open-loop gain of the op amp. A rule of thumb is that the open-loop gain of the op amp should be at least 20 dB (×10) above the amplitude response at the resonant (or cutoff) frequency, including the peaking caused by the Q of the filter. The peaking due to Q will cause an amplitude, A0: A0 = H Q Eq. 5-89 where H is the gain of the circuit. The multiple feedback filter will invert the phase of the signal. This is equivalent to adding the resulting 180° phase shift to the phase shift of the filter itself. The maximum to minimum component value ratios is higher in the multiple feedback case than in the Sallen-Key realization. The design equations for the multiple feedback low pass are given in Figure 5-70. OUT R4 C5 R1 IN − R3 + C2 Figure 5-52: Multiple feedback low pass Comments made about the multiple feedback low pass case apply to the high-pass case as well (see Figure 5-53). Note that resistors and capacitors are again swapped to convert the low pass case to the high pass case. The design equations for the multiple feedback high pass are given in Figure 5-71. The design equations for the multiple feedback band pass case (see Figure 5-54) are given in Figure 5-72. OUT OUT C4 IN C1 R5 C4 R5 IN C3 C3 R1 − − + + R2 R2 Figure 5-53: Multiple feedback high pass Figure 5-54: Multiple feedback band pass 366 Analog Filters This circuit is widely used in low Q (< 20) applications. It allows some tuning of the resonant frequency, F0, by making R2 variable. Q can be adjusted (with R5) as well, but this will also change F0. Tuning of F0 can be accomplished by monitoring the output of the filter with the horizontal channel of an oscilloscope, with the input to the filter connected to the vertical channel. The display will be a Lissajous pattern. This pattern will be an ellipse that will collapse to a straight line at resonance, since the phase shift will be 180°. Output could also be adjusted for maximum output, which will also occur at resonance, but this is usually not as precise, especially at lower values of Q where there is a less pronounced peak. State Variable The state-variable realization (see Reference 11) is shown in Figure 5-55, along with the design equations in Figure 5-73. This configuration offers the most precise implementation, at the expense of many more circuit elements. All three major parameters (gain, Q and ω0) can be adjusted independently, and low pass, high pass, and band pass outputs are available simultaneously. Note that the low pass and high pass outputs are inverted in phase while the band pass output maintains the phase. The gain of each of the outputs of the filter is also independently variable. With an added amplifier section summing the low pass and high pass sections the notch function can also be synthesized. By changing the ratio of the summed sections, low pass notch, standard notch and high pass notch functions can be realized. A standard notch may also be realized by subtracting the band pass output from the input with the added op amp section. An all-pass filter may also be built with the four amplifier configuration by subtracting the band pass output from the input. In this instance, the band pass gain must equal 2. IN R1 LP OUT R2 R3 C1 R4 C2 R5 − − − + + + BP OUT R6 HP OUT R7 Figure 5-55: State-variable filter Since all parameters of the state-variable filter can be adjusted independently, component spread can be minimized. Also, variations due to temperature and component tolerances are minimized. The op amps used in the integrator sections will have the same limitations on op amp gain-bandwidth as described in the multiple feedback section. Tuning the resonant frequency of a state-variable filter is accomplished by varying R4 and R5. While it is not necessary to tune both, if varying over a wide range it is generally preferable. Holding R1 constant, tuning R2 sets the low pass gain and tuning R3 sets the high-pass gain. Band pass gain and Q are set by the ratio of R6 and R7. 367 Chapter Five Since the parameters of a state variable filter are independent and tunable, it is easy to add electronic control of frequency, Q and ω0. This adjustment is accomplished by using an analog multiplier, multiplying DACs (MDACs) or digital pots, as shown in one of the examples in a later section. For the integrator sections adding the analog multiplier or MDAC effectively increases the time constant by dividing the voltage driving the resistor, which, in turn, provides the charging current for the integrator capacitor. This in effect raises the resistance and, in turn, the time constant. The Q and gain can be varied by changing the ratio of the various feedback paths. A digital pot will accomplish the same feat in a more direct manner, by directly changing the resistance value. The resultant tunable filter offers a great deal of utility in measurement and control circuitry. A worked out example is given in Section 8 of this chapter. Biquadratic (Biquad) A close cousin of the state variable filter is the biquad as shown in Figure 5-56. The name of this circuit was first used by J. Tow in 1968 (Reference 11) and later by L. C. Thomas in 1971 (see Reference 12). The name derives from the fact that the transfer function is a quadratic function in both the numerator and the denominator. Hence the transfer function is a biquadratic function. This circuit is a slight rearrangement of the state variable circuit. One significant difference is that there is not a separate high pass output. The band pass output inverts the phase. There are two low pass outputs, one in phase and one out of phase. With the addition of a fourth amplifier section, high pass, notch (low-pass, standard and high-pass) and all-pass filters can be realized. The design equations for the biquad are given in Figure 5-74. Referring to Figure 5-74, the all-pass case of the biquad, R8 = R9/2 and R7 = R9. This is required to make the terms in the transfer function line up correctly. For the high pass output, the input, band pass and second low pass outputs are summed. In this case the constraints are that R1 = R2 = R3 and R7 = R8 = R9. Like the state variable, the biquad filter is tunable. Adjusting R3 will adjust the Q. Adjusting R4 will set the resonant frequency. Adjusting R1 will set the gain. Frequency would generally be adjusted first followed by Q and then gain. Setting the parameters in this manner minimizes the effects of component value interaction. R2 R3 C2 R4 R5 R6 C1 − + + − LP OUT (OUT OF PHASE) LP OUT (IN PHASE) + R1 − IN BP OUT Figure 5-56: Biquad filter 368 Analog Filters Dual Amplifier Band Pass (DAPB) The Dual Amplifier band-pass filter structure is useful in designs requiring high Qs and high frequencies. Its component sensitivity is small, and the element spread is low. A useful feature of this circuit is that the Q and resonant frequency can be adjusted more or less independently. Referring to Figure 5-57, the resonant frequency can be adjusted by R2. R1 can then be adjusted for Q. In this topology it is useful to use dual op amps. The match of the two op amps will lower the sensitivity of Q to the amplifier parameters. It should be noted that the DABP has a gain of 2 at resonance. If lower gain is required, resistor R1 may be split to form a voltage divider. This is reflected in the addendum to the design equations of the DABP, Figure 5-75. OUT + R4 − R5 C R3 R2 IN − R1 + C Figure 5-57: Dual amplifier band-pass filter 369 Chapter Five Twin-T Notch The Twin T is widely used as a general-purpose notch circuit as shown in Figure 5-58. The passive implementation of the twin T (i.e., with no feedback) has a major shortcoming of having a Q that is fixed at 0.25. This issue can be rectified with the application of positive feedback to the reference node. The amount of the signal feedback, set by the R4/R5 ratio, will determine the value of Q of the circuit, which, in turn, determines the notch depth. For maximum notch depth, the resistors R4 and R5 and the associated op amp can be eliminated. In this case, the junction of C3 and R3 will be directly connected to the output. Tuning is not easily accomplished. Using standard 1% components a 60 dB notch is as good as can be expected, with 40 dB–50 dB being more typical. The design equations for the Twin T are given in Figure 5-76. IN R1 R2 OUT + − C3 R4 + − R3 R5 C1 C2 Figure 5-58: Twin-T notch filter Bainter Notch A simple notch filter is the Bainter circuit (see Reference 21). It is composed of simple circuit blocks with two feedback loops as shown in Figure 5-59. Also, the component sensitivity is very low. This circuit has several interesting properties. The Q of the notch is not based on component matching as it is in every other implementation, but is instead only dependant on the gain of the amplifiers. Therefore, the R4 NOTCH OUT C1 R1 R2 R3 R5 − + + − − + IN C2 R7 R8 R6 Figure 5-59: Bainter notch filter 370 Analog Filters notch depth will not drift with temperature, aging, and other environmental factors. The notch frequency may shift, but not the depth. Amplifier open loop gain of 104 will yield a Qz of > 200. It is capable of orthogonal tuning with minimal interaction. R6 tunes Q and R1 tunes ωZ. Varying R3 sets the ratio of ω0/ωZ produces low pass notch (R4 > R3), notch (R4 = R3) or high pass notch (R4 < R3). The design equations of the Bainter circuit are given in Figure 5-77. Boctor Notch The Boctor circuits (see References 22, 23), while moderately complicated, uses only one op amp. Due to the number of components, there is a great deal of latitude in component selection. These circuits also offer low sensitivity and the ability to tune the various parameters more or less independently. There are two forms, a low pass notch (Figure 5-60) and a high-pass notch (Figure 5-61). For the low pass case, the preferred order of adjustment is to tune ω0 with R4, then Q0 with R2, next Qz with R3 and finally ωz with R1. R1 R2 R4 R4 R5 OUT C2 C1 R6 C2 R2 IN − IN + C1 − OUT + R1 R3 R3 R5 R6 Figure 5-60: Boctor low-pass notch filter Figure 5-61: Boctor high-pass filter In order for the components to be realizable we must define a variable, k1, such that: ω02 < k1 < 1 ωZ2 Eq. 5-90 The design equations are given in Figure 5-78 for the low pass case and in Figure 5-79 for the high pass case. In the high-pass case circuit gain is require and it applies only when 1 Q< ω 2 1 − Z2 ω0 Eq. 5-91 but a high pass notch can be realized with one amplifier and only two capacitors, which can be the same value. The pole and zero frequencies are completely in