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Analysis and Design of Analog Integrated Circuits.pdf
Copyright
Preface
Chapter 1: Models for Integrated-Circuit Active Devices
Introduction
Depletion Region of a pn Junction
Depletion-Region Capacitance
Junction Breakdown
Large-Signal Behavior of Bipolar Transistors
Large-Signal Models in the Forward-Active Region
Effects of Collector Voltage on Large-Signal Characteristics in the Forward-Active Region
Saturation and Inverse-Active Regions
Transistor Breakdown Voltages
Dependence of Transistor Current Gain βF on Operating Conditions
Small-Signal Models of Bipolar Transistors
Transconductance
Base-Charging Capacitance
Input Resistance
Output Resistance
Basic Small-Signal Model of the Bipolar Transistor
Collector-Base Resistance
Parasitic Elements in the Small-Signal Model
Specification of Transistor Frequency Response
Large-Signal Behavior of Metal-Oxide-Semiconductor Field-Effect Transistors
Transfer Characteristics of MOS Devices
Comparison of Operating Regions of Bipolar and MOS Transistors
Decomposition of Gate-Source Voltage
Threshold Temperature Dependence
MOS Device Voltage Limitations
Small-Signal Models of MOS Transistors
Transconductance
Intrinsic Gate-Source and Gate-Drain Capacitance
Input Resistance
Output Resistance
Basic Small-Signal Model of the MOS Transistor
Body Transconductance
Parasitic Elements in the Small-Signal Model
MOS Transistor Frequency Response
Short-Channel Effects in MOS Transistors
Velocity Saturation from the Horizontal Field
Transconductance and Transition Frequency
Mobility Degradation from the Vertical Field
Weak Inversion in MOS Transistors
Drain Current in Weak Inversion
Transconductance and Transition Frequency in Weak Inversion
Substrate Current Flow in MOS Transistors
Summary of Active-Device Parameters
Chapter 2: Bipolar, MOS, and BiCMOS Integrated-Circuit Technology
Introduction
Basic Processes in Integrated-Circuit Fabrication
Electrical Resistivity of Silicon
Solid-State Diffusion
Electrical Properties of Diffused Layers
Photolithography
Epitaxial Growth
Ion Implantation
Local Oxidation
Polysilicon Deposition
High-Voltage Bipolar Integrated-Circuit Fabrication
Advanced Bipolar Integrated-Circuit Fabrication
Active Devices in Bipolar Analog Integrated Circuits
Integrated-Circuit npn Transistors
Integrated-Circuit pnp Transistors
Passive Components in Bipolar Integrated Circuits
Diffused Resistors
Epitaxial and Epitaxial Pinch Resistors
Integrated-Circuit Capacitors
Zener Diodes
Junction Diodes
Modifications to the Basic Bipolar Process
Dielectric Isolation
Compatible Processing for High-Performance Active Devices
High-Performance Passive Components
MOS Integrated-Circuit Fabrication
Active Devices in MOS Integrated Circuits
n-Channel Transistors
p-Channel Transistors
Depletion Devices
Bipolar Transistors
Passive Components in MOS Technology
Resistors
Capacitors in MOS Technology
Latchup in CMOS Technology
BiCMOS Technology
Heterojunction Bipolar Transistors
Interconnect Delay
Economics of Integrated-Circuit Fabrication
Yield Considerations in Integrated-Circuit Fabrication
Cost Considerations in Integrated-Circuit Fabrication
SPICE Model-Parameter Files
Chapter 3: Single-Transistor and Multiple-Transistor Amplifiers
Device Model Selection for Approximate Analysis of Analog Circuits
Two-Port Modeling of Amplifiers
Basic Single-Transistor Amplifier Stages
Common-Emitter Configuration
Common-Source Configuration
Common-Base Configuration
Common-Gate Configuration
Common-Base and Common-Gate Configurations with Finite r0
Common-Base and Common-Gate Input Resistance
Common-Base and Common-Gate Output Resistance
Common-Collector Configuration (Emitter Follower)
Common-Drain Configuration (Source Follower)
Common-Emitter Amplifier with Emitter Degeneration
Common-Source Amplifier with Source Degeneration
Multiple-Transistor Amplifier Stages
The CC-CE, CC-CC, and Darlington Configurations
The Cascode Configuration
The Bipolar Cascode
The MOS Cascode
The Active Cascode
The Super Source Follower
Differential Pairs
The dc Transfer Characteristic of an Emitter-Coupled Pair
The dc Transfer Characteristic with Emitter Degeneration
The dc Transfer Characteristic of a Source-Coupled Pair
Introduction to the Small-Signal Analysis of Differential Amplifiers
Small-Signal Characteristics of Balanced Differential Amplifiers
Device Mismatch Effects in Differential Amplifiers
Input Offset Voltage and Current
Input Offset Voltage of the Emitter-Coupled Pair
Offset Voltage of the Emitter-Coupled Pair: Approximate Analysis
Offset Voltage Drift in the Emitter-Coupled Pair
Input Offset Current of the Emitter-Coupled Pair
Input Offset Voltage of the Source-Coupled Pair
Offset Voltage of the Source-Coupled Pair: Approximate Analysis
Offset Voltage Drift in the Source-Coupled Pair
Small-Signal Characteristics of Unbalanced Differential Amplifiers
Elementary Statistics and the Gaussian Distribution
Chapter 4: Current Mirrors, Active Loads, and References
Introduction
Current Mirrors
General Properties
Simple Current Mirror
Bipolar
MOS
Simple Current Mirror with Beta Helper
Bipolar
MOS
Simple Current Mirror with Degeneration
Bipolar
MOS
Cascode Current Mirror
Bipolar
MOS
Wilson Current Mirror
Bipolar
MOS
Active Loads
Motivation
Common-Emitter–Common-Source Amplifier with Complementary Load
Common-Emitter–Common-Source Amplifier with Depletion Load
Common-Emitter–Common-Source Amplifier with Diode-Connected Load
Differential Pair with Current-Mirror Load
Large-Signal Analysis
Small-Signal Analysis
Common-Mode Rejection Ratio
Voltage and Current References
Low-Current Biasing
Bipolar Widlar Current Source
MOS Widlar Current Source
Bipolar Peaking Current Source
MOS Peaking Current Source
Supply-Insensitive Biasing
Widlar Current Sources
Current Sources Using Other Voltage Standards
Self-Biasing
Temperature-Insensitive Biasing
Band-Gap-Referenced Bias Circuits in Bipolar Technology
Band-Gap-Referenced Bias Circuits in CMOS Technology
Matching Considerations in Current Mirrors
Bipolar
MOS
Input Offset Voltage of Differential Pair with Active Load
Bipolar
MOS
Chapter 5: Output Stages
Introduction
The Emitter Follower as an Output Stage
Transfer Characteristics of the Emitter-Follower
Power Output and Efficiency
Emitter-Follower Drive Requirements
Small-Signal Properties of the Emitter Follower
The Source Follower as an Output Stage
Transfer Characteristics of the Source Follower
Distortion in the Source Follower
Class B Push–Pull Output Stage
Transfer Characteristic of the Class B Stage
Power Output and Efficiency of the Class B Stage
Practical Realizations of Class B Complementary Output Stages
All-npn Class B Output Stage
Quasi-Complementary Output Stages
Overload Protection
CMOS Class AB Output Stages
Common-Drain Configuration
Common-Source Configuration with Error Amplifiers
Alternative Configurations
Combined Common-Drain Common-Source Configuration
Combined Common-Drain Common-Source Configuration with High Swing
Parallel Common-Source Configuration
Chapter 6: Operational Amplifiers with Single-Ended Outputs
Applications of Operational Amplifiers
Basic Feedback Concepts
Inverting Amplifier
Noninverting Amplifier
Differential Amplifier
Nonlinear Analog Operations
Integrator, Differentiator
Internal Amplifiers
Switched-Capacitor Amplifier
Switched-Capacitor Integrator
Deviations from Ideality in Real Operational Amplifiers
Input Bias Current
Input Offset Current
Input Offset Voltage
Common-Mode Input Range
Common-Mode Rejection Ratio (CMRR)
Power-Supply Rejection Ratio (PSRR)
Input Resistance
Output Resistance
Frequency Response
Operational-Amplifier Equivalent Circuit
Basic Two-Stage MOS Operational Amplifiers
Input Resistance, Output Resistance, and Open-Circuit Voltage Gain
Output Swing
Input Offset Voltage
Common-Mode Rejection Ratio
Common-Mode Input Range
Power-Supply Rejection Ratio (PSRR)
Effect of Overdrive Voltages
Layout Considerations
Two-Stage MOS Operational Amplifiers with Cascodes
MOS Telescopic-Cascode Operational Amplifiers
MOS Folded-Cascode Operational Amplifiers
MOS Active-Cascode Operational Amplifiers
Bipolar Operational Amplifiers
The dc Analysis of the NE5234 Operational Amplifier
Transistors that Are Normally Off
Small-Signal Analysis of the NE5234 Operational Amplifier
Calculation of the Input Offset Voltage and Current of the NE5234
Chapter 7: Frequency Response of Integrated Circuits
Introduction
Single-Stage Amplifiers
Single-Stage Voltage Amplifiers and the Miller Effect
The Bipolar Differential Amplifier: Differential-Mode Gain
The MOS Differential Amplifier: Differential-Mode Gain
Frequency Response of the Common-Mode Gain for a Differential Amplifier
Frequency Response of Voltage Buffers
Frequency Response of the Emitter Follower
Frequency Response of the Source Follower
Frequency Response of Current Buffers
Common-Base Amplifier Frequency Response
Common-Gate Amplifier Frequency Response
Multistage Amplifier Frequency Response
Dominant-Pole Approximation
Zero-Value Time Constant Analysis
Cascode Voltage-Amplifier Frequency Response
Cascode Frequency Response
Frequency Response of a Current Mirror Loading a Differential Pair
Short-Circuit Time Constants
Analysis of the Frequency Response of the NE5234 Op Amp
High-Frequency Equivalent Circuit of the NE5234
Calculation of the -3-dB Frequency of the NE5234
Nondominant Poles of the NE5234
Relation Between Frequency Response and Time Response
Chapter 8: Feedback
Ideal Feedback Equation
Gain Sensitivity
Effect of Negative Feedback on Distortion
Feedback Configurations
Series-Shunt Feedback
Shunt-Shunt Feedback
Shunt-Series Feedback
Series-Series Feedback
Practical Configurations and the Effect of Loading
Shunt-Shunt Feedback
Series-Series Feedback
Series-Shunt Feedback
Shunt-Series Feedback
Summary
Single-Stage Feedback
Local Series-Series Feedback
Local Series-Shunt Feedback
The Voltage Regulator as a Feedback Circuit
Feedback Circuit Analysis Using Return Ratio
Closed-Loop Gain Using Return Ratio
Closed-Loop Impedance Formula Using Return Ratio
Summary—Return-Ratio Analysis
Modeling Input and Output Ports in Feedback Circuits
Chapter 9: Frequency Response and Stability of Feedback Amplifiers
Introduction
Relation Between Gain and Bandwidth in Feedback Amplifiers
Instability and the Nyquist Criterion
Compensation
Theory of Compensation
Methods of Compensation
Two-Stage MOS Amplifier Compensation
Compensation of Single-Stage CMOS Op Amps
Nested Miller Compensation
Root-Locus Techniques
Root Locus for a Three-Pole Transfer Function
Rules for Root-Locus Construction
Root Locus for Dominant-Pole Compensation
Root Locus for Feedback-Zero Compensation
Slew Rate
Origin of Slew-Rate Limitations
Methods of Improving Slew-Rate in Two-Stage Op Amps
Improving Slew-Rate in Bipolar Op Amps
Improving Slew-Rate in MOS Op Amps
Effect of Slew-Rate Limitations on Large-Signal Sinusoidal Performance
Analysis in Terms of Return-Ratio Parameters
Roots of a Quadratic Equation
Chapter 10: Nonlinear Analog Circuits
Introduction
Analog Multipliers Employing the Bipolar Transistor
The Emitter-Coupled Pair as a Simple Multiplier
The dc Analysis of the Gilbert Multiplier Cell
The Gilbert Cell as an Analog Multiplier
A Complete Analog Multiplier
The Gilbert Multiplier Cell as a Balanced Modulator and Phase Detector
Phase-Locked Loops (PLL)
Phase-Locked Loop Concepts
The Phase-Locked Loop in the Locked Condition
Integrated-Circuit Phase-Locked Loops
Nonlinear Function Synthesis
Chapter 11: Noise in Integrated Circuits
Introduction
Sources of Noise
Shot Noise
Thermal Noise
Flicker Noise (1/f Noise)
Burst Noise (Popcorn Noise)
Avalanche Noise
Noise Models of Integrated-Circuit Components
Junction Diode
Bipolar Transistor
MOS Transistor
Resistors
Capacitors and Inductors
Circuit Noise Calculations
Bipolar Transistor Noise Performance
Equivalent Input Noise and the Minimum Detectable Signal
Equivalent Input Noise Generators
Bipolar Transistor Noise Generators
MOS Transistor Noise Generators
Effect of Feedback on Noise Performance
Effect of Ideal Feedback on Noise Performance
Effect of Practical Feedback on Noise Performance
Noise Performance of Other Transistor Configurations
Common-Base Stage Noise Performance
Emitter-Follower Noise Performance
Differential-Pair Noise Performance
Noise in Operational Amplifiers
Noise Bandwidth
Noise Figure and Noise Temperature
Noise Figure
Noise Temperature
Chapter 12: Fully Differential Operational Amplifiers
Introduction
Properties of Fully Differential Amplifiers
Small-Signal Models for Balanced Differential Amplifiers
Common-Mode Feedback
Common-Mode Feedback at Low Frequencies
Stability and Compensation Considerations in a CMFB Loop
CMFB Circuits
CMFB Using Resistive Divider and Amplifier
CMFB Using Two Differential Pairs
CMFB Using Transistors in the Triode Region
Switched-Capacitor CMFB
Fully Differential Op Amps
A Fully Differential Two-Stage Op Amp
Fully Differential Telescopic Cascode Op Amp
Fully Differential Folded-Cascode Op Amp
A Differential Op Amp with Two Differential Input Stages
Neutralization
Unbalanced Fully Differential Circuits
Bandwidth of the CMFB Loop
Analysis of a CMOS Fully Differential Folded-Cascode Op Amp
DC Biasing
Low-Frequency Analysis
Frequency and Time Responses in a Feedback Application
Index
ANALYSIS AND DESIGN
OF ANALOG INTEGRATED
CIRCUITS
Fifth Edition
PAUL R. GRAY
University of California, Berkeley
PAUL J. HURST
University of California, Davis
STEPHEN H. LEWIS
University of California, Davis
ROBERT G. MEYER
University of California, Berkeley
New York / Chichester / Weinheim / Brisbane / Singapore / Toronto
PUBLISHER
ACQUISITIONS EDITOR
Don Fowley
Daniel Sayre
SENIOR PRODUCTION EDITOR
Valerie A. Vargas
EXECUTIVE MARKETING MANAGER
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PRODUCTION MANAGEMENT SERVICES
Elm Street Publishing Services
EDITORIAL ASSISTANT
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MEDIA EDITOR
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Cover courtesy of Chi Ho Law.
This book was set in 10/12 Times Roman by Thomson Digital and printed and bound by
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This book was printed on acid-free paper. ∞
Copyright 2009 © John Wiley & Sons, 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, scanning
or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States
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books or for customer service please call 1-800-CALL-WILEY (255-5945).
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Library of Congress Cataloging-in-Publication Data
Analysis and design of analog integrated circuits / Paul R. Gray . . . [et al.]. — 5th ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-24599-6 (cloth: alk. paper)
1. Linear integrated circuits-Computer-aided design. 2. Metal oxide
semiconductors-Computer-aided design. 3. Bipolar transistors-Computer-aided design.
I. Gray, Paul R., 1942-
TK7874.A588 2009
621.3815–dc21
Printed in the United States of America
10 9 8 7 6 5 3 2 1
08-043583
To Liz, Barbara, Robin, and Judy
Preface
Since the publication of the first edition of this book, the field of analog integrated circuits has
developed and matured. The initial groundwork was laid in bipolar technology, followed by
a rapid evolution of MOS analog integrated circuits. Thirty years ago, CMOS technologies
were fast enough to support applications only at audio frequencies. However, the continu-
ing reduction of the minimum feature size in integrated-circuit (IC) technologies has greatly
increased the maximum operating frequencies, and CMOS technologies have become fast
enough for many new applications as a result. For example, the bandwidth in some video
applications is about 4 MHz, requiring bipolar technologies as recently as about twenty-three
years ago. Now, however, CMOS easily can accommodate the required bandwidth for video
and is being used for radio-frequency applications. Today, bipolar integrated circuits are used in
some applications that require very low noise, very wide bandwidth, or driving low-impedance
loads.
In this fifth edition, coverage of the bipolar 741 op amp has been replaced with a low-
voltage bipolar op amp, the NE5234, with rail-to-rail common-mode input range and almost
rail-to-rail output swing. Analysis of a fully differential CMOS folded-cascode operational
amplifier (op amp) is now included in Chapter 12. The 560B phase-locked loop, which is no
longer commercially available, has been deleted from Chapter 10.
The SPICE computer analysis program is now readily available to virtually all electrical
engineering students and professionals, and we have included extensive use of SPICE in this
edition, particularly as an integral part of many problems. We have used computer analysis as
it is most commonly employed in the engineering design process—both as a more accurate
check on hand calculations, and also as a tool to examine complex circuit behavior beyond the
scope of hand analysis.
An in-depth look at SPICE as an indispensable tool for IC robust design can be found in
The SPICE Book, 2nd ed., published by J. Wiley and Sons. This text contains many worked
out circuit designs and verification examples linked to the multitude of analyses available in
the most popular versions of SPICE. The SPICE Book conveys the role of simulation as an
integral part of the design process, but not as a replacement for solid circuit-design knowledge.
This book is intended to be useful both as a text for students and as a reference book for
practicing engineers. For class use, each chapter includes many worked problems; the problem
sets at the end of each chapter illustrate the practical applications of the material in the text. All
of the authors have extensive industrial experience in IC design and in the teaching of courses
on this subject; this experience is reflected in the choice of text material and in the problem
sets.
Although this book is concerned largely with the analysis and design of ICs, a considerable
amount of material also is included on applications. In practice, these two subjects are closely
linked, and a knowledge of both is essential for designers and users of ICs. The latter compose
the larger group by far, and we believe that a working knowledge of IC design is a great
advantage to an IC user. This is particularly apparent when the user must choose from among a
number of competing designs to satisfy a particular need. An understanding of the IC structure
is then useful in evaluating the relative desirability of the different designs under extremes of
environment or in the presence of variations in supply voltage. In addition, the IC user is in a
iv
Preface
v
much better position to interpret a manufacturer’s data if he or she has a working knowledge
of the internal operation of the integrated circuit.
The contents of this book stem largely from courses on analog integrated circuits given at
the University of California at the Berkeley and Davis campuses. The courses are senior-level
electives and first-year graduate courses. The book is structured so that it can be used as the
basic text for a sequence of such courses. The more advanced material is found at the end of
each chapter or in an appendix so that a first course in analog integrated circuits can omit this
material without loss of continuity. An outline of each chapter is given below with suggestions
for material to be covered in such a first course. It is assumed that the course consists of three
hours of lecture per week over a fifteen-week semester and that the students have a working
knowledge of Laplace transforms and frequency-domain circuit analysis. It is also assumed
that the students have had an introductory course in electronics so that they are familiar with
the principles of transistor operation and with the functioning of simple analog circuits. Unless
otherwise stated, each chapter requires three to four lecture hours to cover.
Chapter 1 contains a summary of bipolar transistor and MOS transistor device physics.
We suggest spending one week on selected topics from this chapter, with the choice of topics
depending on the background of the students. The material of Chapters 1 and 2 is quite important
in IC design because there is significant interaction between circuit and device design, as will
be seen in later chapters. A thorough understanding of the influence of device fabrication on
device characteristics is essential.
Chapter 2 is concerned with the technology of IC fabrication and is largely descriptive.
One lecture on this material should suffice if the students are assigned the chapter to read.
Chapter 3 deals with the characteristics of elementary transistor connections. The material
on one-transistor amplifiers should be a review for students at the senior and graduate levels and
can be assigned as reading. The section on two-transistor amplifiers can be covered in about
three hours, with greatest emphasis on differential pairs. The material on device mismatch
effects in differential amplifiers can be covered to the extent that time allows.
In Chapter 4, the important topics of current mirrors and active loads are considered. These
configurations are basic building blocks in modern analog IC design, and this material should
be covered in full, with the exception of the material on band-gap references and the material
in the appendices.
Chapter 5 is concerned with output stages and methods of delivering output power to a load.
Integrated-circuit realizations of Class A, Class B, and Class AB output stages are described,
as well as methods of output-stage protection. A selection of topics from this chapter should
be covered.
Chapter 6 deals with the design of operational amplifiers (op amps). Illustrative examples
of dc and ac analysis in both MOS and bipolar op amps are performed in detail, and the limita-
tions of the basic op amps are described. The design of op amps with improved characteristics
in both MOS and bipolar technologies are considered. This key chapter on amplifier design
requires at least six hours.
In Chapter 7, the frequency response of amplifiers is considered. The zero-value time-
constant technique is introduced for the calculations of the –3-dB frequency of complex circuits.
The material of this chapter should be considered in full.
Chapter 8 describes the analysis of feedback circuits. Two different types of analysis are
presented: two-port and return-ratio analyses. Either approach should be covered in full with
the section on voltage regulators assigned as reading.
Chapter 9 deals with the frequency response and stability of feedback circuits and should
be covered up to the section on root locus. Time may not permit a detailed discussion of root
locus, but some introduction to this topic can be given.
vi
Preface
In a fifteen-week semester, coverage of the above material leaves about two weeks for
Chapters 10, 11, and 12. A selection of topics from these chapters can be chosen as follows.
Chapter 10 deals with nonlinear analog circuits and portions of this chapter up to Section
10.2 could be covered in a first course. Chapter 11 is a comprehensive treatment of noise
in integrated circuits and material up to and including Section 11.4 is suitable. Chapter 12
describes fully differential operational amplifiers and common-mode feedback and may be
best suited for a second course.
We are grateful to the following colleagues for their suggestions for and/or evaluation of
this book: R. Jacob Baker, Bernhard E. Boser, A. Paul Brokaw, Iwen Chao, John N. Churchill,
David W. Cline, Kenneth C. Dyer, Ozan E. Erdo˘gan, John W. Fattaruso, Weinan Gao, Edwin
W. Greeneich, Alex Gros-Balthazard, T¨unde Gyurics, Ward J. Helms, Kaveh Hosseini, Tim-
othy H. Hu, Shafiq M. Jamal, John P. Keane, Haideh Khorramabadi, Pak Kim Lau, Thomas
W. Matthews, Krishnaswamy Nagaraj, Khalil Najafi, Borivoje Nikoli´c, Keith O’Donoghue,
Robert A. Pease, Lawrence T. Pileggi, Edgar S´anchez-Sinencio, Bang-Sup Song, Richard R.
Spencer, Eric J. Swanson, Andrew Y. J. Szeto, Yannis P. Tsividis, Srikanth Vaidianathan, T. R.
Viswanathan, Chorng-Kuang Wang, Dong Wang, and Mo Maggie Zhang. We are also grateful
to Darrel Akers, Mu Jane Lee, Lakshmi Rao, Nattapol Sitthimahachaikul, Haoyue Wang, and
Mo Maggie Zhang for help with proofreading, and to Chi Ho Law for allowing us to use on the
cover of this book a die photograph of an integrated circuit he designed. Finally, we would like
to thank the staffs at Wiley and Elm Street Publishing Services for their efforts in producing
this edition.
The material in this book has been greatly influenced by our association with the late
Donald O. Pederson, and we acknowledge his contributions.
Berkeley and Davis, CA, 2008
Paul R. Gray
Paul J. Hurst
Stephen H. Lewis
Robert G. Meyer
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