good book to purchase

7/27/2019 Good Book to Purchase

1/21

FEEDBACK NETWORKSTHEORY AND

CIRCUIT APP LICATIONS

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Advanced Series in Circuits and Systems - Vol. 5

FEEDBACK NETWORKSTHEORY AND

CIRCUIT APPLICATIONS

J ChomaUniversity of Southern California

W K ChenUniversity of Illinois, Chicago

world scientificNEW J ERSEY . SINGAPORE . BEIJ ING . SHANGHAI . HONG KONG . TAIPEI . CHENNAI

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British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.

For photocopying of material in this volume, please pay a copying fee through the CopyrightClearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission tophotocopy is not required from the publisher.

ISBN-13 978-981-02-2770-8ISBN-10 981-02-2770-1

All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,electronic or mechanical, including photocopying, recording or any information storage and retrievalsystem now known or to be invented, without written permission from the Publisher.

Copyright 2007 by World Scientific Publishing Co. Pte. Ltd.

Published by

World Scientific Publishing Co. Pte. Ltd.

5 Toh Tuck Link, Singapore 596224

USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

Printed in Singapore.

FEEDBACK NETWORKS: THEORY AND CIRCUIT APPLICATIONSAdvanced Series in Circuits and Systems Vol. 5

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To our wives, Lorraine and Shiao-Ling, for their constant encouragement, understanding, and patience.

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Preface

Feedback Networks: Theory and Circuit Applications is not an explicit cir-cuit design text, but it is very much a text that forges a foundation for thecreative design of electronic circuits and systems. A circuit design initiativethat culminates by responding positively to the demanding performancespecications of modern data processing, information transmission, andcommunication systems is a challenging and often daunting undertaking.The acquisition of design skills is complicated by the curious fact thatcomputational precision is not the primary objective of design-oriented cir-cuit analysis. Rather, the purpose of analyses undertaken in support of adesign venture is to gain insights into the theoretic and phenomenologicalunderpinnings of the mathematical solutions for the electrical responsesof electronic networks. An insightful understanding is cultivated by solu-tions albeit approximate solutions premised on clearly understood engi-neering presumptions cast in forms that highlight circuit attributes, limi-tations, best case operating features, and worst case performance shortfalls.In short, design skills, methodologies, and guidelines are not necessarilynurtured by elegant and mathematically satisfying circuit solutions. Theyare more likely to derive from approximate circuit solutions that, whenproperly interpreted in light of given applications, paint an understandableengineering picture of pertinent circuit dynamics. A fundamental objec-tive of this textbook is to paint compelling analytical images that sup-

port the innovative design of high frequency and high speed integratedelectronics.Two engineering reasons justify the obvious feedback focus of this

textbook. The rst of these reasons is that feedback signal ow pathsare pervasive of all electronic networks. These feedback paths are either

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viii Feedback Networks: Theory and Circuit Applications

purposefully implemented or parasitically incurred and in many active net-works destined for high frequency or high speed signal processing applica-

tions, both purposeful and parasitic feedback prevails. Included among thenumerous advantages of feedback incorporated explicitly as a design vehi-cle is the realization of electronic circuits and systems exuding broadbandedsteady state frequencyresponses, suitable impedance levels at input andout-putnetwork ports, and acceptable desensitization of input-to-output transfercharacteristics with respect to vagarious circuit elements or active deviceparameters. When feedback is not overtly adopted, it nonetheless prevails,generally in the form of undesirable capacitive coupling between device

terminals or network node pairs, parasitic magnetic coupling between net-work branches, or unwanted conductive coupling between device termi-nals. For example, when an impedance is inserted in series with the sourcelead of a common source amplier, the transistor channel resistance, whichis not very large in deep submicron device technologies, is a bilateral,nonglobal feedback element interconnecting the drain and source terminalsof the device. Rarely is parasitic feedback advantageous to circuit designobjectives. Indeed, it commonly incurs degradation of the forward signal

transmission characteristics, poor transient responses,difculties in achiev-ing maximum signal power gain, and in extreme cases, outright circuitinstability.

A second reason for the expressed focus of this textbook is that the analy-sis of feedback networks is invariably cumbersome, particularly if attentionis directed to high frequency circuit performance. As a result, denitivemanual analyses are obviated in favor of only computer-based investiga-tions that may not impart the circuit insights supportive of accurate, reliable,

and reproducible circuit design. When manual analyses are executed, theirvalue is often limited by unrealistic approximations and assumptions thateither mask requisite insights or produce results that are incapable of mirror-ing engineering reality. In this textbook, a systematic analysis methodologyfor feedback electronics (which is actually a superuous phrase, since feed-back is pervasive of all electronics) is developed and ultimately applied tothe design-oriented analysis of practical electronic networks. Aside frommerely applying the new feedback analysis techniques to the standard cells

of analog electronic systems, the new procedure actually facilitates circuitbroadbanding innovations, as is demonstrated in the nal chapter. In addi-tion to rendering feedback network analysis less daunting and more prac-tical than might be traditionally expected, the new methodology implicitlyaccounts for the facts that the feedback paths of interest may not be global

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Preface ix

and that purposefully implemented or parasitically encountered feedback is invariably bilateral in nature.

Feedback Networks: Theory and Circuit Applicationsis principally anadvanced circuits and systems analysis text that forges a strong ana-

lytical foundation for more design-intensive analog and mixed signalintegrated circuits and systems classes. It teaches students computation-ally efcient manual methods, complemented by meaningful computer-aided assessment and verication strategies, for analyzing the electricaldynamics of active networks destined for monolithic realization in silicon-germanium (SiGe) heterostructure bipolar, and principally complemen-

tary metal-oxide-semiconductor (CMOS) technologies. More than teachingmere analytical problem solving techniques, the text couches analysesin forms that foster the engineering insights underpinning a meaningfulcharacterization and performance assessment of active circuits embeddedin high frequency and/or high speed system applications. These insightsare fundamental to consistently creative circuit and system design, forthey enable realistic comparisons among candidate active devices andamong plausible circuit architectures. They are also indispensable to the

omnipresent design problem of mitigating the deleterious effects that para-sitic energy storage and other high order device and circuit phenomena haveon such performance metrics as bandwidth, signal delay in both time andfrequency domains, gain and phase margins, phase noise, distortion, andtransient step and impulse responses. In short, the formulation of insight-ful design-oriented analysis strategies commensurate with the realizationof modern integrated circuits, and particularly analog high performanceintegrated circuits and systems, is the primary focus of this work.

This textbook is suitable for use in a senior elective circuits course whosestudents have successfully completed courses in basic circuit analysis, basiclinear systems, and an introductory electronics course featuring exposureto linear electronics exploiting bipolar and MOS technology devices. Itcan also be used as a graduate level core course for the electronic circuitsand systems arena. Students using this textbook should be comfortablewith using one of the many available versions of SPICE computer-aidedanalysis software, such as HSPICE, PSPICE, TOPSPICE, Tanner SPICE,

or the circuit analysis tools implicit to the CADENCE design suite.Chapter 1 on Circuit and System Fundamentals offers the student an

overview of the basic theoretic concepts traditionally addressed in sopho-more and junior level circuits and linear systems classes. Although theissues covered in this chapter should not be foreign to senior and graduate

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x Feedback Networks: Theory and Circuit Applications

level electrical engineering students, their interpretation in light of a varietyof conventional circuit design requirements may comprise new material for

neophyte electronic circuit design students. For example, the well-knowntheorems of Thvenin and Norton are reviewed and thence used directlyto dene the basic terminal characteristics of the four types of ampliersencountered in modern electronic systems.Secondorder circuits are studiedthoroughly in both the frequency and the time domains. In a representa-tive graduate electrical engineering class, the instructor may elect to ignoreChapter 1 and proceed directly to Chapter 2. In such an event, the studentis nonetheless strongly encouraged to read Chapter 1 and to attempt sev-

eral of the Exercises at its conclusion to assess his/her ability to utilizefundamental theoretic detail in practical problems.In Chapter 2 on Two-Port Network Models and Analysis , the mod-

els and analysis procedures surrounding the four fundamental types of two-port network characterizations are studied in detail. In the course of this study, the underpinnings of circuit feedback are introduced throughthe introduction of the concepts of open loop and loop gains. Com-putationally efcient methods of studying interconnections of two-port

networks are developed, and power gain in active networks is denedand assessed. The concepts of potential network instability and uncon-ditional network stability are introduced. Chapter 3 on Scattering Param-eters embellishes the contents of Chapter 2 by considering the scatteringparameter characterization of linear two-port networks. These scatteringparameters are carefully interpreted and thence applied to the problem of designing lossless lters, which are commonly deployed in both narrow-band and wideband electronics earmarked for high frequency communica-

tion systems.Chapters 4, 5, and 6 collectively comprise a reasonably exhaustive trea-

tise on the analysis of feedback networks. Chapter 4 on Feedback Circuit and System Theory addresses rst order, second order, and multi-orderfeedback networks from the perspectives, of gain, transfer function sensi-tivity to critical parameters, bandwidth, gain-bandwidth product, and otherperformance metrics. Useful expressions for the gain and phase margins of second order networks are propounded, and the problems of overshoot, set-

tling time, and delay time surrounding feedback network responses to tran-sient step and impulsive inputs are thoroughly examined. Chapter 5, whichconsiders Signal Flow Methods of Feedback Network Analysis , offers ageneral, tractable, and insightful method for analyzing both single loop and

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Preface xi

dual loop feedback ampliers. The theoretic detail underpinning this ana-lytical method, which embodies the analytical notions of null gain, return

ratio, and null return ratio, is applied to the problem of denitively assess-ing the performance attributes and shortfalls indigenous to several typesof traditionally encountered ampliers. Chapter 6 on Multiloop Feedback Ampliers complements the considerations of Chapter 5 by providing thereader with enhanced mathematical rigor. It also embellishes the dual loopdiscourse of Chapter 5 by developing a generalized and powerful mathe-matical technique for analyzing multiloop feedback circuits.

Chapter 7 on Analog MOS Technology Circuits exploits the theoretic

disclosures proffered in preceding chapters by studying the canonic MOStechnology analog cells at both low and high signal frequencies. In advanceof these circuit studies, the circuit level models of MOS transistors, inclu-sive of deep submicron technologies, are studied in reasonably completedetail so that the circuit assessments developed in the chapter can be inter-preted in terms device phenomenological issues and monolithic processingconstraints. Chapter 8 on MOS Technology Operational Ampliers buildson its predecessor chapter by studying, and developing design method-

ologies for, single stage and two-stage operational ampliers destined forutilization in monolithic mixed signal applications.In Chapter 9, Broadband and Radio Frequency MOS Technology Ampli-

ers , the feedback tools developed earlier are applied to the problem of optimizing amplier performance at high signal frequencies. The circuitbroadbanding schemes addressed include resistance-capacitance degener-ation, shunt peaking, multi-order series peaking, and series-shunt peaking.In the course of these discussions, a new broadbanding scheme, premised

on the realization of constant resistance compensation lters, is proposed.Impedance matching in tuned radio frequency ampliers is discussed andcritically assessed.

Almost all of the material included in this textbook has been used severaltimes by Prof. Choma in a graduate level core course on electronic circuitsat the University of Southern California Viterbi School of Engineering.To this end, the text benets from the critique and constructive criticismsof many Viterbi School of Engineering graduate students and particularly,

those unselshly offered by Mr. Jonathan Roderick, who is scheduled tocomplete his electrical engineering doctorate early in 2006. Prof. Chomaalso wishes to acknowledge the enormous benets gleaned from numeroustechnical exchanges he enjoyed with his faculty colleague, Prof. Hossein

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xii Feedback Networks: Theory and Circuit Applications

Hashemi, in the Department of Electrical Engineering-Electrophysics of the USC Viterbi School of Engineering.

John ChomaSan Dimas, California

Wai-Kai ChenFremont, California

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Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII

Chapter One: Circuit and System Fundamentals 11.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 11.2.0. Thvenins and Nortons Theorems . . . . . . . . . 3

1.2.1. Thvenin and Norton Parameters . . . . . . . 71.2.2. Engineering Observations . . . . . . . . . . 9

1.3.0. Dependent Sources and Amplier Concepts . . . . . 201.3.1. Voltage Amplier . . . . . . . . . . . . . . . 211.3.2. Transconductor . . . . . . . . . . . . . . . . 251.3.3. Transresistor . . . . . . . . . . . . . . . . . 271.3.4. Current Amplier . . . . . . . . . . . . . . . 301.3.5. Buffers . . . . . . . . . . . . . . . . . . . . 32

1.3.5.1. Voltage Buffer . . . . . . . . . . . . 341.3.5.2. Current Buffer . . . . . . . . . . . . 40

1.3.6. Load Power Considerations . . . . . . . . . 451.3.6.1. Maximum Power Transfer . . . . . . 481.3.6.2. The dBm Power Measure . . . . . . 501.3.6.3. Match Termination and Tuned

Responses . . . . . . . . . . . . . . 511.4.0. Second Order Circuits and Systems . . . . . . . . . 57

1.4.1. Second Order Filters . . . . . . . . . . . . . 581.4.2. Frequency Response . . . . . . . . . . . . . 63

1.4.2.1. Response Peaking . . . . . . . . . . 651.4.2.2. Bandwidth . . . . . . . . . . . . . . 661.4.2.3. Phase and Delay Responses . . . . . 69

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1.4.3. Poles and Second Order SystemParameters . . . . . . . . . . . . . . . . . . 75

1.4.4. Time Domain Transient Responses . . . . . . 781.4.4.1. Impulse Response . . . . . . . . . . 791.4.4.2. Step Response . . . . . . . . . . . . 82

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Chapter Two: Two-Port Network Modelsand Analysis 111

2.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 111

2.2.0. Two-Port Linearity Issues . . . . . . . . . . . . . . 1122.3.0. Generalized Two-Port Parameters . . . . . . . . . . 117

2.3.1. Hybrid h -Parameters . . . . . . . . . . . . . 1182.3.1.1. Ideal Current Amplier . . . . . . . 1222.3.1.2. Parameter Measurement

Issues . . . . . . . . . . . . . . . . 1242.3.2. Hybrid g -Parameters . . . . . . . . . . . . . 128

2.3.2.1. g - and h -Parameter

Interrelationships . . . . . . . . . . 1302.3.2.2. Ideal Voltage Amplier . . . . . . . 132

2.3.3. Short Circuit y-Parameters . . . . . . . . . . 1352.3.3.1. -Type Network Model . . . . . . . 1372.3.3.2. Ideal Transconductor . . . . . . . . 1412.3.3.3. Indenite Admittance Matrix . . . . 142

2.3.4. Open Circuit z-Parameters . . . . . . . . . . 1462.3.4.1. Tee-Type Network Model . . . . . . 1482.3.4.2. Ideal Transresistor . . . . . . . . . . 149

2.3.5. Transmission Parameters . . . . . . . . . . . 1512.3.5.1. Input and Output Impedances . . . . 1532.3.5.2. Voltage Transfer Function . . . . . . 1542.3.5.3. Cascade Interconnection . . . . . . . 1542.3.5.4. Series and Shunt Branch

Elements . . . . . . . . . . . . . . . 1562.4.0. Two-Port Methods of Circuit Analysis . . . . . . . . 158

2.4.1. Circuit Analysis in Terms of h -Parameters . . . . . . . . . . . . . . . . . 1592.4.1.1. Open Loop Gain and Loop Gain

Concepts . . . . . . . . . . . . . . . 1602.4.1.2. I/O Impedances . . . . . . . . . . . 164

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2.4.2. Circuit Analysis Via g -Parameters . . . . . . 1672.4.3. Circuit Analysis in Terms of y-Parameters . . 169

2.4.4. Circuit Analysis in Terms of z-Parameters . . 1712.4.5. Generalized Analytical Disclosures . . . . . 1762.5.0. Systems of Interconnected Two Ports . . . . . . . . 177

2.5.1. Series-Shunt Feedback Architecture . . . . . 1782.5.2. Shunt-Series Feedback . . . . . . . . . . . . 1862.5.3. Shunt-Shunt Feedback . . . . . . . . . . . . 1882.5.4. Series-Series Feedback . . . . . . . . . . . . 189

2.6.0. Power Flow and Transfer . . . . . . . . . . . . . . . 191

2.6.1. Power Gain Expressions . . . . . . . . . . . 1922.6.2. Stability Considerations . . . . . . . . . . . 1952.6.3. Maximum Transducer Gain . . . . . . . . . 2012.6.4. Unilateralization . . . . . . . . . . . . . . . 204

2.6.4.1. Shunt-Antiphase ShuntCompensation . . . . . . . . . . . . 204

2.6.4.2. Shunt-Antiphase Shunt Network Realization . . . . . . . . . . . . . . 206

References . . . . . . . . . . . . . . . . . . . . . . 208Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Chapter Three: Scattering Parameters 2253.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 2253.2.0. Reection Coefcient . . . . . . . . . . . . . . . . 227

3.2.1. Voltage Scattering . . . . . . . . . . . . . . 228

3.2.2. Power Scattering . . . . . . . . . . . . . . . 2293.2.3. Signicance of the Reection Coefcient . . 230

3.3.0. Two-Port Scattering Parameters . . . . . . . . . . . 2393.3.1. Parameters S 11 and S 21 . . . . . . . . . . . . 2413.3.2. Parameters S 22 and S 12 . . . . . . . . . . . . 2433.3.3. Port Voltage and Current Generalizations . . 2443.3.4. Scattering Analysis of a Generalized

Two-Port . . . . . . . . . . . . . . . . . . . 2443.3.4.1. Input and Output Reection

Coefcients . . . . . . . . . . . . . 2453.3.4.2. Voltage Transfer Function . . . . . . 2473.3.4.3. Other Transfer Functions . . . . . . 249

3.3.5. Scattering and Conventional Parameters . . . 250

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3.3.5.1. S -Parameters in Terms of h -Parameters . . . . . . . . . . . . . 250

3.3.5.2. h -Parameters in Terms of Scattering Parameters . . . . . . . . 2523.4.0. Lossless Two-Port Networks . . . . . . . . . . . . . 255

3.4.1. Average Power Delivered to ComplexLoad . . . . . . . . . . . . . . . . . . . . . 256

3.4.2. Average Power Delivered to Two-PortNetwork . . . . . . . . . . . . . . . . . . . . 258

3.4.3. Lossless, Passive Two-Port Network . . . . . 260


Chapter Four: Feedback Circuit and SystemTheory 277

4.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 2774.2.0. System Level Model of Feedback Circuit . . . . . . 2774.3.0. Feedback Network Frequency Response . . . . . . . 285

4.3.1. Single Pole Open Loop TransferFunction . . . . . . . . . . . . . . . . . . . 286

4.3.2. Second Order Open Loop TransferFunction . . . . . . . . . . . . . . . . . . . 288

4.3.3. Stability Issues . . . . . . . . . . . . . . . . 2914.3.3.1. Phase Margin . . . . . . . . . . . . 2924.3.3.2. Gain Margin . . . . . . . . . . . . . 295

4.3.3.3. Alternative Damping and UndampedFrequency Expressions . . . . . . . 2974.3.4. Compensation for Closed Loop Stability . . . 300

4.4.0. Time Domain Response . . . . . . . . . . . . . . . 3064.4.1. Unit Step Response . . . . . . . . . . . . . . 3064.4.2. Settling Time . . . . . . . . . . . . . . . . . 308References . . . . . . . . . . . . . . . . . . . . . . 312

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

Chapter Five: Signal Flow Methods ofFeedback Network Analysis 321

5.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 3215.2.0. Feedback Network Analysis Fundamentals . . . . . 322

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5.2.1. Calculation of Feedback Network Parameters . . . . . . . . . . . . . . . . . . 326

5.2.1.1. Null Parameter Gain . . . . . . . . . 3275.2.1.2. Normalized Return Ratio . . . . . . 3285.2.1.3. Normalized Null Return Ratio . . . 330

5.2.2. Input and Output Impedances . . . . . . . . 3375.2.2.1 Driving Point Input Impedance . . . 3375.2.2.2 Driving Point Output Impedance . . 340

5.2.3 Output Port-to-Local Port Feedback . . . . . 3455.3.0 Special Case Feedback Network Examples . . . . . 348

5.3.1. Global Feedback . . . . . . . . . . . . . . . 3485.3.1.1. Transimpedance Feedback Amplier . . . . . . . . . . . . . . 348

5.3.1.2. Transadmittance Feedback Amplier . . . . . . . . . . . . . . 352

5.3.1.3. Voltage Feedback Amplier . . . . . 3545.3.1.4. Current Feedback Amplier . . . . . 357

5.3.2. Other Feedback Architectures . . . . . . . . 366

5.3.2.1. Feedback Branch Admittance . . . . 3665.3.2.2. Feedback Branch Impedance . . . . 377

5.3.2. Dual Loop Feedback . . . . . . . . . . . . . 3855.4.1. Series-Series/Shunt-Shunt Feedback . . . . . 388

5.4.1.1. Analysis of the Series-Series/ Shunt-Shunt Feedback Pair . . . . . 390

5.4.1.2. Interpretation of Results and DesignConsiderations . . . . . . . . . . . . 398

5.4.2. Series-Shunt/Shunt-Series Feedback . . . . . 4055.4.2.1. Analysis of the Series-Shunt/

Shunt-Series Feedback Pair . . . . . 4055.4.2.2. Design Restrictions . . . . . . . . . 416


Chapter Six: Multiple Loop Feedback Ampliers 4416.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 4416.2.0. Indenite Admittance Matrix . . . . . . . . . . . . 442

6.2.1. Return Difference . . . . . . . . . . . . . . . 4486.2.2. Null Return Difference . . . . . . . . . . . . 454

6.3.0. Network Functions and Feedback . . . . . . . . . . 456

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6.3.1. Blackmans Formula . . . . . . . . . . . . . 4576.3.2. Sensitivity Function . . . . . . . . . . . . . 463

6.4.0. Measurement of Return Difference . . . . . . . . . 4676.4.1. Blechers Procedure . . . . . . . . . . . . . 4696.4.2. Impedance Measurements . . . . . . . . . . 472

6.5.0. Multiloop Feedback . . . . . . . . . . . . . . . . . 4756.5.1. Multiloop Feedback Theory . . . . . . . . . 4766.5.2. Return Difference Matrix . . . . . . . . . . . 4806.5.3. Null Return Difference Matrix . . . . . . . . 4826.5.4. Transfer Function Matrix . . . . . . . . . . . 484

6.5.5. Sensitivity Matrix . . . . . . . . . . . . . . . 4886.5.6. Multi-Parameter Sensitivity . . . . . . . . . 492References . . . . . . . . . . . . . . . . . . . . . . 495

Chpater Seven: Analog MOS Technology Circuits 4977.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 4977.2.0. MOS Transistor Models . . . . . . . . . . . . . . . 499

7.2.1. Transistor Cross-Section and Electrical

Symbol . . . . . . . . . . . . . . . . . . . . 5007.2.2. Static Volt-Ampere Relationships . . . . . . 504

7.2.2.1. Cutoff . . . . . . . . . . . . . . . . 5057.2.2.2. Ohmic Electrical Regime . . . . . . 5097.2.2.3. Saturation Regime . . . . . . . . . . 512

7.2.3. Small Signal Models . . . . . . . . . . . . . 5147.2.3.1. Small Signal Model At High

Frequencies . . . . . . . . . . . . . 5187.2.3.2. Unity Gain Frequency . . . . . . . . 522

7.3.0. Common Source Amplier . . . . . . . . . . . . . . 5247.3.1. Voltage Transfer Function . . . . . . . . . . 526

7.3.1.1. Poles and Time Constants . . . . . . 5287.3.1.2. Miller-Limited Frequency

Response . . . . . . . . . . . . . . . 5327.3.1.3. Output Port Time Constant

Dominance . . . . . . . . . . . . . . 5407.3.2. Input and Output Impedances . . . . . . . . 5427.3.3. Variants of the Common Source

Topology . . . . . . . . . . . . . . . . . . . 5447.3.3.1. NMOS Load . . . . . . . . . . . . . 5447.3.3.2. PMOS Load . . . . . . . . . . . . . 548

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7.4.0. Common Drain Amplier . . . . . . . . . . . . . . 5527.4.1. Source Follower Transfer Function . . . . . . 555

7.4.2. Source Follower I/O Impedances . . . . . . . 5607.5.0. Common Gate Amplier . . . . . . . . . . . . . . . 5687.5.1. Common Gate I/O Characteristics . . . . . . 5717.5.2. Common Source-Common Gate Cascode . . 5757.5.3. Enhanced Common Gate Cell . . . . . . . . 581

7.5.3.1. Low Frequency CircuitProperties . . . . . . . . . . . . . . 584

7.5.3.2. High Frequency Circuit

Properties . . . . . . . . . . . . . . 5857.5.3.3. Integrator Application . . . . . . . . 591References . . . . . . . . . . . . . . . . . . . . . . 604

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 605

Chapter Eight: MOS Technology OperationalAmpliers 629

8.1.0. Introduction . . . . . . . . . . . . . . . . . . . . . 629

8.2.0. Op-Amp System Architectures . . . . . . . . . . . . 6308.2.1. Single Stage Architecture . . . . . . . . . . . 6308.2.2. Two-Stage Architecture . . . . . . . . . . . 6328.2.3. Input Stage Transconductor . . . . . . . . . 634

8.3.0. CMOS Input Stage Analysis . . . . . . . . . . . . . 6378.3.1. P -Channel Transconductor . . . . . . . . . . 638

8.3.1.1. Transconductor Small SignalAnalysis . . . . . . . . . . . . . . . 640

8.3.1.2. Transconductor OutputMacromodel . . . . . . . . . . . . . 642

8.3.1.3. First Stage Output Macromodel . . . 6518.3.1.4. First Stage Static Analysis . . . . . . 654

8.3.2. N -Channel Transconductor . . . . . . . . . . 6568.4.0. Phase Inverting Second Stage . . . . . . . . . . . . 657

8.4.1. Low Frequency Small Signal Analysis . . . . 6588.4.2. Op-Amp Static Analysis . . . . . . . . . . . 660

8.5.0. Frequency Compensation . . . . . . . . . . . . . . 6618.5.1. Approximate High Frequency Analysis . . . 6628.5.2. Miller Compensation . . . . . . . . . . . . . 6648.5.3. Improved Frequency Compensation . . . . . 669

8.5.3.1. Buffered Capacitive Feedback . . . . 670

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9.7.2. Amplier Bandwidth . . . . . . . . . . . . . 7939.7.3. Input Impedance . . . . . . . . . . . . . . . 795

9.7.4. Input Impedance Compensation . . . . . . . 7979.7.5. Output Impedance . . . . . . . . . . . . . . 8069.8.0. The f T -Doubler . . . . . . . . . . . . . . . . . . . . 812

9.8.1. Small Signal Analysis . . . . . . . . . . . . 8139.8.2. Realization of the f T -Doubler . . . . . . . . 815

9.9.0. Bandpass Feedback Amplier . . . . . . . . . . . . 8169.9.1. Common Source RF Amplier . . . . . . . . 8219.9.2. Impedance and Transfer Characteristics . . . 824

9.9.2.1. Gate Impedance . . . . . . . . . . . 8259.9.2.2. Voltage Transfer Function . . . . . . 832References . . . . . . . . . . . . . . . . . . . . . . 841

Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 842

Index 855

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