FEEDBACK AMPLIFIERS This page intentionally left blank Feedback Amplifiers Theory and Design by Gaetano Palumbo University of Catania and Salvatore Pennisi University of Catania KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 0-306-48042-5 Print ISBN: 0-7923-7643-9 ©2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ©2002 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstore at: http://ebooks.kluweronline.com To our families: Michela and Francesca Stefania, Francesco, and Valeria CONTENTS ACKNOWLEDGEMENTS xi PREFACE xiii 1. INTRODUCTION TO DEVICE MODELING 1 (by Gianluca Giustolisi) 1.1 DOPED SILICON 1 1.2 DIODES 2 1.2.1 Reverse Bias Condition 5 1.2.2 Graded Junctions 6 1.2.3 Forward Bias Condition 7 1.2.4 Diode Small Signal Model 9 1.3 MOS TRANSISTORS 9 1.3.1 Basic Operation 10 1.3.2 Triode or Linear Region 12 1.3.3 Saturation or Active Region 14 1.3.4 Body Effect 15 1.3.5 p-channel Transistors 16 1.3.6 Saturation Region Small Signal Model 16 1.3.7 Triode Region Small Signal Model 21 1.3.8 Cutoff Region Small Signal Model 23 1.3.9 Second Order Effects in MOSFET Modeling 24 1.3.10Sub-threshold Region 28 1.4 BIPOLAR-JUNCTIONTRANSISTORS 29 1.4.1 Basic Operation 31 1.4.2 Early Effect or Base Width Modulation 32 1.4.3 Saturation Region 33 1.4.4 Charge Stored in the Active Region 33 1.4.5 Active Region Small Signal Model 34 REFERENCES 36 2. SINGLE TRANSISTOR CONFIGURATIONS 37 2.1 THE GENERIC ACTIVE COMPONENT 37 2.2 AC SCHEMATIC DIAGRAM AND LINEAR ANALYSIS 39 2.3 COMMON X (EMITTER/SOURCE) CONFIGURATION 41 2.4 COMMON X WITH DEGENERATIVE RESISTANCE 42 2.5 COMMON Y (BASE/GATE) 48 2.6 COMMON Z (COLLECTOR/DRAIN) 51 2.7 FREQUENCY RESPONSE OF SINGLE TRANSISTOR 54 CONFIGURATIONS viii 2.7.1 Common X Configuration 55 2.7.2 Common X with a Degenerative Resistance 56 2.7.3 Common Y and Common Z Configurations 61 3. FEEDBACK 63 3.1 METHOD OF ANALYSIS OF FEEDBACK CIRCUITS 64 3.2 SIGNAL FLOW GRAPH ANALYSIS 67 3.3 THE ROSENSTARK METHOD 69 3.4 THE CHOMA METHOD 72 3.5 THE BLACKMAN THEOREM 74 4. STABILITY - FREQUENCY AND STEP RESPONSE 77 4.1 ONE-POLE FEEDBACK AMPLIFIERS 78 4.2 TWO-POLE FEEDBACK AMPLIFIERS 82 4.3 TWO-POLE FEEDBACK AMPLIFIERS WITH A POLE- 92 ZERO DOUBLET 4.4 THREE-POLE FEEDBACK AMPLIFIERS WITH REAL 97 POLES 4.5 THREE-POLE FEEDBACK AMPLIFIERS WITH A PAIR OF 98 COMPLEX AND CONJUGATE POLES 4.6 TWO-POLE FEEDBACK AMPLIFIERS WITH A ZERO 100 5. FREQUENCY COMPENSATION TECHNIQUES 103 5.1 DOMINANT-POLE COMPENSATION 104 5.2 MILLER (POLE-SPLITTING) COMPENSATION 106 5.3 COMPENSATION OF THE MILLER RHP ZERO 109 5.3.1 Nulling Resistor 110 5.3.2 Voltage Buffer 111 5.3.3 Current Buffer 114 5.4 NESTED MILLER COMPENSATION 116 5.4.1 General Features 116 5.4.2 RHP Cancellation with Nulling Resistors 120 5.5 REVERSED NESTEDMILLER COMPENSATION 126 5.5.1 General Features 126 5.5.2 RHP Cancellation with Nulling Resistors 130 5.5.3 RHP Cancellation with One Real Voltage Buffer 131 5.5.4 RHP Cancellation with One Real Current Buffer 134 6. FUNDAMENTAL FEEDBACK CONFIGURATIONS 137 6.1 SERIES-SHUNT AMPLIFIER 137 6.1.1 Series-shunt Amplifier with Buffer 146 6.2 SHUNT-SERIESAMPLIFIER 148 6.3 SHUNT-SHUNT AMPLIFIER 155 ix 6.4 SERIES-SERIES AMPLIFIER 158 6.5 A GENERAL VIEW OF SINGLE-LOOP AMPLIFIERS 162 6.6 FREQUENCY COMPENSATION OF THE FUNDAMENTAL 165 CONFIGURATIONS 6.6.1 Frequency Compensation of the Series-Shunt Amplifier 166 6.6.2 Frequency Compensation of the Shunt-Series Amplifier 169 6.6.3 Frequency Compensation of the Shunt- Shunt Amplifier 171 6.6.4 Frequency Compensation of the Series-Series Amplifier 172 7.HARMONIC DISTORTION 173 7.1 HARMONIC DISTORTION AT LOW FREQUENCY 176 7.1.1 Nonlinear Amplifier with Linear Feedback 176 7.1.2 Nonlinear Amplifier with Nonlinear Feedback 178 7.2 HARMONIC DISTORTION IN THE FREQUENCY DOMAIN 182 7.2.1 Open-loop Amplifiers 182 7.2.2 Closed-loop Amplifiers 185 7.3 HARMONIC DISTORTION AND COMPENSATION 191 7.3.1 Two-stage Amplifier with Dominant-Pole Compensation 191 7.3.2 Two-stage Amplifier with Miller Compensation 193 7.3.3 Single-stage Amplifiers 199 7.4 AN ALTERNATIVE FREQUENCY ANALYSIS 205 8. NOISE 207 8.1 BASIC CONCEPTS 207 8.2 EQUIVALENT INPUT NOISE GENERATORS 209 8.3 NOISE MODELS OF CIRCUIT COMPONENTS 212 8.4 EFFECT OF FEEDBACK 214 9. EXAMPLES OF FEEDBACK IN INTEGRATED CIRCUITS 221 9.1 THE OUTPUT RESISTANCE OF A DIFFERENTIAL 221 AMPLIFIER WITH CURRENT-MIRROR LOAD 9.2 THE WILSON CURRENT MIRROR 224 9.3 THE CASCODE CURRENT MIRROR 228 9.4 THE CURRENT FEEDBACK OPERATIONAL AMPLIFIER 229 AND ITS HIGH-LEVEL CHARACTERISTICS 9.5 TRANSISTOR-LEVEL ARCHITECTURE, SMALL-SIGNAL 232 MODEL, AND FREQUENCY COMPENSATION OF CFOAS 9.6 INTEGRATORS AND DIFFERENTIATORS WITH CFOAS 236 9.7 CFOA VERSUS VOA 238 x APPENDIX: FREQUENCY ANALYSIS OF RC NETWORKS 243 A.1 TRANSFER FUNCTION OF A GENERIC RCNETWORK 243 A.2 APPROXIMATED POLES 247 REFERENCES 251 ABOUT THE AUTHORS 263 xi ACKNOWLEDGEMENTS The authors wish to thank Massimo Alioto, Walter Aloisi and Rosario Mita for their help during the correction of the draft. A special thank is due to Professor John Choma jr., a scientific leader in feedback theory and feedback amplifiers, for his encouragement and inspiration in the development of this book. We would like to thank our families and parents for their endless support and interest in our careers. Gaetano Palumbo Salvatore Pennisi This page intentionally left blank xiii PREFACE Feedback circuits and their related properties have been extensively investigated since the early days of electronics. From the time scientific and industrial communities started talking about and working with active elements like vacuum tubes or transistors, until today, much literature and many scientific results have been published which reinforce the importance of feedback. Improved features have been implemented in integrated circuits, novel techniques of analysis have been proposed which deeply improve our understanding of the resulting layouts, and new design strategies have been developed to optimise performance. Nevertheless, the genuinely complex subject of feedback and its applications in analog electronics remain obscure even for the majority of graduate electronics students. To this end, the main focus of this book will be to provide the reader with a real and deep understanding of feedback and feedback amplifiers. Whenever possible and without any loss of generality, a simple and intuitive approach will be used to derive simple and compact equations useful in pencil-and-paper design. Complex analytical derivations will be used only when necessary to elucidate fundamental relationships. Consequently, the contents of the book have been kept to a reasonably accessible level. The book is written for use both by graduate and postgraduate students who are already familiar with electronic devices and circuits, and who want to extend their knowledge to cover all aspects of the analysis and design of analog feedback circuits/amplifiers. Although the material is presented in a formal and theoretical manner, much emphasis is devoted to a design perspective. Indeed, the book can become a valid reference for analog IC designers who wish to deal more deeply with feedback amplifier features and their related design strategies, which are often partially –or even incorrectly– presented in the open literature. For this purpose (and despite xiv maturity of the subject), novel formalisms, approaches, and results are described in this book. For instance, a generic small-signal model applicable to a variety of different transistor types operating in the active region is introduced. A new comprehensive approach for the frequency compensation of two-stage and three-stage amplifiers is adopted. Novel and insightful results are reported for harmonic distortion in the frequency domain. The outline of the text is as follows: Chapter 1 provides a brief introduction to the operating principles of Bipolar and MOS transistors together with their small-signal models. This chapter is an invited contribution by Dr. Ginaluca Giustolisi. A general small-signal model for transistors in the active region of operation is derived in Chapter 2. The resulting model helps the reader to acquire a uniform view of the designer’s tasks and sidesteps the impractical distinction traditionally practised between Bipolar and MOS devices. This model is then thoroughly utilised in the rest of the chapter and the book itself. The three basic single-transistor configurations, which are the common-emitter, common-collector, common-base, for the bipolar transistor and common source, common-drain, common-gate for the MOS transistor, are subsequently revisited. General relationships, for both these active components, valid at low and high frequencies are accordingly developed. Feedback is introduced in Chapter 3. Feedback features are discussed in detail with particular emphasis on achievable advantages (and corresponding disadvantages) from a circuit perspective. Moreover, after an overview of the numerous techniques proposed until now to analyse feedback circuits, the two techniques which are the most useful in the authors’ opinion are presented together with Blackman’s theorem which is concerned only with the impedance level change due to feedback.