Operational Amplifiers

Operational Amplifiers

Johan Huijsing Operational Amplifiers Theory and Design Third Edition

Johan Huijsing Faculty of Electrical Engineering Mathematics and Computer Sciences (EEMCS) Delft University of Technology Delft, The Netherlands ISBN 978-3-319-28126-1 ISBN 978-3-319-28127-8 (ebook) DOI 10.1007/978-3-319-28127-8 Library of Congress Control Number: 2016941868 Springer International Publishing Switzerland 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland

To my dear wife Willeke and children Hans, Adriaan, Mirjam, and Reineke, who have given me love and support.

Acknowledgements Simon Middelhoek stimulated me to write this overview book. Wim van Nimwegen drew pictures in a very clear way. Ovidiu Bajdechi wrote the problems and simulation exercises. Anja de Koning and Mary van den Berg typed the original manuscript. Wendy Sturrock and many students helped in correcting the manuscript. Maureen Meekel provided computer support. Thanks to all. Above all, thanks to God through Jesus Christ, who is the Lord of my life. vii

Contents 1 Definition of Operational Amplifiers... 1 1.1 Operational Inverting Amplifier.... 2 1.1.1 Current-to-Voltage Converter..... 3 1.2 Operational Voltage Amplifier........................ 3 1.2.1 Non-inverting Voltage Amplifier............... 3 1.2.2 Voltage Follower... 4 1.3 Operational Current Amplifier........................ 5 1.3.1 Current Amplifier... 5 1.3.2 Current Follower...... 6 1.4 Operational Floating Amplifier..... 7 1.4.1 Voltage-to-Current Converter..... 7 1.4.2 Voltage and Current Follower... 7 1.5 Conclusion... 8 References... 9 2 Macromodels... 11 2.1 Operational Inverting Amplifier.... 11 2.1.1 Definition of Offset Voltage and Current, Input and Output Impedance, Transconductance........ 12 2.2 Operational Voltage Amplifier........................ 13 2.2.1 Definition of Input Bias Current, Input Common-Mode Rejection Ratio............... 13 2.3 Operational Current Amplifier........................ 14 2.3.1 Definition of Output Bias Current, Output Common-Mode Current Rejection Ratio..... 15 2.4 Operational Floating Amplifier..... 15 2.4.1 Using All Definitions...... 16 2.5 Macromodels in SPICE... 16 2.5.1 Macromodel Mathematical.... 17 ix

x Contents 2.5.2 Macromodel Miller-Compensated.............. 17 2.5.3 Macromodel Nested-Miller-Compensated........ 18 2.5.4 Conclusion.... 19 2.6 Measurement Techniques for Operational Amplifiers...... 20 2.6.1 Transconductance Measurement of an OTA....... 20 2.6.2 Voltage Gain Measurement of an OpAmp........ 21 2.6.3 Voltage Gain and Offset Measurements of an OpAmp... 22 2.6.4 General Measurement Setup for an OpAmp.... 22 2.7 Problems and Simulation Exercises...... 24 2.7.1 Problem 2.1.............................. 24 2.7.2 Solution................................. 25 2.7.3 Simulation Exercise 2.1... 27 2.7.4 Simulation Exercise 2.2... 27 References... 28 3 Applications... 29 3.1 Operational Inverting Amplifier.... 30 3.1.1 Current-to-Voltage Converter..... 30 3.1.2 Inverting Voltage Amplifier...... 31 3.2 Operational Voltage Amplifier........................ 32 3.2.1 Non-inverting Voltage Amplifier............... 32 3.2.2 Voltage Follower... 33 3.2.3 Bridge Instrumentation Amplifier..... 33 3.3 Operational Current Amplifier........................ 35 3.3.1 Current Amplifier... 35 3.4 Operational Floating Amplifier..... 36 3.4.1 Voltage-to-Current Converter..... 36 3.4.2 Inverting Current Amplifier..... 37 3.4.3 Differential Voltage-to-Current Converter........ 38 3.4.4 Instrumentation Voltage Amplifier.... 40 3.4.5 Instrumentation Current Amplifier.............. 41 3.4.6 Gyrator Floating........................... 41 3.4.7 Conclusion.... 43 3.5 Dynamic Range..... 43 3.5.1 Dynamic Range over Supply-Power Ratio..... 43 3.5.2 Voltage-to-Current Converter..... 44 3.5.3 Inverting Voltage Amplifier...... 45 3.5.4 Non-inverting Voltage Amplifier............... 46 3.5.5 Inverting Voltage Integrator...... 47 3.5.6 Current Mirror............................ 47 3.5.7 Conclusion Current Mirror................... 48 3.5.8 Nonideal Operational Amplifiers... 49 3.5.9 Conclusion.... 50

Contents xi 3.6 Problems... 51 3.6.1 Problem 3.1.............................. 51 3.6.2 Problem 3.2.............................. 53 3.6.3 Problem 3.3.............................. 54 References... 55 4 Input Stages... 57 4.1 Offset Bias, and Drift.............................. 57 4.1.1 Isolation Techniques........................ 58 4.1.2 Balancing Techniques...... 59 4.1.3 Offset Trimming.......................... 63 4.1.4 Biasing for Constant Transconductance G m Over Temperature......................... 66 4.2 Noise... 69 4.2.1 Isolation Techniques........................ 69 4.2.2 Balancing Techniques...... 71 4.2.3 Conclusion.... 71 4.3 Common-Mode Rejection... 72 4.3.1 Isolation Techniques........................ 72 4.3.2 Balancing Techniques...... 73 4.3.3 Combination of Isolation and Balancing...... 74 4.3.4 Common-Mode Cross-Talk Ratios... 75 4.3.5 Parallel Input Impedance.... 75 4.3.6 Collector or Drain Impedance................. 76 4.3.7 Tail Impedance........................... 77 4.3.8 Collector Base Impedance................... 78 4.3.9 Base Impedance...... 78 4.3.10 Back-Gate Influence... 79 4.3.11 Total CMCR............................. 80 4.3.12 Conclusion... 80 4.4 Rail-to-Rail Input Stages... 81 4.4.1 Constant g m by Constant Sum of Tail-Currents.... 83 4.4.2 Constant g m by Multiple Input Stages in Strong-Inversion CMOS................... 86 4.4.3 Constant g m by Current Spillover Control... 87 4.4.4 Constant g m in CMOS by Saturation Control... 90 4.4.5 Constant g m in Strong-Inversion CMOS by Constant Sum of V GS... 93 4.4.6 Rail-to-Rail in CMOS by Back-Gate Driving... 95 4.4.7 Extension of the Common-Mode Input Range... 95 4.4.8 Conclusion.... 96 4.5 Problems and Simulation Exercises...... 96 4.5.1 Problem 4.1.............................. 96 4.5.2 Problem 4.2.............................. 98 4.5.3 Problem 4.3.............................. 100

xii Contents 4.5.4 Simulation Exercise 4.1... 101 4.5.5 Simulation Exercise 4.2... 101 4.5.6 Simulation Exercise 4.3... 102 References... 103 5 Output Stages... 105 5.1 Power Efficiency of Output Stages... 105 5.2 Classification of Output Stages.... 110 5.3 Feedforward Class-AB Biasing (FFB).................. 112 5.3.1 FFB Voltage Follower Output Stages..... 112 5.3.2 FFB Compound Output Stages..... 117 5.3.3 FFB Rail-to-Rail General-Amplifier Output Stages.... 120 5.3.4 Conclusion.... 129 5.4 Feedback Class-AB Biasing (FBB).................... 129 5.4.1 FBB Voltage-Follower Output Stages........... 130 5.4.2 FBB Compound Output Stages................ 131 5.4.3 FBB Rail-to-Rail General Amplifier Output Stages.... 136 5.4.4 Conclusion.... 141 5.5 Saturation Protection and Current Limitation..... 142 5.5.1 Output Saturation Protection Circuits............ 142 5.5.2 Output Current Limitation Circuits... 144 5.6 Problems and Simulation Exercises...... 147 5.6.1 Problem 5.1.............................. 147 5.6.2 Problem 5.2.............................. 148 5.6.3 Problem 5.3.............................. 149 5.6.4 Problem 5.4.............................. 150 5.6.5 Problem 5.5.............................. 151 5.6.6 Simulation Exercise 5.1... 152 5.6.7 Simulation Exercise 5.2... 152 References... 154 6 Overall Design... 157 6.1 Classification of Overall Topologies... 157 6.1.1 Nine Overall Topologies.... 157 6.1.2 Voltage and Current Gain Boosting...... 162 6.1.3 Input Voltage and Current Compensation... 162 6.2 Frequency Compensation........................... 163 6.2.1 One-GA-Stage Frequency Compensation......... 165 6.2.2 Two-GA-stage Frequency Compensation......... 168 6.2.3 Three-GA-Stage Frequency Compensation........ 179 6.2.4 Four-GA-Stage Frequency Compensation... 186 6.2.5 Multi-GA-stage Compensations...... 191

Contents xiii 6.2.6 Compensation for Low Power and High Capacitive Load... 191 6.2.7 Conclusion.... 199 6.3 Slew Rate....................................... 199 6.4 Nonlinear Distortion............................... 201 6.4.1 Conclusion.... 206 6.5 Problems and Simulation Exercises...... 206 6.5.1 Problem 6.1.............................. 206 6.5.2 Problem 6.2.............................. 208 6.5.3 Problem 6.3.............................. 209 6.5.4 Problem 6.4.............................. 210 6.5.5 Problem 6.5.............................. 211 6.5.6 Simulation Exercise 6.1... 212 6.5.7 Simulation Exercise 6.2... 212 References... 213 7 Design Examples... 215 7.1 GA-CF Configuration... 215 7.1.1 Operational Transconductance Amplifier... 215 7.1.2 Folded-Cascode Operational Amplifier..... 218 7.1.3 Telescopic-Cascode Operational Amplifier... 221 7.1.4 Feedforward HF Compensation................ 222 7.1.5 Input Voltage Compensation..... 224 7.1.6 Input Class-AB Boosting.................... 226 7.1.7 Voltage-Gain Boosting..... 227 7.1.8 Conclusion.... 228 7.2 GA-GA Configuration.............................. 229 7.2.1 Basic Bipolar R-R-Out Class-A Operational Amplifier... 229 7.2.2 Improved Basic Bipolar R-R-Out Class-A Operational Amplifier..... 230 7.2.3 Basic CMOS R-R-Out Class-A Operational Amplifier... 232 7.2.4 Improved Basic CMOS R-R-Out Class-A Operational Amplifier..... 232 7.2.5 Conclusion.... 234 7.3 GA-CF-VF Configuration........................... 234 7.3.1 High-Speed Bipolar Class-AB Operational Amplifier... 234 7.3.2 High-Slew-Rate Bipolar Class-AB Voltage-Follower Buffer... 237 7.3.3 Conclusion.... 238 7.4 GA-GA-VF Configuration... 238 7.4.1 General Bipolar Class-AB Operational Amplifier with Miller Compensation... 239

xiv Contents 7.4.2 μa741 Operational Amplifier with Miller Compensation... 241 7.4.3 Conclusion.... 242 7.5 GA-CF-VF/GA Configuration............. 242 7.5.1 High-Frequency All-NPN Operational Amplifier with Mixed PC and MC...... 243 7.5.2 Conclusion.... 245 7.6 GA-GA-VF/GA Configuration........................ 245 7.6.1 LM101 Class-AB All-NPN Operational Amplifier with MC... 246 7.6.2 NE5534 Class-AB Operational Amplifier with Bypassed NMC... 247 7.6.3 Precision All-NPN Class-AB Operational Amplifier with NMC... 249 7.6.4 Precision HF All-NPN Class-AB Operational Amplifier with MNMC...................... 251 7.6.5 1 GHz, All-NPN Class-AB Operational Amplifier with MNMC...................... 253 7.6.6 2 V Power-Efficient All-NPN Class-AB Operational Amplifier with MDNMC........... 254 7.6.7 Conclusion.... 255 7.7 GA-CF-GA Configuration........................... 255 7.7.1 Compact 1.2 V R-R-Out CMOS Class-A OpAmp with MC...... 255 7.7.2 Compact 2 V R-R-Out CMOS Class-AB OpAmp with MC...... 258 7.7.3 Compact 2 V R-R-In/Out CMOS Class-AB OpAmp with MC...... 260 7.7.4 Compact 1.2 V R-R-Out CMOS Class-AB OpAmp with MC...... 264 7.7.5 Conclusion.... 265 7.8 GA-GA-GA Configuration... 265 7.8.1 1 V R-R-Out CMOS Class-AB OpAmp with MNMC... 265 7.8.2 Compact 1.2 V R-R-Out BiCMOS Class-AB OpAmp with MNMC....................... 268 7.8.3 Bipolar Input and Output Protection............ 270 7.8.4 1.8 V R-R-In/Out Bipolar Class-AB OpAmp (NE5234) with NMC..... 270 7.8.5 Conclusion.... 273 7.9 GA-GA-GA-GA Configuration....................... 273 7.9.1 1 V R-R-In/Out Bipolar Class-AB OpAmp with MNMC... 273 7.9.2 1.2 V R-R-Out CMOS Class-AB OpAmp with MHNMC...... 277 7.9.3 Conclusion.... 280

Contents xv 7.10 Problems and Simulation Exercises..... 280 7.10.1 Problem 7.1.............................. 280 7.10.2 Problem 7.2.............................. 282 7.10.3 Problem 7.3.............................. 283 7.10.4 Problem 7.4.............................. 285 7.10.5 Simulation Exercise 7.1..... 286 7.10.6 Simulation Exercise 7.2..... 287 References... 287 8 Fully Differential Operational Amplifiers... 289 8.1 Fully Differential GA-CF Configuration................. 290 8.1.1 Fully Differential CMOS OpAmp with Linear-Mode CM-Out Control............. 290 8.1.2 Fully Differential Telescopic CMOS OpAmp with Linear-Mode CM-Out Control............. 292 8.1.3 Fully Differential CMOS OpAmp with LTP CM-Out Control........................... 292 8.1.4 Fully Differential GA-CF CMOS OpAmp with Output Voltage Gain Boosters... 294 8.1.5 Fully Differential GA-CF CMOS OpAmp with Input-CM Feedback CM-Out Control... 295 8.1.6 Fully Differential CMOS OpAmp with R-R Buffered Resistive CM-Out Control...... 295 8.2 Fully Differential GA-CF-GA Configuration... 297 8.2.1 Fully Differential CMOS OpAmp with R-R Resistive CM-Out Control... 298 8.2.2 Conclusion.... 300 8.3 Fully Differential GA-GA-GA-GA Configuration.... 300 8.3.1 Fully Differential CMOS OpAmp with Switched-Capacitor CM-Out Control... 300 8.3.2 Conclusion.... 301 8.4 Problems and Simulation Exercises...... 302 8.4.1 Problem 8.1.............................. 302 8.4.2 Problem 8.2.............................. 303 8.4.3 Simulation Exercise 8.1... 304 References... 306 9 Instrumentation Amplifiers and Operational Floating Amplifiers... 307 9.1 Introduction..................................... 307 9.2 Unipolar Voltage-to-Current Converter................. 309 9.2.1 Unipolar Single-Transistor V-I Converter... 310 9.2.2 Unipolar OpAmp-Gain-Boosted Accurate V-I Converter..... 311 9.2.3 Unipolar CMOS Accurate V-I Converter......... 312

xvi Contents 9.2.4 Unipolar Bipolar Accurate V-I Converter... 312 9.2.5 Unipolar OpAmp Accurate V-I Converter... 314 9.2.6 Conclusion.... 315 9.3 Differential Voltage-to-Current Converters.... 315 9.3.1 Differential Simple V-I Converter..... 315 9.3.2 Differential Accurate V-I Converter............ 316 9.3.3 Differential CMOS Accurate V-I Converter... 317 9.4 Instrumentation Amplifiers... 318 9.4.1 Instrumentation Amplifier (Semi) with Three OpAmps................................ 318 9.4.2 Instrumentation Amplifier with a Differential V-I Converter for Input Sensing... 319 9.4.3 Instrumentation Amplifier with Differential V-I Converters for Input and Output Sensing...... 320 9.4.4 Instrumentation Amplifier with Simple Differential V-I Converters for Input and Output Sensing..... 321 9.4.5 Instrumentation Amplifier Bipolar with Common-Mode Voltage Range Including Negative Rail Voltage... 323 9.4.6 Instrumentation Amplifier CMOS with Common-Mode Voltage Range Including Negative Rail Voltage... 324 9.4.7 Instrumentation Amplifier Simplified Diagram and General Symbol..... 325 9.4.8 Conclusion.... 325 9.5 Universal Class-AB Voltage-to-Current Converter Design Using an Instrumentation Amplifier... 326 9.5.1 Universal V-I Converter Design with Semi-instrumentation Amplifier... 327 9.5.2 Universal V-I Converter Design with Real Instrumentation Amplifier..... 328 9.5.3 Conclusion.... 329 9.6 Universal Class-A OFA Design.... 329 9.6.1 Universal Class-A OFA Design with Floating Zener-Diode Supply....... 330 9.6.2 Universal Class-A OFA Design with Supply Current Followers... 330 9.6.3 Universal Class-A OFA Design with Long-Tailed-Pairs...... 332 9.6.4 Conclusion.... 336 9.7 Universal Class-AB OFA Realization with Power-Supply Isolation........................................ 336 9.7.1 Universal Floating Power Supply Design... 337 9.7.2 Conclusion.... 337

Contents xvii 9.8 Universal Class-AB OFA Design... 337 9.8.1 Universal Class-AB OFA Design with Total-Output-Supply-Current Equalization.............................. 338 9.8.2 Universal Class-AB OFA Design with Current Mirrors... 341 9.8.3 Universal Class-AB OFA Design with Output-Current Equalization... 342 9.8.4 Universal Class-AB Voltage-to-Current Converter with Instrumentation Amplifier................ 343 9.8.5 Conclusion.... 344 9.9 Problems... 345 9.9.1 Problem 9.1.............................. 345 9.9.2 Problem 9.2.............................. 347 9.9.3 Problem 9.3.............................. 348 References... 349 10 Low-Noise and Low-Offset Operational and Instrumentation Amplifiers... 351 10.1 Introduction..................................... 351 10.2 Applications of Instrumentation Amplifiers.... 352 10.3 Three-OpAmp Instrumentation Amplifiers.... 354 10.4 Current-Feedback Instrumentation Amplifiers...... 356 10.5 Auto-Zero OpAmps and InstAmps... 358 10.6 Chopper OpAmps and InstAmps.... 362 10.7 Chopper-Stabilized OpAmps and InstAmps.... 367 10.8 Chopper-Stabilized Chopper OpAmps and InstAmps... 373 10.9 Chopper Amplifiers with Ripple-Reduction Loop...... 377 10.10 Chopper Amplifiers with Capacitive-Coupled Input........ 384 10.10.1 Wide-Band Chopper Amplifiers with Capacitive-Coupled Input................ 390 10.10.2 Fully Floating Capacitive-Coupled Input Choppers..... 397 10.11 Gain Accuracy of Instrumentation Amplifiers... 404 10.11.1 Conclusion..... 411 10.12 Summary Low Offset... 411 References... 412 Author Biography... 415 Index... 417

Summary This third edition has completed Chap. 10 on systematic design of μv-offset operational amplifiers and precision instrumentation amplifiers by applying chopping, auto-zeroing, and dynamic element-matching techniques. Wide-band and fast-settling capacitive-coupled operational and instrumentation amplifiers are added. The associated designs of floating input choppers are presented, that facilitate beyond-the-rails CM input voltage ranges. Furthermore, many improvements have been made and errors corrected. A systematic circuit design of operational amplifiers is presented. It is shown that the topology of all operational amplifiers can be divided in nine main overall configurations. These configurations range from one gain stage up to four or more gain stages. Many famous designs are completely evaluated. High-frequency compensation techniques are presented for all nine configurations even at high capacitive loads. Special focus is on low-power low-voltage architectures with rail-to-rail input and output ranges. The design of fully differential operational amplifiers and operational floating amplifiers is being developed. Also, the characterization of operational amplifiers by macromodels and error matrices is presented, together with measurement techniques for their parameters. Problems and simulation exercises have been supplied for self-evaluation. xix

Introduction The goal of this book is to equip the circuit designer with a proper understanding of the theory and design of operational amplifiers (OpAmps). The core of the book presents the systematic design of operational amplifiers. All operational amplifiers can be classified into a periodic system of nine main overall configurations. This division enables the designer to quickly recognize, understand, and choose optimal configurations. Chapter 1 defines four basic types of operational amplifiers on the basis of the external ground connections of the input and output port; and which port needs to be isolated from the ground has a big impact on the circuit design. A complete set of linear parameters, by which each of the above four basic types of operational amplifiers can be quantified, is given in Chap. 2. This chapter also presents macromodels and measurement techniques for OpAmp parameters. A systematic treatment of sources of errors in important applications of the above four basic types of operational amplifiers is presented in Chap. 3. Input stages are evaluated in Chap. 4. Important aspects such as bias, offset, noise, and common-mode rejection are considered. Low-voltage input stages with a rail-to-rail input voltage range are extensively discussed. A classification of push pull output stages is presented in Chap. 5. Three possible topologies are explored: voltage follower stages, compound stages, and rail-to-rail general amplifier stages. Emphasis is on voltage and current efficiency. A classification of operational amplifiers into nine main overall configurations is presented in Chap. 6. The classification consists of 2 two-stage OpAmps, 6 threestage OpAmps, and 1 four- or multi-stage OpAmp. High-frequency compensation techniques are developed for all configurations. Methods are presented for obtaining a maximum bandwidth over power ratio for certain high capacitive load conditions. Slew-rate and distortion are also considered. Chapter 7 presents design examples of each of the nine main configurations. Many well-known OpAmps are fully elaborated. Among them are simple CMOS OpAmps, high-frequency bipolar OpAmps, Low-voltage CMOS and bipolar OpAmps. xxi

xxii Introduction The design of fully differential operational amplifiers with common-mode feedback is developed in Chap. 8. Special focus is on low-voltage architectures. The design of the most universal active network element: the operational floating amplifier (OFA) is presented in Chap. 9. It has both the output and input port isolated from ground. The concept of this OFA gives the designer the freedom to work with current signals as well as voltage signals. An additional Chap. 10 has been added on the systematic design of μv-offset operational amplifiers and precision instrumentation amplifiers by applying chopping, auto-zeroing, and dynamic element-matching techniques. Capacitive coupling at the input gives these chopper amplifiers input CM ranges that reach far beyond the supply-rail voltages. The design of associated floating choppers is presented. Problems and simulation exercises have been supplied for most of the chapters to facilitate self-evaluation of the understanding and design skills of the user of this book.

Notation OpAmp OA OIA OVA OCA OFA GA VF CF CM IA a A v A vo β B v C Ch C ox C M C P D ƒ ƒ T ƒ o g m i I I B Operational amplifier Operational amplifier Operational inverting amplifier Operational voltage amplifier Operational current amplifier Operational floating amplifier General amplifier stage Voltage follower stage Current follower stage Current mirror stage Instrumentation amplifier Temperature coefficient Voltage gain DC voltage gain Current gain of bipolar transistor Voltage attenuation of feedback network Capacitor value Chopper Specific capacitance of gate oxide Miller capacitor value Parallel capacitor value Distortion Frequency Transit frequency of a transistor Zero-dB frequency Transconductance of a transistor Small-signal current Current Bias current (continued) xxiii

xxiv Notation I C I D I E I S I Q Collector current Drain current Emitter current Supply current Quiescent current k Boltzman s constant K ¼ μc ox W/L L Length of gate in MOS transistors M CMOS transistor R Resistor value S Signal S Switch S r Slew rate T Generalized transistor Q Bipolar transistor v Small-signal voltage V Voltage V B Bias voltage V CC Positive supply voltage with bipolar transistors V DD Positive supply voltage with MOS transistors V EE Negative supply voltage with bipolar transistors V G Generator voltage V GS Gate-source voltage V GT Active gate-source voltage (V GS V TH ) V S Total-supply voltage V SN Negative supply voltage V SP Positive supply voltage V SS Negative supply voltage with MOS transistors V T Thermal voltage kt/q V TH Threshold voltage of MOS device W Width of gate in MOS transistors μ Mobility of change carriers Extrinsic device parameters R L C L C M R D R C R G R B R S R E

Notation xxv Intrinsic small-signal transistor parameters r ds r ce r o r gs r be r s r e c ds c ce c gs c be g m g m μ n μ p β n β p