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Головна Microelectronic Circuits
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Microelectronic Circuits, 7th-2015_(Adel S. Sedra, Kenneth C. Smith).pdf
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Microelectronic Circuits Sedra_FM_BM.indd 1 9/30/2014 9:36:10 PM THE OXFORD SERIES IN ELECTRICAL AND COMPUTER ENGINEERING Adel S. Sedra, Series Editor Allen and Holberg, CMOS Analog Circuit Design, 3rd edition Bobrow, Elementary Linear Circuit Analysis, 2nd edition Bobrow, Fundamentals of Electrical Engineering, 2nd edition Campbell, Fabrication Engineering at the Micro- and Nanoscale, 4th edition Chen, Digital Signal Processing Chen, Linear System Theory and Design, 4th edition Chen, Signals and Systems, 3rd edition Comer, Digital Logic and State Machine Design, 3rd edition Comer, Microprocessor-Based System Design Cooper and McGillem, Probabilistic Methods of Signal and System Analysis, 3rd edition Dimitrijev, Principles of Semiconductor Device, 2nd edition Dimitrijev, Understanding Semiconductor Devices Fortney, Principles of Electronics: Analog & Digital Franco, Electric Circuits Fundamentals Ghausi, Electronic Devices and Circuits: Discrete and Integrated Guru and Hiziroğlu, Electric Machinery and Transformers, 3rd edition Houts, Signal Analysis in Linear Systems Jones, Introduction to Optical Fiber Communication Systems Krein, Elements of Power Electronics Kuo, Digital Control Systems, 2nd edition Lathi, Linear Systems and Signals, 2nd edition Lathi and Ding, Modern Digital and Analog Communication Systems, 4th edition Lathi, Signal Processing and Linear Systems Martin, Digital Integrated Circuit Design Miner, Lines and Electromagnetic Fields for Engineers Parhami, Computer Architecture Parhami, Computer Arithmetic, 2nd edition Roberts and Sedra, SPICE, 2nd edition Roberts, Taenzler, and Burns, An Introduction to Mixed-Signal IC Test and Measurement, 2nd edition Roulston, An Introduction to the Physics of Semiconductor Devices Sadiku, Elements of Electromagnetics, 6th edition Santina, Stubberud, and Hostetter, Digital Control System Design, 2nd edition Sarma, Introduction to Electrical Engineering Schaumann, Xiao, and Van Valkenburg, Design of Analog Filters, 3rd edition Schwarz and Oldham, E; lectrical Engineering: An Introduction, 2nd edition Sedra and Smith, Microelectronic Circuits, 7th edition Stefani, Shahian, Savant, and Hostetter, Design of Feedback Control Systems, 4th edition Tsividis/McAndrew, Operation and Modeling of the MOS Transistor, 3rd edition Van Valkenburg, Analog Filter Design Warner and Grung, Semiconductor Device Electronics Wolovich, Automatic Control Systems Yariv and Yeh, Photonics: Optical Electronics in Modern Communications, 6th edition Żak, Systems and Control Sedra_FM_BM.indd 2 9/30/2014 9:36:22 PM SEVENTH EDITION Microelectronic Circuits Adel S. Sedra University of Waterloo Kenneth C. Smith University of Toronto New York Oxford OXFORD UNIVERSITY PRESS Sedra_FM_BM.indd 3 9/30/2014 9:36:34 PM Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Copyright © 2015, 2010, 2004, 1998 by Oxford University Press; 1991, 1987 Holt, Rinehart, and Winston, Inc.; 1982 CBS College Publishing For titles covered by Section 112 of the US Higher Education Opportunity Act, please visit www.oup.com/us/he for the latest information about pricing and alternate formats. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016 http://www.oup.com Oxford is a registered trade mark of Oxford University Press. 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 permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Sedra, Adel S., author. Microelectronic circuits / Adel S. Sedra, University of Waterloo, Kenneth C. Smith, University of Toronto. — Seventh edition. pages cm. — (The Oxford series in electrical and computer engineering) Includes bibliographical references and index. ISBN 978–0–19–933913–6 1. Electronic circuits. 2. Integrated circuits. I. Smith, Kenneth C. (Kenneth Carless), author. II. Title. TK7867.S39 2014 621.3815—dc232014033965 Multisim and National Instruments are trademarks of National Instruments. The Sedra/Smith, Microelectronic Circuits, Seventh Edition book is a product of Oxford University Press, not National Instruments Corporation or any of its affiliated companies, and Oxford University Press is solely responsible for the Sedra/Smith book and its content. Neither Oxford University Press, the Sedra/Smith book, nor any of the books and other goods and services offered by Oxford University Press are official publications of National Instruments Corporation or any of its affiliated companies, and they are not affiliated with, endorsed by, or sponsored by National Instruments Corporation or any of its affiliated companies. OrCad and PSpice are trademarks of Cadence Design Systems, Inc. The Sedra/Smith, Microelectronic Circuits, Seventh Edition book is a product of Oxford University Press, not Cadence Design Systems, Inc., or any of its affiliated companies, and Oxford University Press is solely responsible for the Sedra/Smith book and its content. Neither Oxford University Press, the Sedra/Smith book, nor any of the books and other goods and services offered by Oxford University Press are official publications of Cadence Design Systems, Inc. or any of its affiliated companies, and they are not affiliated with, endorsed by, or sponsored by Cadence Design Systems, Inc. or any of its affiliated companies. Cover Photo: This 3D IC system demonstrates the concept of wireless power delivery and communication through multiple layers of CMOS chips. The communication circuits were demonstrated in an IBM 45 nm SOI CMOS process. This technology is designed to serve a multi-Gb/s interconnect between cores spread across several IC layers for high-performance processors. (Photo Credit: The picture is courtesy of Professor David Wentzloff, Director of the Wireless Integrated Circuits Group at the University of Michigan, and was edited by Muhammad Faisal, Founder of Movellus Circuits Incorporated.) Printing number: 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper Sedra_FM_BM.indd 4 9/30/2014 9:36:34 PM BRIEF TABLE OF CONTENTS Tables xvi "Expand-Your-Perspective" Notes xvii Preface xix PART I 1 2 3 4 5 6 7 2 Signals and Amplifiers 4 Operational Amplifiers 58 Semiconductors 134 Diodes 174 MOS Field-Effect Transistors (MOSFETs) Bipolar Junction Transistors (BJTs) 304 Transistor Amplifiers 366 PART II 8 9 10 11 12 13 DEVICES AND BASIC CIRCUITS 246 INTEGRATED-CIRCUIT AMPLIFIERS 506 Building Blocks of Integrated-Circuit Amplifiers Differential and Multistage Amplifiers 594 Frequency Response 696 Feedback 806 Output Stages and Power Amplifiers 920 Operational Amplifier Circuits 994 PART III DIGITAL INTEGRATED CIRCUITS 508 1086 14 CMOS Digital Logic Circuits 1088 15 Advanced Topics in Digital Integrated-Circuit Design 16 Memory Circuits 1236 PART IV FILTERS AND OSCILLATORS 1166 1288 17 Filters and Tuned Amplifiers 1290 18 Signal Generators and Waveform-Shaping Circuits 1378 Appendices A–L Index IN-1 v Sedra_FM_BM.indd 5 9/30/2014 9:36:37 PM CONTENTS Tables xvi "Expand-Your-Perspective" Notes xvii Preface xix DEVICES AND BASIC CIRCUITS 2 PART I 1 Signals and Amplifiers 4 Introduction 5 1.1 Signals 6 1.2 Frequency Spectrum of Signals 9 1.3 Analog and Digital Signals 12 1.4 Amplifiers 15 1.4.1 Signal Amplification 15 1.4.2 Amplifier Circuit Symbol 16 1.4.3 Voltage Gain 17 1.4.4 Power Gain and Current Gain 17 1.4.5 Expressing Gain in Decibels 18 1.4.6 The Amplifier Power Supplies 18 1.4.7 Amplifier Saturation 21 1.4.8 Symbol Convention 22 1.5 Circuit Models for Amplifiers 23 1.5.1 Voltage Amplifiers 23 1.5.2 Cascaded Amplifiers 25 1.5.3 Other Amplifier Types 28 1.5.4 Relationships between the Four Amplifier Models 28 1.5.5 Determining Ri and Ro 29 1.5.6 Unilateral Models 29 1.6 Frequency Response of Amplifiers 33 1.6.1 Measuring the Amplifier Frequency Response 33 1.6.2 Amplifier Bandwidth 34 1.6.3 Evaluating the Frequency Response of Amplifiers 34 1.6.4 Single-Time-Constant Networks 35 1.6.5 Classification of Amplifiers Based on Frequency Response 41 Summary 44 Problems 45 2 Operational Amplifiers 58 Introduction 59 2.1 The Ideal Op Amp 60 2.1.1 The Op-Amp Terminals 60 2.1.2 Function and Characteristics of the Ideal Op Amp 61 2.1.3 Differential and Common-Mode Signals 63 2.2 The Inverting Configuration 64 2.2.1 The Closed-Loop Gain 65 2.2.2 Effect of the Finite Open-Loop Gain 67 2.2.3 Input and Output Resistances 68 2.2.4 An Important Application—The Weighted Summer 71 2.3 The Noninverting Configuration 73 2.3.1 The Closed-Loop Gain 73 2.3.2 Effect of Finite Open-Loop Gain 75 2.3.3 Input and Output Resistance 75 2.3.4 The Voltage Follower 75 2.4 Difference Amplifiers 77 2.4.1 A Single-Op-Amp Difference Amplifier 78 2.4.2 A Superior Circuit—The Instrumentation Amplifier 82 2.5 Integrators and Differentiators 87 2.5.1 The Inverting Configuration with General Impedances 87 2.5.2 The Inverting Integrator 89 2.5.3 The Op-Amp Differentiator 94 2.6 DC Imperfections 96 2.6.1 Offset Voltage 96 2.6.2 Input Bias and Offset Currents 100 2.6.3 Effect of VOS and IOS on the Operation of the Inverting Integrator 103 2.7 Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance 105 2.7.1 Frequency Dependence of the Open-Loop Gain 105 2.7.2 Frequency Response of Closed-Loop Amplifiers 107 vi Sedra_FM_BM.indd 6 9/30/2014 9:36:41 PM Contents vii 2.8 Large-Signal Operation of Op Amps 110 2.8.1 Output Voltage Saturation 110 2.8.2 Output Current Limits 110 2.8.3 Slew Rate 112 2.8.4 Full-Power Bandwidth 114 Summary 115 Problems 116 3 Semiconductors 134 Introduction 135 3.1 Intrinsic Semiconductors 136 3.2 Doped Semiconductors 139 3.3 Current Flow in Semiconductors 142 3.3.1 Drift Current 142 3.3.2 Diffusion Current 145 3.3.3 Relationship between D and μ 148 3.4 The pn Junction 148 3.4.1 Physical Structure 149 3.4.2 Operation with Open-Circuit Terminals 149 3.5 The pn Junction with an Applied Voltage 155 3.5.1 Qualitative Description of Junction Operation 155 3.5.2 The Current–Voltage Relationship of the Junction 158 3.5.3 Reverse Breakdown 162 3.6 Capacitive Effects in the pn Junction 164 3.6.1 Depletion or Junction Capacitance 164 3.6.2 Diffusion Capacitance 166 Summary 168 Problems 171 4 Diodes 174 Introduction 175 4.1 The Ideal Diode 176 4.1.1 Current–Voltage Characteristic 176 4.1.2 A Simple Application: The Rectifier 177 4.1.3 Another Application: Diode Logic Gates 180 4.2 Terminal Characteristics of Junction Diodes 184 4.2.1 The Forward-Bias Region 184 4.2.2 The Reverse-Bias Region 189 4.2.3 The Breakdown Region 190 4.3 Modeling the Diode Forward Characteristic 190 Sedra_FM_BM.indd 7 4.3.1 The Exponential Model 190 4.3.2 Graphical Analysis Using the Exponential Model 191 4.3.3 Iterative Analysis Using the Exponential Model 191 4.3.4 The Need for Rapid Analysis 192 4.3.5 The Constant-Voltage-Drop Model 193 4.3.6 The Ideal-Diode Model 194 4.3.7 The Small-Signal Model 195 4.3.8 Use of the Diode Forward Drop in Voltage Regulation 200 4.4 Operation in the Reverse Breakdown Region—Zener Diodes 202 4.4.1 Specifying and Modeling the Zener Diode 203 4.4.2 Use of the Zener as a Shunt Regulator 204 4.4.3 Temperature Effects 206 4.4.4 A Final Remark 207 4.5 Rectifier Circuits 207 4.5.1 The Half-Wave Rectifier 208 4.5.2 The Full-Wave Rectifier 210 4.5.3 The Bridge Rectifier 212 4.5.4 The Rectifier with a Filter Capacitor—The Peak Rectifier 213 4.5.5 Precision Half-Wave Rectifier—The Superdiode 219 4.6 Limiting and Clamping Circuits 221 4.6.1 Limiter Circuits 221 4.6.2 The Clamped Capacitor or DC Restorer 224 4.6.3 The Voltage Doubler 226 4.7 Special Diode Types 227 4.7.1 The Schottky-Barrier Diode (SBD) 227 4.7.2 Varactors 228 4.7.3 Photodiodes 228 4.7.4 Light-Emitting Diodes (LEDs) 228 Summary 229 Problems 230 5 MOS Field-Effect Transistors (MOSFETs) 246 Introduction 247 5.1 Device Structure and Physical Operation 248 5.1.1 Device Structure 248 5.1.2 Operation with Zero Gate Voltage 250 9/30/2014 9:36:41 PM viii Contents 5.1.3 Creating a Channel for Current Flow 250 5.1.4 Applying a Small v DS 252 5.1.5 Operation as v DS Is Increased 256 5.1.6 Operation for v DS ≥ VOV: Channel Pinch-Off and Current Saturation 258 5.1.7 The p-Channel MOSFET 261 5.1.8 Complementary MOS or CMOS 263 5.1.9 Operating the MOS Transistor in the Subthreshold Region 264 5.2 Current–Voltage Characteristics 264 5.2.1 Circuit Symbol 264 5.2.2 The iD –v DS Characteristics 265 5.2.3 The iD –v GS Characteristic 267 5.2.4 Finite Output Resistance in Saturation 271 5.2.5 Characteristics of the p-Channel MOSFET 274 5.3 MOSFET Circuits at DC 276 5.4 The Body Effect and Other Topics 288 5.4.1 The Role of the Substrate—The Body Effect 288 5.4.2 Temperature Effects 289 5.4.3 Breakdown and Input Protection 289 5.4.4 Velocity Saturation 290 5.4.5 The Depletion-Type MOSFET 290 Summary 291 Problems 292 6 Bipolar Junction Transistors (BJTs) 304 Introduction 305 6.1 Device Structure and Physical Operation 306 6.1.1 Simplified Structure and Modes of Operation 306 6.1.2 Operation of the npn Transistor in the Active Mode 307 6.1.3 Structure of Actual Transistors 315 6.1.4 Operation in the Saturation Mode 316 6.1.5 The pnp Transistor 318 6.2 Current–Voltage Characteristics 320 6.2.1 Circuit Symbols and Conventions 320 6.2.2 G raphical Representation of Transistor Characteristics 325 Sedra_FM_BM.indd 8 6.2.3 D ependence of iC on the Collector Voltage—The Early Effect 326 6.2.4 A n Alternative Form of the CommonEmitter Characteristics 329 6.3 BJT Circuits at DC 333 6.4 Transistor Breakdown and Temperature Effects 351 6.4.1 Transistor Breakdown 351 6.4.2 Dependence of β on IC and Temperature 353 Summary 354 Problems 355 7 Transistor Amplifiers 366 Introduction 367 7.1 Basic Principles 368 7.1.1 The Basis for Amplifier Operation 368 7.1.2 Obtaining a Voltage Amplifier 369 7.1.3 The Voltage-Transfer Characteristic (VTC) 370 7.1.4 Obtaining Linear Amplification by Biasing the Transistor 371 7.1.5 The Small-Signal Voltage Gain 374 7.1.6 Determining the VTC by Graphical Analysis 380 7.1.7 Deciding on a Location for the Bias Point Q 381 7.2 Small-Signal Operation and Models 383 7.2.1 The MOSFET Case 383 7.2.2 The BJT Case 399 7.2.3 Summary Tables 420 7.3 Basic Configurations 423 7.3.1 The Three Basic Configurations 423 7.3.2 Characterizing Amplifiers 424 7.3.3 The Common-Source (CS) and Common-Emitter (CE) Amplifiers 426 7.3.4 The Common-Source (CommonEmitter) Amplifier with a Source (Emitter) Resistance 431 7.3.5 The Common-Gate (CG) and the Common-Base (CB) Amplifiers 439 7.3.6 The Source and Emitter Followers 442 7.3.7 Summary Tables and Comparisons 452 9/30/2014 9:36:41 PM Contents ix 7.3.8 When and How to Include the Transistor Output Resistance ro 453 7.4 Biasing 454 7.4.1 The MOSFET Case 455 7.4.2 The BJT Case 461 7.5 Discrete-Circuit Amplifiers 467 7.5.1 A Common-Source (CS) Amplifier 467 7.5.2 A Common-Emitter (CE) Amplifier 470 7.5.3 A Common-Emitter Amplifier with an Emitter Resistance Re 471 7.5.4 A Common-Base (CB) Amplifier 473 7.5.5 An Emitter Follower 475 7.5.6 The Amplifier Frequency Response 477 Summary 479 Problems 480 INTEGRATED-CIRCUIT AMPLIFIERS 506 PART II 8 Building Blocks of IntegratedCircuit Amplifiers 508 Introduction 509 8.1 IC Design Philosophy 510 8.2 IC Biasing—Current Sources, Current Mirrors, and Current-Steering Circuits 511 8.2.1 The Basic MOSFET Current Source 512 8.2.2 MOS Current-Steering Circuits 515 8.2.3 BJT Circuits 518 8.2.4 Small-Signal Operation of Current Mirrors 523 8.3 The Basic Gain Cell 525 8.3.1 The CS and CE Amplifiers with Current-Source Loads 525 8.3.2 The Intrinsic Gain 527 8.3.3 Effect of the Output Resistance of the Current-Source Load 530 8.3.4 Increasing the Gain of the Basic Cell 536 8.4 The Common-Gate and Common-Base Amplifiers 537 8.4.1 The CG Circuit 537 8.4.2 Output Resistance of a CS Amplifier with a Source Resistance 541 Sedra_FM_BM.indd 9 8.4.3 The Body Effect 542 8.4.4 The CB Circuit 543 8.4.5 Output Resistance of an EmitterDegenerated CE Amplifier 546 8.5 The Cascode Amplifier 546 8.5.1 Cascoding 546 8.5.2 The MOS Cascode Amplifier 547 8.5.3 Distribution of Voltage Gain in a Cascode Amplifier 552 8.5.4 Double Cascoding 555 8.5.5 The Folded Cascode 555 8.5.6 The BJT Cascode 557 8.6 C urrent-Mirror Circuits with Improved Performance 559 8.6.1 Cascode MOS Mirrors 559 8.6.2 The Wilson Current Mirror 560 8.6.3 The Wilson MOS Mirror 563 8.6.4 The Widlar Current Souce 565 8.7 Some Useful Transistor Pairings 567 8.7.1 The CC–CE, CD–CS, and CD–CE Configurations 567 8.7.2 The Darlington Configuration 571 8.7.3 The CC–CB and CD–CG Configurations 572 Summary 575 Problems 576 9 Differential and Multistage Amplifiers 594 Introduction 595 9.1 The MOS Differential Pair 596 9.1.1 Operation with a Common-Mode Input Voltage 597 9.1.2 Operation with a Differential Input Voltage 601 9.1.3 Large-Signal Operation 602 9.1.4 Small-Signal Operation 607 9.1.5 The Differential Amplifier with Current-Source Loads 611 9.1.6 Cascode Differential Amplifier 612 9.2 The BJT Differential Pair 614 9.2.1 Basic Operation 614 9.2.2 Input Common-Mode Range 616 9.2.3 Large-Signal Operation 617 9.2.4 Small-Signal Operation 620 9.3 Common-Mode Rejection 627 9.3.1 The MOS Case 628 9.3.2 The BJT Case 634 9.4 DC Offset 637 9/30/2014 9:36:42 PM x Contents 9.4.1 Input Offset Voltage of the MOS Differential Amplifier 637 9.4.2 Input Offset Voltage of the Bipolar Differential Amplifier 640 9.4.3 Input Bias and Offset Currents of the Bipolar Differential Amplifier 643 9.4.4 A Concluding Remark 644 9.5 The Differential Amplifier with a Current-Mirror Load 644 9.5.1 Differential to Single-Ended Conversion 644 9.5.2 The Current-Mirror-Loaded MOS Differential Pair 645 9.5.3 Differential Gain of the Current-Mirror-Loaded MOS Pair 647 9.5.4 The Bipolar Differential Pair with a Current-Mirror Load 651 9.5.5 Common-Mode Gain and CMRR 655 9.6 Multistage Amplifiers 659 9.6.1 A Two-Stage CMOS Op Amp 659 9.6.2 A Bipolar Op Amp 664 Summary 672 Problems 674 10 Frequency Response 696 Introduction 697 10.1 Low-Frequency Response of Discrete-Circuit CommonSource and Common-Emitter Amplifiers 699 10.1.1 The CS Amplifier 699 10.1.2 The Method of Short-Circuit Time-Constants 707 10.1.3 The CE Amplifier 707 10.2 Internal Capacitive Effects and the High-Frequency Model of the MOSFET and the BJT 711 10.2.1 The MOSFET 711 10.2.2 The BJT 717 10.3 High-Frequency Response of the CS and CE Amplifiers 722 10.3.1 The Common-Source Amplifier 722 10.3.2 The Common-Emitter Amplifier 728 10.3.3 Miller's Theorem 732 10.3.4 Frequency Response of the CS Amplifier When Rsig Is Low 735 Sedra_FM_BM.indd 10 10.4 Useful Tools for the Analysis of the High-Frequency Response of Amplifiers 739 10.4.1 The High-Frequency Gain Function 739 10.4.2 Determining the 3-dB Frequency fH 740 10.4.3 The Method of Open-Circuit Time Constants 743 10.4.4 Application of the Method of Open-Circuit Time Constants to the CS Amplifier 744 10.4.5 Application of the Method of Open-Circuit Time Constants to the CE Amplifier 748 10.5 High-Frequency Response of the Common-Gate and Cascode Amplifiers 748 10.5.1 High-Frequency Response of the CG Amplifier 748 10.5.2 High-Frequency Response of the MOS Cascode Amplifier 754 10.5.3 High-Frequency Response of the Bipolar Cascode Amplifier 759 10.6 High-Frequency Response of the Source and Emitter Followers 760 10.6.1 The Source-Follower Case 761 10.6.2 The Emitter-Follower Case 767 10.7 High-Frequency Response of Differential Amplifiers 768 10.7.1 Analysis of the Resistively Loaded MOS Amplifier 768 10.7.2 Analysis of the Current-MirrorLoaded MOS Amplifier 772 10.8 Other Wideband Amplifier Configurations 778 10.8.1 Obtaining Wideband Amplification by Source and Emitter Degeneration 778 10.8.2 The CD–CS, CC–CE, and CD–CE Configurations 781 10.8.3 The CC–CB and CD–CG Configurations 786 Summary 788 Problems 789 11 Feedback 806 Introduction 807 11.1 The General Feedback Structure 808 11.1.1 Signal-Flow Diagram 808 11.1.2 The Closed-Loop Gain 809 9/30/2014 9:36:42 PM Contents xi 11.1.3 The Loop Gain 810 11.1.4 Summary 814 11.2 Some Properties of Negative Feedback 815 11.2.1 Gain Desensitivity 815 11.2.2 Bandwidth Extension 816 11.2.3 Interference Reduction 817 11.2.4 Reduction in Nonlinear Distortion 819 11.3 The Feedback Voltage Amplifier 820 11.3.1 The Series–Shunt Feedback Topology 820 11.3.2 Examples of Series–Shunt Feedback Amplifiers 821 11.3.3 Analysis of the Feedback Voltage Amplifier Utilizing the Loop Gain 823 11.3.4 A Final Remark 828 11.4 Systematic Analysis of Feedback Voltage Amplifiers 828 11.4.1 The Ideal Case 829 11.4.2 The Practical Case 831 11.5 Other Feedback Amplifier Types 840 11.5.1 Basic Principles 840 11.5.2 The Feedback Transconductance Amplifier (Series–Series) 844 11.5.3 The Feedback Transresistance Amplifier (Shunt–Shunt) 855 11.5.4 The Feedback Current Amplifier (Shunt–Series) 865 11.6 Summary of the Feedback Analysis Method 871 11.7 The Stability Problem 871 11.7.1 Transfer Function of the Feedback Amplifier 871 11.7.2 The Nyquist Plot 873 11.8 Effect of Feedback on the Amplifier Poles 875 11.8.1 Stability and Pole Location 875 11.8.2 Poles of the Feedback Amplifier 876 11.8.3 Amplifier with a Single-Pole Response 877 11.8.4 Amplifier with a Two-Pole Response 878 11.8.5 Amplifiers with Three or More Poles 883 11.9 Stability Study Using Bode Plots 885 11.9.1 Gain and Phase Margins 885 11.9.2 Effect of Phase Margin on Closed-Loop Response 886 Sedra_FM_BM.indd 11 11.9.3 An Alternative Approach for Investigating Stability 887 11.10 Frequency Compensation 889 11.10.1 Theory 889 11.10.2 Implementation 891 11.10.3 Miller Compensation and Pole Splitting 892 Summary 895 Problems 896 12 Output Stages and Power Amplifiers 920 Introduction 921 12.1 Classification of Output Stages 922 12.2 Class A Output Stage 923 12.2.1 Transfer Characteristic 924 12.2.2 Signal Waveforms 925 12.2.3 Power Dissipation 926 12.2.4 Power-Conversion Efficiency 928 12.3 Class B Output Stage 929 12.3.1 Circuit Operation 929 12.3.2 Transfer Characteristic 929 12.3.3 Power-Conversion Efficiency 930 12.3.4 Power Dissipation 931 12.3.5 Reducing Crossover Distortion 933 12.3.6 Single-Supply Operation 934 12.4 Class AB Output Stage 935 12.4.1 Circuit Operation 935 12.4.2 Output Resistance 937 12.5 Biasing the Class AB Circuit 940 12.5.1 Biasing Using Diodes 940 12.5.2 Biasing Using the VBE Multiplier 942 12.6 Variations on the Class AB Configuration 945 12.6.1 Use of Input Emitter Followers 945 12.6.2 Use of Compound Devices 946 12.6.3 Short-Circuit Protection 949 12.6.4 Thermal Shutdown 950 12.7 CMOS Class AB Output Stages 950 12.7.1 The Classical Configuration 950 12.7.2 An Alternative Circuit Utilizing Common-Source Transistors 953 12.8 IC Power Amplifiers 961 12.8.1 A Fixed-Gain IC Power Amplifier 962 9/30/2014 9:36:42 PM xii Contents 12.8.2 T he Bridge Amplifier 966 12.9 Class D Power Amplifiers 967 12.10 Power Transistors 971 12.10.1 Packages and Heat Sinks 971 12.10.2 Power BJTs 972 12.10.3 Power MOSFETs 974 12.10.4 Thermal Considerations 976 Summary 982 Problems 983 13 Operational-Amplifier Circuits 994 Introduction 995 13.1 The Two-Stage CMOS Op Amp 996 13.1.1 The Circuit 997 13.1.2 Input Common-Mode Range and Output Swing 998 13.1.3 DC Voltage Gain 999 13.1.4 Common-Mode Rejection Ratio (CMRR) 1001 13.1.5 Frequency Response 1002 13.1.6 Slew Rate 1007 13.1.7 Power-Supply Rejection Ratio (PSRR) 1008 13.1.8 Design Trade-Offs 1009 13.1.9 A Bias Circuit for the Two-Stage CMOS Op Amp 1010 13.2 T he Folded-Cascode CMOS Op Amp 1016 13.2.1 The Circuit 1016 13.2.2 Input Common-Mode Range and Output Swing 1018 13.2.3 Voltage Gain 1020 13.2.4 Frequency Response 1021 13.2.5 Slew Rate 1022 13.2.6 Increasing the Input CommonMode Range: Rail-to-Rail Input Operation 1024 13.2.7 Increasing the Output Voltage Range: The Wide-Swing Current Mirror 1026 13.3 The 741 BJT Op Amp 1028 13.3.1 The 741 Circuit 1028 13.3.2 DC Analysis 1032 13.3.3 Small-Signal Analysis 1038 13.3.4 Frequency Response 1051 13.3.5 Slew Rate 1053 13.4 Modern Techniques for the Design of BJT Op Amps 1054 Sedra_FM_BM.indd 12 13.4.1 Special Performance Requirements 1054 13.4.2 Bias Design 1056 13.4.3 Design of the Input Stage to Obtain Rail-to-Rail VICM 1058 13.4.4 Common-Mode Feedback to Control the DC Voltage at the Output of the Input Stage 1064 13.4.5 Output-Stage Design for Near Rail-to-Rail Output Swing 1069 13.4.6 Concluding Remark 1073 Summary 1073 Problems 1074 DIGITAL INTEGRATED CIRCUITS 1086 PART III 14 CMOS Digital Logic Circuits 1088 Introduction 1089 14.1 CMOS Logic-Gate Circuits 1090 14.1.1 Switch-Level Transistor Model 1090 14.1.2 The CMOS Inverter 1091 14.1.3 General Structure of CMOS Logic 1091 14.1.4 The Two-Input NOR Gate 1094 14.1.5 The Two-Input NAND Gate 1095 14.1.6 A Complex Gate 1096 14.1.7 Obtaining the PUN from the PDN and Vice Versa 1096 14.1.8 The Exclusive-OR Function 1097 14.1.9 Summary of the Synthesis Method 1098 14.2 Digital Logic Inverters 1100 14.2.1 The Voltage-Transfer Characteristic (VTC) 1100 14.2.2 Noise Margins 1101 14.2.3 The Ideal VTC 1103 14.2.4 Inverter Implementation 1103 14.3 The CMOS Inverter 1114 14.3.1 Circuit Operation 1114 14.3.2 The Voltage-Transfer Characteristic (VTC) 1117 14.3.3 The Situation When QN and QP Are Not Matched 1120 14.4 Dynamic Operation of the CMOS Inverter 1125 9/30/2014 9:36:42 PM Contents xiii 14.4.1 Propagation Delay 1125 14.4.2 Determining the Propagation Delay of the CMOS Inverter 1129 14.4.3 Determining the Equivalent Load Capacitance C 1136 14.5 Transistor Sizing 1139 14.5.1 Inverter Sizing 1139 14.5.2 Transistor Sizing in CMOS Logic Gates 1141 14.5.3 Effects of Fan-In and Fan-Out on Propagation Delay 1145 14.5.4 Driving a Large Capacitance 1146 14.6 Power Dissipation 1149 14.6.1 Sources of Power Dissipation 1149 14.6.2 Power–Delay and Energy–Delay Products 1152 Summary 1154 Problems 1156 15 Advanced Topics in Digital Integrated-Circuit Design 1166 Introduction 1167 15.1 Implications of Technology Scaling: Issues in Deep-Submicron Design 1168 15.1.1 Silicon Area 1169 15.1.2 Scaling Implications 1169 15.1.3 Velocity Saturation 1171 15.1.4 Subthreshold Conduction 1177 15.1.5 Temperature, Voltage, and Process Variations 1178 15.1.6 Wiring: The Interconnect 1178 15.2 Digital IC Technologies, Logic-Circuit Families, and Design Methodologies 1179 15.2.1 Digital IC Technologies and Logic-Circuit Families 1180 15.2.2 Styles for Digital System Design 1182 15.2.3 Design Abstraction and Computer Aids 1182 15.3 Pseudo-NMOS Logic Circuits 1183 15.3.1 The Pseudo-NMOS Inverter 1183 15.3.2 Static Characteristics 1184 15.3.3 Derivation of the VTC 1186 15.3.4 Dynamic Operation 1188 15.3.5 Design 1189 15.3.6 Gate Circuits 1189 Sedra_FM_BM.indd 13 15.3.7 Concluding Remarks 1190 15.4 Pass-Transistor Logic Circuits 1192 15.4.1 An Essential Design Requirement 1193 15.4.2 Operation with NMOS Transistors as Switches 1194 15.4.3 Restoring the Value of VOH to VDD 1198 15.4.4 The Use of CMOS Transmission Gates as Switches 1199 15.4.5 Examples of Pass-Transistor Logic Circuits 1206 15.4.6 A Final Remark 1208 15.5 Dynamic MOS Logic Circuits 1208 15.5.1 The Basic Principle 1209 15.5.2 Nonideal Effects 1212 15.5.3 Domino CMOS Logic 1216 15.5.4 Concluding Remarks 1217 15.6 Bipolar and BiCMOS Logic Circuits 1217 15.6.1 Emitter-Coupled Logic (ECL) 1218 15.6.2 BiCMOS Digital Circuits 1223 Summary 1226 Problems 1227 16 Memory Circuits 1236 Introduction 1237 16.1 Latches and Flip-Flops 1238 16.1.1 The Latch 1238 16.1.2 The SR Flip-Flop 1240 16.1.3 CMOS Implementation of SR Flip-Flops 1241 16.1.4 A Simpler CMOS Implementation of the Clocked SR Flip-Flop 1247 16.1.5 D Flip-Flop Circuits 1247 16.2 Semiconductor Memories: Types and Architectures 1249 16.2.1 Memory-Chip Organization 1250 16.2.2 Memory-Chip Timing 1252 16.3 Random-Access Memory (RAM) Cells 1253 16.3.1 Static Memory (SRAM) Cell 1253 16.3.2 Dynamic Memory (DRAM) Cell 1260 16.4 Sense Amplifiers and Address Decoders 1262 16.4.1 The Sense Amplifier 1263 9/30/2014 9:36:42 PM xiv Contents 16.4.2 The Row-Address Decoder 1271 16.4.3 The Column-Address Decoder 1273 16.4.4 Pulse-Generation Circuits 1274 16.5 Read-Only Memory (ROM) 1276 16.5.1 A MOS ROM 1276 16.5.2 Mask Programmable ROMs 1278 16.5.3 Programmable ROMs (PROMs, EPROMs, and Flash) 1279 16.6 CMOS Image Sensors 1281 Summary 1282 Problems 1283 FILTERS AND OSCILLATORS 1288 PART IV 17 Filters and Tuned Amplifiers 1290 Introduction 1291 17.1 Filter Transmission, Types, and Specification 1292 17.1.1 Filter Transmission 1292 17.1.2 Filter Types 1293 17.1.3 Filter Specification 1293 17.2 The Filter Transfer Function 1296 17.3 Butterworth and Chebyshev Filters 1300 17.3.1 The Butterworth Filter 1300 17.3.2 The Chebyshev Filter 1304 17.4 First-Order and Second-Order Filter Functions 1307 17.4.1 First-Order Filters 1308 17.4.2 Second-Order Filter Functions 1311 17.5 The Second-Order LCR Resonator 1316 17.5.1 The Resonator Natural Modes 1316 17.5.2 Realization of Transmission Zeros 1317 17.5.3 Realization of the Low-Pass Function 1317 17.5.4 Realization of the High-Pass Function 1319 17.5.5 Realization of the Bandpass Function 1319 17.5.6 Realization of the Notch Functions 1319 17.5.7 Realization of the All-Pass Function 1321 17.6 Second-Order Active Filters Based on Inductor Replacement 1322 Sedra_FM_BM.indd 14 17.6.1 The Antoniou InductanceSimulation Circuit 1322 17.6.2 The Op Amp–RC Resonator 1323 17.6.3 Realization of the Various Filter Types 1325 17.6.4 The All-Pass Circuit 1325 17.7 Second-Order Active Filters Based on the Two-Integrator-Loop Topology 1330 17.7.1 Derivation of the Two-IntegratorLoop Biquad 1330 17.7.2 Circuit Implementation 1332 17.7.3 An Alternative Two-IntegratorLoop Biquad Circuit 1334 17.7.4 Final Remarks 1335 17.8 Single-Amplifier Biquadratic Active Filters 1336 17.8.1 Synthesis of the Feedback Loop 1336 17.8.2 Injecting the Input Signal 1339 17.8.3 Generation of Equivalent Feedback Loops 1341 17.9 Sensitivity 1344 17.10 Transconductance-C Filters 1347 17.10.1 Methods for IC Filter Implementation 1347 17.10.2 Transconductors 1348 17.10.3 Basic Building Blocks 1349 17.10.4 Second-Order Gm −C Filter 1351 17.11 Switched-Capacitor Filters 1354 17.11.1 The Basic Principle 1354 17.11.2 Practical Circuits 1356 17.11.3 Final Remarks 1359 17.12 Tuned Amplifiers 1359 17.12.1 The Basic Principle 1360 17.12.2 Inductor Losses 1362 17.12.3 Use of Transformers 1363 17.12.4 Amplifiers with Multiple Tuned Circuits 1365 17.12.5 The Cascode and the CC–CB Cascade 1366 17.12.6 Synchronous Tuning and Stagger Tuning 1367 Summary 1368 Problems 1369 18 Signal Generators and Waveform-Shaping Circuits 1378 Introduction 1379 18.1 Basic Principles of Sinusoidal Oscillators 1380 9/30/2014 9:36:42 PM Contents xv 18.1.1 The Oscillator Feedback Loop 1380 18.1.2 The Oscillation Criterion 1381 18.1.3 Analysis of Oscillator Circuits 1382 18.1.4 Nonlinear Amplitude Control 1385 18.1.5 A Popular Limiter Circuit for Amplitude Control 1386 18.2 Op Amp–RC Oscillator Circuits 1388 18.2.1 The Wien-Bridge Oscillator 1388 18.2.2 The Phase-Shift Oscillator 1391 18.2.3 The Quadrature Oscillator 1392 18.2.4 The Active-Filter-Tuned Oscillator 1394 18.2.5 A Final Remark 1396 18.3 LC and Crystal Oscillators 1396 18.3.1 The Colpitts and Hartley Oscillators 1396 18.3.2 The Cross-Coupled LC Oscillator 1400 18.3.3 Crystal Oscillators 1402 18.4 Bistable Multivibrators 1404 18.4.1 The Feedback Loop 1405 18.4.2 Transfer Characteristic of the Bistable Circuit 1406 18.4.3 Triggering the Bistable Circuit 1407 18.4.4 The Bistable Circuit as a Memory Element 1407 18.4.5 A Bistable Circuit with Noninverting Transfer Characteristic 1408 18.4.6 Application of the Bistable Circuit as a Comparator 1409 18.4.7 Making the Output Levels More Precise 1411 18.5 Generation of Square and Triangular Waveforms Using Astable Multivibrators 1412 18.5.1 Operation of the Astable Multivibrator 1413 18.5.2 Generation of Triangular Waveforms 1415 Sedra_FM_BM.indd 15 18.6 Generation of a Standardized Pulse: The Monostable Multivibrator 1417 18.7 Integrated-Circuit Timers 1419 18.7.1 The 555 Circuit 1419 18.7.2 Implementing a Monostable Multivibrator Using the 555 IC 1420 18.7.3 An Astable Multivibrator Using the 555 IC 1420 18.8 Nonlinear Waveform-Shaping Circuits 1424 18.8.1 The Breakpoint Method 1424 18.8.2 The Nonlinear-Amplification Method 1426 Summary 1428 Problems 1428 Appendices A. VLSI Fabrication Technology (on website) A-1 B. SPICE Device Models and Design and Simulation Examples Using PSpice® and MultisimTM (on website) B-1 C. Two-Port Network Parameters (on website) C-1 D. Some Useful Network Theorems (on website) D-1 E. Single-Time-Constant Circuits (on website) E-1 F. s-Domain Analysis: Poles, Zeros, and Bode Plots (on website) F-1 G. Comparison of the MOSFET and the BJT (on website, also Table G.3 in text) G-1 H. Design of Stagger-Tuned Amplifiers (on website) H-1 I. Bibliography (on website) I-1 J. Standard Resistance Values and Unit Prefixes J-1 K. Typical Parameter Values for IC Devices Fabricated in CMOS and Bipolar Processes K-1 L. Answers to Selected Problems (on website) L-1 Index IN-1 9/30/2014 9:36:43 PM TABLES FOR REFERENCE AND STUDY Table 1.1 The Four Amplifier Types 28 Table 1.2 Frequency Response of STC Networks 36 Table 2.1 Characteristics of the Ideal Op Amp 62 Table 3.1 Summary of Important Semiconductor Equations 169 Table 5.1 Regions of Operation of the NMOS Transistor 266 Table 5.2 Regions of Operation of the PMOS Transistor 275 Table 6.1 BJT Modes of Operation 307 Table 6.2 Summary of the BJT Current–Voltage Relationships in the Active Mode 322 Table 6.3 Simplified Models for the Operation of the BJT in DC Circuits 334 Table 7.1 Systematic Procedure for the Analysis of Transistor Amplifier Circuits 421 Table 7.2 Small-Signal Models of the MOSFET 421 Table 7.3 Small-Signal Models of the BJT 422 Table 7.4 Characteristics of MOSFET Amplifiers 452 Table 7.5 Characteristics of BJT Amplifiers 453 Table 8.1 Gain Distribution in the MOS Cascode Amplifier for Various Values of R L 554 Table 10.1 The MOSFET High-Frequency Model 716 Table 10.2 The BJT High-Frequency Model 722 Table 11.1 Summary of the Parameters and Formulas for the Ideal Feedback-Amplifier Structure of Fig. 11.1 815 Table 11.2 Summary of Relationships for the Four FeedbackAmplifier Topologies 872 Table 13.1 DC Collector Currents of the 741 Circuit (μA) 1038 Table 14.1 Important Parameters of the VTC of the Logic Inverter 1102 Table 14.2 Summary of Important Characteristics of the CMOS Logic Inverter 1155 Table 15.1 Implications of Device and Voltage Scaling 1170 Table 15.2 Regions of Operation of the Pseudo-NMOS Inverter 1187 Table 17.1 Design Data for the Circuits Based on Inductance Simulation (Fig 17.22) 1328 Table 17.2 Design Data for the Tow-Thomas Biquad Circuit in Fig 17.26 1335 Table G.3 Comparison of the MOSFET and the BJT G-1 Table J.1 Standard Resistance Values J-1 Table J.2 SI Unit Prefixes J-2 Table J.3 Meter Conversion Factors J-2 Table K.1 Typical Values of CMOS Device Parameters K-1 Table K.2 Typical Parameter Values for BJTs K-1 xvi Sedra_FM_BM.indd 16 9/30/2014 9:36:47 PM "EXPAND-YOUR-PERSPECTIVE" NOTES Chapter 1: Analog vs. Digital Circuit Engineers 15 Chapter 1: Bode Plots 37 Chapter 2: Integrated Instrumentation Amplifiers 85 Chapter 2: Early Op Amps and Analog Computation 88 Chapter 3: LCDs, the Face of Electronics 139 Chapter 4: The Earliest Semiconductor Diode 219 Chapter 4: From Indication to Illumination 229 Chapter 5: The First Field-Effect Devices 248 Chapter 5: Gordon Moore—His Law 288 Chapter 6: The Invention of the BJT 320 Chapter 7: Shockley and Silicon Valley 405 Chapter 7: Lee de Forest—a Father of the Electronics Age 454 Chapter 8: Solid Circuits with "Flying Wires" 511 Chapter 8: The Integrated Circuit 525 Chapter 9: The Long-Tailed Pair 612 Chapter 9: The International Solid-State Circuits Conference (ISSCC) 659 Chapter 10: John Milton Miller—Capacitance Multiplication 735 Chapter 10: RFID—Identification at a Distance 772 Chapter 11: Feedback—Historical Note 823 Chapter 11: Harry Nyquist—A Diverse Electronics Fundamentalist 875 Chapter 12: Early Power-Op-Amp Product 962 Chapter 12: Hans Camenzind—the Inventor of the Class D Amplifier 968 Chapter 13: The Genie of Analog 996 Chapter 13: The Creator of the μA741—David Fullagar 1031 Chapter 14: Frank Marion Wanless—the Inventor of CMOS 1117 Chapter 14: Federico Faggin—a Pioneer in Microprocessor Electronics 1141 Chapter 15: The Invisible Computer 1182 Chapter 15: Grand-Scale Graphics 1213 Chapter 16: Flip-Flop Fact 1240 Chapter 16: Blinding Flash 1282 Chapter 17: A Brief History of Analog Filters 1295 Chapter 17: Early Filter Pioneers—Cauer and Darlington 1348 Chapter 18: The Wien-Bridge Oscillator 1390 Chapter 18: Oscillator Pioneers 1400 xvii Sedra_FM_BM.indd 17 9/30/2014 9:36:50 PM Sedra_FM_BM.indd 18 9/30/2014 9:36:50 PM PREFACE Microelectronic Circuits, Seventh Edition, is intended as a text for the core courses in electronic circuits taught to majors in electrical and computer engineering. It should also prove useful to engineers and other professionals wishing to update their knowledge through self-study. As was the case with the first six editions, the objective of this book is to develop in the reader the ability to analyze and design electronic circuits, both analog and digital, discrete and integrated. While the application of integrated circuits is covered, emphasis is placed on transistor circuit design. This is done because of our belief that even if the majority of those studying this book were not to pursue a career in IC design, knowledge of what is inside the IC package would enable intelligent and innovative application of such chips. Furthermore, with the advances in VLSI technology and design methodology, IC design itself has become accessible to an increasing number of engineers. Prerequisites The prerequisite for studying the material in this book is a first course in circuit analysis. As a review, some linear circuits material is included here in the appendices: specifically, two-port network parameters in Appendix C; some useful network theorems in Appendix D; single-time-constant circuits in Appendix E; and s-domain analysis in Appendix F. In addition, a number of relevant circuit analysis problems are included at the beginning of the end-of-chapter problems section of Chapter 1. No prior knowledge of physical electronics is assumed. All required semiconductor device physics is included, and Appendix A provides a brief description of IC fabrication. All these appendices can be found on the book's website. Emphasis on Design It has been our philosophy that circuit design is best taught by pointing out the various tradeoffs available in selecting a circuit configuration and in selecting component values for a given configuration. The emphasis on design has been retained in this edition. In addition to design examples, and design-oriented exercises and end-of-chapter problems (indicated with a D), the book includes on its website an extensive appendix (Appendix B) where a large number of simulation and design examples are presented. These emphasize the use of SPICE, the most valuable circuit-design aid. xix Sedra_FM_BM.indd 19 9/30/2014 9:36:53 PM xx Preface New to the Seventh Edition While maintaining the philosophy and pedagogical approach of the first six editions, several changes have been made to both organization and coverage. Our goal in making structural changes has been to increase modularity and thus flexibility for the instructor, without causing disturbance to courses currently using the sixth edition. Changes in coverage are necessitated by the continuing advances in technology which make some topics of greater relevance and others of less interest. As well, advances in IC process technology require that the numbers used in the examples, exercises and end-of-chapter problems be updated to reflect the parameters of newer generations of IC technologies (e.g., some problems utilize the parameters of the 65-nm CMOS process). This ensures that students are acquiring a real-world perspective on technology. To improve presentation, a number of chapters and sections have been rewritten for greater clarity. Specific, noteworthy changes are: 1. New End-of-Chapter Problems and a New Instructor's Solutions Manual. The number of the end-of-chapter problems has increased by about 50. Of the resulting 1532 problems, 176 are entirely new and 790 have new data. The new Instructor's Solutions Manual is written by Adel Sedra. 2. Expand-Your-Perspective Notes. This is a new feature providing historical and application perspectives. About two such notes are included in each chapter. Most are focused on notable circuit engineers and key inventions. 3. Greater Flexibility in Presenting the MOSFET and the BJT. Two short and completely parallel chapters present the MOSFET (Chapter 5) and the BJT (Chapter 6). Here the focus is on the device structure and its physical operation, its current-voltage characteristics, and its application in dc circuits. The order of coverage of these two chapters is entirely at the instructor's discretion as they have been written to be completely independent of each other. 4. A Unified Treatment of Transistor Amplifiers. The heart of a first course in electronics is the study of transistor amplifiers. The seventh edition provides a new approach to this subject: A new Chapter 7 begins with the basic principles that underlie the operation of a transistor of either type as an amplifier, and presents such concepts as small-signal operation and modeling. This is followed by the classical configurations of transistor amplifiers, biasing methods, and practical discrete-circuit amplifiers. The combined presentation emphasizes the unity of the basic principles while allowing for separate treatment of the two device types where this is warranted. Very importantly, we are able to compare the two devices and to draw conclusions about their unique areas of application. 5. Improved Presentation of Cascoding. Chapter 8 dealing with the basic building blocks of IC amplifiers has been rewritten to improve presentation. Specifically, the development of cascoding and the key circuit building blocks, the cascode amplifier and the cascode current source, is now much clearer. 6. Clearer and Simplified Study of Feedback. The feedback chapter has been rewritten to improve, simplify and clarify the presentation of this key subject. 7. Streamlined Presentation of Frequency Response. While keeping the treatment of frequency response all together, the chapter has been rewritten to streamline its flow, and simplify and clarify the presentation. 8. Updated Treatment of Output Stages and Power Amplifiers. Here, we have updated the material on MOS power transistors and added a new section on the increasingly important class-D switching power amplifier. 9. A More Contemporary Approach to Operational Amplifier Circuits. While maintaining coverage of some of the enduring features and subcircuits of the classical 741 op amp, its total coverage is somewhat reduced to make room for modern IC op amp design techniques. Sedra_FM_BM.indd 20 9/30/2014 9:36:54 PM Preface xxi 10. Better Organized and Modernized Coverage of Digital IC Design. Significant improvements have been made to the brief but comprehensive coverage of digital IC design in Part III. These include a better motivated study of CMOS logic circuits (Chapter 14) which now begins with logic gate circuits. The material on logic circuit technologies and design methodologies as well as the advanced topic of technology scaling and its implications have been moved to Chapter 15. This modularly structured chapter now deals with a selection of advanced and somewhat specialized topics. Since bipolar is hardly ever used in new digital design, coverage of ECL has been significantly reduced. Similarly, BiCMOS has become somewhat of a specialty topic and its coverage has been correspondingly reduced. Nevertheless, the complete material on both ECL and BiCMOS is now available on the book's website. Finally, we have added a new section on image sensors to Chapter 16 (Memory Circuits). 11. Increased Emphasis on Integrated-Circuit Filters and Oscillators. A section on a popular approach to integrated-circuit filter design, namely, Transconductance-C filters, has been added to Chapter 17. To make room for this new material, the subsection on stagger-tuned amplifiers has been removed and placed in Appendix H, on the website. The cross-coupled LC oscillator, popular in IC design, has been added to Chapter 18. The section on precision diode circuits has been removed but is still made available on the website. 12. A Useful and Insightful Comparison of the MOSFET and the BJT. This is now included in Appendix G, available on the website. The Book's Website A Companion Website for the book has been set up at www.oup.com/us/sedrasmith. Its content will change frequently to reflect new developments. The following material is available on the website: 1. Data sheets for hundreds of useful devices to help in laboratory experiments as well as in design projects. 2. Links to industrial and academic websites of interest. 3. A message center to communicate with the authors and with Oxford University Press. 4. Links to the student versions of both Cadence PSpice® and National Instruments Multisim™. 5. The input files for all the PSpice® and Multisim™ examples of Appendix B. 6. Step-by-step guidance to help with the simulation examples and the end-of-chapter problems identified with a SIM icon. 7. Bonus text material of specialized topics which are either not covered or covered briefly in the current edition of the textbook. These include: • Junction Field-Effect Transistors (JFETs) • Gallium Arsenide (GaAs) Devices and Circuits • Transistor-Transistor Logic (TTL) Circuits • Emitter-Coupled Logic (ECL) Circuits • BiCMOS Circuits • Precision Rectifier Circuits 8. Appendices for the Book: • Appendix A: VLSI Fabrication Technology • Appendix B: SPICE Device Models and Design and Simulation Examples Using PSpice® and Multisim™ • Appendix C: Two-Port Network Parameters • Appendix D: Some Useful Network Theorems • Appendix E: Single-Time-Constant Circuits • Appendix F: s-domain Analysis: Poles, Zeros, and Bode Plots • Appendix G: Comparison of the MOSFET and the BJT Sedra_FM_BM.indd 21 9/30/2014 9:36:54 PM xxii Preface • Appendix H: Design of Stagger-Tuned Amplifiers • Appendix I: Bibliography • Appendix L: Answers to Selected Problems Exercises and End-of-Chapter Problems Over 475 Exercises are integrated throughout the text. The answer to each exercise is given below the exercise so students can check their understanding of the material as they read. Solving these exercises should enable the reader to gauge his or her grasp of the preceding material. In addition, more than 1530 end-of-chapter Problems, 65% of which are new or revised in this edition, are provided. The problems are keyed to the individual chapter sections and their degree of difficulty is indicated by a rating system: difficult problems are marked with an asterisk (*); more difficult problems with two asterisks (**); and very difficult (and/or time consuming) problems with three asterisks (***). We must admit, however, that this classification is by no means exact. Our rating no doubt depended to some degree on our thinking (and mood!) at the time a particular problem was created. Answers to sample problems are given in Appendix L (on the website), so students have a checkpoint to tell if they are working out the problems correctly. Complete solutions for all exercises and problems are included in the Instructor's Solutions Manual, which is available from the publisher to those instructors who adopt the book. As in the previous six editions, many examples are included. The examples, and indeed most of the problems and exercises, are based on real circuits and anticipate the applications encountered in designing real-life circuits. This edition continues the use of numbered solution steps in the figures for many examples, as an attempt to recreate the dynamics of the classroom. Course Organization The book contains sufficient material for a sequence of two single-semester courses, each of 40-50 lecture hours. The modular organization of the book provides considerable flexibility for course design. In the following, we suggest content for a sequence of two classical or standard courses. We also describe some variations on the content of these two courses and specify supplemental material for a possible third course. The First Course The first course is based on Part I of the book, that is, Chapters 1–7. It can be taught, most simply by starting at the beginning of Chapter 1 and concluding with the end of Chapter 7. However, as guidance to instructors who wish to follow a different order of presentation or a somewhat modified coverage, or to deal with situations where time might be constrained, we offer the following remarks: The core of the first course is the study of the two transistor types, Chapters 5 and 6, in whatever order the instructor wishes, and transistor amplifiers in Chapter 7. These three chapters must be covered in full. Another important part of the first course is the study of diodes (Chapter 4). Here, however, if time does not permit, some of the applications in the later part of the chapter can be skipped. We have found it highly motivational to cover op amps (Chapter 2) near the beginning of the course. This provides the students with the opportunity to work with a practical integrated circuit and to experiment with non-trivial circuits. Coverage of Chapter 1, at least of the amplifier sections, should prove helpful. Here the sections on signals can be either covered in class or assigned as reading material. Section 1.6 on frequency response is needed if the frequency-response of op-amp circuits is to be studied; otherwise this section can be delayed to the second course. Sedra_FM_BM.indd 22 9/30/2014 9:36:54 PM Preface xxiii Finally, if the students have not taken a course on physical electronics, Chapter 3 needs to be covered. Otherwise, it can be used as review material or skipped altogether. The Second Course The main subject of the second course is integrated-circuit amplifiers and is based on Part II of the book, that is, Chapters 8-13. Here also, the course can be taught most simply by beginning with Chapter 8 and concluding with Chapter 13. However, this being a second course, considerable flexibility in coverage is possible to satisfy particular curriculum designs and/or to deal with time constraints. First, however, we note that the core material is presented in Chapters 8-11 and these four chapters must be covered, though not necessarily in their entirety. For instance, some of the sections near the end of a chapter and identified by the "advanced material" icon can be skipped, usually with no loss of continuity. Beyond the required chapters, (8-11), the instructor has many possibilities for the remainder of the course. These include one or both of the two remaining chapters in Part II, namely, Output Stages and Power Amplifier (Chapter 12), and Op-Amp Circuits (Chapter 13). Another possibility, is to include an introduction to digital integrated circuits by covering Chapter 14, and if time permits, selected topics of Chapters 15 and 16. Yet another possibility for the remainder of the second course is selected topics from the filters chapter (17) and/or the oscillators chapter (18). A Digitally Oriented First Course A digitally-oriented first course can include the following: Chapter 1 (without Section 1.6), Chapter 2, Chapter 3 (if the students have not had any exposure to physical electronics), Chapter 4 (perhaps without some of the later applications sections), Chapter 5, selected topics from Chapter 7 emphasizing the basics of the application of the MOSFET as an amplifier, Chapter 14, and selected topics from Chapters 15 and 16. Such a course would be particularly suited for Computer Engineering students. Supplemental Material/Third Course Depending on the selection of topics for the first and second courses, some material will remain and can be used for part of a third course or as supplemental material to support student design projects. These can include Chapter 12 (Output Stages and Power Amplifiers), Chapter 13 (Op-Amp Circuits), Chapter 17 (Filters) and Chapter 18 (Oscillators), which can be used to support a third course on analog circuits. These can also include Chapters 14, 15 and 16 which can be used for a portion of a senior-level course on digital IC design. The Accompanying Laboratory Courses in electronic circuits are usually accompanied by laboratory experiments. To support the laboratory component for courses using this book, Professor Vincent Gaudet of the University of Waterloo has, in collaboration with K.C. Smith, authored a laboratory manual. Laboratory Explorations, together with an Instructor's Manual, is available from Oxford University Press. Another innovative laboratory instruction system, designed to accompany this book, has been recently developed. Specifically, Illuster Technologies Inc. has developed a digitally controlled lab platform, AELabs. The platform is realized on printed circuit boards using surface mount devices. A wide variety of circuits can be configured on this platform through a custom graphical user interface. This allows students to conduct many experiments relatively quickly. More information is available from Illuster (see link on the Companion Website). Sedra_FM_BM.indd 23 9/30/2014 9:36:54 PM xxiv Preface An Outline for the Reader Part I, Devices and Basic Circuits, includes the most fundamental and essential topics for the study of electronic circuits. At the same time, it constitutes a complete package for a first course on the subject. Chapter 1. The book starts with an introduction to the basic concepts of electronics in Chapter 1. Signals, their frequency spectra, and their analog and digital forms are presented. Amplifiers are introduced as circuit building blocks and their various types and models are studied. This chapter also establishes some of the terminology and conventions used throughout the text. Chapter 2. Chapter 2 deals with operational amplifiers, their terminal characteristics, simple applications, and practical limitations. We chose to discuss the op amp as a circuit building block at this early stage simply because it is easy to deal with and because the student can experiment with op-amp circuits that perform nontrivial tasks with relative ease and with a sense of accomplishment. We have found this approach to be highly motivating to the student. We should point out, however, that part or all of this chapter can be skipped and studied at a later stage (for instance, in conjunction with Chapter 9, Chapter 11, and/or Chapter 13) with no loss of continuity. Chapter 3. Chapter 3 provides an overview of semiconductor concepts at a level sufficient for understanding the operation of diodes and transistors in later chapters. Coverage of this material is useful in particular for students who have had no prior exposure to device physics. Even those with such a background would find a review of Chapter 3 beneficial as a refresher. The instructor can choose to cover this material in class or assign it for outside reading. Chapter 4. The first electronic device, the diode, is studied in Chapter 4. The diode terminal characteristics, the circuit models that are used to represent it, and its circuit applications are presented. Depending on the time available in the course, some of the diode applications (e.g. Section 4.6) can be skipped. Also, the brief description of special diode types (Section 4.7) can be left for the student to read. Chapters 5 and 6. The foundation of electronic circuits is established by the study of the two transistor types in use today: the MOS transistor in Chapter 5 and the bipolar transistor in Chapter 6. These two chapters have been written to be completely independent of one another and thus can be studied in either order, as desired. Furthermore, the two chapters have the same structure, making it easier and faster to study the second device, as well as to draw comparisons between the two device types. Each of Chapters 5 and 6 begins with a study of the device structure and its physical operation, leading to a description of its terminal characteristics. Then, to allow the student to become very familiar with the operation of the transistor as a circuit element, a large number of examples are presented of dc circuits utilizing the device. The last section of each of Chapters 5 and 6 deals with second-order effects that are included for completeness, but that can be skipped if time does not permit detailed coverage. Chapter 7. The heart of a first course in electronics is the study of transistor amplifiers. Chapter 7 (new to this edition) presents a unified treatment of the subject. It begins with the basic principles that underlie the operation of a transistor, of either type, as an amplifier, and proceeds to present the important concepts of small-signal operation and modeling. This is followed by a study of the basic configurations of single-transistor amplifiers. After a presentation of dc biasing methods, the chapter concludes with practical examples of discrete-circuit amplifiers. The combined presentation emphasizes the unity of the basic principles while allowing for separate treatment of the two device types where this is warranted. Very importantly, we are able to compare the two devices and to draw conclusions about their unique areas of application. After the study of Part I, the reader will be fully prepared to study either integrated-circuit amplifiers in Part II, or digital integrated circuits in Part III. Part II, Integrated-Circuit Amplifiers, is devoted to the study of practical amplifier circuits that can be fabricated in the integrated-circuit (IC) form. Its six chapters constitute a coherent treatment of IC amplifier design and can thus serve as a second course in electronic circuits. MOS and Bipolar. Throughout Part II, both MOS and bipolar circuits are presented side-by-side. Because the MOSFET is by far the dominant device, its circuits are presented first. Bipolar circuits are discussed to the same depth but occasionally more briefly. Sedra_FM_BM.indd 24 9/30/2014 9:36:54 PM Preface xxv Chapter 8. Beginning with a brief introduction to the philosophy of IC design, Chapter 8 presents the basic circuit building blocks that are used in the design of IC amplifiers. These include current mirrors, current sources, gain cells, and cascode amplifiers. Chapter 9. The most important IC building block, the differential pair, is the main topic of Chapter 9. The last section of Chapter 9 is devoted to the study of multistage amplifiers. Chapter 10. Chapter 10 presents a comprehensive treatment of the important subject of amplifier frequency response. Here, Sections 10.1, 10.2, and 10.3 contain essential material; Section 10.4 provides an in-depth treatment of very useful new tools; and Sections 10.5 to 10.8 present the frequency response analysis of a variety of amplifier configurations that can be studied as and when needed. A selection of the latter sections can be made depending on the time available and the instructor's preference. Chapter 11. The fourth of the essential topics of Part II, feedback, is the subject of Chapter 11. Both the theory of negative feedback and its application in the design of practical feedback amplifiers are presented. We also discuss the stability problem in feedback amplifiers and treat frequency compensation in some detail. Chapter 12. In Chapter 12 we switch gears from dealing with small-signal amplifiers to those that are required to handle large signals and large amounts of power. Here we study the different amplifier classes—A, B, and AB—and their realization in bipolar and CMOS technologies. We also consider power BJTs and power MOSFETs, and study representative IC power amplifiers. A brief study of the increasingly popular Class D amplifier is also presented. Depending on the availability of time, some of the later sections can be skipped in a first reading. Chapter 13. Finally, Chapter 13 brings together all the topics of Part II in an important application; namely, the design of operational amplifier circuits. We study both CMOS and bipolar op amps. In the latter category, besides the classical and still timely 741 circuit, we present modern techniques for the design of low-voltage op amps (Section 13.4). Part III, Digital Integrated Circuits, provides a brief but nonetheless comprehensive and sufficiently detailed study of digital IC design. Our treatment is almost self-contained, requiring for the most part only a thorough understanding of the MOSFET material presented in Chapter 5. Thus, Part III can be studied right after Chapter 5. The only exceptions to this are the last section in Chapter 15 which requires knowledge of the BJT (Chapter 6). Also, knowledge of the MOSFET internal capacitances (Section 10.2.2) will be needed. Chapter 14. Chapter 14 is the foundation of Part III. It begins with the motivating topic of CMOS logic-gate circuits. Then, following a detailed study of digital logic inverters, we concentrate on the CMOS inverter; its static and dynamic characteristics and its design. Transistor sizing and power dissipation round out the topics of Chapter 14. The material covered in this chapter is the minimum needed to learn something meaningful about digital circuits. Chapter 15. Chapter 15 has a modular structure and presents six topics of somewhat advanced nature. It begins with a presentation of Moore's law and the technology scaling that has made the multi-billion-transistor chip possible. This is followed by an overview of digital IC technologies, and the design methodologies that make the design of super-complex digital ICs possible. Four different logic-circuit types are then presented. Only the last of these includes bipolar transistors. Chapter 16. Digital circuits can be broadly divided into logic and memory circuits. The latter is the subject of Chapter 16. Part IV, Filters and Oscillators, is intentionally oriented toward applications and systems. The two topics illustrate powerfully and dramatically the application of both negative and positive feedback. Chapter 17. Chapter 17 deals with the design of filters, which are important building blocks of communication and instrumentation systems. A comprehensive, design-oriented treatment of the subject is presented. The material provided should allow the reader to perform a complete filter design, starting from specification and ending with a complete circuit realization. A wealth of design tables is included. Chapter 18. Chapter 18 deals with circuits for the generation of signals with a variety of waveforms: sinusoidal, square, and triangular. We also present circuits for the nonlinear shaping of waveforms. Sedra_FM_BM.indd 25 9/30/2014 9:36:54 PM xxvi Preface Appendices. The twelve appendices contain much useful background and supplementary material. We wish to draw the reader's attention in particular to the first two: Appendix A provides a concise introduction to the important topic of IC fabrication technology including IC layout. Appendix B provides SPICE device models as well as a large number of design and simulation examples in PSpice® and Multisim™. The examples are keyed to the book chapters. These Appendices and a great deal more material on these simulation examples can be found on the Companion Website. Ancillaries A complete set of ancillary materials is available with this text to support your course. For the Instructor The Ancillary Resource Center (ARC) at www.oup-arc.com/sedrasmith is a convenient destination for all the instructor resources that accompany Microelectronic Circuits. Accessed online through individual user accounts, the ARC provides instructors with access to up-to-date ancillaries at any time while guaranteeing the security of grade-significant resources. The ARC replaces the Instructor's Resource CD that accompanied the sixth edition. On the ARC, you will find: • An electronic version of the Instructor's Solutions Manual. • PowerPoint-based figure slides that feature all the images and summary tables from the text, with their captions, so they can easily be displayed and explained in class. • Detailed instructor's support for the SPICE circuit simulations in Multisim™ and PSpice®. The Instructor's Solutions Manual (ISBN 978-0-19-933915-0), written by Adel Sedra, contains detailed solutions to all in-text exercises and end-of-chapter problems found in Microelectronic Circuits. The Instructor's Solutions Manual for Laboratory Explorations to Accompany Microelectronic Circuits (ISBN 978-0-19-933926-6) contains detailed solutions to all the exercises and problems found in this student's laboratory guide. For the Student and Instructor A Companion Website at www.oup.com/us/sedrasmith features permanently cached versions of device datasheets, so students can design their own circuits in class. The website also contains SPICE circuit simulation examples and lessons. Bonus text topics and the Appendices are also featured on the website. The Laboratory Explorations to Accompany Microelectronic Circuits (ISBN 978-0-19-933925-9) invites students to explore the realm of real-world engineering through practical, hands-on experiments. Keyed to sections in the text and taking a "learn-by-doing" approach, it presents labs that focus on the development of practical engineering skills and design practices. Acknowledgments Many of the changes in this seventh edition were made in response to feedback received from instructors who adopted the sixth edition. We are grateful to all those who took the time to write to us. In addition, many of the reviewers provided detailed commentary on the sixth edition and suggested a number of the changes that we have incorporated in this edition. They are listed later; to all of them, we extend our sincere thanks. Adel Sedra is also grateful for the feedback received from the students who have taken his electronics courses over the past number of years at the University of Waterloo. Sedra_FM_BM.indd 26 9/30/2014 9:36:54 PM Preface xxvii A number of individuals made significant contributions to this edition. Vincent Gaudet of the University of Waterloo contributed to Part III as well as co-authoring the laboratory manual. WaiTung Ng of the University of Toronto contributed to Chapter 12 and updated Appendix A (of which he is the original author). Muhammad Faisal of the University of Michigan updated Appendix B, which he helped create for the sixth edition; helped in obtaining the cover photo, and has over a number of years been the source of many good ideas. Olivier Trescases and his students at the University of Toronto pioneered the laboratory system described elsewhere in the Preface. Jennifer Rodrigues typed all the revisions, as she did for a number of the previous editions, with tremendous skill and good humour. Chris Schroeder was of great assistance to Adel Sedra with local logistics. Laura Fujino assisted in many ways and in particular with the "Expand-Your-Perspective" notes. To all of these friends and colleagues we say thank you. Over the recent years we have benefited greatly from discussions with a number of colleagues and friends. In particular we are very grateful to the following: James Barby, University of Waterloo; David Nairn, University of Waterloo; Anthony Chan Carusone, University of Toronto; David Johns, University of Toronto; Ken Martin, University of Toronto; Khoman Phang, University of Toronto; Gordon Roberts, McGill University; Ali Sheikholeslami, University of Toronto; and Amir Yazdani, Ryerson University. The cover photograph shows a 3D IC system, which demonstrates the concept of wireless power delivery and communication through multiple layers of CMOS chips. The communication circuits were demonstrated in an IBM 45 nm SOI CMOS process. This technology is designed to serve a multi-Gb/s interconnect between cores spread across several IC layers for high-performance processors. We are grateful to Professor David Wentzloff, Director of the Wireless Integrated Circuits Group at the University of Michigan, who allowed us to use this image, and to Muhammad Faisal, Founder of Movellus Circuits Incorporated, who edited the image. A large number of people at Oxford University Press contributed to the development of this edition and its various ancillaries. We would like to specifically mention Marketing Manager David Jurman, Marketing Director Frank Mortimer, Higher Ed Sales Director Bill Marting, Copywriter Kristin Maffei, Art Director Michele Laseau, Production Manager Lisa Grzan, Team Leader Amy Whitmer, and Senior Production Editor Jane Lee. We wish to extend special thanks to our Publisher at Oxford University Press, John Challice, and the Editorial Director, Patrick Lynch. Both have always shown great interest in this book and have provided considerable guidance and support throughout the process of preparing this edition. The Senior Acquisitions Editor, Nancy Blaine, and Associate Editor, Christine Mahon, have done a truly outstanding job. It has been a pleasure to work with both of them, both as professionals and as highly thoughtful individuals; we owe them much gratitude. On the production side, Barbara Mathieu, Senior Production Editor, has been superb: her attention to detail and emphasis on quality is without par. Finally, we wish to thank our families for their support and understanding, and to thank all the students and instructors who have valued this book throughout its history. Adel S. Sedra Kenneth C. (KC) Smith Waterloo, Ontario, Canada August 2014 Sedra_FM_BM.indd 27 9/30/2014 9:36:54 PM xxviii Preface Reviewers of Seventh Edition Junseok Chae, Arizona State University, Tempe, AZ Liang Dong, Baylor University, Waco, TX Muhammad Faisal, University of Michigan, Ann Arbor, MI Patrick Fay, University of Notre Dame, Notre Dame, IN Vincent Gaudet, University of Waterloo, Waterloo, Canada Elmer A Grubbs, Northern Arizona University, Flagstaff, AZ Serhiy Levkov, New Jersey Institute of Technology, Newark, NJ Leda Lunardi, North Carolina State University, Raleigh, NC Phyllis R. Nelson, California State Polytechnic University, Pomona, CA Robert W. Newcomb, University of Maryland, College Park, MD Toshikazu Nishida, University of Florida, Gainesville, FL Matthew Swabey, Purdue University, West Lafayette, IN Khalid Hasan Tantawi, University of Alabama, Huntsville, AL Farid M. Tranjan, University of North Carolina, Charlotte, NC Mustapha C.E. Yagoub, University of Ottawa, Ottawa, Canada Justin Jackson, Weber State University, Ogden, UT John Mankowski, Texas Tech University, Lubbock, TX Chris Mi, University of Michigan, Dearborn, MI Reviewers of Prior Editions Maurice Aburdene, Bucknell University, Lewisburg, PA Michael Bartz, University of Memphis, TN Elizabeth Brauer, Northern Arizona University, Flagstaff, AZ Martin Brooke, Duke University, Durham, NC Patrick L. Chapman, University of Illinois, Urbana– Champaign, IL Yun Chiu, University of Illinois, Urbana–Champaign, IL Roy H. Cornely, New Jersey Institute of Technology, Newark, NJ Norman Cox, Missouri University of Science and Technology, Rolla, MO Dale L. Critchlow, University of Vermont, Burlingon, VT Robert Bruce Darling, University of Washington, Seattle, WA Artice Davis, San Jose State University, CA John Davis, University of Texas, Austin, TX Christopher DeMarco, University of Wisconsin, Madison, WI Robert Engelken, Arkansas State University, Jonesboro, AR Ethan Farquhar, University of Tennessee, Knoxville, TN Eby G. Friedman, University of Rochester, NY Paul M. Furth, New Mexico State University, Las Cruces, NM Rhett T. George, Jr., Duke University, Durham, NC Roobik Gharabagi, St. Louis University, MO George Giakos, University of Akron, OH John Gilmer, Wilkes University, Wilkes-Barre, PA Michael Green, University of California, Irvine, CA Steven de Haas, California State University, Sacramento, CA Anas Hamoui, McGill University, Montreal, Canada Reza Hashemian, Northern Illinois University, DeKalb, IL William Harrell, Clemson University, SC Reid Harrison, University of Utah, Salt Lake City, UT Ward J. Helms, University of Washington, Seattle, WA Richard Hornsey, York University, Toronto, Canada Timothy Horiuchi, University of Maryland, College Park, MD Sedra_FM_BM.indd 28 Hsiung Hsu, The Ohio State University, Columbus, OH Robert Irvine, California State Polytechnic University, Pomona, CA Mohammed Ismail, The Ohio State University, Columbus, OH Paul Israelsen, Utah State University, Logan UT Steve Jantzi, Broadcom, CA Zhenhua Jiang, University of Miami, FL Marian Kazimierczuk, Wright State University, Dayton, OH John Khoury, Columbia University, New York, NY Jacob B. Khurgin, The Johns Hopkins University, Baltimore, MD Seongsin M. Kim, University of Alabama, Tuscaloosa, AL Roger King, University of Toledo, OH Clark Kinnaird, Southern Methodist University, Dallas, TX Robert J. Krueger, University of Wisconsin, Milwaukee, WI Joy Laskar, Georgia Institute of Technology, Atlanta, GA Tsu-Jae King Liu, University of California, Berkeley, CA Yicheng Lu, Rutgers University, Piscataway, NJ David Luke, University of New Brunswick, Fredericton, Canada Thomas Matthews, California State University, Sacramento, CA Un-Ku Moon, Oregon State University, Corvallis, OR Bahram Nabet, Drexel University, Philadelphia, PA Dipankar Nagchoudhuri, Indian Institute of Technology, Delhi, India David Nairn, University of Waterloo, Waterloo, Canada Joseph H. Nevin, University of Cincinnati, OH Ken Noren, University of Idaho, Moscow, ID Brita Olson, California Polytechnic University, Pomona, CA Martin Peckerar, University of Maryland, College Park, MD Khoman Phang, University of Toronto, Canada Mahmudur Rahman, Santa Clara University, CA Rabin Raut, Concordia University, Montreal, Canada John A. Ringo, Washington State University, Pullman, WA Zvi S. Roth, Florida Atlantic University, Boca Raton, FL Mulukutla Sarma, Northeastern University, Boston, MA John Scalzo, Louisiana State University, Baton Rouge, LA Norman Scheinberg, City College, New York, NY Pierre Schmidt, Florida International University, Miami, FL Richard Schreier, Analog Devices, Toronto, Canada Dipankar Sengupta, Royal Melbourne Institute of Technology, Australia Ali Sheikholeslami, University of Toronto, Canada Kuang Sheng, Rutgers University, Piscataway, NJ Michael L. Simpson, University of Tennessee, Knoxville, TN Karl A. Spuhl, Washington University in St. Louis, MO Charles Sullivan, Dartmouth College, Hanover, NH Andrew Szeto, San Diego State University, CA Joel Therrien, University of Massachusetts, Lowell, MA Len Trombetta, University of Houston, TX Daniel van der Weide, University of Delaware, Newark, DE Gregory M. Wierzba, Michigan State University, East Lansing, MI Donna Yu, North Carolina State University, Raleigh, NC Jiann-Shiun Yuan, University of Central Florida, Orlando, FL Sandra Yost, University of Detroit, Mercy, MI Alex Zaslavsky, Brown University, Providence, RI Jianhua (David) Zhang, University of Illinois, Urbana– Champaign, IL 9/30/2014 9:36:54 PM Microelectronic Circuits Sedra_FM_BM.indd 1 9/30/2014 9:36:54 PM PART I Devices and Basic Circuits CHAPTER 1 Signals and Amplifiers 4 CHAPTER 2 Operational Amplifiers 58 CHAPTER 3 Semiconductors 134 CHAPTER 4 Diodes 174 CHAPTER 5 MOS Field-Effect Transistors (MOSFETs) 246 CHAPTER 6 Bipolar Junction Transistors (BJTs) 304 CHAPTER 7 Transistor Amplifiers 366 P art I, Devices and Basic Circuits, includes the most fundamental and essential topics for the study of electronic circuits. At the same time, it constitutes a complete package for a first course on the subject. The heart of Part I is the study of the three basic semiconductor devices: the diode (Chapter 4), the MOS transistor (Chapter 5), and the bipolar transistor (Chapter 6). In each case, we study the device operation, its characterization, and its basic circuit applications. Chapter 7 then follows with a study of the most fundamental application of the two transistor types; namely, their use in amplifier design. This side-by-side study of MOSFET and BJT amplifiers allows us to see similarities between these amplifiers and to compare them, which in turn highlights the distinct areas of applicability of each, as well as showing the unity of the basic principles that underlie the use of transistors as amplifiers. For those who have not had a prior course on device physics, Chapter 3 provides an overview of semiconductor concepts at a level sufficient for the study of electronic circuits. A review of Chapter 3 should prove useful even for those with prior knowledge of semiconductors. Since the purpose of electronic circuits is the processing of signals, it is essential to understand signals, their characterization in the time and frequency domains, and their analog and digital representations. The basis for such understanding is provided in Chapter 1, which also introduces the most common signal-processing function, amplification, and the characterization and types of amplifiers. Besides diodes and transistors, the basic electronic devices, the op amp is studied in Part I. Although not an electronic device in the most fundamental sense, the op amp is commercially available as an integrated circuit (IC) package and has well-defined terminal characteristics. Thus, even though the op amp's internal circuit is complex, typically incorporating 20 or more transistors, its almost-ideal terminal behavior makes it possible to treat the op amp as a circuit element and to use it in the design of powerful circuits, as we do in Chapter 2, without any knowledge of its internal construction. We should mention, however, that the study of op amps can be delayed until a later point, and Chapter 2 can be skipped with no loss of continuity. The foundation of this book, and of any electronics course, is the study of the two transistor types in use today: the MOS transistor in Chapter 5 and the bipolar transistor in Chapter 6. These two chapters have been written to be completely independent of each other and thus can be studied in either order, as desired. After the study of Part I, the reader will be fully prepared to undertake the study of either integrated-circuit amplifiers in Part II or digital integrated circuits in Part III. 3 CHAPTER 1 Signals and Amplifiers Introduction 5 1.1 Signals 6 1.5 Circuit Models for Amplifiers 23 1.6 Frequency Response of Amplifiers 33 1.2 Frequency Spectrum of Signals 9 Summary 44 1.3 Analog and Digital Signals 12 Problems 45 1.4 Amplifiers 15 IN THIS CHAPTER YOU WILL LEARN 1. That electronic circuits process signals, and thus understanding electrical signals is essential to appreciating the material in this book. 2. The Thévenin and Norton representations of signal sources. 3. The representation of a signal as the sum of sine waves. 4. The analog and digital representations of a signal. 5. The most basic and pervasive signal-processing function: signal amplification, and correspondingly, the signal amplifier. 6. How amplifiers are characterized (modeled) as circuit building blocks independent of their internal circuitry. 7. How the frequency response of an amplifier is measured, and how it is calculated, especially in the simple but common case of a single-time-constant (STC) type response. Introduction The subject of this book is modern electronics, a field that has come to be known as microelectronics. Microelectronics refers to the integrated-circuit (IC) technology that at the time of this writing is capable of producing circuits that contain billions of components in a small piece of silicon (known as a silicon chip) whose area is on the order of 100 mm2 . One such microelectronic circuit, for example, is a complete digital computer, which accordingly is known as a microcomputer or, more generally, a microprocessor. The microelectronic circuits you will learn to design in this book are used in almost every device we encounter in our daily lives: in the appliances we use in our homes; in the vehicles and transportation systems we use to travel; in the cell phones we use to communicate; in the medical equipment we need to care for our health; in the computers we use to do our work; and in the audio and video systems, the radio and TV sets, and the multitude of other digital devices we use to entertain ourselves. Indeed, it is difficult to conceive of modern life without microelectronic circuits. In this book we shall study electronic devices that can be used singly (in the design of discrete circuits) or as components of an integrated-circuit (IC) chip. We shall study the design and analysis of interconnections of these devices, which form discrete and integrated 5 6 Chapter 1 Signals and Amplifiers circuits of varying complexity and perform a wide variety of functions. We shall also learn about available IC chips and their application in the design of electronic systems. The purpose of this first chapter is to introduce some basic concepts and terminology. In particular, we shall learn about signals and about one of the most important signal-processing functions electronic circuits are designed to perform, namely, signal amplification. We shall then look at circuit representations or models for linear amplifiers. These models will be employed in subsequent chapters in the design and analysis of actual amplifier circuits. In addition to motivating the study of electronics, this chapter serves as a bridge between the study of linear circuits and that of the subject of this book: the design and analysis of electronic circuits. 1.1 Signals Signals contain information about a variety of things and activities in our physical world. Examples abound: Information about the weather is contained in signals that represent the air temperature, pressure, wind speed, etc. The voice of a radio announcer reading the news into a microphone provides an acoustic signal that contains information about world affairs. To monitor the status of a nuclear reactor, instruments are used to measure a multitude of relevant parameters, each instrument producing a signal. To extract required information from a set of signals, the observer (be it a human or a machine) invariably needs to process the signals in some predetermined manner. This signal processing is usually most conveniently performed by electronic systems. For this to be possible, however, the signal must first be converted into an electrical signal, that is, a voltage or a current. This process is accomplished by devices known as transducers. A variety of transducers exist, each suitable for one of the various forms of physical signals. For instance, the sound waves generated by a human can be converted into electrical signals by using a microphone, which is in effect a pressure transducer. It is not our purpose here to study transducers; rather, we shall assume that the signals of interest already exist in the electrical domain and represent them by one of the two equivalent forms shown in Fig. 1.1. In Fig. 1.1(a) the signal is represented by a voltage source v s (t) having a source resistance Rs . In the alternate representation of Fig. 1.1(b) the signal is represented by a current source is (t) having a source resistance Rs . Although the two representations are equivalent, that in Fig. 1.1(a) (known as the Thévenin form) is preferred when Rs is low. The representation of Fig. 1.1(b) (known as the Norton form) is preferred when Rs is high. The reader will come to appreciate this point later in this chapter when we study the different types of amplifiers. For the time being, it is important to be familiar with Thévenin's and Norton's theorems (for a Rs vs(t) (a) is(t) Rs (b) Figure 1.1 Two alternative representations of a signal source: (a) the Thévenin form; (b) the Norton form. 1.1 Signals 7 brief review, see Appendix D) and to note that for the two representations in Fig. 1.1 to be equivalent, their parameters are related by v s (t) = Rs is (t) Example 1.1 The output resistance of a signal source, although inevitable, is an imperfection that limits the ability of the source to deliver its full signal strength to a load. To see this point more clearly, consider the signal source when connected to a load resistance RL as shown in Fig. 1.2. For the case in which the source is represented by its Thévenin equivalent form, find the voltage v o that appears across RL , and hence the condition that Rs must satisfy for v o to be close to the value of v s . Repeat for the Norton-represented source; in this case finding the current io that flows through RL and hence the condition that Rs must satisfy for io to be close to the value of is . Rs io vs RL vo is Rs RL (a) (b) Figure 1.2 Circuits for Example 1.1. Solution For the Thévenin-represented signal source shown in Fig. 1.2(a), the output voltage v o that appears across the load resistance RL can be found from the ratio of the voltage divider formed by Rs and RL , vo = vs RL RL + Rs From this equation we see that for vo vs the source resistance Rs must be much lower than the load resistance RL , Rs RL Thus, for a source represented by its Thévenin equivalent, ideally Rs = 0, and as Rs is increased, relative to the load resistance RL with which this source is intended to operate, the voltage v o that appears across the load becomes smaller, not a desirable outcome. 8 Chapter 1 Signals and Amplifiers Example 1.1 continued Next, we consider the Norton-represented signal source in Fig. 1.2(b). To obtain the current io that flows through the load resistance RL , we utilize the ratio of the current divider formed by Rs and RL , io = is Rs Rs + RL From this relationship we see that for io is the source resistance Rs must be much larger than RL , Rs RL Thus for a signal source represented by its Norton equivalent, ideally Rs = ∞, and as Rs is reduced, relative to the load resistance RL with which this source is intended to operate, the current io that flows through the load becomes smaller, not a desirable outcome. Finally, we note that although circuit designers cannot usually do much about the value of Rs , they may have to devise a circuit solution that minimizes or eliminates the loss of signal strength that results when the source is connected to the load. EXERCISES 1.1 For the signal-source representations shown in Figs. 1.1(a) and 1.1(b), what are the open-circuit output voltages that would be observed? If, for each, the output terminals are short-circuited (i.e., wired together), what current would flow? For the representations to be equivalent, what must the relationship be between v s , is , and Rs ? Ans. For (a), v oc = v s (t); for (b), v oc = Rs is (t); for (a), isc = v s (t)/Rs ; for (b), isc = is (t); for equivalency, v s (t) = Rs is (t) 1.2 A signal source has an open-circuit voltage of 10 mV and a short-circuit current of 10 μA. What is the source resistance? Ans. 1 k 1.3 A signal source that is most conveniently represented by its Thévenin equivalent has v s = 10 mV and Rs = 1 k. If the source feeds a load resistance RL , find the voltage v o that appears across the load for RL = 100 k, 10 k, 1 k, and 100 . Also, find the lowest permissible value of RL for which the output voltage is at least 80% of the source voltage. Ans. 9.9 mV; 9.1 mV; 5 mV; 0.9 mV; 4 k 1.4 A signal source that is most conveniently represented by its Norton equivalent form has is = 10 μA and Rs = 100 k. If the source feeds a load resistance RL , find the current io that flows through the load for RL = 1 k, 10 k, 100 k, and 1 M. Also, find the largest permissible value of RL for which the load current is at least 80% of the source current. Ans. 9.9 μA; 9.1 μA; 5 μA; 0.9 μA; 25 k 1.2 Frequency Spectrum of Signals Figure 1.3 An arbitrary voltage signal v s (t). From the discussion above, it should be apparent that a signal is a time-varying quantity that can be represented by a graph such as that shown in Fig. 1.3. In fact, the information content of the signal is represented by the changes in its magnitude as time progresses; that is, the information is contained in the "wiggles" in the signal waveform. In general, such waveforms are difficult to characterize mathematically. In other words, it is not easy to describe succinctly an arbitrary-looking waveform such as that of Fig. 1.3. Of course, such a description is of great importance for the purpose of designing appropriate signal-processing circuits that perform desired functions on the given signal. An effective approach to signal characterization is studied in the next section. 1.2 Frequency Spectrum of Signals An extremely useful characterization of a signal, and for that matter of any arbitrary function of time, is in terms of its frequency spectrum. Such a description of signals is obtained through the mathematical tools of Fourier series and Fourier transform.1 We are not interested here in the details of these transformations; suffice it to say that they provide the means for representing a voltage signal v s (t) or a current signal is (t) as the sum of sine-wave signals of different frequencies and amplitudes. This makes the sine wave a very important signal in the analysis, design, and testing of electronic circuits. Therefore, we shall briefly review the properties of the sinusoid. Figure 1.4 shows a sine-wave voltage signal v a (t), v a (t) = Va sin ωt (1.1) where Va denotes the peak value or amplitude in volts and ω denotes the angular frequency in radians per second; that is, ω = 2π f rad/s, where f is the frequency in hertz, f = 1/T Hz, and T is the period in seconds. The sine-wave signal is completely characterized by its peak value Va , its frequency ω, and its phase with respect to an arbitrary reference time. In the case depicted in Fig. 1.4, the time 1 The reader who has not yet studied these topics should not be alarmed. No detailed application of this material will be made until Chapter 10. Nevertheless, a general understanding of Section 1.2 should be very helpful in studying early parts of this book. 9 10 Chapter 1 Signals and Amplifiers Figure 1.4 Sine-wave voltage signal of amplitude Va and frequency f = 1/T Hz. The angular frequency ω = 2π f rad/s. Figure 1.5 A symmetrical square-wave signal of amplitude V . origin has been chosen so that the phase angle is 0. It should be mentioned that it is common to express the amplitude of a sine-wave signal√in terms of its root-mean-square (rms) value, which is equal to √the peak value divided by 2. Thus the rms value of the sinusoid v a (t) of Fig. 1.4 is Va / 2. For instance, when we speak of the wall √ power supply in our homes as being 120 V, we mean that it has a sine waveform of 120 2 volts peak value. Returning now to the representation of signals as the sum of sinusoids, we note that the Fourier series is utilized to accomplish this task for the special case of a signal that is a periodic function of time. On the other hand, the Fourier transform is more general and can be used to obtain the frequency spectrum of a signal whose waveform is an arbitrary function of time. The Fourier series allows us to express a given periodic function of time as the sum of an infinite number of sinusoids whose frequencies are harmonically related. For instance, the symmetrical square-wave signal in Fig. 1.5 can be expressed as v(t) = 4V 1 1 (sin ω0 t + sin 3ω0 t + sin 5ω0 t + · · · ) π 3 5 (1.2) where V is the amplitude of the square wave and ω0 = 2π /T (T is the period of the square wave) is called the fundamental frequency. Note that because the amplitudes of the harmonics progressively decrease, the infinite series can be truncated, with the truncated series providing an approximation to the square waveform. The sinusoidal components in the series of Eq. (1.2) constitute the frequency spectrum of the square-wave signal. Such a spectrum can be graphically represented as in Fig. 1.6, where the horizontal axis represents the angular frequency ω in radians per second. 1.2 Frequency Spectrum of Signals Figure 1.6 The frequency spectrum (also known as the line spectrum) of the periodic square wave of Fig. 1.5. Figure 1.7 The frequency spectrum of an arbitrary waveform such as that in Fig. 1.3. The Fourier transform can be applied to a nonperiodic function of time, such as that depicted in Fig. 1.3, and provides its frequency spectrum as a continuous function of frequency, as indicated in Fig. 1.7. Unlike the case of periodic signals, where the spectrum consists of discrete frequencies (at ω0 and its harmonics), the spectrum of a nonperiodic signal contains in general all possible frequencies. Nevertheless, the essential parts of the spectra of practical signals are usually confined to relatively short segments of the frequency (ω) axis—an observation that is very useful in the processing of such signals. For instance, the spectrum of audible sounds such as speech and music extends from about 20 Hz to about 20 kHz—a frequency range known as the audio band. Here we should note that although some musical tones have frequencies above 20 kHz, the human ear is incapable of hearing frequencies that are much above 20 kHz. As another example, analog video signals have their spectra in the range of 0 MHz to 4.5 MHz. We conclude this section by noting that a signal can be represented either by the manner in which its waveform varies with time, as for the voltage signal v a (t) shown in Fig. 1.3, or in terms of its frequency spectrum, as in Fig. 1.7. The two alternative representations are known as the time-domain representation and the frequency-domain representation, respectively. The frequency-domain representation of v a (t) will be denoted by the symbol Va (ω). 11 12 Chapter 1 Signals and Amplifiers EXERCISES 1.5 Find the frequencies f and ω of a sine-wave signal with a period of 1 ms. 3 Ans. f = 1000 Hz; ω = 2π × 10 rad/s −3 1.6 What is the period T of sine waveforms characterized by frequencies of (a) f = 60 Hz? (b) f = 10 Hz? (c) f = 1 MHz? Ans. 16.7 ms; 1000 s; 1 μs 1.7 The UHF (ultra high frequency) television broadcast band begins with channel 14 and extends from 470 MHz to 806 MHz. If 6 MHz is allocated for each channel, how many channels can this band accommodate? Ans. 56; channels 14 to 69 1.8 When the square-wave signal of Fig. 1.5, whose Fourier series is given in Eq. (1.2), is applied T 2 to a resistor, the total power dissipated may be calculated directly using the relationship P = 1/T 0 (v /R) dt or indirectly by summing the contribution of each of the harmonic components, that is, P = P1 + P3 + P5 + . . . , which may be found directly from rms values. Verify that the two approaches are equivalent. What fraction of the energy of a square wave is in its fundamental? In its first five harmonics? In its first seven? First nine? In what number of harmonics is 90% of the energy? (Note that in counting harmonics, the fundamental at ω0 is the first, the one at 2ω0 is the second, etc.) Ans. 0.81; 0.93; 0.95; 0.96; 3 1.3 Analog and Digital Signals The voltage signal depicted in Fig. 1.3 is called an analog signal. The name derives from the fact that such a signal is analogous to the physical signal that it represents. The magnitude of an analog signal can take on any value; that is, the amplitude of an analog signal exhibits a continuous variation over its range of activity. The vast majority of signals in the world around us are analog. Electronic circuits that process such signals are known as analog circuits. A variety of analog circuits will be studied in this book. An alternative form of signal representation is that of a sequence of numbers, each number representing the signal magnitude at an instant of time. The resulting signal is called a digital signal. To see how a signal can be represented in this form—that is, how signals can be converted from analog to digital form—consider Fig. 1.8(a). Here the curve represents a voltage signal, identical to that in Fig. 1.3. At equal intervals along the time axis, we have marked the time instants t0 , t1 , t2 , and so on. At each of these time instants, the magnitude of the signal is measured, a process known as sampling. Figure 1.8(b) shows a representation of the signal of Fig. 1.8(a) in terms of its samples. The signal of Fig. 1.8(b) is defined only at the sampling instants; it no longer is a continuous function of time; rather, it is a discrete-time signal. However, since the magnitude of each sample can take any value in a continuous range, the signal in Fig. 1.8(b) is still an analog signal. Now if we represent the magnitude of each of the signal samples in Fig. 1.8(b) by a number having a finite number of digits, then the signal amplitude will no longer be continuous; rather, 1.3 Analog and Digital Signals 13 (a) Figure 1.8 Sampling the continuous-time analog signal in (a) results in the discrete-time signal in (b). it is said to be quantized, discretized, or digitized. The resulting digital signal then is simply a sequence of numbers that represent the magnitudes of the successive signal samples. The choice of number system to represent the signal samples affects the type of digital signal produced and has a profound effect on the complexity of the digital circuits required to process the signals. It turns out that the binary number system results in the simplest possible digital signals and circuits. In a binary system, each digit in the number takes on one of only two possible values, denoted 0 and 1. Correspondingly, the digital signals in binary systems need have only two voltage levels, which can be labeled low and high. As an example, in some of the digital circuits studied in this book, the levels are 0 V and +5 V. Figure 1.9 shows the time variation of such a digital signal. Observe that the waveform is a pulse train with 0 V representing a 0 signal, or logic 0, and +5 V representing logic 1. If we use N binary digits (bits) to represent each sample of the analog signal, then the digitized sample value can be expressed as D = b0 20 + b1 21 + b2 22 + · · · + bN−1 2N−1 (1.3) where b0 , b1 , . . . , bN−1 , denote the N bits and have values of 0 or 1. Here bit b0 is the least significant bit (LSB), and bit bN−1 is the most significant bit (MSB). Conventionally, this binary number is written as bN−1 bN−2 . . . b0 . We observe that such a representation quantizes N the analog sample into one of 2 levels. Obviously the greater the number of bits (i.e., the larger the N), the closer the digital word D approximates the magnitude of the analog sample. That is, increasing the number of bits reduces the quantization error and increases the resolution of the 14 Chapter 1 Signals and Amplifiers v (t) (V) 5 Logic values 0 1 0 1 1 0 1 0 0 Time, t Figure 1.9 Variation of a particular binary digital signal with time. Analog v input A A/D converter b0 b1 bN1 Digital output Figure 1.10 Block-diagram representation of the analog-to-digital converter (ADC). analog-to-digital conversion. This improvement is, however, usually obtained at the expense of more complex and hence more costly circuit implementations. It is not our purpose here to delve into this topic any deeper; we merely want the reader to appreciate the nature of analog and digital signals. Nevertheless, it is an opportune time to introduce a very important circuit building block of modern electronic systems: the analog-to-digital converter (A/D or ADC) shown in block form in Fig. 1.10. The ADC accepts at its input the samples of an analog signal and provides for each input sample the corresponding N-bit digital representation (according to Eq. 1.3) at its N output terminals. Thus although the voltage at the input might be, say, 6.51 V, at each of the output terminals (say, at the ith terminal), the voltage will be either low (0 V) or high (5 V) if bi is supposed to be 0 or 1, respectively. The dual circuit of the ADC is the digital-to-analog converter (D/A or DAC). It converts an N-bit digital input to an analog output voltage. Once the signal is in digital form, it can be processed using digital circuits. Of course digital circuits can deal also with signals that do not have an analog origin, such as the signals that represent the various instructions of a digital computer. Since digital circuits deal exclusively with binary signals, their design is simpler than that of analog circuits. Furthermore, digital systems can be designed using a relatively few different kinds of digital circuit blocks. However, a large number (e.g., hundreds of thousands or even millions) of each of these blocks are usually needed. Thus the design of digital circuits poses its own set of challenges to the designer but provides reliable and economic implementations of a great variety of signal-processing functions, many of which are not po