FOURTH EDITION
`
` wicgpnee
`
`tos
`
`:
`
`y
`
`‘4
`
`>
`
`Adel‘S. ‘edaABN
`
`Ay oneiteM
`
`University of Toronto
`
`Kenneth C. Smith
`University of Toronto and Hong Kong
`University of Science and Technology
`
`New York Oxford
`OXFORD UNIVERSITY PRESS
`1998
`
`Page 1 of 326
`
`Volkswagen Exhibit 1007
`
`Page 1 of 326
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`Volkswagen Exhibit 1007
`
`

`

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`Library of Congress Cataloging-in-Publication Data
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`General Library System
`j
`University of Wisconsi
`728 Stat
`nsin - Madison
`ate Street
`Madison WI 53706-
`U.S.A ,
`6-1494
`
`Sedra, Adel S.
`Microelectronic circuits / Adel S. Sedra, Kenneth C. Smith. — 4th ed.
`p.
`em. — (Oxford series in electrical and computer engineering)
`Includes bibliographical references and index.
`ISBN 0-19-511663-1
`2. Integrated circuits.
`1. Electronic circuits.
`Kenneth Carless.
`II, Title.
`Il. Series.
`TK7867.839
`1997
`621.381—de21
`
`], Smith,
`
`97-11254
`cir
`
`20 19 18 17 16 [5 t4 13 12 1110
`
`Printed in the United States of America on acid-free paper
`
`Cover Illustration: The chip shownis the ADXL-50 surface-micromachined accelerometer. For the first time, sensor
`and signal conditioning are combined on a single monolithic chip. In its earliest application, it was a key factor in
`the improved reliability and reduced cost of modern automotive airbag systems. Photo reprinted with permission of
`Analog Devices, Inc.
`
`Page 2 of 326
`
`Page 2 of 326
`
`

`

`(\_{\_DRTAILED TABLE OF CONTENTS
`
`PREFACE
`
`P
`
`Chapter 1
`
`INTRODUCTION TO ELectronics
`
`I
`
`Introduction
`
`J
`
`1.1
`L.2
`L.3
`14
`1.5
`1.6
`1.7
`
`3
`
`2
`Signals
`Frequency Spectrum of Signals
`Analog and Digital Signals
`6
`Amplifiers
`9
`29
`Circuit Models for Amplifiers
`Frequency Response of Amplifiers
`The Digital Logic Inverter 39
`Summary
`47
`Bibliography
`Problems
`48
`
`48
`
`28
`
`PART I DEVICES AND BASIC CIRCUITS 58
`
`Chapter 2
`
`OPERATIONAL AMPLIFIERS
`
`60
`
`Introduction
`60
`The Op-Amp Terminals 6/
`The Ideal Op Amp
`62
`Analysis of Circuits Containing Ideal Op Amps—TheInverting Configuration
`Other Applications of the Inverting Configuration
`71
`2.4.1 The Inverting Configuration with General Impedances Z, and Z,
`2.4.2. The Inverting Integrator
`73
`2.4.3. The Op Amp Differentiator
`2.4.4 The Weighted Summer
`80
`2.5
`The Noninverting Configuration
`87
`2.6
`Examples of Op-Amp Circuits
`85
`2.7
`92
`Effect of Finite Open-Loop Gain and Bandwidth on Circuit Performance
`2.8
`Large-Signal Operation of Op Amps=97
`2.9
`DC Imperfections
`101
`Summary
`168
`Bibliography 09
`Problems
`JI@
`
`64
`
`7J
`
`78
`
`2.1
`2.2
`2.3
`24
`
`xiv
`
`Page 3 of 326
`
`Page 3 of 326
`
`

`

`DETAILED TABLE OF CONTENTS
`
`x¥
`
`Chapter 3
`
`Diopes
`
`i122
`
`3.1
`3.2
`3.3
`
`3.4
`3.5
`3.6
`3.7
`3.8
`3.9
`3.10
`
`131
`
`143
`146
`
`J5J
`
`122
`Introduction
`123
`The Ideal Diode
`Termina] Characteristics of Junction Diodes
`Physical Operation of Diodes
`137
`138
`3.3.1 Basic Semiconductor Concepts
`3.3.2 The pn Junction Under Open-Circuit Conditions
`3.3.3 The pn Junction Under Reverse-Bias Conditions
`3.3.4 The pr Junction in the Breakdown Region
`149
`3.3.5 The pr Junction Under Forward-Bias Conditions
`3.3.6 Summary
`155
`155
`Analysis of Diode Circuits
`163
`The Small-Signal Model and Its Application
`Operation in the Reverse Breakdown Region—Zener Diodes
`Rectifier Circuits
`179
`Limiting and Clamping Circuits
`Special Diode Types
`196
`The SPICE Diode Model and Simulation Examples
`Summary
`206
`Bibliography 206
`Problems
`207
`
`291
`
`172
`
`£99
`
`Chapter 4
`
`Birocar Juncrion Transistors (BJTs) 22]
`
`4.1
`42
`43
`44
`45
`4.6
`/4d
`48
`49
`
`, 4.10
`, 4.11
`4.12
`4,13
`4.14
`4.15
`4.16
`
`Introduction 22]
`Physical Structure and Modes of Operation 222
`Operation of the npn Transistor in the Active Mode 223
`The pap Transistor
`232
`Circuit Symbols and Conventions 234
`Graphical Representation of Transistor Characteristics 238
`Analysis of Transistor Circuits at DC 241
`The Transistor as an Amplifier
`253
`Small-Signal Equivalent Circuit Models 259
`Graphical Analysis
`272
`Biasing the BJT for Discrete-Circuit Design 276
`282
`Basic Single-Stage BJT Amplifier Configurations
`295
`The Transistor as a Switch—Cutoff and Saturation
`A General Large-Signal Model for the BJT: The Ebers-Moll (EM) Model
`The Basic BJT Logic Inverter 320
`Complete Static Characteristics, Internal Capacitances, and Second-Order Effects 315
`The SPICE BJT Model and Simulation Examples 326
`Summary
`337
`Bibliography
`332
`Problems
`333
`
`343
`
`Page 4 of 326
`
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`
`

`

`xvi
`
`DETAILED TABLE OF CONTENTS
`
`Chapter 5
`
`FiaLp-Errect Transistors (FETs}
`
`353
`
`5.1
`5.2
`5.3
`5.4
`5.5
`5.6
`
`$.7
`
`5.8
`5.9
`5.10
`5.11
`5.12
`5.13
`
`408
`
`353
`Introduction
`Structure and Physical Operation of the Enhancement-Type MOSFET 354
`Current-Voltage Characteristics of the Enhancement MOSFET 366
`The Deletion-Type MOSFET 376
`MOSFETCircuits at DC 380
`389
`The MOSFET as an Amplifier
`400
`Biasing in MOS Amplifier Circuits
`400
`5.6.1 Biasing of Discrete MOSFET Amplifiers
`402
`5.6.2 Biasing in Integrated-Circuit MOS Amplifiers
`Basic Configurations of Single-Stage IC MOS Amplifiers
`5.7.1. The CMOS Common-Source Amplifier 409
`5.7.2. The CMOS Common-Gate Amplifier
`423
`5.7.3 The Common-Drain or Source-Follower Configuration 416
`5.74 Al-NMOS Amplifier Stages 479
`5.7.5 A Final Remark 425
`425
`The CMOSDigital Logic Inverter
`436
`The MOSFETas an Analog Switch
`The MOSFETIntemal Capacitances and High-Frequency Model
`The Junction Field-Effect Transistor (JFET) 447
`Gallium Arsenide (GaAs) Devices—The MESFET 452
`The SPICE MOSFET Mode] and Simulation Examples
`Summary
`464
`Bibliography 464
`Problems
`466
`
`447
`
`458
`
`PART II ANALOG CIRCUITS 484
`
`Chapter 6
`
`DIFFERENTIAL AND MULTISTAGE AMPLIFIERS
`
`487
`
`6.1
`6.2
`6.3
`6.4
`65
`6.6
`6.7
`6.8
`6.9
`6.10
`
`Introduction 487
`The BIT Differential Pair 487
`492
`Small-Signal Operation of the BJT Differential Amplifier
`Other Nonideal Characteristics of the Differential Amplifier 504
`Biasing in BJT Integrated Circuits
`508
`The BJT Differential Amplifier with Active Load
`MOSDifferential Amplifiers 327
`BiCMOS Amplifiers
`537
`GaAs Amplifiers
`542
`351
`Multistage Amplifiers
`SPICE Simulation Example
`Summary
`563
`Bibliography
`364
`Problems
`564
`
`338
`
`522
`
`Page 5 of 326
`
`Page 5 of 326
`
`

`

`DETAILED TABLE OF CONTENTS
`
`xvii
`
`Chapter 7
`
`FREQUENCY RESPONSE S83
`
`7.)
`7.2
`73
`
`74
`
`73
`7.6
`77
`7.8
`79
`
`Introduction
`583
`s-Domain Analysis: Poles, Zeros, and Bode Plots 584
`The Amplifier Transfer Function
`590
`Low-Frequency Response of the Common-Source and Common-Emitter
`Amplifiers
`602
`High-Frequency Response of the Common-Source and Common-Emitter
`Amplifiers
`670
`The Common-Base, Common-Gate, and Cascode Configurations
`Frequency Response ofthe Emitter and Source Followers
`626
`The Common-Collector Common-Emitter Cascade
`630
`Frequency Response.of the Differential Amplifier 635
`SPICE Simulation Examples
`645
`Summary
`649
`Bibliography
`650
`Problems
`650
`
`629
`
`Chapter 8
`
`FEEDBACK 667
`
`8.]
`8.2
`8.3
`8.4
`8.5
`8.6
`. 87
`8.8
`8.9
`8.10
`8.11
`8.12
`
`667
`Introduction
`The General Feedback Structure
`668
`670
`SomeProperties of Negative Feedback
`675
`The Four Basic Feedback Topologies
`679
`The Series-Shunt Feedback Amplifier
`688
`The Series-Series Feedback Amplifier
`The Shunt-Shunt and the Shunt-Series Feedback Amplifiers
`Determining the Loop Gain
`708
`The Stability Problem 7/3
`Effect of Feedback on the Amplifier Poles
`Stability Study Using Bode Plots
`725
`Frequency Compensation
`729
`SPICE Simulation Examples
`735
`Summary
`746
`Bibliography
`740
`Problems
`74f
`
`725
`
`696
`
`Chapter 9
`
`Ourpur STAGES AND POWER AMPLIFIERS
`
`751
`
`Introduction
`
`751
`
`9.1
`9.2
`9.3
`
`Classification of Output Stages
`Class A Output Stage
`753
`Class B Output Stage
`758
`
`752
`
`Page 6 of 326
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`

`

`xviii
`
`DETAILED TABLE OF CONTENTS
`
`9.4
`9.5
`9.6
`97
`9.8
`9.9
`9.10
`
`764
`Class AB Output Stage
`Biasing the Class AB Circuit
`Power BJTs
`773
`
`767
`
`Variations on the Class AB Configuration
`IC Power Amplifiers
`785
`MOSPowerTransistors
`792
`
`780
`
`SPICE Simulation Example
`Summary
`802
`Bibliography
`802
`Problems
`803
`
`797
`
`Chapter 10
`
`ANALOG INTEGRATED Circuits
`
`870
`
`Introduction
`
`sid
`
`10.1
`10,2
`10,3
`10.4
`10.5
`10.6
`10.7
`10,8
`10.9
`10.10
`10.11
`10.12
`
`411
`The 741 Op-Amp Circuit
`815
`DC Analysis of the 741
`Small-Signal Analysis of the 741 Input Stage
`Small-Signal Analysis of the 741 Second Stage
`Analysis of the 74.1 Output Stage
`830
`Gain and Frequency Response of the 741
`CMOS OpAmps 840
`Alternative Configurations for CMOS and BiCMOS Op Amps
`Data Converters—AnIntroduction 856
`D/A Converter Circuits &60
`A/D Converter Circuits &6¢4
`
`822
`828
`
`835
`
`856
`
`SPICE Simulation Example
`Summary
`874
`Bibliography
`875
`Problems
`876
`
`870
`
`Chapter 11
`
`FILTERS AND TUNED AMPLIFIERS
`
`884
`
`Introduction &84
`Filter Transmission, Types, and Specification
`The Filter Transfer Function
`889
`
`892
`Butterworth and Chebyshev Filters
`First-Order and Second-Order Filler Functions
`The Second-Order LCR Resonator
`909
`
`885
`
`900
`
`Second-Order Active Filters Based on Inductor Replacement 9/5
`Second-Order Active Filters Based on the Two-Integrator-Loop Topology
`Single-Amplifier Biquadratic Active Filters 929
`Sensitivity
`938
`
`923
`
`{Ll
`112
`113
`11.4
`11.5
`{1.6
`11.7
`11.8
`11.9
`
`Page 7 of 326
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`
`

`

`DETAILED TABLE OF CONTENTS
`
`xix
`
`11.10
`11.11
`11.12
`
`Switched-Capacitor Filters
`Tuned Amplifiers
`946
`SPICE Simulation Examples
`Summary
`965
`Bibliography
`966
`Problems
`967
`
`941
`
`959
`
`Chapter 12
`
`SIGNAL GENERATORS AND WAVEFORM-SHAPING CIRCUITS
`
`973
`
`12.1
`12.2
`12.3
`12.4
`12.5
`
`12.6
`12.7
`12.8
`12.9
`12.10
`
`974
`
`Introduction
`973
`Basic Principles of Sinusoidal Oscillators
`Op Amp-RC Oscillator Circuits
`980
`LC and Crystal Oscillators
`988
`Bistabie Multivibrators
`994
`Generation of Square and Triangular Waveforms Using Astable
`Multivibrators
`1002
`Generation of a Standardized Pulse—The Monostable Multivibrator
`Integrated-Circuit Timers
`1009
`Nonlinear Waveform-Shaping Circuits
`1074
`Precision Rectifier Circuits
`7018
`SPICE Simulation Examples
`1026
`Summary
`1030
`Bibliography
`1030
`Problems
`1031
`
`7007
`
`PART IIT DIGITAL CIRCUITS 1040
`MGS Diarrac CIRcuITs
`1042
`
`Chapter 13
`
`Introduction
`1042
`Digital Circuit Design: An Overview 1043
`13.1.1 Digital IC Technologies and Logic-Circuit Families
`13.1.2 Logic-Circuit Characterization
`7645
`13.1.3.
`Styles for Digital System Design
`1048
`1048
`13.1.4 Design Abstraction and Computer Aids
`Design and Performance Analysis of the CMOSInverter
`CMOSLogic-Gate Circuits
`1058
`Pseudo-NMOS Logic Circuits
`1070
`Pass-Transistor Logic Circuits
`1080
`Dynamic Logic Circuits
`1090
`Latches and Flip-Flops
`1097
`Multivibrator Circuits 1/06
`Semiconductor Memories: Types and Architectures 11/3
`
`13.1
`
`13.2
`13.3
`13.4
`13.5
`13.6
`13.7
`13.8
`13.9
`
`1043
`
`1049
`
`Page 8 of 326
`
`Page 8 of 326
`
`

`

`1125
`13.11.1 The Sense Amplifier
`13.11.2 The Row-Address Decoder 1/31
`(3.11.3 The Coltumn-Address Decoder
`1133
`
`-
`
`13.12 Read-Only Memory (ROM)
`13.13 SPICE Simulation Example
`Summary
`I144
`Bibliography
`1146
`Problems
`£146
`
`1133
`114@
`
`Chapter 14
`
`BIPOLAR AND ADVANCED-TECHNOLOGY DiartraL Circurts
`
`7158
`
`Introduction
`
`7158
`
`2759
`14.1 Dynamic Operation of the BIT Switch
`1163
`14.2 Early Forms of BJT Digital Circuits
`14.3 Transistor-Transistor Logic (TTL or T°L)
`14.4 Characteristics of Standard TTL 71780
`
`1167
`
`1187
`
`14.5 TTL Families with Improved Performance
`14.6 Emitter-Coupled Logic (ECL)
`1195
`14.7 BiCMOSDigital Circuits
`1211
`14.8 Gallium-Arsenide Digital Circuits
`14.9 SPICE Simulation Example
`1224
`Summary
`1230
`Bibliography
`123]
`Problems
`1232
`
`1216
`
`APPENDIXES
`
`VLSI FABRICATION TECHNOLOGY A-I
`Two-Port Nerwork PARAMETERS B-I
`AN INTRODUCTION To SPICE C-T
`INpuT FILES FOR THE SPICE Exampies D-?
`Some UseruL Network THEeorems
`£E-I
`SINGLE-TIME-CONSTANT Circuits F-J
`DETERMINING THE PARAMETER WALUES OF THE HyBrip-7 BJT Model G-1
`STANDARD RESISTANCE VALUES AND Unit Prerixes H-J
`ANSWERS TO SELECTED PROBLEMS 1-I
`
`InpeEx
`
`JIN-I
`
`Page 9 of 326
`
`Page 9 of 326
`
`

`

`
`
`Introduction to Electronics
`
`:
`
`a
`Introduction
`1.6
`Frequency Response of
`Signals
`Amplifiers.
`,
`1.1
`Frequency Spectrum of Signals
`1.7. The Digital Logic Inverter
`1.2.
`1.3. Analog and Digital Signals
`Summary
`1.4 Amplifiers
`Bibliography
`1.5 Circuit Models for Amplifiers
`Problems
`EE
`
`‘
`
`INTRODUCTION
`a
`The subject of this book is modern electronics, a field that has come to be known as
`microelectronics. Microelectronics refers to the integrated-circuit (C) technology that at
`the time of this writing is capable of producing circuits that contain millions of components
`in a small piece of silicon (known as a silicon chip) whose area is in the order of 100
`mm?. One such microelectronic circuit, for example, is a complete digital computer, which
`accordingly is known as a microcomputer or, more generally, a microprocessor.
`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
`circuits of varying complexity and perform a wide variety of functions. Weshall also learn
`about available IC chips and their application in the design of electronic systems.
`The purpose ofthis 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 amplifica-
`tion. We shall then look at models for linear amplifiers. These models will be employed in
`subsequentchapters in the design and analysis of actual amplifier circuits.
`Whereas the amplifier is the basic element of analog circuits, the logic inverter plays
`this role in digital circuits. We shall therefore take a preliminary look at the digital inverter,
`its circuit function, and important characteristics.
`l
`
`Page 10 of 326
`
`Page 10 of 326
`
`

`

`2
`
`INTRODUCTION TO ELECTRONICS
`
`In addition to motivating the study of electronics, this chapter serves as a bridge be-
`tween the study oflinear 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 announcerreading 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.
`
`
`
`us
`fori
`7 For instance,
`e sound waves generated by a human can be converted
`into electric signals using a mi-
`
`crophone, which is in effect a pressure transducer.
`It is not our purpose here to study
`transducers: rather, we shall assumethat the signals of interest already exist in the electrical
`domain and represent them by one of the two equivalent forms shownin Fig, 1.1. In Fig.
`1.1(a) the signal is represented by a voltage source u(t) having a source resistance R,. In
`the alternate representation of Fig. 1.1(b) the signal
`is represented by a current source
`i,(t) having a source resistance.
`h the two representations are equivalent, that in
`
`Fig. 1.1(a) _Therepresentation(HOWHIaS
`
`
`of Fig. 1.1(b)
`form.
`
`Fig. 1.1 Two alternative
`representations of a signal
`source:
`(a) the Thévenin
`form, and
`(b) the Norton
`
`(a)
`
`(b)
`
`From the discussion above, it should be apparentthata signalis a time-varying quantity
`that can be represented by a graph such as that shown in Fig. 1.2. In fact, the information
`contentofthe signal is represented by the changesinits magnitudeas 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 asthat of Fig. 1.2. 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.
`
`Page 11 of 326
`
`Page 11 of 326
`
`

`

`1.2.
`
`FREQUENCY SPECTRUM OF SIGNALS
`
`3
`
`u(t)
`
`Fig. 1.2 An arbitrary voltage signal v(t).
`
`1.2 FREQUENCY SPECTRUM OF SIGNALS
`ATrextremely usefurcharacterizationofa"aSignal,andforiarmagerofanyarbitraryfunction”
`
`offinte; is in terms fitsSfrecuency”§“Spevtrunt.runt.Such aadlescripfion of‘sifuials is obtained 7]
`“ifrough the-ntathématieal“tools “of"Fourierseries and: Forriti“transforifiWe aténot
`interestedatthis ‘pointin’ thé detailSofthésetransformauions, suffice it to say that they
`provide the means for representing a voltage signal »,(f} or a currentsignal i,(f) 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 1.3 shows a sine-wave voltage signal v,(4),
`(1.1)
`in(O.Visio
`
`(here.re.¥,denotes,thepeakaloe-ormamplitude~iffvolts "and’@deridtestheangularfrequeticyy
`_inradiansper.SCOUTPhat-isowen27sad/s;wherefoisil“is_thefrequency. in-hertz,f,= VE i
`(CHz,.and77isthe.periadinsecands4
`
`rad/s,
`
`Sine-wavevoltage
`Fig. 1.3
`signal of amplitude V, and
`frequency f = 1/T Hz. The
`angular frequency w = 2xf
`
`' The reader who has not yet studied these topics should not be alarmed. No detailed application of this
`* material will be made until Chapter 7. Nevertheless, a general understanding of Section 1.2 should be very helpful
`when studying early parts of this book.
`
`Page 12 of 326
`
`Page 12 of 326
`
`

`

`4
`
`INTRODUCTION TO ELECTRONICS
`
`The sine-wave signal is completely characterized by its peak value ¥,, its frequency w,
`and its phase with respect to an arbitrary reference time. In this case thetime origin has
`been chosen so that the phase angle is 0. It should be mentioned that“itis.comman ip
`Xpresstheampubue,ofasine-wave-signal-in, terms-of-itsHookmean-squareThtis)VANE,
`WhichSeeqiaToUSTSSEvalue,dividedby“Wd,gthosWefins value of the sinusoid ¥,(0)
`of Fig. 1.3 is V,/V2. 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 120V2 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 when the signalis
`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.
`aninfinitenumberoksinusoidswhosetreqenciesare harmonically elatedFor ingame,
`‘The.Fourier-series~allows-us-to-express-a-givenperiodic function"oftiiig as The
`theSynimetncalsquare-wavesignalinFig.1.4 can bé expressed
`as
`(1.2)
`vu) = in sot + 4sin 3aot + dsinS@of + °°)
`whereVis the amplitude of the square wave and 99"2alT“(rigtheperiod ofshesquare
`~>
`aveiscANedthéfuridiinentalfrequency-jNote that because the amplitudes of the har- °
`fionics progressively decrease, the infinite series can be truncated, with the truncatedseries
`providing an approximation to the square waveform.
`
`amplitude V.
`
`Fig. 1.4 A symmetrical
`square-wave signal of
`
`The sinusoidal componentsin 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. 1.5,
`where the horizontal axis represents the angular frequency w in radians per second.
`The Fourier transform can be applied to a nonperiodic function of time, such as that
`depicted in Fig, 1.2, and provides its frequency spectrum as a continuous function of fre-
`quency, as indicated in Fig. 1.6. Unlike the case of periodic signals, where the spectrum
`consists of discrete frequencies (at #9 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
`(w) 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
`
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`

`

`1.2.
`
`PREQUENCY SPECTRUM OFSIGNALS
`
`5
`
`
`
`ag
`
`ay
`
`Sip
`
`Targ
`
`w (rad/s)
`
`Fig. 1.5 The frequency spectrum (also known as the line spectrum) of the periodic square wave
`of Fig. 1.4.
`‘
`
`although some musical tones have frequencies above 20 kHz, the humanearis incapable
`of hearing frequencies that are much above 20 kHz.
`Weconclude this section by noting that g-signal-carrberepresentedeitherbythemarinér{
`Grnifs Waveformvaries‘withtime,As for the voltage signal v,(2) shown in Fig. 1.2,
`as in Fig. 1.6. The two alternative representations are
`in tefhisofitsfrequencyspectrum)
`knownas theLihe-domainrepresentationanethefrequency-domainTepiesehaliah, respec-
`tively. The frequency-domain representationofu,(f) will be denoted by the symbol V,(w).
`
`
`
`Frequencyspectrum¥,(w)involts
`
`oO
`
`Fig. 1.6 The frequency
`spectrum of an arbitrary
`waveform such as that in
`Fig. 1.2.
`
`_ w (rad/s)
`
`Exercises
`
`1.1 Find the frequencies f and w of a sine-wave signal with a period of | ms.
`
`Ans. f = 1000 Hz; w = 2 X 10° rad/s
`
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`

`

`6
`
`INTRODUCTION TO ELECTRONICS
`
`1.2 What
`107? Hz?
`
`is the period T of sine waveforms characterized by frequencies of
`(c) f = 1 MHz?
`
`(a) f= 60Hz? O)f=
`
`Ans. 16.7 ms; 1000s; 1 us
`1.3 Whenthe square-wave signal of Fig. 1.4, whose Fourier series is given in Eq, (1.2), is applied to a resistor,
`T
`A the total power dissipated may be calculated directly using the relationship P = wT|(IR) dt, or indirectly
`Qo
`by summing the contribution of each of the harmonic components, that is, P = Pi + Py + Ps + +++, which
`may be found directly from rms values. Verify that the two approaches are equivalent. What fraction of the
`#
`
`
`
`energy of a square waveis 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 wo is the
`
`tl
`
`first, the one at 2mis 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. 1.2 is called an analog signal. The namederives from
`the fact that such a signal is analégous to the physical signal that it represents. The mag-
`nitude of an analog signal can take on ‘any value; that is,heaiipiitadeof-an-analog stptar"y
`rexhibits e-continuods‘variition Syeriisrange,Ofwctivity Je
`ajority_of signalsinthe/
`omni
`veal
`eerere wie
`.
`7
`_
`.
`(rorid=around"ws “are analogyElectronic circuits that
`process such signals are known as
`
`eineraTahara “ . . . . . a
`
`
`
`
`
`analog circuits, A variety of analog circuits will be studiedinthis book.
`Je TormotSignalrepresemananis_that of.a-sequencentWibens,.<acbt
`AuberrepresentingthesignalmagnitedEatan instantok (uneUiheresultipesignali$Caley
`To see how a signal can be represented in this form—that is, how signals
`
`
` sital sien.
`can be converted from analog to digital form—consider Fig. 1.7(a). Here the curve repre-
`sents a voltage signal, identical to that in Fig. 1.2. At equal intervals along the time axis
`we have marked the time instants fo, fi, 2, and so on. At each of these time instants the
`magnitude of the signalis measured, a process known as sampling. Figure 1.7(b) shows a
`representation of the signal of Fig. 1.7(a) in terms of its samples. The signal of Fig. 1.7(b)
`is defined only at the sampling instants, it no longer is a continuous function of time, but
`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. 1.7(b) is still an analog signal.
`Now if we represent the magnitude of each of the signal samples in Fig. 1.7(b) by a
`number having a finite number of digits, then the signal amplitude will no longer be con-
`tinuous; rather, 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 10 represent the signal samples affects the type of digital
`signal produced and has a profound effect on the complexity of the digital cireuits 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
`
`Page 15 of 326
`
`Page 15 of 326
`
`

`

`1.3.
`
`ANALOG AND DIGITAL SIGNALS
`
`7
`
`wt)
`
`fo fy ta fy ve
`
`
`
`(a)
`
`ud)
`
`
`
`ty by ta tg
`
`
`
`(b)
`Fig. 1.7 Sampling the continuous-time analog signal in {a} results in the discrete-time signal
`in (b).
`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 1.8 shows the time variation of such a digital signal. Observe that the wave-
`form is a pulse train with 0 V representing a 0 signal, or logic 0, and +5 V representing
`logic 1.
`
`+5
`
`vf
`
`0
`1
`0
`1
`i
`0
`Logic values 2 i
`Fig. 1.8 Variation of a particular binary digital signal with time.
`
`0
`
`Time, t
`
`Page 16 of 326
`
`Page 16 of 326
`
`

`

`where bo, by,..-, 2v—1, denote the ¥ bits and have values of 0 or 1. Here bit &p is the
`least significant bit (LSB), and bit by—1 is the most significant bit (MSB). Conventionally,
`this binary numberis written as by-1bw-2 .
`.
`. Bp. We observe that such a representation
`quantizes the analog sample into one of 2" levels. Obviously the greater the numberofbits
`(i.e., the larger the N), the closer the digital word D approximates the magnitude of the
`analog sample. That is,rincresSing,dhe OMMheeoFDitsreducesWe"qiairizMion efroratid
`
`Hcreasestreresolution’of theanalog-to-digitalconversion} "Tis improve penis, Weve]
`Waalohtained._at iE-expenseofToreTOMplexandhence"more-costly_CirkMitiiiplemen- 7
`Ciationszlt 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 importantcircuit building block of modem electronic systems: the
`analog-to-digital converter (A/D or ADC) shown in block form in Fig. 1.9. 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 ; is supposed
`to be 0 or 1, respectively. We shall study the ADC andits dual circuit the digital-to-analog
`converter (D/A or DAC) in Chapter 10.
`
`Analog ¢
`
`input *
`
`Fig. 1.9 Block-diagram
`representation of the analog-
`to-digital converter (ADC).
`
`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.
`ciremi
`akexclusively-with-binary-signals;-their design-is-simpler thanj
`ThalDfaeatog vicarsrurthermore;digitdl-sVstéms-can-be-désigned=usingarelativelytew/
`AIVeFentbinaBFightcreatTock. However, a largenumber(e.g..hundreds-of thou-;
`andsorevenmillionsy-oleach of these“blocksareusually fgéded:Thus the"designof
`Weill circuits"poses"its"owir-setOf challenges~to-the-designer,butprovidesfelrable andy
`. ae ae
`its ater
`are,
`
`ic ipplementonsOb.2prea-variescorsigaal-processififunctions, somé ofwhich?
`(CHIE“notpossible swithanalogcifcujts} At the present time, more andmore of the signal
`processing functions are being performed digitally. Examples around us abound: from the
`digital watch and the calculator to digital audio systems and, very soon, digital television.
`Moreover, some longstanding analog systems such as the telephone communication system
`are now almost entirely digital. And we should not forget the most important of all digital
`systems, the digital computer.
`
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`

`

`1.4
`
`AMPLIFIERS
`
`9
`
`The basic building blocks of digital systems are logic circuits and memory circuits. We
`shall study both in this book, beginning in Section 1.7 with the most fundamental digital
`circuit, the digital logic inverter.
`One final remark: Although the digital processing of signals is at presentall-pervasive,
`there remain many signal processing functions that are best performed by analog circuits.
`Indeed, many electronic systems include both analog anddigital parts. It follows that a good
`electronics engineer must be proficient in the design of both analog and digital circuits.
`Such is the aim of this book.
`
`
`Exercise
`
`a 1.4 Consider a 4-bit digital word D = b3byb,bo(see Eg. 1.3) used to represent an analog signal v4 that varies
`. between 0 V and +15 V.
`
`‘
`
`»
`
`(a) Give D corresponding to vg = 0 V,
`
`1 V, 2 V, and 15 V.
`
`(b) What change in wv, causes a change from 0to |
`
`in: (i) bo, (ii) b), Gii) b2, and (iv) by?
`
`(c)
`
`If vw = 5.2 V, what do you expect D to be? What is the resulting error in representation?
`
`© Ans. (a) 0000, 0001, 0010, 1111;
`
`(©) O101, 4%
`(b) +1. V, +2, +4V. +8.V;
`
`
`1.4 AMPLIFIERS
`
`In this section, we shall introduce a fundamental signal-processing function that is employed
`in some form in almost every electronic system, namely, signal amplification.
`
`Signal Amplification
`
`From a conceptual point of view the simplest signal-processing task is that of signal am-
`plification. The needfor/amplification arises because transducers provide signals that are
`said to be “‘weak,’? that is,
`in the microvolt (uwV) or millivolt (mV) range and possessing
`little energy. Such signals are too small for reliable processing, and processing is much,
`easier if the signal magnitude is made larger! The functional block that accomplishesthis
`1s
`.
`
`screeneeeeEONT TR the need for linearity in amplifiers. When
`amplifying a signal, caremust be exercised so that the information contained in thesignal
`is not changed and no new information is introduced. Thus whenfeeding the signal shown
`in Fig. 1.2 to anamplifier, we want the output signaloftheamplifier tobean exact replica
`of ‘that atthe input, except of course for having larger magnitude. In other words, the
`“wiggles” in the output waveform must be identical to those in the input waveform. Any
`change in waveform is considered to be distortion and is obviously undesirable:
`An amplifier that preserves the details of the signal waveform is characterized by the
`relationship
`
`Ul) = Av,{t)
`
`(1.4)
`
`Page 18 of 326
`
`Page 18 of 326
`
`

`

`where v; and v, are the input and output signals, respectively, and A is a constant repre-
`senting the magnitude of amplification, known as amplifier gain. Equation (1.4) is a linear
`relationship; hence the amplifier it describes is a/limear amplifier. It should be easy to see
`that if the relationship between v, and v; contains higher powers of v;, then the waveform
`of v, will no longer be identical to that of v;. The amplifier is then said to exhibit nonlinear
`distortion.
`The amplifiers discussed so far are primarily intended to operate on very small input
`signals, Their purpose is to make the signal magnitude larger and therefore are thought of —
`as voltage amplifiers. The preamplifier in the home stereo system is an example of a
`voltage amplifier. However, it usually does more than just amplify the signal; specifically,
`i