Electronics. Circuits, Amplifiers and Gates

326 Pages·2006·2.41 MB·English

by  David Bugg

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Electronics
Circuits, Amplifiers and Gates
Second Edition
DV Bugg
Emeritus Professor, Queen Mary,
University of London
InstituteofPhysicsPublishing
BristolandPhiladelphia
Copyright © 2005 IOP Publishing Ltd.
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©IOPPublishingLtd2005
All rights reserved. No part of this publication may be reproduced, stored in a
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Firstedition1991
Reprinted1995,1996,1999
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Contents
Preface ix
1 Voltage, Current and Resistance 1
1.1 Basic Notions 1
1.2 Waveforms 3
1.3 Ohm’s Law 6
1.4 Diodes 6
1.5 Kirchhoff’s Laws 8
1.6 Node Voltages 14
1.7 EARTHS 15
1.8 Superposition 16
1.9 Summary 19
2. Thevenin and Norton 24
2.1 Thevenin’s Theorem 24
2.2 How to Measure V and R 28
EQ EQ
2.3 Current Sources 30
2.4 Norton’s Theorem 31
2.5 General Remarks on Thevenin’s Theorem and Norton’s 34
2.6 Matching 35
2.7 Amplifiers 36
2.8 Systems 38
2.9 Summary 38
3. Capacitance 44
3.1 Charge and Capacitance 44
3.2 Energy Stored in a Capacitor 46
3.3 The Effect of a Dielectric 46
3.4 Capacitors in Parallel 47
3.5 Capacitors in Series 48
3.6 The CR Transient 48
3.7 AC Coupling and Baseline Shift 53
3.8 Stray Capacitance 55
3.9 Integration and Differentiation 55
3.10 Thevenin’s Theorem Again 56
3.11 Summary 57
4. Alternating Current (AC); Bandwidth 61
4.1 Introduction 61
4.2 Power in a Resistor: RMS Quantities 61
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vi Contents
4.3 Phase Relations 62
4.4 Response of a Capacitor to AC 64
4.5 Simple Filter Circuits 65
4.6 Power Factor 70
4.7 Amplifiers 71
4.8 Bandwidth 73
4.9 Noise and Bandwidth 73
4.10 Summary 75
5. Inductance 78
5.1 Faraday’s Law 78
5.2 Self-inductance 79
5.3 LR Transient 80
5.4 Energy Stored in an Inductor 82
5.5 Stray Inductance 83
5.6 Response of an Inductor to Alternating Current 84
5.7 Phasors 84
5.8 Summary 85
6. Complex Numbers: Impedance 89
6.1 Complex Numbers 89
6.2 AC Voltages and Currents 93
6.3 Inductance 95
6.4 Summary on Impedance 96
6.5 Impedances in Series 96
6.6 Impedances in Parallel 98
6.7 Power 101
6.8 Bridges 102
7. Operational Amplifiers and Negative Feedback 109
7.1 Introduction 109
7.2 Series Voltage Feedback 111
∗
7.3 Approximations in Voltage Feedback 115
7.4 Shunt Feedback 115
7.5 The Analogue Adder 118
7.6 The Differential Amplifier 119
7.7 Gain-Bandwidth Product 120
7.8 Offset Voltage and Bias Current 123
7.9 Complex Feedback Loops 125
7.10 Impedance Transformation 127
7.11 Input and Output Impedances with Feedback 128
7.12 Stabilised Current Supplies 132
∗
7.13 Input Impedance with Shunt Feedback 133
7.14 Oscillation 135
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Contents vii
8. Integration and Differentiation 143
8.1 Integration 143
8.2 The Miller Effect 146
8.3 Compensation 148
8.4 Differentiation 149
8.5 The Charge Sensitive Amplifier 149
9. The Diode and the Bipolar Transistor 155
9.1 Conductors 155
9.2 Semiconductors and Doping 157
9.3 The pn Junction Diode 160
9.4 The Diode as a Switch 167
9.5 The npn Bipolar Transistor 169
9.6 Simple Transistor Circuits 171
9.7 Voltage Amplification 173
9.8 Biasing 175
10. The Field Effect Transistor (FET) 180
10.1 Gate Action 180
10.2 Simple FET Amplifiers 183
10.3 MOSFETs 186
10.4 Fabrication of Transistors and Integrated Circuits 188
10.5 CMOS 190
11. Equivalent Circuits for Diodes and Transistors 192
11.1 Introduction: the Diode 192
11.2 An Equivalent Circuit for the Bipolar Transistor 194
11.3 The Hybrid-π Equivalent Circuit 199
11.4 The FET 200
11.5 The Common Emitter Amplifier 201
11.6 Performance of the Common Emitter Amplifier 202
11.7 Emitter Follower 206
11.8 FETs 210
12. Gates 219
12.1 Introduction 219
12.2 Logic Combinations of A and B 220
12.3 Boolean Algebra 223
12.4 De Morgan’s Theorems 224
12.5 The Full Adder 225
12.6 The Karnaugh Map 226
12.7 Don’t Care or Can’t Happen Conditions 230
12.8 Products of Karnaugh Maps 231
12.9 Products of Sums 232
12.10 Use of NOR and NAND Gates 233
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viii Contents
12.11 Decoders and Encoders 235
12.12 Multiplexing 237
13. Sequential Logic 241
13.1 The RS Flip-Flop 241
13.2 Clocks 242
13.3 The JK Flip-Flop 244
13.4 A Scale-of-4 Counter 246
13.5 State Diagrams 249
13.6 Trapping Sequences: Pattern Recognition 252
13.7 The Monostable 254
13.8 The Pulse Generator 256
14. Resonance and Ringing 261
14.1 Introduction 261
14.2 Resonance in a Series LCR Circuit 261
14.3 Transient in a CL Circuit 265
14.4 Transient in the Series LCR Circuit 266
14.5 Parallel LCR 269
∗
14.6 Poles and Zeros 273
15. Fourier’s Theorem 277
15.1 Introduction 277
15.2 A Square Wave applied to a CR Filter 278
15.3 How to Find Fourier Coefficients 279
15.4 The Heterodyne Principle 281
15.5 Broadcasting 282
15.6 Frequency Modulation (FM) 284
15.7 Frequency Multiplexing 285
15.8 Time Division Multiplexing 286
15.9 Fourier Series using Complex Exponentials 288
15.10 Fourier Transforms 289
15.11 Response to an impluse 290
15.12 Fourier analysis of a Damped Oscillator 291
15.13 The Perfect Filter 292
16. Transformers and 3-Phase Supplies 298
16.1 Introduction 298
16.2 Energy Stored in a Transformer 300
16.3 Circuit Equations and Equivalent Circuits 301
16.4 Three Phase Systems 304
16.5 Balanced Loads 306
Appendix A: Thevenin’s Theorem 313
Appendix B: Exponentials 315
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Preface
Industryandresearchdependheavilyonelectricalinstrumentsandtechniques.
Trouble-shooting invariably involves using multimeters and oscilloscopes. For
many students, experience with these instruments begins in first year courses at
UniversitiesandCollegesandthereaftercontinuestoexpandformanyyears. The
objectiveofthisbookistoaccompanyfirst-yearcoursesandgojustbeyondthat
for completeness. The aim is a rigorous but introductory treatment. I have fre-
quentlytaughtcoursesforengineersandhaveincludedthematerialtheyneed-for
example3-phasepowersupplies. Inthepresentperiloussituationinwhichmany
departmentsfindthemselves,closercooperationbetweenengineeringandphysics
faculties may be the way forward. I therefore hope the book may be helpful to
bothphysicistsandengineers.
Over90%ofthematerialincludedherehasbeenusedinpracticalclasses. The
necessarykitconsistsofa2-beamoscilloscope,abreadboard,apowersupplywith
twoindependentoutputsupto12V,andageneratorwhichprovidessinewavesand
pulsetrainsupto∼106Hz. ComputerpackagesforFourieranalysisandFourier
transformsareagreathelptoo. Studentprojectsbeyondthebasiccourseworkare
tobeencouraged. Theyhaveaknackofuncoveringknottyproblems.
The new Edition is a slimmed down version of the first. Integrated circuits
cannowbeboughtsocheaplythattheyreplaceattemptsatdo-it-yourselfdesign
of electronics. This has made the more advanced parts of the earlier Edition
redundant. However,Iclingtotheideathatallstudentsneedpracticalexperience
ofhowtransistorsamplifycurrentsandvoltagesinafewrudimentaryexamples.
The volume has been kept as slim as possible so that students can afford it, and
canalsocarryitaround!
Exercises graded in difficulty are provided with most chapters. Students are
encouragedtochecksolutionsinthelab. Manyexercisescomefromexamination
paperssetincollegesofLondonUniversity,andIamgratefultotheUniversityfor
permissiontoreproducethem.Answersaremineandhavebeenmultiplychecked,
thoughIwouldbegratefultohearaboutanysurvivingerrors.
Within the text, tricky questions are posed every now and then in italics. No
answers are given, deliberately. I find that such unanswered teasers provoke as
muchthoughtanddiscussionasdetailedexercisesandIconsiderthemanintegral
partofthelearningprocess.
Forme,ithasbeenalifetimeoffuntacklingphysicsproblemsandIhopethis
volumewillbesomereturntothecommunity,encouragingnewstudentstofollow
asimilarpath. Ioweagreatdebttomywifeforenduringthetribulationsofdoing
physics.
DavidBugg
February2005
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1
Voltage, Current and Resistance
1.1 BasicNotions
Athunderstormisadramaticelectricalspectacle. Whocoulddoubttherealityof
voltages and currents when confronted by such a display? The storm separates
electricalchargesbetweentopandbottomofthecloud. Theenergyrequiredfor
thisseparationcomesfromwarmmoistairwhichrisesandcondenses. Inawell
developedstorm,avoltageof≈200millionvoltsbuildsupbetweenthecloudand
the earth. Eventually the air breaks down when the electric field at the base of
the cloud approaches 106 V m−1. In the ensuing lightning stroke the current is
104–105amps.
B
A
2 × 108 V
Earth
Fig.1.1. Thundercloudandlightning.
The physics of a thunderstorm is complicated. For present purposes this
example serves to focus attention on basic notions of charge, current, voltage
andenergy. Whatdothenumbersmean? Howarevoltageandcurrentdefined?
Firstlet’sgetcleartherelationbetweenvoltageandenergy. IfachargeQis
movedfrompointAinthecloudatvoltageVA to pointB at voltageVB, (figure 1.2),
1
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2 Voltage,CurrentandResistance
V
B
B
Q
V
A
A
Fig.1.2.Workdone=Q(VB −VA).
theworkdoneonthechargeisQ×(VB−VA). InSIunits,itrequiresonejoule(J)
tomoveonecoulomb(C)ofchargethroughonevolt(V):
Energy(J)=Charge(C)×Potentialdifference(V). (1.1)
When the thundercloud discharges, this energy is liberated as heat, thunder and
electromagneticradiation. Ifthecloudcarriesachargeof10C,theenergyliberated
inacompletedischargeis10×2×108J=2×109Jor2GJ(Gigajoules).
In an electrical circuit, a battery likewise provides a potential difference and
a source of energy. A fully charged 12 V car battery can deliver a charge of
typically 3 × 105 C from chemical reactions and an energy of 3.6 × 106 J or
3.6MJ(megajoules).
A third familiar example will illustrate these ideas. Figure 1.3 shows schema-
ticallythelayoutofanoscilloscope. Electronsareemittedfromaheatedcathode
andarethenacceleratedthroughalargevoltageV,typically1–5kV(kilovolts).
TheyacquirekineticenergyinfallingthroughthepotentialdifferenceV andreach
avelocityvgivenby
eV = 1mv2 (1.2)
2
where e and m are the charge and mass of the electron. We must distinguish
betweenthevoltagedifferenceV throughwhichthebeamisacceleratedandthe
energy eV acquired by each electron. If V = 5 kV, this energy is 1.6×10−19
×5×103J=8×10−16J.
Next,whatistherelationbetweencurrentandcharge? Themovingelectrons
carryacurrent,whosemagnitudeisdefinedbythechargeQpassingthroughthe
controlgridinunittime: 1Ampere=1Coulombpersecond. Sincethecurrent
mayvarywithtime,itneedstobeexpressedintermsofdifferentialquantities:
dQ(C)=I(A)×dt(s)
or
I =dQ/dt. (1.3)
Forexample,abeamof1013electrons/scarriesacurrentof−1.6×10−19×1013
A = −1.6 ×10−6A or −1.6 µA (microamps). The minus sign arises because
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Waveforms 3
heated cathode at
potential −V control grid Vy Vx
electron beam
Y plates X plates
focusing coils
screen
− V +
Fig.1.3. Schematicofanoscilloscope.
electrons are negatively charged; conventional current flows in the opposite di-
rectiontotheelectrons. Thecurrentmaybemeasuredusingtheforceonitina
magneticfield. Youcandemonstratethisforcebyholdingabarmagnetuptoan
oscilloscopeoraTVsetandwatchingthebeamdeflect. TheAmpere,theabsolute
unit of current, is actually defined in terms of the force between two current-
carrying coils. Then the Coulomb is derived from the Ampere using equation
(1.3).
Another important electrical quantity is power P. It is defined as the rate of
changeofenergy,E:
P =dE/dt. (1.4)
Itmayberelatedtovoltageandcurrentusingequation(1.1).AchargedQfalling
through potential V gains energy dE = VdQ, so a current I flowing through
potentialdifferenceV generatespower
dQ
P =V =VI. (1.5)
dt
This is the familiar result for power dissipated in a resistor. Power is measured
inwatts(W):onewatt= 1joule/second. Ineachstrokeofalightningdischarge,
powerisdissipatedfor≈100µsatarateofabout5×1012W.Bycomparison,a
largepowerstationgenerates2000MW=2×109W.
1.2 Waveforms
This chapter is concerned mostly with constant voltages and currents. Such a
situationisreferredtoasDC,meaningdirectcurrent. However, theprinciples
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