Fundamentals of Modern Electric Circuit Analysis and Filter Synthesis. A Transfer Function Approach

689 Pages·2023·19.856 MB·English

by  Afshin Izadian

Afshin Izadian
Fundamentals
of Modern Electric
Circuit Analysis and
Filter Synthesis
A Transfer Function Approach
Second Edition
Fundamentals of Modern Electric Circuit Analysis
and Filter Synthesis
Afshin Izadian
Fundamentals of Modern
Electric Circuit Analysis
and Filter Synthesis
A Transfer Function Approach
Second Edition
AfshinIzadian
AssociateProfessor
PurdueUniversity
Indianapolis,IN,USA
ISBN978-3-031-21907-8 ISBN978-3-031-21908-5 (eBook)
https://doi.org/10.1007/978-3-031-21908-5
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To
Pardis, Anahita, and Atousa
Preface
Inthesecondedition,thecontentofeachchapterhasbeenenhancedwithnumerous
solvedproblems.Sometopicshavebeenaddedtocovermostofthematerialtaught
in electric circuits for undergraduate students. The end-of-chapter problems have
been advanced to provide a guided study for students. However, each chapter’s
depthofsolvedproblemslaysoutthefoundationexpectedformostundergraduate-
level circuit requirements. The focus on filters and their transfer functions has
advancedtounderstandthesubjectsbetter.
The book can cover two semesters of electric circuits. The first course may
include Chaps. 1, 2, 3, 4, 5, and 6, emphasizing electric circuits’ foundations. The
secondpart,Chaps.7,8,9,10,11,and12,coverstheanalysisofelectriccircuitsin
thefrequencydomainwiththetransferfunctionapproach.
Chapter1coverselectriccircuits’basicsbyintroducingsomemeasurementunits
and their conversions. Circuit elements and their schematics are introduced, and
several examples of electric circuits are provided. Students familiarize themselves
with the units used in the book and understand the importance and application of
electriccircuits.
Chapter 2 covers the circuit elements, OHM’s law, and the voltage-current
relations in each electric circuit element. Resistors, inductors, and capacitors can
be connected in various ways. Series, parallel, delta, and star and their equivalent
modelsarecoveredforeachcircuitelement.However,analysisofRL,RC,andRLC
is introduced in Chapters 4 and 5. Several switching elements are introduced with
their detailed operations. Mechanical and electrical switches and their applications
are discussed. Dependent and independent sources are introduced. Linear time-
invariantcircuitsandsuperpositionareintroducedthroughseveralexamples.
Chapter 3 covers fundamental waveforms, their analysis, and mathematical
expressions. Sinusoidal waveform, phasor, and rectangular-polar coordinations are
introduced.TheapplicationofphasorsincircuitanalysisisintroducedinChapter5.
Chapter4coverstheconceptoftheorderofacircuit.Thefirst-ordercircuitsand
second-ordercircuitsareintroducedasanintroductiontotime-basedcircuitanalysis.
Several examples are introduced to help students classify the circuits and predict
vii
viii Preface
their behavior. Natural response and forced response are discussed. Students also
learntoobtainthecircuitparametersbyanalyzingthetime-basedresponses.
Chapter 5 covers thebasicsof sinusoidalACcircuit analysis in LTI. Thisstarts
withacoverageofcomplexmathcalculations.Thefoundationsofphaseshift,lead,
and lag circuits are discussed. The idea of reactance is introduced, and several
circuits are analyzed. Accordingly, the power factor and resonance are introduced
throughseveralexamples.ThepowercalculationsinACcircuitsareintroducedand
coveredin-depth.ThissectionalsoincludestheThevenin-NortonequivalentforAC
circuits.ThemaximumpowertransferfortheACcircuitsisalsointroduced.
Chapter 6 covers the fundamentals of mutual inductance and their equivalent
circuits. The concept of induced voltage through mutual inductance is introduced.
Accordingly,transformersareintroduced,andtheirpower,voltage,andcurrentare
analyzed.
Chapter 7 covers the fundamentals of the Laplace transformation and its appli-
cationincircuitanalysis.BasicmathematicalanalysisoftheLaplacetransformations
andoperationsarealsointroducedforsignalsandwaveforms.Theyareidentifiedas
theinputandoutputofthecircuitstoprepareforthetransferfunctionanalysis.The
frequencydomainanalysisofsimplecircuitswithvariousinputsisintroduced.
Chapter8coversthetransferfunctions,theirdefinition,variousformsofsystem
combination,andfeedbacksystems.Thetransferfunctionisobtainedforsingle-loop
systemsandsystemswithmultipleinputsandmultipleoutputs.Theinitialandfinal
valuetheoremsareintroduced,andthesystems’steady-stateresponsesareanalyzed
accordingly.First-ordersystemtransferfunctionssecondordersystemsareanalyzed
in the frequency domain. The frequency response of the systems is analyzed, and
theirBodediagramsareobtained.Thischapteralsocoversthestatespacerepresen-
tationofthesystems.
Chapter 9 covers the design and analysis of passive filters. Various filters are
introducedanddesignedintheformofhardware(circuits)andsoftware(computer
code).Filtertransferfunctionsareanalyzed,andtheirbasicoperationsareimproved
to design better filters. A free-style software design that matches the filter circuit
transferfunctionsisintroduced.RLCresonantcircuitisusedforthispurposetoform
filters. Butterworth filters are designed to improve their operation. Higher-order
filtersarealsodesignedtoobtainthedesiredperformance.
Chapter10coverstheprinciplesofoperationalamplifiers.Severaldesignprinci-
plesarecovered,andsimplecircuitsareintroducedtohelpstudentsunderstandthe
approach to analyzing the Opamp circuits. Opamps are also utilized to solve
differential equations. This chapter introduces the design of analog computers and
PIDcontrollers.
Chapter11coverstheactivefiltersinvariousforms.Simplecircuitsaredesigned
withtheapproachtocontrolthefeedbackimpedanceortheinputimpedance.Filter
hardware is analyzed, and the transfer functions are obtained. Non-resonant-based
filtersareintroduced,andtheircircuitsareanalyzed.MultiFeedBack(MFB)circuits
areintroduced,andmethodstoobtainvariousfiltersarediscussed.
Preface ix
Chapter12coverstwo-portnetworks.Severalrepresentationmethodsinimped-
ance,admittance,andtransmissionmatricesareintroduced.Thesematricesareoften
obtainedthroughseveralmethodsexplainedinnumerousexamples.
Theneweditionofthistextbookisintendedtobeusefulforallengineeringand
othermajors.ThankstoMs.HanShi,whotirelesslyhelpedpreparethefigures.The
contentofthisbookisconstantlyinimprovement.Yourfeedbackenrichesthetopics
and sheds light on shortcomings. Therefore, please forward your suggestions to
improvethebooktomyinstitutionalemailaddressorSpringer.
Sincerely
Indianapolis,IN,USA AfshinIzadian
Contents
1 IntroductiontoElectricCircuits. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
ElectricCircuitTopologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
HingedCircuits. . . .. . . . . .. . . . . .. . . . . .. . . . .. . . . . .. . . . . .. . 4
MeasurementUnits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
ScalesandUnits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
MostCommonElectricCircuitSymbols.. . . . .. . . . .. . . .. . . . .. 7
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 CircuitComponents,Voltage,andCurrentLaws. . . . . . . . . . . . . . 11
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
DefinitionofVoltage.. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. . . . .. 11
DefinitionofCurrent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Resistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Conductors,Insulators,andSemiconductors. . . . . . . . . . . . . . . . . . . . 14
EffectofTemperatureonResistance. . . . . . . . . . . . . . . . . . . . . . . . . 14
ParallelConnectionofCircuitElements. . . . . . . . . . . . . . . . . . . . . . . 16
MixedConnectionofCircuitElements. . . . . . . . . . . . . . . . . . . . . . . . 16
Mesh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Node. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Ohm’sLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
KirchhoffVoltageLaw(KVL). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
KirchhoffCurrentLaw(KCL). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
TheEquivalentofResistorsinSeries. . . . . . . . . . . . . . . . . . . . . . . . . 25
TheEquivalentofResistorsinParallel. . . . . . . . . . . . . . . . . . . . . . . . 26
Delta(Δ)andStar(Y)Connection. . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Y→ΔConversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Δ→YConversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
PowerandEnergyinResistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
DefinitionofaShortCircuit. . . .. . . . .. . . . . .. . . . .. . . . .. . . . . .. 33
WhatIsanInductor?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
xi
xii Contents
Inductor’sVoltageandCurrentRelation. . . . . . . . . . . . . . . . . . . . 34
EnergyandPowerofanInductor. . . . . . . . . . . . . . . . . . . . . . . . . . 35
TheEquivalentofInductorsinSeries. . . . . . . . . . . . . . . . . . . . . . . 36
TheEquivalentofInductorsinParallel. . . . . . . . . . . . . . . . . . . . . . 37
WhatIsaCapacitor?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Capacitor’sVoltageandCurrentRelation. . . . . . . . . . . . . . . . . . . . 39
EnergyandPowerofaCapacitor. . . . . . . . . . . . . . . . . . . . . . . . . . 41
TheEquivalentofCapacitorsinSeries. . . . . . . . . . . . . . . . . . . . . . 43
TheEquivalentofCapacitorsinParallel. . . . . . . . . . . . . . . . . . . . . 44
Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
IndependentVoltageSource. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
IndependentCurrentSource. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
DependentSources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Switches. . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . . . . . . .. . . . . . .. . 59
MechanicalRelaysandContactors. . . . . . . . . . . . . . . . . . . . . . . . . . . 61
ElectricallyOperatedorSolid-StateSwitches. . . . . . . . . . . . . . . . . . . 62
Diode’sPeakInverseVoltage(PIV). . . . . . . . . . . . . . . . . . . . . . . . . . 66
DiodeCurrentCarryingCapacityandOperatingFrequency. . . . . . . . . 68
LinearTime-InvariantCircuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
SuperpositioninCircuits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
3 WaveformandSourceAnalyses. . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
WaveformAnalysis. . .. . . . . . .. . . . . .. . . . . . .. . . . . . .. . . . . .. . 111
ImpulseFunctionf(t)=δ(t). . . .. . . . . . . . . . . .. . . . . . . . . . . .. . 111
UnitStepFunctionf(t)=u(t). . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
RampFunctionf(t)=r(t). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
PowerFunctionfðtÞ=AtnuðtÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
n!
ExponentialFunctionf(t)=Aeαtu(t). . . . . . . . . . . . . . . . . . . .. . . . 130
SinusoidalFunctionf(t)=Asin(ωt+φ). . . . . . . . . . . . . . . . . . . . 131
PolartoCartesian(Rectangle)Conversion. . . . . . . . . . . . . . . . . . . 132
Cartesian(Rectangle)toPolarConversion. . . . . . . . . . . . . . . . . . . 133
MathematicalOperationofPolarandComplex
Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
DampedSinusoidalFunction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
PeriodicWaveformMathematicalExpression. . . . . . . . . . . . . . . . . . . 145
AverageofaSignal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
RootMeanSquare(RMS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
CircuitSimplificationTechniques. . . .. . . . . . .. . . . . . . .. . . . . . . .. 152
VoltageDivision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
CurrentDivision. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
SourceConversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
TheveninEquivalentCircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
NortonEquivalentCircuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159