Fundamentals of Modern Electric Circuit Analysis and Filter Synthesis. A Transfer Function Approach PDF
Preview Fundamentals of Modern Electric Circuit Analysis and Filter Synthesis. A Transfer Function Approach
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 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNatureSwitzerland AG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseof illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similarordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors, and the editorsare safeto assume that the adviceand informationin this bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland 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
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