Introductory Circuit Theory

300 Pages·2020·10.622 MB·English

by  D. Sundararajan

D. Sundararajan
Introductory
Circuit Theory
Introductory Circuit Theory
D. Sundararajan
Introductory Circuit Theory
D.Sundararajan
FormerlyatConcordiaUniversity
Montreal,QC,Canada
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Preface
Circuit theory is fundamental to the study of important engineering applications such as power
systems and communication. As such, it forms part of the first course to engineering and science
students in several disciplines. This book is written for engineering, computer science and physics
students,andengineersandscientists.Boththetheoryandpracticebyprogrammingandinlaboratory
aretwoimportantaspectsofthelearningprocessofcircuittheory.Theobjectiveinwritingthisbook
is to present the fundamentals of circuit theory systematically in a clear and concise textbook and
provide the required programming part online. Hopefully, this approach is expected to improve the
readability and understandability of the theory without clutter. Plenty of examples, figures, tables,
programs,analogy,andphysicalexplanationsmakeiteasyforthereadertogetagoodgroundingin
thebasicsofcircuittheoryandsomeofitsapplications.
The learning of the circuit theory requires calculus, linear algebra, transform analysis, program-
ming, and laboratory practice. These tools are also required for other courses and in professional
careerlater.However,thesetopicsaredifficultfornewstudents.But,throughthemethodssuggested,
studentscanlearnwellthisall-importantsubjectwithsufficientpractice.Further,thelearningprocess
forthissubjectwillcertainlyhelpthestudentsintheirensuingstudyoftheothersubjects.
Learning of the circuit theory consists of four aspects: (1) systematic presentation of the
mathematical methods inthe text; (2) verification of the analytically obtained results by coding; (3)
verification of the results by simulation; and (4) verification of the results using actual components
in laboratory experiments. The last component gives physical appreciation of the circuit elements
andtheirvaluesinpractice,thevoltages,currents,frequencies,measuringinstruments,andallother
practical aspects involved. Students must take a coordinated laboratory course. Both coding and
simulationoftheanalysisofcircuitsarepresentedintheonlineprogrammingpart.Eachstudentcan
practiceusingthesefourmethodsasmuchasitisrequiredforagoodunderstandingofthesubject.
Thisbookisintendedtobeatextbookforthefirstcourseincircuittheorytothenewundergraduate
studentsinseveraldisciplinesofengineeringandscience,whichincludestheprimarydisciplinesof
electricalandelectronicsengineering.Forengineeringprofessionals,thisbookwillbeusefulforself-
study. In addition, this book will be a reference for anyone, student or professional, specializing in
practicalapplicationsofcircuittheory.Theprerequisiteforreadingthisbookisagoodknowledgeof
physicsandcalculusatthehighschoollevel.
Asmentionedalready,programmingisanimportantcomponentinlearningandpracticingcircuit
theory, as well as other subjects. While several software packages are available, it is better to use a
popular general-purpose software package that the students are likely to use in their other courses
and ensuing professional carrier in several areas of engineering and science. Therefore, learning of
only one package is required. The programming part is presented using the popular, user-friendly
(cid:2)
and widely used, both in universities and industries, MATLABR software package. While the use
ofasoftwarepackageisinevitableinmostapplications,itisbettertousethesoftwareinadditionto
v
vi Preface
self-developedprograms.Theeffectiveuseofasoftwarepackageortodevelopownprogramsrequires
agoodgroundinginthebasicprinciplesofthecircuittheory.Answerstoselectedexercisesmarked
∗aregivenattheendofthebook.ASolutionsManualandslidesareavailableforinstructorsatthe
websiteofthebook.
Iassumetheresponsibilityforalltheerrorsinthisbookandwouldverymuchappreciatereceiving
readers’ suggestions and pointing out any errors (email:[email protected]). I am grateful
tomyEditorandtherestoftheteamatSpringerfortheirhelpandencouragementincompletingthis
project.Ithankmyfamilyfortheirsupportduringthisendeavor.
D.Sundararajan
Contents
1 BasicConcepts................................................................ 1
1.1 Ohm’sLaw .............................................................. 3
1.2 ResistorsConnectedinSeries............................................... 4
1.3 ResistorsConnectedinParallel.............................................. 7
1.4 ResistorsConnectedinSeriesandParallel .................................... 9
1.5 Kirchhoff’sVoltageandCurrentLaws........................................ 11
1.6 Applications ............................................................. 13
1.7 Summary................................................................ 13
2 DCCircuits .................................................................. 19
2.1 MeshAnalysis ........................................................... 20
2.2 NodalAnalysis ........................................................... 27
2.3 Examples................................................................ 29
2.3.1 LinearityPropertyofCircuits......................................... 37
2.3.2 AnalysisofaCircuitwithaControlledVoltageSource ................... 40
2.3.3 AnalysisofaCircuitwithaControlledCurrentSource ................... 44
2.3.4 Y −(cid:2)and(cid:2)−Y Transformations.................................... 55
2.4 CircuitTheorems ......................................................... 59
2.4.1 Thévenin’sTheoremandNorton’sTheorem............................. 59
2.4.2 MaximumPowerTransferTheorem ................................... 65
2.5 Application .............................................................. 67
2.5.1 StrainGaugeMeasurement........................................... 67
2.6 Summary................................................................ 68
3 ACCircuits................................................................... 77
3.1 Sinusoids................................................................ 77
3.1.1 TheRectangularFormofSinusoids.................................... 79
3.1.2 TheComplexSinusoids ............................................. 79
3.2 ACCircuitAnalysis....................................................... 80
3.2.1 Time-andFrequency-DomainRepresentationsofCircuitElements ......... 80
3.2.2 Time-DomainAnalysisofaSeriesRCCircuit........................... 82
3.2.3 Frequency-DomainAnalysisofaRCCircuit............................ 84
3.2.4 ImpedancesConnectedinSeries ...................................... 85
3.2.5 ImpedancesConnectedinParallel..................................... 91
3.2.6 ImpedancesConnectedinSeriesandParallel............................ 93
3.2.7 AnalysisofTypicalCircuits .......................................... 94
3.2.8 LinearityPropertyofCircuits......................................... 105
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3.3 CircuitTheorems ......................................................... 122
3.3.1 Thévenin’sTheorem ................................................ 122
3.3.2 Norton’sTheorem .................................................. 130
3.3.3 MaximumAveragePowerTransferTheorem............................ 131
3.3.4 SourceTransformation .............................................. 133
3.4 Application .............................................................. 135
3.4.1 Filters ............................................................ 135
3.5 Summary................................................................ 137
4 Steady-StatePower............................................................ 149
4.1 EnergyinReactiveElementswithSinusoidalSources........................... 150
4.2 PowerRelationsinaCircuit ................................................ 151
4.3 Power-FactorCorrection ................................................... 159
4.4 Application .............................................................. 173
4.5 Summary................................................................ 173
5 MagneticallyCoupledCircuits.................................................. 177
5.1 MutualInductance ........................................................ 177
5.2 StoredEnergy ............................................................ 178
5.3 Examples................................................................ 181
5.4 Application .............................................................. 198
5.4.1 Transformers ...................................................... 198
5.5 Summary................................................................ 199
6 Three-PhaseCircuits .......................................................... 203
6.1 Three-PhaseVoltages...................................................... 203
6.1.1 TheInstantaneousPower ............................................ 205
6.2 TheThree-PhaseBalancedY −Y Circuit..................................... 205
6.3 TheThree-PhaseBalancedY −(cid:2)Circuit..................................... 207
6.4 TheThree-PhaseBalanced(cid:2)−Y Circuit..................................... 210
6.5 TheThree-PhaseBalanced(cid:2)−(cid:2)Circuit .................................... 211
6.6 Application .............................................................. 212
6.7 Summary................................................................ 212
7 Two-PortNetworks............................................................ 215
7.1 ImpedanceParameters..................................................... 215
7.2 AdmittanceParameters .................................................... 221
7.3 HybridParameters ........................................................ 224
7.4 TransmissionParameters................................................... 225
7.5 Examples................................................................ 226
7.5.1 Analysisofaπ Circuit .............................................. 226
7.5.2 AnalysisofaCommon-EmitterTransistorAmplifier ..................... 228
7.5.3 AnalysisofaBridgeCircuit.......................................... 230
7.5.4 LadderCircuit ..................................................... 231
7.6 Application .............................................................. 233
7.6.1 Digital-to-AnalogConverter:TheR−2RLadderCircuit ................. 233
7.7 Summary................................................................ 236
Contents ix
8 TransformAnalysisandTransientResponse ..................................... 239
8.1 FourierSeries ............................................................ 240
8.1.1 FourierSeriesofaRectifiedSineWave ................................ 242
8.1.2 GibbsPhenomenon ................................................. 246
8.2 FourierTransform ........................................................ 246
8.2.1 TheTransferFunctionandtheFrequencyResponse ...................... 248
8.3 TransientResponse........................................................ 249
8.3.1 TheUnit-ImpulseandUnit-StepSignals................................ 250
8.4 LaplaceTransform ........................................................ 252
8.4.1 PropertiesoftheLaplaceTransform ................................... 253
8.4.2 Time-Differentiation ................................................ 254
8.4.3 Integration ........................................................ 254
8.4.4 InitialValue ....................................................... 255
8.4.5 FinalValue ........................................................ 255
8.4.6 CircuitAnalysisintheFrequency-Domain.............................. 255
8.5 Application .............................................................. 269
8.6 Summary................................................................ 271
A Matrices ..................................................................... 275
A.1 Determinants............................................................. 277
B ComplexNumbers ............................................................ 281
AnswerstoSelectedExercises...................................................... 285
Bibliography .................................................................. 291
Index ........................................................................... 293
Abbreviations
AC Alternatingcurrent,sinusoidallyvaryingcurrentorvoltage
DC Directcurrent,sinusoidwithfrequencyzero,constantcurrentorvoltage
FS Fourierseries
FT Fouriertransform
Im Imaginarypartof
KCL Kirchhoff’sCurrentLaw
KVL Kirchhoff’sVoltageLaw
LTI Lineartime-invariant
pf Powerfactor
RC Circuitcomprisingaresistorandacapacitorinseries
Re Realpartof
RL Circuitcomprisingaresistorandaninductorinseries
RLC Circuitcomprisingaresistor,acapacitor,andaninductorinseries
RMS Root-mean-squarevalue
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