Computational Electronic Circuits: Simulation and Analysis with MATLAB®

457 Pages·2021·24.288 MB·English

by  Sotoudeh Hamedi-Hagh

Sotoudeh Hamedi-Hagh
Computational
Electronic Circuits
SSiimmuullaattiioonn aanndd AAnnaallyyssiiss wwiitthh MMAATTLLAABB®®
Computational Electronic Circuits
Sotoudeh Hamedi-Hagh
Computational Electronic
Circuits
®
Simulation and Analysis with MATLAB
SotoudehHamedi-Hagh
SanJoseStateUniversity
SanJose,CA,USA
ISBN978-3-030-75567-6 ISBN978-3-030-75568-3 (eBook)
https://doi.org/10.1007/978-3-030-75568-3
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Preface
Writing a full-scale circuit simulator is a very intriguing and satisfying task, espe-
ciallyforstudents.Intheprocessofwritingacircuitsimulator,studentswillbetter
understandandlearnthecircuittheoryandanalysis.Thesearethemotivationsthat
promptmetowritethisbook.Acircuitsimulatorhastwomainparts.Thefirstpartis
the generation of a graphical user interface for drawing circuits and interconnects.
This is called the schematic editor. The second part is translating the circuit into
codesthatcanbemathematicallycomputed.Thisiscalledthecircuitanalyzer.Both
the graphical user interface and the computational engine are integrated into a
compiler called the circuit simulator. The compiler is written using a computer
programming language like C and includes an extensive library of different func-
tionsthatuserscanexecute,suchasmovingacircuitcomponenttoanewlocation
androtatingitorcreatingnetlistfromthecircuitandperformingaspecificsimulation
followedbycalculatingsomecharacteristics,suchasthetime-domainaverageofa
signalorthefrequency-domaingroupdelayofavoltage-gaintransferfunction.
Writing a compiler using a programming language is not in the scope of this
book.Instead,aversatilecompilersuchasMATLABisusedinthisbookinorderto
showthegeneration ofacircuitgraphicaluser interface, translatingthecircuit into
codes thatcanbecomputationallycalculated aswellascreating alibraryofcircuit
analysis functions. The generation of the graphical user interface and translating
circuitsintonetlistsaredemonstratedattheendofChap.1aftercircuitcomponents
and their characteristics are studied. Although the generation of a graphical user
interfaceisveryfunandhelpfulforcreatingacircuitsimulator,itisnotessentialin
learning circuit theories and analyses. As a result, this first part of the circuit
simulatorisonlystudiedinChap.1.Themainemphasizeintheremainingchapters
is to show how to create computational codes required by the second part of the
circuitsimulatorinordertoanalyzecircuitsandextracttheircharacteristics.
The universal adaptability of computational codes is considered throughout his
book.Asanexample,insteadofaskingstudentstohandcalculatethevoltage-gain
transfer functions of different filters before plotting them using MATLAB, the
voltage-gain transfer functions for circuits with different number of nodes and
vii
viii Preface
configurationsareautomaticallycalculatedusingCramer’srulesandLaplaceexpan-
sionsappliedtoadmittancematrices.Asaresult,thecodesandthemethodsadopted
in this book can be used in a universal circuit simulator rather than a specific-task
simulation. Utilizing custom simulation functions such as calculating fast Fourier
transform andnumerical analysis ofsystems ofequationsarealsoused throughout
this book instead of relying on pre-existing MATLAB functions, such as FFT or
solvecommands.Mostofthecomputationalbooksinengineeringtopicsuseexten-
siveamountsofmaththatcaneasilyforceareadertolosethecomprehensionandthe
interestinthetopic.Whileanextensiveamountofsimulationmethodsiscoveredin
thisbook,theamountofmathiskeptataminimumlevel.
Circuitanalysiscan bedone using nodalcurrents, mesh voltages, or both. Each
methodifappliedproperlycananalyzeanykindofcircuits.Thenodalanalysisbased
on Kirchhoff’s current law is used throughout this book to analyze circuits. The
signalnotationsusedinthisbookincludepresentingtheinstantaneousvoltageand
currentsignalsby“V ”and“I ”(capitalletterfollowedbycapitalsubscript),the
TR TR
DC components of the signals by “v ” and “i ” (lowercase letter followed by
DC DC
capital subscript), and presenting the AC components of the signals by “vac” and
“iac”(lowercaseitalicletterfollowedbylowercasesubscript).IntheabsenceofAC
signalsinDCanalysis,theDCandinstantaneoussignalsbecomeequalandtheDC
voltages and currents might optionally be shown with the instantaneous signal
notation.
Circuit analysis is done using two distinct numerical and symbolic approaches.
Both methods are covered in this book. The numerical approach generates a
component-obscure result after each simulation but is very computer-memory effi-
cient because when multiple numbers are added, subtracted, multiplied, or divided
together, the result will be just a number. The symbolic approach generates a
component-visibleresultthatshowshowthecircuitcharacteristicchangesbyvary-
ing each component but is very computer-memory inefficient because as different
symbolicvariablesareadded,subtracted,multiplied,ordividedtogether,themath-
ematicalexpressionsexpandinsize.Forsmallcircuitsorsimplebuildingblocksthat
arestudiedinelectroniccourses,thesymbolicanalysisisadvantageousinteaching
students how the circuits work. For large circuits, full symbolic analysis becomes
impracticalandthenumericalanalysisbecomestheonlypracticalchoiceincreating
circuitsimulators.
Themodelingandcharacteristicsofcircuitcomponentsandcreatingcircuitsand
netlists are studied in Chap. 1. The DC analysis of linear and nonlinear circuits is
studied in Chap. 2. The calculation of inverse matrix, Laplace expansion, LU
decomposition, Gaussian elimination, and iterative methods such as conjugate
gradient, Gauss-Seidel, and Newton-Raphson are demonstrated in this chapter.
The transient analysis of linear and nonlinear circuits is studied in Chap. 3. The
calculation offinite difference and finite integrals, Laplace transforms, partial frac-
tiondecomposition,andfastFouriertransformaredemonstratedinthischapter.The
AC analysis of linearized circuits is studied in Chap. 4. The Cramer’s rules and
Laplace expansion, Taylorseriesexpansion,nodeelimination,extractionofadmit-
tancematrixandtransferfunctions,powergains,Y-,Z-,andS-parametersandtheir
Preface ix
conversions, poles and zeros, impulse and step responses, Bode, Nyquist and
Nichols plots, root locus and Smith charts are demonstrated in this chapter. The
noiseanalysisoflinearizedcircuitsisstudiedinChap.5.Thetransientandspectral
noisecharacteristics,noisematrices,noisetransformation,inputandoutputreferred
noise calculations, noise factors, and noise and power tradeoff are demonstrated in
thischapter.Finally,thebehavioralanalysisofcircuitswherespecific-taskmodeling
andalgorithmsareappliedtodifferentcircuitsinordertostudytheirfunctionalityis
studiedinChap.6.Anoverviewofchaptertopicsislistedinthefollowingtable.
Signals Schematic Composing
Ch. 1 Framework
Components DC, Transient, AC and Noise modeling Netlisting
DC Linear Equations Direct Methods
Ch. 2 DC Circuit Model
Analysis Nonlinear Equations Iterative Methods
Transient Linear Circuits Aperiodic and Periodic Signals Laplace Transform
Ch. 3
Analysis Nonlinear Circuits Switching Circuits Differential Equations
AC
Ch. 4 Linearized s-domain Model Matrix Calculations Transfer Function Characteristics
Analysis
Noise
Ch. 5 Linearized s-domain Model Noise Matrix Calculations Noise Transformation
Analysis
Behavioral
Ch. 6 Block-Level Modeling Accuracy and Speed Tradeoff
Analysis
Incontrarytothecurrentcomputationalmethodsforsomeengineeringfieldssuch
as electromagnetics and antenna where different methods and approaches are
required for simulating different open boundary or closed boundary systems, the
circuitanalysisisverywellstructuredanddeveloped.Forexample,asingletransient
analysiscansolve anytype oflinearornonlinear circuitswith anytype ofcompo-
nents with any number of nodes and meshes with any number and types of signal
sources. A simulation algorithm works for all types of circuits. All fundamental
knowledge and skills required for students in order to develop their own circuit
simulator are included in this book with the hope to make circuit and electronic
coursesveryenjoyableandmemorableforall.
SanJose,CA,USA SotoudehHamedi-Hagh
Contents
1 Framework. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 NumericandSymbolicAnalyses. . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 FiniteIntegral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 FiniteDifference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 LaplaceTransformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 BasicSignals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.2 MultiplicationandConvolution. . . . . . . . . . . . . . . . . . . 8
1.4.3 Scaling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4.4 Shifting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.5 Differentiation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.6 Integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.7 MultiplicationbyTime. . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.8 ConjugateProperty. . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.9 InitialandFinalValues. . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.10 Periodicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Waveforms. . . . . . . . .. . . . . . . . . .. . . . . . . . .. . . . . . . . . .. . 11
1.6 Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.1 Ground. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.2 Short. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.3 Open. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.4 IdealSwitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6.5 Resistors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.6.6 Capacitors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.6.7 NonidealSwitch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.8 Inductors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.6.9 Transformers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.6.10 NonidealSources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
1.6.11 DependentSources. . . . . . . . .. . . . . . . . .. . . . . . . . .. 30
1.6.12 Diodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
xi
xii Contents
1.6.13 BipolarJunctionTransistors. . . . . . . . . . . . . . . . . . . . . 37
1.6.14 MetalOxideSemiconductorFieldEffectTransistors. . . 44
1.7 LTI/LTV/NTI/NTV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
1.8 SchematicEditor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
1.8.1 Netlisting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
1.9 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Q.1.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Q.1.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Q.1.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Q.1.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Q.1.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Q.1.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Q.1.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Q.1.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Q.1.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Q.1.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2 DCAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
2.1 AnalysisAlgorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.2 InverseMatrixCalculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.3 DeterminantRatiosObtainedbyLaplaceExpansion. . . . . . . . . . 81
2.4 DeterminantRatiosObtainedbyLUDecomposition. . . . . . . . . . 86
2.5 GaussianElimination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
2.6 ConjugateGradientIterations. . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.7 Gauss-SeidelIterativeMethod. . . . . . . . . . . . . . . . . . . . . . . . . . 102
2.8 Newton-Raphson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
2.9 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Questions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Q.2.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Q.2.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Q.2.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
Q.2.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Q.2.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Q.2.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Q.2.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Q.2.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3 TransientAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.1 PartialFractionDecomposition. . . . . . . . . . . . . . . . . . . . . . . . . 121
3.2 AperiodicCapacitiveCircuits. . . . . . . . . . . . . . . . . . . . . . . . . . 122
3.3 AperiodicInductiveCircuits. . . . . . . . . . . . . . . . . . . . . . . . . . . 126
3.4 PeriodicTransformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
3.5 PeriodicCapacitiveCircuits. . . . . . . . . . . . . . . . .. . . . . . . . . . . 131
3.5.1 Circuit1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131