Table Of Content(cid:2)
CIRCUIT ORIENTED
ELECTROMAGNETIC
MODELING USING
THE PEEC TECHNIQUES
ALBERTE.RUEHLI
MissouriUniversityofScienceandTechnology,Rolla,MO
GIULIOANTONINI
UniversitàdegliStudidell’Aquila,Italy
LIJUNJIANG
TheUniversityofHongKong,Pokfulam,HongKong
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Copyright©2017byTheInstituteofElectricalandElectronicsEngineers,Inc.
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey.
PublishedsimultaneouslyinCanada.
LibraryofCongressCataloging-in-PublicationData:
Names:Ruehli,A.E.(AlbertE.),1937-author.|Antonini,Giulio,1969-
author.|Jiang,Lijun1970-author.
Title:Thepartialelementequivalentcircuitmethodforelectro-magneticand
circuitproblems:aparadigmforEMmodeling/AlbertE.Ruehli,Giulio
Antonini,LijunJiang.
Description:Hoboken,NewJersey:JohnWiley&Sons,2016.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2016026830(print)|LCCN2016049198(ebook)|ISBN
9781118436646(cloth)|ISBN9781119078395(pdf)|ISBN9781119078401
(epub)
Subjects:LCSH:Electriccircuits–Mathematicalmodels.|
Electromagnetism–Mathematicalmodels.
Classification:LCCTK3001.R682016(print)|LCCTK3001(ebook)|DDC
621.301/51–dc23
LCrecordavailableathttps://lccn.loc.gov/2016026830
CoverDesign:Wiley
CoverImage:©Vectorig/Gettyimages
Typesetin10/12pt,TimesLTStdbySPiGlobal,Chennai,India.
PrintedintheUnitedStatesofAmerica.
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CONTENTS
DEDICATION xv
PREFACE xvii
ACKNOWLEDGEMENTS xxi
(cid:2) ACRONYMS xxv (cid:2)
1 Introduction 1
References, 6
2 CircuitAnalysisforPEECMethods 9
2.1 CircuitAnalysisTechniques, 9
2.2 OverallElectromagneticandCircuitSolverStructure, 9
2.3 CircuitLaws, 11
2.3.1 Kirchoff’sCurrentLaw, 11
2.3.2 Kirchoff’sVoltageLaw, 11
2.3.3 BranchImpedances, 12
2.3.4 IncompleteKirchhoff’sCurrentLaw, 12
2.4 FrequencyandTimeDomainAnalyses, 13
2.5 FrequencyDomainAnalysisFormulation, 14
2.6 TimeDomainAnalysisFormulations, 17
2.6.1 NumericalIntegrationofTimeDomainDifferentialEquations, 18
2.6.2 ListofIntegrationMethodsforPEECSolver, 20
2.6.3 InitialConditionsforTimeSolverwithDelays, 22
2.7 GeneralModifiedNodalAnalysis(MNA), 22
2.7.1 MatrixKirchhoff’sCurrentLawandStamps, 23
2.7.2 MatrixKirchhoff’sVoltageLaw, 24
2.7.3 MatrixKCLSolutionofMNAEquationsforPEEC, 25
2.7.4 MatrixKCLforConductorExample, 27
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2.8 IncludingFrequencyDependentModelsinTimeDomainSolution, 28
2.9 IncludingFrequencyDomainModelsinCircuitSolution, 31
2.9.1 EquivalentCircuitforRationalApproximationofTransfer
Functions, 31
2.9.2 InclusionofFrequencyDomainModelsinaTimeDomainCircuit
Solver, 34
2.9.3 GeneralInclusionofFrequencyDomainAdmittanceModels, 36
2.9.4 State-SpaceandDescriptorRepresentations, 37
2.10 RecursiveConvolutionSolution, 39
2.10.1 ConventionalConvolution, 39
2.10.2 RecursiveConvolution, 40
2.11 CircuitModelswithDelaysorRetardation, 41
2.11.1 InclusionofDelaysintheCircuitDomain, 42
Problems, 43
References, 44
3 Maxwell’sEquations 47
3.1 Maxwell’sEquationsforPEECSolutions, 47
3.1.1 Maxwell’sEquationsintheDifferentialForm, 47
3.1.2 Maxwell’sEquationsintheIntegralForm, 49
3.1.3 Maxwell’sEquationsandKirchhoff’sCircuitLaws, 50
3.1.4 BoundaryConditions, 51
3.2 AuxiliaryPotentials, 52
(cid:2) 3.2.1 MagneticVectorPotentialAandElectricScalarPotentialΦ , 52 (cid:2)
e
3.2.2 ElectricVectorPotentialFandMagneticScalarPotentialΦ , 53
m
3.2.3 ImportantFundamentalRelationships, 54
3.3 WaveEquationsandTheirSolutions, 54
3.3.1 WaveEquationsforEandH, 54
3.3.2 WaveEquationsforA,F,andΦ , 55
e
3.3.3 SolutionoftheHelmholtzEquation, 56
3.3.4 ElectricFieldIntegralEquation, 57
3.4 Green’sFunction, 58
3.4.1 NotationUsedforWaveNumberandFourierTransform, 58
3.4.2 FullWaveFreeSpaceGreen’sFunction, 59
3.5 EquivalencePrinciples, 60
3.5.1 VolumeEquivalencePrinciple, 61
3.5.2 Huygens’EquivalencePrinciple, 62
3.6 NumericalSolutionofIntegralEquations, 63
Problems, 65
References, 66
4 CapacitanceComputations 67
4.1 MulticonductorCapacitanceConcepts, 68
4.2 CapacitanceModels, 69
4.2.1 CapacitanceModelsforMulticonductorGeometries, 69
4.2.2 ShortCircuitCapacitances, 70
4.2.3 CoefficientofPotentialMatrixPp, 71
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4.2.4 CapacitanceofConductorSystems, 72
4.2.5 EliminationofaFloatingConductorNode, 72
4.2.6 FloatingorReferenceFreeCapacitances, 73
4.3 SolutionTechniquesforCapacitanceProblems, 74
4.3.1 DifferentialEquation(DE)MethodsforCapacitance
Computations, 76
4.4 MeshingRelatedAccuracyProblemsforPEECModel, 79
4.4.1 ImpactofMeshingonCapacitancesandStabilityandPassivity, 80
4.5 RepresentationofCapacitiveCurrentsforPEECModels, 82
4.5.1 QuasistaticCapacitance–basedModel, 82
4.5.2 CurrentSource-BasedModelfortheCapacitances, 82
4.5.3 Potential-BasedModelfortheCapacitances, 84
Problems, 85
References, 86
5 InductanceComputations 89
5.1 LoopInductanceComputations, 90
5.1.1 LoopInductanceComputationinTermsofPartialInductances, 91
5.1.2 CircuitModelforPartialInductanceLoop, 93
5.2 InductanceComputationUsingaSolutionoraCircuitSolver, 95
5.3 FluxLoopsforPartialInductance, 95
5.4 InductancesofIncompleteStructures, 96
5.4.1 Open-LoopInductances, 96
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5.4.2 Open-LoopMacromodels, 97
5.4.3 ExamplesforOpen-LoopInductances, 98
5.5 ComputationofPartialInductances, 99
5.5.1 ApproximateFormulasforPartialInductances, 100
5.5.2 InductanceComputationsforLargeAspectRatioConductors, 101
5.6 GeneralInductanceComputationsUsingPartialInductancesandOpenLoop
Inductance, 107
5.6.1 ClosingtheLoopforOpen-LoopProblems, 108
5.7 DifferenceCellPairInductanceModels, 109
5.7.1 InductancesforTransmissionLine-TypeGeometries, 109
5.7.2 ApproximateInductiveCouplingCalculationBetweenDifferenceCell
Pairs, 111
5.7.3 InductanceofFiniteandSemi-InfiniteLengthTL, 113
5.7.4 PlanePairPEECModelsBasedonDifferenceCurrents, 114
5.7.5 ParallelPlanePEECModeling, 114
5.7.6 PEECInductancePlaneModelwithOrthogonalMeshing, 115
5.7.7 MeshReductionWithoutCouplingsofNonparallelInductances, 117
5.8 PartialInductanceswithFrequencyDomainRetardation, 119
5.8.1 ThinWireExampleforRetardedPartialInductances, 122
5.8.2 GeneralCaseforSeparatedConductorPartialInductanceswith
Retardation, 123
Problems, 125
References, 131
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6 BuildingPEECModels 133
6.1 ResistiveCircuitElementsforManhattan-TypeGeometries, 134
6.2 Inductance–Resistance(Lp,R)PEECModels, 136
6.2.1 Inductance–Resistance(L,R)PEECModelforBarConductor, 137
6.3 General(Lp,Pp,R)PEECModelDevelopment, 138
6.3.1 ContinuityEquationandKCL, 139
6.3.2 RelaxationTimeforChargetoSurface, 140
6.3.3 PhysicalAspectoftheCapacitanceModel, 141
6.3.4 EquivalentCircuitsforPEECCapacitances, 143
6.3.5 (Pp,R)PEECResistiveCapacitiveInductor-LessModels, 146
6.3.6 Delayed(Lp,Pp,R,τ)PEECModels, 146
6.3.7 SimpleFull-Wave(Lp,Pp,R,τ)PEECModelsImplementation, 147
6.4 CompletePEECModelwithInputandOutputConnections, 148
6.4.1 Full-WaveModels, 149
6.4.2 QuasistaticPEECModels, 149
6.4.3 InputandOutputSelectors, 150
6.4.4 Power/EnergyTypeCircuitModel, 151
6.4.5 Resistances,Inductance,andCapacitiveTerms, 153
6.5 TimeDomainRepresentation, 154
Problems, 154
References, 155
7 NonorthogonalPEECModels 157
(cid:2) 7.1 RepresentationofNonorthogonalShapes, 158 (cid:2)
7.1.1 HexahedralBodies, 160
7.1.2 DerivativesoftheLocalCoordinates, 162
7.2 SpecificationofNonorthogonalPartialElements, 163
7.2.1 DiscretizationofConductorandDielectricGeometries, 164
7.2.2 ContinuityEquationandKCLforNonorthogonalGeometries, 168
7.3 EvaluationofPartialElementsforNonorthogonalPEECCircuits, 169
7.3.1 AnalyticSolutionforQuadrilateralCellsinaPlane, 172
7.3.2 GeneralCaseforEvaluationofIntegralI , 174
p
7.3.3 EvaluationofIntegralI WhenTwoSideslCoincide, 178
p
Problems, 181
References, 182
8 GeometricalDescriptionandMeshing 185
8.1 GeneralAspectsofPEECModelMeshingRequirements, 186
8.2 OutlineofSomeMeshingTechniquesAvailableToday, 187
8.2.1 MeshingExampleforRectangularBlock, 188
8.2.2 MultiblockMeshingMethods, 189
8.2.3 MeshingofNonorthogonalSubproblems, 190
8.2.4 AdjustmentofBlockBoundaryNodes, 190
8.2.5 ContactsBetweentheEMandCircuitParts, 191
8.2.6 NonorthogonalCoordinateSystemforGeometries, 192
8.3 SPICETypeGeometryDescription, 194
8.3.1 ShortingofAdjoiningBodies, 196
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8.4 DetailedPropertiesofMeshingAlgorithms, 196
8.4.1 NonuniformMeshingAlgorithmforEfficientPEECModels, 197
8.4.2 𝛼CellProjectionAlgorithm, 199
8.4.3 SmoothingandTolerancing, 200
8.4.4 NodeRelaxation, 200
8.5 AutomaticGenerationofGeometricalObjects, 202
8.5.1 AutomaticMeshingTechniquesforThinandOtherObjects, 202
8.5.2 LoopingAlgorithmExample, 203
8.6 MeshingofSomeThreeDimensionalPre-determinedShapes, 205
8.6.1 GenerationTechniquesandMeshingofSpecialShapesLike
Circles, 205
8.6.2 BodiesGeneratedbyUsingGeneratrices, 206
8.7 ApproximationswithSimplifiedMeshes, 207
8.8 MeshGenerationCodes, 208
Problems, 209
References, 210
9 SkinEffectModeling 213
9.1 TransmissionLineBasedModels, 214
9.1.1 AnomalousSkin-EffectLossandSurfaceRoughness, 214
9.1.2 CurrentFlowDirectionandCoordinateDependence, 215
9.2 OneDimensionalCurrentFlowTechniques, 215
9.2.1 Analytical1DCurrentFlowModels, 215
(cid:2) 9.2.2 NarrowBandHigh-FrequencySkin-EffectModels, 216 (cid:2)
9.2.3 ApproximateGSIThinConductorSkin-EffectModel, 217
9.2.4 Physics-BasedMacromodel, 220
9.2.5 FrequencyDomainSolverforPhysics-BasedMacromodel, 222
9.2.6 ApproximateThinWireSkin-EffectLossModel, 223
9.3 3DVolumeFilament(VFI)Skin-EffectModel, 227
9.3.1 Approximate3DVFIModelwith1DCurrentFlow, 228
9.3.2 ShortsattheIntersections, 228
9.3.3 ProximityEffect, 229
9.3.4 CircuitEquationsforProximityEffectStudy, 230
9.3.5 Full3DCurrentFlowSkin-EffectModels, 234
9.3.6 EquivalentCircuitfor3DVFIModel, 234
9.3.7 SurfaceEquivalenceTheorem-BasedSkin-EffectModel, 236
9.4 ComparisonsofDifferentSkin-EffectModels, 238
9.4.1 ThinConductorResults, 240
9.4.2 ThickConductorResults, 240
9.4.3 ComparisonofExampleResults, 241
Problems, 244
References, 246
10 PEECModelsforDielectrics 249
10.1 ElectricalModelsforDielectricMaterials, 249
10.1.1 FrequencyandTimeDomainModelsforDielectricMaterials, 249
10.1.2 ModelsforLossyDielectricMaterials, 250
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10.1.3 PermittivityPropertiesofDielectrics, 251
10.1.4 ElectricalPermittivityModelforTimeDomain, 251
10.1.5 CausalModelsforDispersiveandLossyDielectrics, 252
10.2 CircuitOrientedModelsforDispersiveDielectrics, 254
10.2.1 SimpleDebyeMediumCircuitModelforDielectricBlock, 254
10.2.2 SimpleCapacitanceModelforLorentzMedia, 256
10.3 Multi-PoleDebyeModel, 257
10.3.1 CombinedDebyeandLorentzDielectricModel, 259
10.4 IncludingDielectricModelsinPEECSolutions, 260
10.4.1 ModelsforUniform,LosslessDielectrics, 260
10.4.2 Green’sFunctionsforDielectricLayersBasedontheImage
Theory, 261
10.4.3 Green’sFunctionforOneDielectricInterface, 263
10.4.4 ThreeDielectricLayersGreen’sFunctions, 266
10.4.5 DielectricModelBasedontheVolumeEquivalenceTheorem, 270
10.4.6 DiscretizationofDielectrics, 272
10.4.7 DispersiveDielectricsIncludedintheVolumeEquivalenceTheorem
Model, 274
10.4.8 DispersiveDielectricswithFiniteElectricalConductivity, 274
10.4.9 ConvolutionFormulationforGeneralDispersiveMedia, 275
10.5 ExampleforImpactofDielectricPropertiesintheTimeDomain, 276
10.5.1 On-ChipTypeInterconnect, 276
10.5.2 MicrostripLinewithDispersive,Lossydielectric, 277
10.5.3 CoplanarMicrostripLineExample, 280
(cid:2) Problems, 281 (cid:2)
References, 281
11 PEECModelsforMagneticMaterial 285
11.1 InclusionofProblemswithMagneticMaterials, 285
11.1.1 MagneticCircuitsforClosedFluxTypeClassofProblems, 285
11.1.2 ExampleforInductanceComputation, 287
11.1.3 MagneticReluctanceResistanceComputation, 289
11.1.4 InductanceComputationforMultipleMagneticPaths, 289
11.1.5 EquivalentCircuitforTransformer-TypeElement, 291
11.2 ModelforMagneticBodiesbyUsingaMagneticScalarPotentialand
MagneticChargeFormulation, 292
11.2.1 MagneticScalarPotential, 292
11.2.2 ArtificialMagneticCharge, 292
11.2.3 MagneticChargeIntegralEquationforSurfacePoleDensity, 293
11.2.4 MagneticVectorPotential, 294
11.3 PEECFormulationIncludingMagneticBodies, 295
11.3.1 ModelforMagneticBody, 295
11.3.2 ComputationofInductiveMagneticCoupling, 297
11.3.3 RelationBetweenMagneticField,Current,andMagnetization, 298
11.4 SurfaceModelsforMagneticandDielectricMaterialSolutionsinPEEC, 300
11.4.1 PEECVersionofMagneticFieldIntegralEquation(MFIE), 301
11.4.2 CombinedIntegralEquationforMagneticandDielectricBodies, 302
Problems, 307
References, 308
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12 IncidentandRadiatedFieldModels 309
12.1 ExternalIncidentFieldAppliedtoPEECModel, 310
12.2 Far-FieldRadiationModelsbyUsingSensors, 312
12.2.1 RadiatedElectricFieldCalculationsUsingSensors, 313
12.2.2 Evaluationofz-DirectionInductiveCouplingTermfortheE-Field
Sensor, 314
12.2.3 PotentialCoefficientCouplingContribution, 315
12.2.4 SummaryofE-FieldCalculationwitheSensor, 316
12.2.5 MagneticFieldCalculationUsingSensors, 316
12.2.6 TimeDomainSolutionforH-FieldSensor, 317
12.2.7 FrequencyDomainSolutionforH-FieldSensor, 318
12.3 DirectFar-FieldRadiationComputation, 318
12.3.1 GeneralRadiatedField, 319
12.3.2 RadiatedFieldComputationBasedonthePEECComputation
Results, 320
12.3.3 ApproximateComputationofFarFields, 320
Problems, 322
References, 322
13 StabilityandPassivityofPEECModels 325
13.1 FundamentalStabilityandPassivityConcepts, 327
13.1.1 TimeDomainStability, 328
13.1.2 TimeDomainPassivity, 328
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13.1.3 Causality, 329
13.1.4 PositiveRealFunctionandPassivity, 331
13.1.5 ExampleCircuitforNon-orLimitedPassivity, 331
13.2 AnalysisofPropertiesofPEECCircuits, 332
13.2.1 PortsandNodalPotentials(Voltages), 332
13.2.2 PassivityforQuasistaticPEECPortImpedance, 333
13.3 ObservabilityandControllabilityofPEECCircuits, 334
13.3.1 GeneralProperties, 335
13.3.2 PassivityatPortsforPEECCircuitintheFrequencyDomain, 335
13.3.3 TimeDomainStabilityandPassivityIssues, 336
13.4 PassivityAssessmentofSolution, 337
13.4.1 Port-BasedPassivityAssessmentinFrequencyDomain, 337
13.4.2 Port-BasedPassivityAssessmentinTimeDomain, 340
13.5 SolverBasedStabilityandPassivityEnhancementTechniques, 342
13.5.1 SolverEnhancementTechniquesforTimeandFrequency
Domains, 343
13.5.2 PassivityEnhancementbySubdivisionofPartialElements, 344
13.5.3 PassivityEnhancementUsingResistiveDamping, 346
13.5.4 PartialElementsDelayMacromodelsforPassivityEnhancement, 348
13.5.5 PassivityEnhancementforModelwithVFISkin-EffectModels, 353
13.5.6 Physics-BasedSkin-EffectMacromodelforPartialElements, 353
13.5.7 MutualCouplingInductanceTermswithRetardation, 355
13.6 TimeDomainSolverIssuesforStabilityandPassivity, 359
13.6.1 ImpactofTimeIntegrationonStability, 359
13.6.2 ImpactofNumericalDampingofIntegrationMethod, 361
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13.6.3 DigitalWaveformFiltering, 362
Acknowledgment, 364
Problems, 364
References, 365
A TableofUnits 369
A.1 CollectionofVariablesandConstantsforDifferentApplications, 369
B ModifiedNodalAnalysisStamps 373
B.1 ModifiedNodalAnalysisMatrixStamps, 373
B.1.1 Resistor, 373
B.1.2 Capacitor, 375
B.1.3 IndependentVoltageSource, 376
B.1.4 IndependentVoltageSourcewithSeriesElements, 376
B.1.5 IndependentCurrentSource, 377
B.1.6 ShortCircuitConnection, 377
B.1.7 CoupledInductances, 378
B.1.8 IdealTransformerModel, 379
B.2 ControlledSourceStamps, 380
B.2.1 CurrentControlledVoltageSource(CCVS), 380
B.2.2 VoltageControlledVoltageSource(VCVS), 380
B.2.3 CurrentControlledCurrentSource(CCCS), 380
(cid:2) B.2.4 VoltageControlledCurrentSource(VCCS), 382 (cid:2)
References, 382
C ComputationofPartialInductances 383
C.1 PartialInductanceFormulasforOrthogonalGeometries, 385
C.1.1 Lp forTwoParallelFilaments, 385
12
C.1.2 Lp forRoundWire, 386
11
C.1.3 Lp forFilamentandCurrentSheet, 388
12
C.1.4 Lp forRectangularZeroThicknessCurrentSheet, 389
11
C.1.5 Lp forTwoParallelZeroThicknessCurrentSheets, 389
12
C.1.6 Lp forTwoOrthogonalRectangularCurrentSheets, 390
12
C.1.7 Lp forRectangularFiniteThicknessBar, 392
11
C.1.8 Lp forTwoRectangularParallelBars, 394
12
C.1.9 1/R3KernelIntegralforParallelRectangularSheets, 395
C.1.10 1/R3KernelIntegralforOrthogonalRectangularSheets, 397
C.2 PartialInductanceFormulasforNonorthogonalGeometries, 398
C.2.1 RotationforDifferentNonorthogonalConductorOrientations, 398
C.2.2 LpforArbitraryOrientedWiresintheSamePlanez=0, 399
C.2.3 LpforWireFilamentswithanArbitraryDirection, 401
C.2.4 LpforTwoCellsorBarswithSameCurrentDirection, 403
C.2.5 LpforArbitraryHexahedralPartialSelf-Inductance, 403
C.2.6 LpforArbitraryHexahedralPartialMutualInductance, 404
References, 407
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