Analysis of Multiconductor Transmission Lines 2Ed.pdf

Analysis of Multiconductor Transmission Lines 2Ed.pdf

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ANALYSISOFMULTICONDUCTORTRANSMISSIONLINESSecondEditionCLAYTONR.PAULProfessorofElectricalandComputerEngineeringMercerUniversityMacon,GA31207andEmeritusProfessorofElectricalEngineeringUniversityofKentuckyLexington,KY40506Copyright2008byJohnWiley&Sons,Inc.AllrightsreservedPublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJerseyPublishedsimultaneouslyinCanadaNopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanning,orotherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropriateper-copyfeetotheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,（978）750-8400,fax（978）750-4470,oronthewebat.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,（201）748-6011,fax（201）748-6008,oronlineathttp:

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/.LibraryofCongressCataloging-in-PublicationDataPaul,ClaytonR.Analysisofmulticonductortransmissionlines/byClaytonR.Paul.2nded.p.cm.ISBN978-0-470-13154-1（cloth）1.Multiconductortransmissionlines.2.ElectriccircuitanalysisDataprocessing.I.Title.TK7872.T74P382008621.319?

2dc222007013722PrintedintheUnitedStatesofAmerica10987654321ThistextbookisdedicatedtothehumaneandcompassionatetreatmentofanimalsAmanistrulyethicalonlywhenheobeysthecompulsiontohelpalllifewhichheisabletoassist,andshrinksfrominjuringanythingthatlives.AlbertSchweitzerItillbecomesustoinvokeinourdailyprayerstheblessingsofGod,thecompassionate,itweinturnwillnotpracticeelementarycompassiontowardsourfellowcreatures.GandhiWecanjudgetheheartofmanbyhistreatmentofanimals.ImmanuelKantCONTENTSPrefacexvii1Introduction11.1ExamplesofMulticonductorTransmission-LineStructures51.2PropertiesoftheTEMModeofPropagation81.3TheTransmission-LineEquations:

APreview181.3.1UniqueDefinitionofVoltageandCurrentfortheTEMModeofPropagation191.3.2DefiningthePer-Unit-LengthParameters221.3.3ObtainingtheTransmission-LineEquationsfromtheTransverseElectromagneticFieldEquations281.3.4PropertiesofthePer-Unit-LengthParameters301.4ClassificationofTransmissionLines321.4.1UniformversusNonuniformLines331.4.2HomogeneousversusInhomogeneousSurroundingMedia351.4.3LosslessversusLossyLines361.5RestrictionsontheApplicabilityoftheTransmission-LineEquationFormulation371.5.1HigherOrderModes381.5.1.1TheInfinite,Parallel-PlateTransmissionLine38viiviiiCONTENTS1.5.1.2TheCoaxialTransmissionLine431.5.1.3Two-WireLines441.5.2Transmission-LineCurrentsversusAntennaCurrents451.6TheTimeDomainversustheFrequencyDomain471.6.1TheFourierSeriesandTransform501.6.2SpectraandBandwidthofDigitalWaveforms521.6.3ComputingtheTime-DomainResponseofTransmissionLinesHavingLinearTerminationsUsingFourierMethodsandSuperposition56Problems61References692TheTransmission-LineEquationsforTwo-ConductorLines712.1DerivationoftheTransmission-LineEquationsfromtheIntegralFormofMaxwellsEquations712.2DerivationoftheTransmission-LineEquationsfromthePer-Unit-LengthEquivalentCircuit772.3PropertiesofthePer-Unit-LengthParameters782.4IncorporatingFrequency-DependentLosses792.4.1PropertiesoftheFrequency-DomainPer-Unit-LengthImpedancez（）andAdmittancey（）81Problems85References883TheTransmission-LineEquationsforMulticonductorLines893.1DerivationoftheMulticonductorTransmission-LineEquationsfromtheIntegralFormofMaxwellsEquations893.2DerivationoftheMulticonductorTransmission-LineEquationsfromthePer-Unit-LengthEquivalentCircuit993.3SummaryoftheMTLEquations1013.4IncorporatingFrequency-DependentLosses1023.5PropertiesofthePer-Unit-LengthParameterMatricesL,C,G103Problems108References1094ThePer-Unit-LengthParametersforTwo-ConductorLines1104.1DefinitionsofthePer-Unit-LengthParametersl,c,andg111CONTENTSix4.2LinesHavingConductorsofCircular,CylindricalCrossSection（Wires）1134.2.1FundamentalSubproblemsforWires1134.2.1.1TheMethodofImages1184.2.2Per-Unit-LengthInductanceandCapacitanceforWire-TypeLines1194.2.3Per-Unit-LengthConductanceandResistanceforWire-TypeLines1304.3LinesHavingConductorsofRectangularCrossSection（PCBLands）1444.3.1Per-Unit-LengthInductanceandCapacitanceforPCB-TypeLines1454.3.2Per-Unit-LengthConductanceandResistanceforPCB-TypeLines148Problems156References1585ThePer-Unit-LengthParametersforMulticonductorLines1605.1DefinitionsofthePer-Unit-LengthParameterMatricesL,C,andG1615.1.1TheGeneralizedCapacitanceMatrixC1675.2MulticonductorLinesHavingConductorsofCircular,CylindricalCrossSection（Wires）1715.2.1Wide-SeparationApproximationsforWiresinHomogeneousMedia1715.2.1.1n+1Wires1735.2.1.2nWiresAboveanInfinite,PerfectlyConductingPlane1735.2.1.3nWiresWithinaPerfectlyConductingCylindricalShield1745.2.2NumericalMethodsfortheGeneralCase1765.2.2.1ApplicationstoInhomogeneousDielectricMedia1815.2.3ComputedResults:

RibbonCables1875.3MulticonductorLinesHavingConductorsofRectangularCrossSection1895.3.1MethodofMoments（MoM）Techniques1905.3.1.1ApplicationstoPrintedCircuitBoards1995.3.1.2ApplicationstoCoupledMicrostripLines2115.3.1.3ApplicationstoCoupledStriplines219xCONTENTS5.4FiniteDifferenceTechniques2235.5Finite-ElementTechniques229Problems237References2396Frequency-DomainAnalysisofTwo-ConductorLines2406.1TheTransmission-LineEquationsintheFrequencyDomain2416.2TheGeneralSolutionforLosslessLines2426.2.1TheReflectionCoefficientandInputImpedance2446.2.2SolutionsfortheTerminalVoltagesandCurrents2476.2.3TheSPICE（PSPICE）SolutionforLosslessLines2506.2.4VoltageandCurrentasaFunctionofPositionontheLine2526.2.5MatchingandVSWR2556.2.6PowerFlowonaLosslessLine2566.3TheGeneralSolutionforLossyLines2586.3.1TheLow-LossApproximation2606.4Lumped-CircuitApproximateModelsoftheLine2656.5AlternativeTwo-PortRepresentationsoftheLine2696.5.1TheChainParameters2706.5.2ApproximatingAbruptlyNonuniformLineswiththeChain-ParameterMatrix2736.5.3TheZandYParameters275Problems2787Frequency-DomainAnalysisofMulticonductorLines2827.1TheMTLTransmission-LineEquationsintheFrequencyDomain2827.2TheGeneralSolutionforAn（n+1）-ConductorLine2847.2.1DecouplingtheMTLEquationsbySimilarityTransformations2847.2.2SolutionforLineCategories2917.2.2.1PerfectConductorsinLossy,HomogeneousMedia2927.2.2.2LossyConductorsinLossy,HomogeneousMedia2937.2.2.3PerfectConductorsinLossless,InhomogeneousMedia2967.2.2.4TheGeneralCase:

LossyConductorsinLossy,InhomogeneousMedia2987.2.2.5Cyclic-SymmetricStructures298CONTENTSxi7.3IncorporatingtheTerminalConditions3057.3.1TheGeneralizedTheveninEquivalent3057.3.2TheGeneralizedNortonEquivalent3087.3.3MixedRepresentations3107.4Lumped-CircuitApproximateCharacterizations3127.5Alternative2n-PortCharacterizations3147.5.1AnalogyoftheFrequency-DomainMTLEquationstoState-VariableEquations3147.5.2CharacterizingtheLineasa2n-PortwiththeChain-ParameterMatrix3167.5.3PropertiesoftheChain-ParameterMatrix3187.5.4ApproximatingNonuniformLineswiththeChain-ParameterMatrix3227.5.5TheImpedanceandAdmittanceParameterMatrixCharacterizations3237.6PowerFlowandtheReflectionCoefficientMatrix3277.7ComputedandExperimentalResults3327.7.1RibbonCables3327.7.2PrintedCircuitBoards335Problems338References3428Time-DomainAnalysisofTwo-ConductorLines3438.1TheSolutionforLosslessLines3448.1.1WaveTracingandtheReflectionCoefficients3468.1.2SeriesSolutionsandtheDifferenceOperator3568.1.3TheMethodofCharacteristicsandaTwo-PortModeloftheLine3618.1.4TheSPICE（PSPICE）SolutionforLosslessLines3658.1.5TheLaplaceTransformSolution3688.1.5.1LineswithCapacitiveandInductiveLoads3708.1.6Lumped-CircuitApproximateModelsoftheLine3738.1.6.1WhenistheLineElectricallyShortintheTimeDomain?

3748.1.7TheTime-DomaintoFrequency-Domain（TDFD）TransformationMethod3758.1.8TheFinite-Difference,Time-Domain（FDTD）Method3798.1.8.1TheMagicTimeStep385xiiCONTENTS8.1.9MatchingforSignalIntegrity3928.1.9.1WhenisMatchingRequired?

3988.1.9.2EffectsofLineDiscontinuities3998.2IncorporationofLosses4068.2.1RepresentingFrequency-DependentLosses4088.2.1.1RepresentingLossesintheMedium4088.2.1.2RepresentingLossesintheConductorsandSkinEffect4108.2.1.3ConvolutionwithFrequency-DependentLosses4158.2.2TheTime-Domainto