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1、818IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.51,NO.3,MARCH2003AnalysisofaLargeNumberofViasandDifferentialSignalinginMultilayeredStructuresHoufeiChen,QinLi,LeungTsang,Fellow,IEEE,Chung-ChiHuang,andVikramJandhyala,Member,IEEEAbstract—Amethodispresentedforfull-wavemodelingofver-
2、ticalviasinmultilayeredintegratedcircuits.Theanalysisofthein-teriorproblemisbaseduponthecylindricalwaveexpansionofthemagneticfieldGreen’sfunction.ThemultipleinteractionamongverticalviasismodeledbytheFoldy–Laxscatteringformula.Mul-tilayeredeffectsareincludedbyusingcascadednetworkofthes
3、ingle-layercomponents.Theexteriorproblemoftheviaandthetransmissionlineisanalyzedusingthemethodofmomentsap-proach.Theexteriorandinteriorproblemsarecombinedintoasystemofequationstofacilitatethesolutionofalargenumberofvias.Usingthisapproach,thescatteringmatrixofproblemsofFig.1.Typicalmul
4、ti-viastructureincludingapairofdifferentialsignalingvias,shortingviasintheneighborhoodtoreducecouplingandalsomanyotherseveralthousandviascanbecalculatedwithmoderateCPUandidleviasonthePCB.memoryrequirement.Numericalresultshavebeenobtainedfordifferentviaconfigurationsandforalargerangeof
5、frequency.Alsoillustratedareresultsforcommonanddifferentialmodeindiffer-entialsignalingwithsurroundingidleandshortingvias.IndexTerms—Differentialsignaling,scatteringparameter,via-coupling.I.INTRODUCTIONECAUSEOFTHEever-increasingspeed,density,andBroutingcomplexityinintegratedcircuit(IC
6、)design,viastructureisextensivelyusedtoconnectsignaltracesresidingondifferentlayers.Theimpedancedifferencebetweenviasandsignaltracesintroducesreflection.Thenatureofthemultilay-eredgeometryintroducestheparallelplatewaveguideeffect,whichresultsinsignificantcouplingamongvias.Couplingthro
7、ughparallelplatewaveguidemodesgenerallydecaysFig.2.Decompositionofverticalviastructure.slowlyasthesquarerootofdistanceandposesasignificantchallengetoreliable,high-speedICoperation.Numerousprob-approach[3]–[5]orempiricalformulas[6].Acircularlysym-lemsarisingthere(suchaslargerdelays,los
8、sofsi
