Comsol电容矩阵计算

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1、SolvedwithCOMSOLMultiphysics4.2a.CapacitancematrixIntroductionThecapacitancematrixofanelectricalsystemallowsustoevaluatecrosstalkbetweenexcitationports.Forexample,inFigure1weseeathree-terminalsysteminwhichwecanexciteoneterminalandsettheothertwotoground.Ifwerepeatthism

2、ethodofexcitingoneterminalatatime,sincetherearethreeterminals,wecanevaluateninepossiblevaluesofcapacitance.ThecapacitancecomponentC11isthecapacitanceevaluatedbetweenthegroundedterminalsandTerminal1.ThiscanbecalculatedbyexcitingTerminal1.ThecapacitancebetweenTerminals1

3、and2wouldbeC21.ThiscanbecalculatedoncewehaveinformationaboutC11andC22.ThismeanswewouldneedtosolvethemodelonceagainbyexcitingTerminal2.Bydefinition,C21andC12wouldbeequal.Thismeansthatathree-terminalsystemwillhavesixuniquevaluesofcapacitance.Thecapacitancevalues,termina

4、lchargesandterminalvoltagesarelinkedbythefollowingmatrixrelation:QCCCV11112131Q=CCCV22122232QCCCV33132333Terminal1Terminal2VV2,Q21,Q1Terminal3V3,Q3Figure1:Pictorialrepresentationofamulti-terminalelectricalsystem.CAPACITANCEMATRIX

5、1SolvedwithCOMSOLMultiphysics4.2a.Inth

6、istutorialwewillfindouthowtofindthecapacitancematrixofathree-terminalsystem.Thesameideacanbeextendedtoasmanyterminalsasrequired.ThismodelrequirestheACDCModule.ThemethodologyusedtoevaluatethecomponentsofthecapacitancematrixiselaboratedintheACDCModuleUser’sGuide.ModelDe

7、finitionInthistutorialwewillmodela2Dregionofairsurroundingthreemetallicterminals.ThistutorialwilluseCOMSOL’sElectrostaticsinterfacetosolvethePoisson’sequationshowninEquation1inordertofindthespatialdistributionofelectricpotentialinthemodelingregion.Theonlymaterialprope

8、rtyrequiredtosolvethismodelistherelativepermittivityofair.Introductionofadditionaldielectricmaterialswillautomaticallyaffectthecapacitancevalues.–∇•()εε∇V=00r(1)Wewillcreategeometriclayersaroundtheairdomain.TheselayerswillbeassignedtotheInfiniteElementsfeature.Thisfea

9、tureimplementsthepresenceofaninfinitelyextendedregionhencethemodelwouldyieldmoreaccuratevaluesofcapacitance.Theboundarycondi