Comsol电容矩阵计算

SolvedwithCOMSOLMultiphysics4.2a.CAPACITANCEMATRIX|1CapacitancematrixIntroductionThecapacitancematrixofanelectricalsystemallowsustoevaluatecrosstalkbetweenexcitationports.Forexample,inFigure1weseeathree-terminalsysteminwhichwecanexciteoneterminalandsettheothertwotoground.Ifwerepeatthismethodofexcitingoneterminalatatime,sincetherearethreeterminals,wecanevaluateninepossiblevaluesofcapacitance.ThecapacitancecomponentC11isthecapacitanceevaluatedbetweenthegroundedterminalsandTerminal1.ThiscanbecalculatedbyexcitingTerminal1.ThecapacitancebetweenTerminals1and2wouldbeC21.ThiscanbecalculatedoncewehaveinformationaboutC11andC22.ThismeanswewouldneedtosolvethemodelonceagainbyexcitingTerminal2.Bydefinition,C21andC12wouldbeequal.Thismeansthatathree-terminalsystemwillhavesixuniquevaluesofcapacitance.Thecapacitancevalues,terminalchargesandterminalvoltagesarelinkedbythefollowingmatrixrelation:Figure1:Pictorialrepresentationofamulti-terminalelectricalsystem.Q1Q2Q3C11C12C13C21C22C23C31C32C33V1V2V3=V1,Q1V2,Q2V3,Q3Terminal1Terminal2Terminal3SolvedwithCOMSOLMultiphysics4.2a.2|CAPACITANCEMATRIXInthistutorialwewillfindouthowtofindthecapacitancematrixofathree-terminalsystem.Thesameideacanbeextendedtoasmanyterminalsasrequired.ThismodelrequirestheACDCModule.ThemethodologyusedtoevaluatethecomponentsofthecapacitancematrixiselaboratedintheACDCModuleUser’sGuide.ModelDefinitionInthistutorialwewillmodela2Dregionofairsurroundingthreemetallicterminals.ThistutorialwilluseCOMSOL’sElectrostaticsinterfacetosolvethePoisson’sequationshowninEquation1inordertofindthespatialdistributionofelectricpotentialinthemodelingregion.Theonlymaterialpropertyrequiredtosolvethismodelistherelativepermittivityofair.Introductionofadditionaldielectricmaterialswillautomaticallyaffectthecapacitancevalues.(1)Wewillcreategeometriclayersaroundtheairdomain.TheselayerswillbeassignedtotheInfiniteElementsfeature.Thisfeatureimplementsthepresenceofaninfinitelyextendedregionhencethemodelwouldyieldmoreaccuratevaluesofcapacitance.TheboundaryconditionfortheouteredgesofthelayerswillbesettothedefaultZeroChargeconditionwhichwillensurethatthedisplacementcurrentdoesnotdiverge.FordetailedinformationonInfiniteElements,pleaserefertotheACDCModuleUser’sGuide.InthistutorialyouwillusetheTerminalboundaryconditionwhichautomaticallycalculatesthecapacitancebetweengroundandtheexcitedTerminal.YouwillalsolearntousethePortSweepfunctionalitywhichwillallowyoutosweeptheexcitationoverdifferentterminals,oneatatime,inamulti-terminalsystem.Notethatinthistutorialwedonotassignafixedgroundinthegeometry.Thegroundautomaticallyfloatsbetweenthethreeterminalsasaresultoftheportsweep.However,formostcasesitisingeneralagoodpracticetoassigntheelectricalgroundtoappropriateboundarieswhichrepresentzeroelectricpotential.Notethatinordertocalculatethecapacitance,itisnecessarytoknowtheout-of-planethicknessina2Dmodel.Inthistutorialwewillusethedefaultvalueofunitthickness(i.e.1m).Thevalueofout-of-planethicknesscanbealteredinthesettingsoftheElectrostaticsinterfaceinCOMSOL.ε0εrV∇()∇•–0=SolvedwithCOMSOLMultiphysics4.2a.CAPACITANCEMATRIX|3ResultsandDiscussionThedefaultplotobtainedaftersolvingthemodelisshowninFigure2.Thisplotshowsthedistributionofelectricpotentialinthemodelingregion.ThedefaultplotrepresentsthecasewhenTerminal3isexcited.NotehowtheInfiniteElementsfeaturestretchthesolutiontowhatitshouldbeataninfinitedistancewithinthethicknessofthegeometriclayer.Figure3showsthecasewhenTerminal1isexcited.SimilarlyyoucanalsoinspectthevoltagedistributionwhenTerminal2isexcited.Sinceweonlymodeltheregionofairaroundtheterminalsandassumedthattheterminalsareatisopotentialcondition,thesolutionprecludestheisopotentialregionsinsidetheterminals.Thecapacitancematrixevaluated(innF)forthistutorialproblemisshownbelow.Figure2:SurfaceplotofelectricpotentialwhenTerminal3isexcitedwith1V.0,02140,0125–0,0089–0,0125–0,02770,0152–0,0089–0,0152–0,0242SolvedwithCOMSOLMultiphysics4.2a.4|CAPACITANCEMATRIXFigure3:SurfaceplotofelectricpotentialwhenTerminal1isexcitedwith1V.ModelLibrarypath:ACDC_Module/Tutorials/capacitance_matrixModelingInstructionsMODELWIZARD1GototheModelWizardwindow.2Clickthe2Dbutton.3ClickNext.4IntheAddphysicstree,selectAC/DCElectrostatics(es).5ClickNext.6FindtheStudiessubsection.Inthetree,selectPresetStudiesStationary.7ClickFinish.SolvedwithCOMSOLMultiphysics4.2a.CAPACITANCEMATRIX|5GEOMETRY1Square1(sq1)1IntheModelBuilderwindow,right-clickModel1(mod1)Geometry1andchooseSquare.2GototheSettingswindowforSquare.3LocatethePositionsection.FromtheBaselist,chooseCenter.4ClicktoexpandtheLayerssection.5Inthetable,enterthefollowingsettings:6SelecttheLayerstotheleftcheckbox.7SelecttheLayerstotherightcheckbox.8SelecttheLayersontopcheckbox.9ClicktheBuildSelectedbutton.Rectangle1(r1)1IntheModelBuilderwindow,right-clickGeometry1andchooseRectangle.2GototheSettingswindowforRectangle.3LocatethePositionsection.Inthexeditfield,type-0.3.4Intheyeditfield,type0.2.5LocatetheSizesection.IntheWidtheditfield,type0.2.6IntheHeighteditfield,type0.1.Rectangle2(r2)1IntheModelBuilder