電能設(shè)備英文

{設(shè)備管理}電能設(shè)備英文Section1EMCOFELECTRICALPOWEREQUIPMENTMUTUALINDUCTANCEBETWEENWIRESINHELICALLYTWISTEDPOWERCABLESBERNDW.JAEKEL,GERMANYSiemensAG,AutomationandDrives,Germany,e-mail:@Abstract.Thearrangementoftheconductorsinamulti-corepowercableleadstoasituationwherevariousconductorloopsarebuiltup.Oneorseveralloopsareformedbythephaseandneutralconductorswiththeoperationalcurrentflowingintheseconductors.Afurtherloopisbuiltupbytheprotectiveearthconductorwhichisconnectedtotheequipotentialbondingsystematseverallocations.Theareaofthisloopisessentiallyarrangedoutsideofthepowercable.Theinductivecouplingfromthephaseconductorloopsintothatloopcausesmonmodevoltagesintheprotectiveearthsystemwithconsequentmonmodecurrents.Itcanbedemonstratedthatthiseffecteventakesplaceinthecaseofbalancedphasecurrentsinthecable.Numericalsimulationsandparameterstudieswerecarriedoutinordertodescribethiseffectquantitativelyandtoinvestigatetheinfluenceofdifferentcableparametersontotheresultingmonmodevoltages.IntroductionalmechanismscanbeidentifiedwhichneverthelessPowercablesrepresentponentsofanentirepowersuleadtothegenerationofmonmodevoltagesandmonmopplynetworkwhichcanbecarriedoutindifferenttydecurrentseveninthecaseofbalancedloadedTN-pes.Ifanearthedsystemisrequired,i.e.asystemwSpowernetsystems.hichisconnectedtothelocalreferenceearth,mainLowVoltagePowerCableslytwotypesofsupplynetworkscanbedistinguishedMulti-:TN-CandTN-S.FromanEMCpointofviewaTN-corelowvoltagepowercablesconsistofthephasecoSpowernetworkshoulddefinitelybepreferred[1].nductorsand–Inthistypeofnetworktheneutralandprotectiveeadependingonthegroundingarrangementofthepowerrth(PE)conductorsarestrictlyseparatedexceptasupplynetwork–tonenetpointwherebothconductorsareconnected,ofaneutralconductorand/oraPEconductor.Anexamnormallyatthetransformerortheswitchgear.ThispleforthestructureofapowercableisshowninFig.typeofinstallationpreventsthatanyoperational1foracableoftypeNYY.Eachoftheconductorsaswelcurrentsflowoutsideofthephaseandneutralcondulastheentireconductorarrangementarecoveredbyctors.Nocablenetcurrentsshouldexistandtherefaninsulationforwhichamaterialischosendependioretheequipotentialbondingsystemisgenerallyangonthespecificrequirementsandfieldsofapplicssumedtobefreeofanyoperationalcurrents.Butwhations[2].enlookinginmoredetailatthistypeofnetworkandaThenindividualinsulatedconductorsaretwistedttthephysicalstructureofpowercablessomephysicogetherandeachconductorcanberepresentedbyahelicalline.Anappropriatecylindricalcoordinatepotentialbondingsystem.Thiseffectcanbeexplaisystemfordescribingthespatialarrangementofacnedbymeansofaschematicsketchofa4-onductorisshowninFig.2togetherwiththerelevanconductorcableasshowninFig.3.Forreasonsofclatparameterssuchasaastheradiusofthehelicallinritythetwistingoftheconductorsisnotshowninthewithrespecttothecentrelineofthecableandthepefigure.itchdistancepasthetwistlengthofthecable,i.e.Fig.2:Atwistedconductor(helicalline)inacylinthelengthofthecableperrotationoftheconductordricalcoordinatesystem[3]s.ForsimplicityreasonsonlyoneconductorisshowTheconductorsL1,L2forexampleformaspatialloopn.Thefurthern-inwhichthephasecurrentIL1-1conductorscanberepresentedassimilarlinesandL2flows.Correspondingloopsarebuiltupbythearratheyarerotatedbyanangle=3600/nwithrespecttongementofconductorsL1-L3andL2-thatoneshowninFig.2.L3withtheloopcurrentsIL1-L3andIL2-Fig.1:Multi-corepowercableoftypeNYYL3,respectively.AfurtherloopresultsfromthePEcCommonModeVoltagesinPowerCablesonductorwhichisconnecttotheequipotentialbondThemagneticfluxdensityBcausedbythecurrentsiningsystembyconductivestructures.ThisloopisshtheindividualconductorscanbecalculatedbymeanownasPE-LoopinFig.3.softheBiot-Fig.3:MechanismforgenerationofmonmodevoltageSavartlaw,aslongasthesituationatthepowerfreqsuencyrangeisconsidered:TheinducedvoltageUPEinthePE-Loopcanbederivedbymeansofthemutualinductance(1)sbetweenthevariousphaseconductorloopsandthePIrepresentsthephasoroftheexcitingalternatingE-current,rwithitscylindricalcoordinatesr,,zLooporaccordinglybythemutualinductancebetweedenotestheobservationpointandr’withitscylinnthecurrentcarryingphaseconductorsandthePE-dricalcoordinatesr’,’,z’meansavariablepLoop:ointonthelinecurrent.Thoughthisexpressioncan(2beeasilysolvedinthecaseofstraightwires,thesi)tuationisrelativelyplexinthecaseofpowercablewiththemutualinductancesMLi-swherethevariousconductorsaretwistedandeachcPE(i=1,2,3)tobederivedbyonductorcanberepresentedbyahelicalsolenoid(s(3)eeFig.2).BLirepresentsthemagneticfluxdensitycausedbythInpowercableswhereaprotectiveearthconductor(ecurrentIiinconductorLi(i=1,2,3)andStheareaofPE-thePE-Loop[4].conductor)istwistedalongwiththephaseconductoFig.3showsthesituationforafour-rsaninductivecouplingexistsbetweenthephasecoconductorcable.Fromthecross-nductorloopsandaloopbuiltupbythePE-sectionoftheentirecableconfigurationitcanbesconductoranditsconnectingstructurestotheequieenthatthereisnototalsymmetrywhenlookingatthethreemutualinductancesbetweenthephaseconducsgiventheretoestimatethefieldstrengthversusdtorsandtheprotectiveearthloop.Henceanetmutuaistancetothetwistedphaseconductorarrangementlinductanceresultsleadingtoanetinducedmonmod.evoltage–Therearedifferentpossibilitiestodeterminetheandamonmodecurrentinthecaseofaclosedloop,resamplitudeoftheinducedvoltageUPE:pectively.byanalyticallyperformedintegrationtecTheBiot-hniquesSavartintegral(1)neededinordertodetermineBLi,bynumericalsimulationsorhowever,cannotbecalculatedanalyticallyforacubymeasurements.rrentinahelicalconductorarrangement.ThemagneTheintegrationofthemagneticfluxdensityacrossticvectorpotentialhastobeusedandaseriesexpantheareaofthePEloopresultsinthetotalmagneticfsionofthereciprocaldistancebetweentheobservaluxandsubsequentlyintheinducedvoltage.Thisaptionpointandavariablepointontheconductorhastproach,however,representsaveryplextask,becauobeintroduced.Usingsomewell-seontheonehandtheexpressions(4),(5)and(6)witknowntrigonometrictheoremstogetherwithBesselhtheBesselfunctionshavetobeintegratedandonthfunctionsthefollowingequationsforthediffereneothersidetheseequationswhicharevalidforobsetponentsofthemagneticfluxdensityvectorcanbedrvationpointsoutsidethecablehavetobeconsidererivedforobservationpointsoutside(r>a)theheledaswellascorrespondingequationswhichdescribicalarrangement[5]:ethesituationinsidethepowercable[5].Noanalyticalresultsorapproximateprocedureswerefoundi(4nthetechnicalliteraturewhichoffersolutions.)NumericalSimulationsWithintheframeofnumericalsimulationsthetwist(5edconductorsaswellasthegeneratedPE-)loophavetobemodelledspatially.Aschematicrepresentationforthephysicalmodelofatwistedpower(6cableisgiveninFig.4.Forthesimulationsthegeom)etricaldataofacableoftype4x25mm2areusedwherewithatwistlength(pitch)of0.4mwasconsidered.ThePE-isthecoordinateofthepointwherethehelixintersconductorofthecableisconnectedtoconductivestectstheplaneructures(ofequipotentialbondingsystem)andacl:modifiedBesselfunctionsoffirstandsecondkindosedloopresults.Thedimensionsofthelooparelenofordern():theirderivatives)gthLandwidthW.In[5]thecorrespondinginvestigationsareexpandedtothesituationofatwistedthree-phasearrangement.FurthermoreanapproximationiTheinducedvoltagelinearlyincreaseswithincrea(a)singlongitudinallengthLoftheloop.ThisbehaviotwistedcablewithPE-loopWurcanbeexpectedduetotheresultingconductorconfigurationwherethearrangementofthePEconductorisconstantwithrespecttothephaseconductors.HencethePE-(b)detailof(a)showingindividualtwistedconductorsandconnectionofPE-

loopisexposedtoconstantmagneticfieldsalongth

loopconductorsoutsidethecableecablelengthresultinginaconstantinducedvolta

Fig.4:Spatialmodelofapowercablegeperlengthunit.Thisbehaviourwasfoundalsobym

Thesimulationswereperformedbymeansoftheputereansofexperimentalinvestigations[7].Fromthes

programCONCEPTwhichbasesontheMethodofMomentslopeofthelineacoefficientcanbederivedwhichex

[6].Thismethodandprogramallowsmodellingofallpressestheinducedvoltagepercable/looplengtha

theconductivestructuresofthearrangementunderndwhichisabout0.44μVm/Hz.consideration.ThephaseconductorsareexcitedbyInthecaseofabalancedthreephasesystemwithphas

meansofathreephasevoltagesourceandallthevoltecurrentIandtakingintoaccountthephaserelatioagesandcurrentscanbecalculatedwhichareinducenship,equation(2)canbesimplifiedinordertodes

dinanyconductiveelementofthemodel.cribetherelationbetweentheinducedvoltageUPE,t

Theamplitudeoftheinducedmonmodevoltagedependhefrequencyfofthecurrentsandtheiramplitudes:sontheactualcableparametersandthecableinstal(7)lationcondition.InafirststepthedependencyontwithMNETasthenetmutualinductancederivedfromth

hephasecurrentamplitudesandthephasecurrentfresuperpositionoftheindividualmutualinductanc

equenciesintherangefromseveralHztoseveralhunes.AccordingtothisrelationamutualinductanceM

dredsofHz,heelectricallylowfrequencyr’NET=70nHpermeterlengthresultswhentheinduced

angewereinvestigated.InbothcasesalinearcorrevoltageUPEisconsideredasderivedabove.lationbetweeninducedvoltageandcurrentandfreqThemutualinductanceisexpectedtodependonsever

uency,respectively,couldbefound.Thisclearlyialcableparameters.Correspondinginvestigation

ndicatesthatthephysicalmechanismwhichcausestsconcerningtheamplitudesoftheinducedvoltageU

heinducedvoltageisaninductivecouplingbetweenPEwereperformedforvariouscableparametersandca

thecurrentcarryingphaseconductorsandthePE-bleconfigurations[8].Fromthoseresultscanbede

loop.rivedthatthereisnearlynodependencyonthetwist

FurthermorethevoltageinducedintothePE-length(pitch)ofthepowercableconductorsatleas

loopwascalculatedforvaryinglengthsoftheloopstforpracticaltwistlengthsofmorethanabout40cm

,i.e.forvaryinglongitudinaldimensionsofthere.Furthermorethereisonlyasmallimpactoftheheli

sultingloopbuiltupbythePE-calradiusofthepowercableconductors.Thisfactw

conductorofthepowercableandtheequipotentialbasfoundalsobymeansofmeasurementswheretheresu

ondingsystem.TheresultsaregiveninFig.5.ltsofa4x95mm2powercablearenearlythesameasint

Fig.5:InducedvoltageversuslengthLofthePE-hepresentcaseofa4x25mm2powercable[7].

loopSincetheinductivecouplinghastoconsiderthePE-onductor(seeFig.7)inafiveconductorarrangemenloopdimensionsasignificantimpactoftheloopwidtwhereonlythreephaseconductorscarryacurrent.thWmightbeexpected.ForthesamepowercableasdesConclusioncribedabove(4x25mm2,40cmpitchlength)thewidthInpowercableswithtwistedPEconductorsamonmodeofthePE-voltageisinducedbythecurrentsinthephaseconduloopwasvariedintherangebetween5cmand100cm.Thctors.ThisisvalideveninthecaseofbalancedcurrisvariationreflectspotentialinfluencesduetoventsandisduetothefactthatthePEconductorhasacariationofthecablelayingabovegroundoraboveeqertainasymmetrywithrespecttothephaseconductouivalentequipotentialbondingstructures.ThecorsresultinginanetmagneticfluxthroughtheloopbrrespondingresultsconcerningthevoltageinduceuiltupbythePEconductorandstructuresoftheequidinthePE-potentialbondingsystem.loopareshowninFig.6.TheinducedvoltageandhencFig.7:Arrangementofconductorsinafive-ealsothemutualinductanceMNETdoesnotshowanysigconductorpowercablenificantchangewithvaryingPEloopwidth.TheamplitudeoftheinducedvoltagedependsstrongFig.6:InducedvoltageversuswidthWoftheloopforlyonthelooplengthbutonlyslightlyontheloopwidtwoexemplarylooplengthsof1.2mand2mthandoncableparameterssuchastwistlengthorconThisresultcanbeexplainedbythefactthatthemostductorcross-dominantpartofthevoltageisinducedbythosemagnsection.Henceamutualinductanceperunitlengthceticfieldsintheveryclosevicinityofthephasecoanbederivedtoexpresstheinducedvoltage.Itisinnductors.Themagneticfluxdensitywhichresultsftherangeofabout70–romallthephaseconductorsdecreasesrapidlyandn100nH/mandcanbeusedtoestimateinducedmonmodecorelevantcontributionsexistfordistancesofmorurrents.ethansomehelicalconductorradiibecausetheresuItshallbementionedthatthisphenomenontakesplaltantmagneticfluxdensitydecreasesnearlyexponceforcableswithtwistedPEconductorsonly.Itdoeentiallywithincreasingdistancefromthecable[9snotexistinthecaseofcableswithconcentricPEco].HenceforpracticalestimationstheinfluenceofnductorswhichthereforeshouldpreferablybeusedtheloopwidthWcanbeneglected.whenlowmagneticstrayfieldsarerequired.FurthermorethesituationwasinvestigatedwhenfiReferencesveconductors(5x25mm2)areusedinsteadoffour.Th1.IEC60364-4-isvariationreflectstheusageoffive-44:Electricalinstallationsofbuildings–conductorcablesusedinTN-Part4-44:Protectionforsafety–SnetworkswheretheNandPEconductorseparationisProtectionagainstvoltagedisturbancesandelectestablished.Simulationresultsaredescribedin[romagneticdisturbances,2001-088]andamutualinductanceMNET=95nHpermeterlength2.HeinholdL.,PowerCablesandtheirApplicacanbederivedfromthose.Thishighervalueandhenction,SiemensAktiengesellschaft,BerlinandMuniehighervaluesforinducedvoltagesUPEcanbeexplaich,1990nedqualitativelybythehigherasymmetryofthePEc3.Petterson,P.andSchonborg,N.,Predictingthemagneticfieldfromtwistedthree-,Paper87M2phasearrangement,IEEE1997InternationalSympos7.MesserR.,InvestigationoflowfrequencymiumonElectromagneticCompatibility,Austin,TX,agneticstrayfieldsofpowercablesandtheircouplUSA,1997,pp.513-17ingtogroundingloops,Projectreport,University4.TescheF.M.,IanozM.V.andKarlssonT.,EMCofYork,UK,1994AnalysisMethodsandComputationalModels,JohnWi8.Jaekel,B.,Investigationsoninducedmonmley&Sons,Inc.,NewYork,1997odevoltagesinpowercables,17thInternationalWro5.Hagel,R.,Gong.L.andUnbehauen,R.,OntheclawSymposiumandExhibitiononElectromagneticCMagneticFieldofanInfinitelyLongHelicalLineCuompatibility,Wroclaw,Poland,2004,pp.182-187rrent,IEEETransactionsonMagnetics,Vol.30,No.9.HaberF.,TheMagneticFieldintheVicinity1,pp.80-84,Jan1994ofParallelandTwistedThree-6.MaderT.andBrünsH.-WireCableCarryingBalancedThree-D.,EFIEAnalysisofArbitraryMetallicStructuresPhasedCurrent,IEEETransactionsonEMC,Vol.EMC-intheAreaofEMC,9thInt.ZurichSymposiumandTech16,No.2,1974,pp.76-82.nicalExhibitiononEMC,Zurich,Switzerland,1991EFFECTIVENESSOFPERIODICALFREQUENCYSHIFTFORRADIOFREQUENCYEMISSIONSUPPRESSIONINDC/DCCONVERTERALEXANDERWORSHEVSKY,PETRWORSHEVSKY,RUSSIASaint-PetersburgMarineTechnicalUniversity,e-mail:a.a.worshevsky@Abstract.ADC/DCconverteristhesourceofradiofrequencynoise.Emissionreductionbyswitchingfrequencyshiftsisproposed.Frequencyshiftsupto30%cangivemorethan20dBnoisereductionintheory.Frequencyshifts40-70%arelesseffectiveduetohigherharmonicsposition.Experimentsshow10dBnoisereductionfor20%frequencyshifts.1.IntroductionDC/DCswitchconverter(fig.1)consumespulsecurrSemiconductorconvertersgeneratepulsevoltagesenti(t)fromDCsource.Itleadstovoltagechangeininelectricalmainsduetoswitchingprocess.Thespelectricalmains:ectrumofpulseperturbationsspreadsuptoradiofru=E-Ldi/dt,equencies.Electromagneticpatibility(EMC)normwhereLisaninductanceofvoltagesource.shavetoreduceconductedandradiatednoise.TheusPulsevoltageamplitudesU1,U2areproportionaltoteofstaticconvertersisinconstantprogress;theyhederivativeofi(t).Pulsedurationst1andt2areeqadaptthemainpowertothereapplications,asswitcualtocurrentrisetimeanddecaytime(fig.2).Perihedmodepowersuppliesandmotorcontrol.EmissionodofrepetitionisequalT=1/f,wherefistheswitchrequirementsobligeconstructorstoimplementsolfrequency.Polarityofpulsesaredifferentduetodutionsfornoisesuppression.ifferentpolarityofthederivative.2.SpectrumanalysisofpulsenoiseFig.1.EquivalentcircuitforcalculationofpulsenoisegeneratedbyDC/DCconverter.Noisereduction(suppression)coefficientcalculThespectrumofonepolaritypulsesisshowninfig.3atedfordifferentfrequencyshiftsandharmonicsa.Harmonicshavekffrequency,wherek=1,2,3...Harreshowninfig.6,7.Measuringbandis9kHz.Switchfmonicsvaluecanbecalculatedwiththefollowingforequencyf=100kHz.rmular:Fig.6.Noisereductioncoefficientforharmonicsw.ithN=1,2,3,4,5,6,7viafrequencyshiftsdf/f.TheminimumharmonicsamplitudeinthespectrumcorFig.7.Noisereductioncoefficientforfrequencysrespondto2n/t1frequencies,wheren=1,2,3...hiftsdf/f=10,20,30,40,50%viaharmonicsnumber.Thesequenceofdifferentpolarityvoltagepulses(Noisereductioncoefficientvalueforlowharmonfig.2)givesthepositionoftwospectrums.icsbeeshigherwhenthefrequencyshiftsrise.BuFig.2.Currentandvoltageinthecircuit.tthecoefficientforhighharmonicsisalmosttheTheresultofthepositioncanbecalculatedas:sameduetoshiftedharmonicsposition.Frequencwhereyshifts40-;;;.70%arelesseffectiveduetoaddingofshiftedharFig.3.Spectrumofonepolaritypulsesgeneratedwimonicswithnumbermorethan5.Frequencyshiftsuthfrequencyf.pto30%cangivemorethan20dBnoisereductionintThespectrumcalculatedfort1=1s,t2=0.3s,t3=3heory.Itcanberemendedtousebinationofduratis,T=10sisshowninfig.4.Theswitchfrequencyisonandfrequencyshiftsatthesametime.f=100kHz,butitcanbedifferent.RandomshiftsarebetterthandeterminedchangesofFig.4.Spectrumofdifferentpolaritypulsesgenerpulsesequenceparameters[2].Thelastsequenceofatedwithfrequencyf.pulsesinfig.5isbetterthanthemiddle.TheeffectEmissionmeasurementsareperformedwithradiofreoffrequencymodulationishigherforhigherswitchquencyanalyzerormeasuringreceiver.Frequencybfrequency.andis9kHzfor150kHz-4.Measurementofnoisereduction30MHzfrequencies.ItmeansthateverymomentonlyoSomeresultsofexperimentswithfrequencyshiftsaneharmonicisinmeasuringwindow.reshowninfig.9,10.Pulsecurrentsequenceisgene3.EMIreductionratedwiththehelpofputercontrolledsignalgenerTosatisfyEMCrequirementsforconductedperturbaator.Itwasused50dBattenuatorinmeasuringsystetionsinDC/DCconvertersandtoreducenoisesineacm.Thereallevelofnoiseis50dBhigherthanshowninhfrequencyitispossibletousepulsewidthmodulatfigures.ThenoisespectrumforordinaryDC/DCconvioninaperiodicmode[1].Switchfrequencyshifts(erterisshowninfig.9a,10a.20%frequencymodulatfig.5)leadstofrequencyshiftsofeveryharmonic.iondecreasethenoiselevelsatmainharmonicfrequHarmonicsareinfrequencybandonlypartofmeasuriencies(fig.9b,10b).Thelevelsofharmonicsbeeslngtime.Theaveragelevelofvoltagenoisebeesloweower,butthebandofeveryharmonicbeeswider.Therr.eisbinationofneighboringharmonicsathighfrequFig.5.Pulsesequencesfordifferentswitchfrequeencies.Itwasmeasured10dBnoisereductionofmaxincymodulationmumlevelharmonics.a)rethan20dBnoisereduction.Frequencyshifts40-b)70%arelesseffectiveduetohigherharmonicspositFig.9.SpectrumofDC/DCconverternoisea)withoution.Experimentsshow10dBnoisereductionfor20%ffrequencyshifts,b)with20%frequencyshifts.requencyshifts.ExperimentsgivesadditionalinformationaboutefReferencesfectivenessofthistypeofnoisereduction.Randomizedsequencesoffrequencyshiftsgivebetterresultsthansimplefrequencyvariations.a)b)Fig.10.SpectrumofDC/DCconverternoisea)withoutfrequencyshifts,b)with20%frequencyshifts.5.ConclusionEmissionrequirementsobligeconstructorstoimplementsolutionsfornoisesuppressioninDC/DCconverters.30%switchfrequencymodulationcangivemoANAPPROACHTOINDUCTANCEMODELLINGFORPOWERPCBINTERCONNECTIONS:FDTDMODEL-BASEDEXTRACTIONG.KLARICFELICANDR.EVANS,AUSTRALIATheUniversityofMelbourne,DepartmentofElectricalandElectronicEngineeringe-mail:Abstract.Thesignificanceofparasiticimpedancesoftheconnectingstructuresinpowerelectronicconverters(PCBinterconnects)increaseswithfrequencyandswitchingspeedandinfluencestransientsandradiatedEMI.Designaspectssuchasphysicallayoutandinterconnectroutingrequiresaccurateextractionofparasiticparameters.Thispaperpresentsaputationalprocedureforpartlyachievingthisfortypicalpowerconvertersystems.IntroductionlparametersthatcanbeputedusingnumericaltechnTheinterconnectioninductancemodelofaPCBmountiques.Typically,numericaltechniquessuchastheedchoppercontainsamutationloopandponentleadiFiniteElementMethod(FEM)andPartialElementEqunductances.ToextracttheinductanceofthemutatiivalentCircuit(PEEC)areusedtogenerateapatibloncurrentloop,analyticalandnumericalapproachenetlistforacircuitsimulatorsuchasPSPICEorSaescanbeapplied[1],[2],[3].Analyticalapproachberin[1]and[8].esprovideclosed-ElectromagneticmodellingofVLSIcircuitsisbaseforminductanceexpressionsthatarebasedonthepadonnumericaltechniques[6],[7]sinceanalyticalrtialinductanceconcept[4]oronmagneticenergyrformulaecannotprovideaccurateresultsforsuchpelationsgivenbyNeumann'sformula[5].Closed-lexstructures.BasicparametersforpowerelectroformexpressionsforparasiticextractioncanbeusnicstructuressuchasPCBinterconnectionswithsiedtoobtainalumpedmodelofconnectingstructuresmplelargeconductorsandrightanglebendsinconduthatconsistsofresistive,inductiveandcapacitictorscanbeobtainedfromanalyticalclosed-veponents[8].Theiradvantageisintheirdirectreformexpressions.However,thetrendtowardsincrelationtothephysicaldimensionsoftheconnectingasingswitchingfrequencyandminiaturizedandplestructurehencetheyeasilyrelatetodesign.HowevxPCBstructuresproducesEMCproblemsthatcannotbertheyareonlyapplicabletosimplestructureswiteeasilyaccountedforinclosed-huniformcurrentdistributionandsmalldimensionformexpressions.Thechallengesfacingsuchsysteswithrespecttotheoperatingwavelengths.msaresimilartotheissuesinVLSIparasiticanalysTheuseofnumericalmodellingapproachinpowereleisandtheyrequiretheapplicationofnumericalmetctronicsismainlygovernedbytheneedtopredictthhodssuchasthefiniteelementorfinitedifferenceeEMIemissionlevelofacircuit.EMIpredictionisbmethods.asedonequivalentcircuitsconsistingofthehighfThispaperpresentsaprocedureforloopinductancerequencyparametersofpowerponents,theelementvestimationbasedonFDTDputation[9]andleastsquaaluesoflineimpedancestabilisationnetworks(LIrescircuitmodelling.TheFDTDmodelisbasedontheSN)usedinstandardEMImeasurementsandstructuraspecificfeaturesofpowerelectronicsinterconnectionsi.e.relativelylargepowerPCBconductorsa1.2GHz(Figure4and5)andthenextractedfromthepundsimplegeometrieswithrightangles.Theinductatedinputimpedance(theFDTDputeddataset).nceofrectangularshapedloopsmountedonapowerPCTheFDTDputeddataset(realandimaginarypartsofiBisextractedfromtheFDTDimpedanceputationsusinputimpedance)whichcapturesfrequencydependenngfrequencydomainidentificationandcircuitsyntperformanceofaPCBinterconnectionisapproximathesismethods.Typicalanalyticalapproachesandtedusinganonlinearleastsquares(NLS)estimateformulaethatcalculateinductanceisusedtoestim(1)atetheinductancesofPCBloopsandvalidatetheFDTandtheGauss-NewtonandLevenberg-Dsimulatedmodels.Marquardtmethods[12]whereri(x)denotestheithpInductanceModellingusingFDTDMethodonentfunctionoftheresidualR(x)thatisnonlineaInordertomodelandestimatetheinductanceusingFrinthedesignvariablex,FdenotesthemodelfunctiDTD,thetracesofthepowerPCBundergoingrapidcuron(data‘fit’function)andyistheputeddatasetrenttransitionsareconstructedintheformofaloo.pandexcitedbyavoltageorcurrentsourcethenthee(2)lectricandmagneticfieldsandtransientvoltagesForthegivenexample(Figure2)thevectorvaluedfuandcurrentsareputed.TheFDTDmodelofaPCBloopstnctionFrepresentsaseriesconnectionofparallelructurewithdistributedparametersisconsideredLCelementswithafiniteresistanceR(Figure3).asalinearone-Figure3RLCnetworkportnetwork(Figure1),whichcanberepresentedwiTximationoftheinputimpedancedatathatreflecFigure1One-portnetwork.tresonantbehaviourofPCBloops,i.e.approximatiTheFDTDapproachisappliedtoaPCBloop(Figure2)wonatfrequenciesaroundresonancefrequency.ithasquareshapedPEC(perfectelectricconductorToapproximatetheputedinputimpedancedataobtai)structuremountedonthedielectricstructureintnedforthePCBloopshowninFigure2asecondorderRLhree-Cnetworkisused.TheabsolutevalueandthephaseofdimensionalFDTDputationalspace.Thetotalsizeotheapproximateddata(RLC-ftheFDTDspaceis50×50×40cells.Thecellsizeis(2fit)andFDTDputeddataareshowninFigures4and5.mm×2mm×2mm)soviatheCourantconditionthetimestFigure4MagnitudeofinputimpedanceFDTDputeddatepsizeis3.8ps[9].ThestructureisexcitedbyaGaua(dots)andapproximateddata(line).ssiancurrentpulseattheportwithapulsewidthof3Figure5Phaseofinputimpedance,FDTDputeddata(d00timesstepsmeasuredbetweenthehalfamplitudepots)andapproximateddata(line)oints.ThisprovidesaccurateresultsforfrequencAsshownintheabovefigurestheRLCfitgivesaverygiesupto2GHz.oodcorrelationinmagnitudeandphaseatresonanceFigure2StudiedPCBloop.frequency.However,thediscrepancybetweentheRLFrequencyDomainIdentificationCfitandtheFDTDdataincreasesatthefrequencieswTheimpedanceisputedfromthevoltage-to-ellbelowtheresonancefrequency,astheFDTDdoesncurrentratiooverthefrequencyrangefrom10MHztootputethedataatDCandfrequencybelow10MHz.ThesizeofFDTDcellsandmonconstraintof10cellsperwaxaminehowthestrayinductanceofplexloopsinfluevelengthdeterminesthatthesideofeachcellshoulncesEMIweapplyFDTDmodellingtoacoplanarstripldbe(1/(10))orlessatthehighestfrequency(shortayoutofthediode-estwavelength)ofinterest.transistormutationcircuits.TheFDTDmodeloftheThecalculatedloopinductancesforthesquareloopdiode-withthesidesfrom10mmto50mmand2mmthicktracesbtransistormutationloopofFigure7appliesfortheasedontheanalyticalformulaeandFDTDextractediturn-nductancesareplottedinFigure6.Themeasuredindoffintervalwherethecurrentinpowerdevice(MOSFuctancesforthesquareloopswiththesides27mm,35ET)isdecreasingandgeneratesatransientvoltagemm,40mmand45mmarealsoplottedinFigure6.acrosstheinductanceofthePCBtraces.ThemodelcoFigure6Comparisonofanalyticalcalculations(funsistsofthePCBtraces,adielectricboardandtheelllines),FDTDextracted(boxpointmarker)andmeaxcitationport.Liaoabsorbingboundaryconditionsuredinductances(diamondpointmarker).s[9]areusedsothatwithsufficientspacingtotheoTheinductanceismeasuredusingHewlett-uterboundarytheputationalspaceconsistsof110×Packard8753Cvectornetworkanalyserconfigureda80×40cellsof2mmx1mmx1mmsize.s300kHzto1GHzmeasurementrangeand300HzbandwidTheimpedanceisputedfromthevoltage-to-th.Thereisagoodagreementbetweenthecalculatedcurrentratiooverthefrequencyrange10MHz-,measuredandFDTDextractedinductancesforarang1.2GHzandapproximatedwithanimpedancefunctioneofsquareloopgeometries.However,thecableconnofanequivalentcircuit(network)consistingofthectorsintheexperimentalset-reeparallelRLCcircuits(Figure3).uphaveimpactonthemeasuredvaluesthatresultinincreasedinductance.SincetheanalyticalinductaFigure7FDTDmodelofdiode-nceexpressionsarebasedontheassumptionthatthetransistormutationloop.electricalsizesofthePCBtracesaremuchsmallerthanthesignalwavelengthsthediscrepancybetweenurttheresultsincreaseswiththesizeoftheloops.ThereforewhenthedimensionsofPCBsareshortparedtothesignalwavelengths(lowfrequency)analyticalexpressionscanbeused.AthighfrequencythePCBdimensionsareparabletothewavelengthsandthepropagationeffectsmustbetakenintoaccountrequirinFigure8FDTDputedandapproximatedmagnitudeofthgnumericalapproach.einputimpedance,FDTDputeddata(dots),approximModellingofComplexStructuresateddata(line)andLLSapproximation(+).Thegeometricmodelsofpracticaldiode-Figure9showsthephaseoftheputedandapproximatetransistormutationcircuitsandgatecontrolcircdinputimpedance.uitsaretypicallymoreplexthanthesquareorrectaClearly,LLSapproximationprovidesabetterfittongularshapedmodelsconsideredsofar.InordertoetheFDTDputeddata.However,theequivalentcircuitresultsinnon-physical,negativeparametervalues.Theparametersofthemodelfunctionappr