平板变压器设计详解

Ferroxcube1ContentsIntroduction3Designprocedure4Designexamples-flyback8-forward10Formulas13Layerdesign14DesignofPlanarPowerTransformersFerroxcube2ExplodedviewofaplanartransformerFerroxcube3Planartransformerscanbeconstructedasstandalonecomponents,withastackedlayerdesignorasmallmultilayerPCB,orintegratedintoamultilayerboardofthepowersupply.Importantadvantagesofplanarmagneticsare:-verylowprofile-excellentthermalcharacteristics.-lowleakageinductance-excellentrepeatabilityofpropertiesMeasurementsonplanarEcoretransformersunderoperatingconditionswithwindingsinmultilayerPCBsshowthatthethermalresistanceissubstantiallylower(upto50%)comparedtoconventionalwirewoundtransformerswiththesameeffectivecorevolumeVe.Thisiscausedbytheimprovedsurfacetovolumeratio.Theresultofthisbettercoolingcapabilityisthatplanartransformerscanhandlehigherthroughputpowerdensities,whilethetemperatureriseisstillwithinacceptablelimits.Thisbrochurepresentsafastandeasymethodtomakedesignsforplanarpowertransformers.Exampleswhichhavebeendesignedwiththisfastprocedurewillbediscussed.Testsunderoperatingconditionsshowthatthemeasuredresultsareingoodagreementwiththepredictedtemperaturerise.Introductionlayer1layer2layer3layer41/2planarECore1/2planarEcoremultilayerPCBstandalonetransformerintegratedintoPCBPlanarprinciplesFerroxcube41.CalculationofmaximumfluxdensityThecoreandcopperlossesinatransformerunderoperatingconditionswillinduceatemperaturerise.Thisrisemuststaybelowamaximumallowablevaluetoavoiddamagetothetransformerortherestofthecircuitry.Inthermalequilibriumthetotallossesinthetransformer,Ptrafo,canberelatedtoatemperaturerise∆TofthetransformerwithananalogonofOhm’slawby:Ptrafo=∆TRth[1]InthisformulaRthrepresentsthethermalresistanceofthetransformer.Ptrafocaninfactbeinterpretedasthecoolingcapabilityofthetransformer.Previouswork(1),showedthatitispossibletoestablishanempiricalformulawhichrelatesthevalueofthermalresistanceofatransformerdirectlytothevalueoftheeffectivemagneticvolumeVeoftheferritecoreused.ThisempiricalformulaisvalidforwirewoundtransformerswithcoreshapeslikeRMandETD.AsimilarrelationhasnowbeenfoundforplanarEtransformers.Thisrelationcanbeusedtoestimatethetemperatureriseofthetransformerasafunctionoffluxdensityinthecore.Becauseofthelimitedavailablewindingspaceitisrecommendedtousethemaximumallowedfluxdensitiesinplanarmagnetics.Withtheassumptionthathalfofthetotaltransformerlossiscoreloss,itispossibletoexpressthemaximumcorelossdensityPcoreasafunctionoftheallowedtemperaturerise∆Tofthetransformeras:Pcore=12.∆TVe(cm3)[2][mW/cm3]Powerlossesinourferriteshavebeenmeasuredasafunctionoffrequency(finHz),peakfluxdensity(BinT)andtemperature(Tin°C).Corelossdensitycanbeapproximated(2)bythefollowingformula:Pcore=Cm.fx.By.(ct0-ct1T+ct2T2)=Cm.CT.fx.By[3][mW/cm3]peakpeakInthisformulaCm,x,y,ct0,ct1andct2areparameterswhichhavebeenfoundbycurvefittingofthemeasuredpowerlossdata.Theseparametersarespecificforaferritematerial.Theyaredimensionedinsuchawaythatat100°CthevalueofCTisequalto1.Intable1fitparametersarelistedforseveralFerroxcubepowerferrites.MaximumallowedPcoreiscalculatedwithequation[2].Thisvalueisinsertedinequation[3].MaximumallowedfluxdensityBpeakcannowbecalculatedbyrewritingequation[3]:Bpeak=[4]PcoreCm.CT.fx1/y[T]Designprocedureferritef(kHz)Cmxyct2ct1ct03C3020-1007.13.10-31.423.023.65.10-46.65.10-24100-2007.13.10-31.423.024.10-46.8.10-23.83C9020-2003.2.10-31.462.751.65.10-43.1.10-22.453C9420-2002.37.10-31.462.751.65.10-43.1.10-22.45200-4002.10-92.62.751.65.10-43.1.10-22.453F3100-3000.25.10-31.632.450.79.10-41.05.10-21.26300-5002.10-51.82.50.77.10-41.05.10-21.28500-10003.6.10-92.42.250.67.10-40.81.10-21.143F4500-100012.10-41.752.90.95.10-41.1.10-21.151000-30001.1.10-112.82.40.34.10-40.01.10-20.67Table1:FitparameterstocalculatethepowerlossdensityB2.BpeakBpeakintheformulasishalfthepeaktopeakfluxexcursioninthecore.Ferroxcube5Note:ThemaximumallowedvalueforBcanalsobefoundinanotherway.Formula[3]togetherwiththefitparameterscanbeinsertedintoacomputerprogramwhichmakesitpossibletocalculatethepowerlossesforarbitrarywaveforms(3).AdvantageisthattherealwaveshapeofBcanbesimulatedtocalculatethelossesandthatitispossibletoselecttheoptimumferritefortheconcernedapplication.2.RecommendationsfordistributionoftheturnsinthewindingspaceOncethevalueforthemaximumpeakfluxdensityisdetermined,establishedformulasapplicabletotheconvertertopologyandtransformertype(e.g.flybackorforward)canbeusedtocalculatethenumberofprimaryandsecondaryturns.Adecisionhastobemadehowthewindingswillbedividedovertheavailablelayers.CurrentsinthetrackswillinduceatemperatureriseofthePCB.Itisrecommendedtodistributethewindingturnsintheouterlayerssymmetricallywithrespecttotheturnsintheinnerlayersforreasonsofthermalexpansion.Fromamagneticpointofviewtheoptimumwouldbetosandwichtheprimaryandsecondarylayers.Thiswillreducethesocalledproximityeffect(seepage6).HowevertheavailablewindingheightinthePCBsandtherequirednumberofturnsfortheapplicationwillnotalwaysallowanoptimumdesign.Forcostpricereasonsitisrecommendedtochooseastandardthicknessofth