Nominal Output Voltage: VOUT. 3. Maximum Output Current: IOUT(max). 4. Integrated Circuit used to build the boost converter. This is necessary, because some
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ApplicationReportSLVA372CŒNovember2009ŒRevisedJanuary2014BasicCalculationofaBoostConverter’sPowerStageBrigitteHauke..LowPowerDC/DCApplicationABSTRACTThisapplicationnotegivestheequationstocalculatethepowerstageofaboostconverterbuiltwithanICwithintegratedswitchandoperatingincontinuousconductionmode.Itisnotintendedtogivedetailsonthefunctionalityofaboostconverter(seeReference1)orhowtocompensateaconverter.Seethereferencesattheendofthisdocumentifmoredetailisneeded.Fortheequationswithoutdescription,Seesection8.1BasicConfigurationofaBoostConverterFigure1showsthebasicconfigurationofaboostconverterwheretheswitchisintegratedintheusedIC.Oftenlowerpowerconvertershavethediodereplacedbyasecondswitchintegratedintotheconverter.Ifthisisthecase,allequationsinthisdocumentapplybesidesthepowerdissipationequationofthediode.Figure1.BoostConverterPowerStage1.1NecessaryParametersofthePowerStageThefollowingfourparametersareneededtocalculatethepowerstage:1.InputVoltageRange:VIN(min)andVIN(max)2.NominalOutputVoltage:VOUT3.MaximumOutputCurrent:IOUT(max)4.IntegratedCircuitusedtobuildtheboostconverter.Thisisnecessary,becausesomeparametersforthecalculationshavetobetakenoutofthedatasheet.Iftheseparametersareknownthecalculationofthepowerstagecantakeplace.1SLVA372CŒNovember2009ŒRevisedJanuary2014BasicCalculationofaBoostConverter’sPowerStageSubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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CalculatetheMaximumSwitchCurrentwww.ti.com2CalculatetheMaximumSwitchCurrentThefirststeptocalculatetheswitchcurrentistodeterminethedutycycle,D,fortheminimuminputvoltage.Theminimuminputvoltageisusedbecausethisleadstothemaximumswitchcurrent.(1)VIN(min)=minimuminputvoltageVOUT=desiredoutputvoltage=efficiencyoftheconverter,e.g.estimated80%Theefficiencyisaddedtothedutycyclecalculation,becausetheconverterhastodeliveralsotheenergydissipated.Thiscalculationgivesamorerealisticdutycyclethanjusttheequationwithouttheefficiencyfactor.Eitheranestimatedfactor,e.g.80%(whichisnotunrealisticforaboostconverterworstcaseefficiency),canbeusedorseetheTypicalCharacteristicssectionoftheselectedconverter’sdatasheet(Reference3and4).Thenextsteptocalculatethemaximumswitchcurrentistodeterminetheinductorripplecurrent.IntheconvertersdatasheetnormallyaspecificinductororarangeofinductorsisnamedtousewiththeIC.Soeitherusetherecommendedinductorvaluetocalculatetheripplecurrent,aninductorvalueinthemiddleoftherecommendedrangeor,ifnoneisgiveninthedatasheet,theonecalculatedintheInductorSelectionsectionofthisapplicationnote.(2)VIN(min)=minimuminputvoltageD=dutycyclecalculatedinEquation1fS=minimumswitchingfrequencyoftheconverterL=selectedinductorvalueNowithastobedeterminediftheselectedICcandeliverthemaximumoutputcurrent.(3)ILIM(min)=minimumvalueofthecurrentlimitoftheintegratedswitch(giveninthedatasheet)IL=inductorripplecurrentcalculatedinEquation2D=dutycyclecalculatedinEquation1IfthecalculatedvalueforthemaximumoutputcurrentoftheselectedIC,IMAXOUT,isbelowthesystemsrequiredmaximumoutputcurrent,anotherICwithahigherswitchcurrentlimithastobeused.OnlyifthecalculatevalueforIMAXOUTisjustalittlesmallerthantheneededone,itispossibletousetheselectedICwithaninductorwithhigherinductanceifitisstillintherecommendedrange.AhigherinductancereducestheripplecurrentandthereforeincreasesthemaximumoutputcurrentwiththeselectedIC.Ifthecalculatedvalueisabovethemaximumoutputcurrentoftheapplication,themaximumswitchcurrentinthesystemiscalculated:(4)IL=inductorripplecurrentcalculatedinEquation2IOUT(max)=maximumoutputcurrentnecessaryintheapplicationD=dutycyclecalculatedinEquation1Thisisthepeakcurrent,theinductor,theintegratedswitch(es)andtheexternaldiodehastowithstand.2BasicCalculationofaBoostConverter’sPowerStageSLVA372CŒNovember2009ŒRevisedJanuary2014SubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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www.ti.comInductorSelection3InductorSelectionOftendatasheetsgivearangeofrecommendedinductorvalues.Ifthisisthecase,itisrecommendedtochooseaninductorfromthisrange.Thehighertheinductorvalue,thehigheristhemaximumoutputcurrentbecauseofthereducedripplecurrent.Thelowertheinductorvalue,thesmalleristhesolutionsize.NotethattheinductormustalwayshaveahighercurrentratingthanthemaximumcurrentgiveninEquation4becausethecurrentincreaseswithdecreasinginductance.Forpartswherenoinductorrangeisgiven,thefollowingequationisagoodestimationfortherightinductor:(5)VIN=typicalinputvoltageVOUT=desiredoutputvoltagefS=minimumswitchingfrequencyoftheconverterIL=estimatedinductorripplecurrent,seebelowTheinductorripplecurrentcannotbecalculatedwithEquation1becausetheinductorisnotknown.Agoodestimationfortheinductorripplecurrentis20%to40%oftheoutputcurrent.(6)IL=estimatedinductorripplecurrentIOUT(max)=maximumoutputcurrentnecessaryintheapplication4RectifierDiodeSelectionToreducelosses,Schottkydiodesshouldbeused.Theforwardcurrentratingneededisequaltothemaximumoutputcurrent:(7)IF=averageforwardcurrentoftherectifierdiodeIOUT(max)=maximumoutputcurrentnecessaryintheapplicationSchottkydiodeshaveamuchhigherpeakcurrentratingthanaveragerating.Thereforethehigherpeakcurrentinthesystemisnotaproblem.Theotherparameterthathastobecheckedisthepowerdissipationofthediode.Ithastohandle:(8)IF=averageforwardcurrentoftherectifierdiodeVF=forwardvoltageoftherectifierdiode3SLVA372CŒNovember2009ŒRevisedJanuary2014BasicCalculationofaBoostConverter’sPowerStageSubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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OutputVoltageSettingwww.ti.com5OutputVoltageSettingAlmostallconverterssettheoutputvoltagewitharesistivedividernetwork(whichisintegratediftheyarefixedoutputvoltageconverters).Withthegivenfeedbackvoltage,VFB,andfeedbackbiascurrent,IFB,thevoltagedividercanbecalculated.Figure2.ResistiveDividerforSettingtheOutputVoltageThecurrentthroughtheresistivedividershallbeatleast100timesasbigasthefeedbackbiascurrent:(9)IR1/2=currentthroughtheresistivedividertoGNDIFB=feedbackbiascurrentfromdatasheetThisaddslessthan1%inaccuracytothevoltagemeasurement.Thecurrentcanalsobealothigher.Theonlydisadvantageofsmallerresistorvaluesisahigherpowerlossintheresistivedivider,buttheaccuracywillbealittleincreased.Withtheaboveassumption,theresistorsarecalculatedasfollows:(10)(11)R1,R2=resistivedivider,seeFigure2.VFB=feedbackvoltagefromthedatasheetIR1/2=currentthroughtheresistivedividertoGND,calculatedinEquation9VOUT=desiredoutputvoltage6InputCapacitorSelectionTheminimumvaluefortheinputcapacitorisnormallygiveninthedatasheet.Thisminimumvalueisnecessarytostabilizetheinputvoltageduetothepeakcurrentrequirementofaswitchingpowersupply.thebestpracticeistouselowequivalentseriesresistance(ESR)ceramiccapacitors.ThedielectricmaterialshouldbeX5Rorbetter.Otherwise,thecapacitorcanelosemuchofitscapacitanceduetoDCbiasortemperature(seereferences7and8).Thevaluecanbeincreasediftheinputvoltageisnoisy.4BasicCalculationofaBoostConverter’sPowerStageSLVA372CŒNovember2009ŒRevisedJanuary2014SubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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www.ti.comOutputCapacitorSelection7OutputCapacitorSelectionBestpracticeistouselowESRcapacitorstominimizetherippleontheoutputvoltage.CeramiccapacitorsareagoodchoiceifthedielectricmaterialisX5Rorbetter(seereference7and8).Iftheconverterhasexternalcompensation,anycapacitorvalueabovetherecommendedminimuminthedatasheetcanbeused,butthecompensationhastobeadjustedfortheusedoutputcapacitance.Withinternallycompensatedconverters,therecommendedinductorandcapacitorvaluesshouldbeusedortherecommendationsinthedatasheetforadjustingtheoutputcapacitorstotheapplicationshouldbefollowedfortheratioofL×C.Withexternalcompensation,thefollowingequationscanbeusedtoadjusttheoutputcapacitorvaluesforadesiredoutputvoltageripple:(12)COUT(min)=minimumoutputcapacitanceIOUT(max)=maximumoutputcurrentoftheapplicationD=dutycyclecalculatedwithEquation1fS=minimumswitchingfrequencyoftheconverterVOUT=desiredoutputvoltagerippleTheESRoftheoutputcapacitoraddssomemoreripple,givenwiththeequation:(13)VOUT(ESR)=additionaloutputvoltagerippleduetocapacitorsESRESR=equivalentseriesresistanceoftheusedoutputcapacitorIOUT(max)=maximumoutputcurrentoftheapplicationD=dutycyclecalculatedwithEquation1IL=inductorripplecurrentfromEquation2orEquation65SLVA372CŒNovember2009ŒRevisedJanuary2014BasicCalculationofaBoostConverter’sPowerStageSubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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EquationstoCalculatethePowerStageofaBoostConverterwww.ti.com8EquationstoCalculatethePowerStageofaBoostConverter(14)VIN(min)=minimuminputvoltageVOUT=desiredoutputvoltage=efficiencyoftheconverter,e.g.estimated85%(15)VIN(min)=minimuminputvoltageD=dutycyclecalculatedinEquation14fS=minimumswitchingfrequencyoftheconverterL=selectedinductorvalue(16)ILIM(min)=minimumvalueofthecurrentlimitoftheintegratedwitch(giveninthedatasheet)IL=inductorripplecurrentcalculatedinEquation15D=dutycyclecalculatedinEquation14(17)IL=inductorripplecurrentcalculatedinEquation15IOUT(max)=maximumoutputcurrentnecessaryintheapplicationD=dutycyclecalculatedinEquation14(18)VIN=typicalinputvoltageVOUT=desiredoutputvoltagefS=minimumswitchingfrequencyoftheconverterIL=estimatedinductorripplecurrent,seeEquation19(19)IL=estimatedinductorripplecurrentIOUT(max)=maximumoutputcurrentnecessaryintheapplication(20)IOUT(max)=maximumoutputcurrentnecessaryintheapplication(21)IF=averageforwardcurrentoftherectifierdiodeVF=forwardvoltageoftherectifierdiode(22)IFB=feedbackbiascurrentfromdatasheet(23)6BasicCalculationofaBoostConverter’sPowerStageSLVA372CŒNovember2009ŒRevisedJanuary2014SubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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Referenceswww.ti.com9References1.UnderstandingBoostPowerStagesinSwitchmodePowerSupplies(SLVA061)2.VoltageModeBoostConverterSmallSignalControlLoopAnalysisUsingtheTPS61030(SLVA274)3.DatasheetofTPS65148(SLVS904)4.DatasheetofTPS65130andTPS65131(SLVS493)5.RobertW.Erickson:FundamentalsofPowerElectronics,KluwerAcademicPublishers,19976.Mohan/Underland/Robbins:PowerElectronics,JohnWiley&SonsInc.,SecondEdition,19957.ImproveYourDesignswithLargeCapacitanceValueMulti-LayerCeramicChip(MLCC)CapacitorsbyGeorgeM.Harayda,AkiraOmi,andAxelYamamoto,Panasonic8.ComparisonofMultilayerCeramicandTantalumCapacitorsbyJeffreyCain,Ph.D.,AVXCorporationSpacerRevisionHistoryChangesfromBRevision(July2010)toCRevision..PageŁChangedVINtoVOUTinFigure2..4NOTE:Pagenumbersforpreviousrevisionsmaydifferfrompagenumbersinthecurrentversion.ChangesfromARevision(April2010)toBRevision.PageŁChangedIOUT(max)x(1ŒD)To:IOUT(max)xDinEquation12.5ŁChangedIOUT(max)x(1ŒD)To:IOUT(max)xDinEquation25.7NOTE:Pagenumbersforpreviousrevisionsmaydifferfrompagenumbersinthecurrentversion.ChangesfromOriginal(November2009)toARevisionPageŁAddedVOUT/VIN(Typical)toEquation63ŁaddedVOUT/VIN(Typical)toEquation19..6NOTE:Pagenumbersforpreviousrevisionsmaydifferfrompagenumbersinthecurrentversion.8RevisionHistorySLVA372CŒNovember2009ŒRevisedJanuary2014SubmitDocumentationFeedbackCopyright©2009Œ2014,TexasInstrumentsIncorporated
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