Basic Calculation of a Boost Converter ... - Texas Instruments

1 VINVOUTIINIOUTCINCOUTLDSWA pplicationReportSLVA372C November2009 RevisedJanuary2014 BasicCalculationof a BoostConverter's PowerDC/DCApplicationABSTRACTThis applicationnotegivesthe equationsto calculatethe powerstageof a boostconverterbuilt with an ICwith integratedswitchand operatingin is not intendedto give detailsonthe functionalityof a boostconverter(seeReference1) or howto compensatea the end of this documentif moredetailis the equationswithoutdescription,See a BoostConverterFigure1 showsthe basicconfigurationof a boostconverterwherethe switchis integratedin the diodereplacedby a secondswitchintegratedinto the is the case,all equationsin this documentapplybesidesthe powerdissipationequationof the the PowerStageThe followingfour parametersare neededto calculatethe powerstage:1.

2 InputVoltageRange:VIN(min)and VIN(max)2. NominalOutputVoltage:VOUT3. MaximumOutputCurrent:IOUT(max)4. IntegratedCircuitusedto buildthe is necessary,becausesomeparametersforthe calculationshaveto be takenout of the theseparametersare knownthe calculationof the powerstagecan take November2009 RevisedJanuary2014 BasicCalculationof a BoostConverter's PowerStageSubmitDocumentationFeedbackCop yright 2009 2014,TexasInstrumentsIncorporatedOUT(max )LSW(max)I!II=+21 D-LMAXOUTLIM(min)!II= I(1 D)2 - - IN(m in)LSVD!I =fL IN(min)OUTV D = 1V -Calculatethe MaximumSwitchCurrentThe first step to calculatethe switchcurrentis to determinethe duty cycle,D, for the minimuminputvoltageis usedbecausethis leadsto the maximumswitchcurrent.

3 (1)VIN(min)= minimuminputvoltageVOUT= desiredoutputvoltage = efficiencyof the Converter , estimated80%The efficiencyis addedto the duty cyclecalculation,becausethe converterhas to deliveralso the calculationgivesa morerealisticduty cyclethanjust the equationwithoutthe estimatedfactor, 80%(whichis not unrealisticfor a boostconverterworstcaseefficiency),can be usedor see theTypicalCharacteristicssectionof the selectedconverter'sdatasheet( Reference3 and 4).The next step to calculatethe maximumswitchcurrentis to determinethe theconvertersdatasheetnormallya specificinductoror a rangeof inductorsis namedto use with the IC.

4 Soeitheruse the recommendedinductorvalueto calculatethe ripplecurrent,an inductorvaluein the middleof the recommendedrangeor, if noneis givenin the datasheet,the one calculatedin theInductorSelectionsectionof this applicationnote.(2)VIN(min)= minimuminputvoltageD = duty cyclecalculatedin Equation1fS= minimumswitchingfrequencyof the converterL = selectedinductorvalueNowit has to be determinedif the selectedIC can deliverthe maximumoutputcurrent.(3)ILIM(min)= minimumvalueof the currentlimit of the integratedswitch(givenin the datasheet)

5 IL= inductorripplecurrentcalculatedin Equation2D = duty cyclecalculatedin Equation1If the calculatedvaluefor the maximumoutputcurrentof the selectedIC, IMAXOUT, is belowthe systemsrequiredmaximumoutputcurrent,anot herIC with a higherswitchcurrentlimit has to be the calculatevaluefor IMAXOUTis just a little smallerthanthe neededone,it is possibleto use theselectedIC with an inductorwith higherinductanceif it is still in the higherinductancereducesthe ripplecurrentand thereforeincreasesthe maximumoutputcurrentwith the calculatedvalueis abovethe maximumoutputcurrentof the application,the maximumswitchcurrentin the systemis calculated.

6 (4) IL= inductorripplecurrentcalculatedin Equation2 IOUT(max)= maximumoutputcurrentnecessaryin the applicationD = duty cyclecalculatedin Equation1 This is the peakcurrent,the inductor,the integratedswitch(es)and the externaldiodehas to a BoostConverter's PowerStageSLVA372C November2009 RevisedJanuary2014 SubmitDocumentationFeedbackCopyright 2009 2014,TexasInstrumentsIncorporatedDFFP = IV FO UT (m ax)I = IOUTLOUT(max)INV!I = ( to )IV ()INOUTINLSOUTV VVL =!IfV- a rangeof this is the case,it is recommendedtochoosean inductorfromthis higherthe inductorvalue,the higheris the maximumoutputcurrentbecauseof the lowerthe inductorvalue,the smalleris the the inductormustalwayshaveahighercurrentrati ngthanthe maximumcurrentgivenin Equation4 becausethe partswhereno inductorrangeis given,the followingequationis a goodestimationfor the rightinductor.

7 (5)VIN= typicalinputvoltageVOUT= desiredoutputvoltagefS= minimumswitchingfrequencyof the Converter IL= estimatedinductorripplecurrent,see belowThe inductorripplecurrentcannotbe calculatedwith Equation1 becausethe inductoris not the inductorripplecurrentis 20%to 40%of the outputcurrent.(6) IL= estimatedinductorripplecurrentIOUT(max)= maximumoutputcurrentnecessaryin the application4 RectifierDiodeSelectionTo reducelosses,Schottkydiodesshouldbe forwardcurrentratingneededis equalto themaximumoutputcurrent:(7)IF= averageforwardcurrentof the rectifierdiodeIOUT(max)= maximumoutputcurrentnecessaryin the applicationSchottkydiodeshavea higherpeakcurrentin the systemis not a otherparameterthat has to be checkedis the powerdissipationof the has to handle.

8 (8)IF= averageforwardcurrentof the rectifierdiodeVF= forwardvoltageof the rectifierdiode3 SLVA372C November2009 RevisedJanuary2014 BasicCalculationof a BoostConverter's PowerStageSubmitDocumentationFeedbackCop yright 2009 2014,TexasInstrumentsIncorporatedOUT12 FBVR = R1V - FB2R1/2VR =IR1/2 FBI100 I R1R2IR1 convertersset the outputvoltagewith a resistivedividernetwork(whichis integratedif they arefixedoutputvoltageconverters).Withthe givenfeedbackvoltage,VFB, and feedbackbias current,IFB, the voltagedividercan be ResistiveDividerfor Settingthe OutputVoltageThe currentthroughthe resistivedividershallbe at least100 timesas big as the feedbackbias current.

9 (9)IR1/2= currentthroughthe resistivedividerto GNDIFB= feedbackbias currentfromdatasheetThis addsless than1% inaccuracyto the currentcan also be a lot disadvantageof smallerresistorvaluesis a higherpowerloss in the resistivedivider,but theaccuracywill be a little aboveassumption,the resistorsare calculatedas follows:(10)(11)R1,R2= resistivedivider,see feedbackvoltagefromthe datasheetIR1/2= currentthroughthe resistivedividerto GND,calculatedin Equation9 VOUT= desiredoutputvoltage6 InputCapacitorSelectionThe minimumvaluefor the inputcapacitoris normallygivenin the minimumvalueisnecessaryto stabilizethe inputvoltagedue to the peakcurrentrequirementof a best practiceis to use low equivalentseriesresistance(ESR)

10 Dielectricmaterialshouldbe X5 Ror ,the capacitorcanelose muchof its capacitancedue to DCbias or temperature(seereferences7 and 8).The valuecan be increasedif the inputvoltageis a BoostConverter's PowerStageSLVA372C November2009 RevisedJanuary2014 SubmitDocumentationFeedbackCopyright 2009 2014,TexasInstrumentsIncorporatedOUT(max )LOUT(ESR)I!I!V= ESR+1 D2 - OUT(max)OUT(min)SOUTIDC=f!V to use low ESRcapacitorsto minimizethe rippleon the a goodchoiceif the dielectricmaterialis X5 Ror better(seereference7 and 8).