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

1 (max)VMaximum Duty Cycle: D =V OUTINVINVOUTIINIOUTCINCOUTLDSWA pplicationReportSLVA477B December2011 RevisedAugust2015 BasicCalculationof a BuckConverter's PowerDC/DCApplicationsABSTRACTT hisapplicationreportgivesthe formulasto calculatethe powerstageof a buckconverterbuiltwith anintegratedcircuithavinga integratedswitchandoperatingin is notintendedto givedetailson the functionalityof a buckconverteror howto compensatea ,see the referencesat the end of this containsthe a BuckConverterFigure1 showsthe basicconfigurationof a buckconverterwherethe switchis integratedin the selectedintegratedcircuit( IC). Someconvertershavethe diodereplacedby a secondswitchintegratedinto theconverter(synchronousconverters).If this is the case,all equationsin this documentapplybesidesthepowerdissipatione quationof 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 necessarybecausesomeparametersfor thecalculationsmustbe derivedfromthe theseparametersare known,the powerstagecan be MaximumSwitchCurrentThe first step to calculatethe switchcurrentis to determinethe duty cycle,D, for the maximuminputvoltageis usedbecausethis leadsto the maximumswitchcurrent.(1)VIN(max)= maximuminputvoltageVOUT= outputvoltage1 SLVA477B December2011 RevisedAugust2015 BasicCalculationof a BuckConverter's PowerStageSubmitDocumentationFeedbackCop yright 2011 2015,TexasInstrumentsIncorporated()O UTINOUTLSINV VVL =!IV- fLS W(max)O UT(max)!IA pplication specific m axim um switc h current: I=+ I2 LMAXOUTL IM(min)!IMaxim um output current of the selec ted IC: I= I2-()IN (m ax)OU TLSVVDI nductor ripple Current: !

3 I =L- = efficiencyof the Converter , ,estimated90%The efficiencyis addedto the duty cyclecalculation,becausethe converteralso has to deliverthe calculationgivesa morerealisticduty cyclethanjust the formulawithoutthe eitheran estimatedfactor, ,90%(whichis not unrealisticfor a buckconverterworst-caseefficiency),or see theTypicalCharacteristicssectionof the datasheetof the next step in calculatingthe maximumswitchcurrentis to determinethe theconverter'sdatasheet;normally,a specificinductoror a rangeof inductorsare namedfor use with the , use the recommendedinductorvalueto calculatethe ripplecurrent,an inductorvaluein the middleofthe recommendedrange,or if noneis givenin the datasheet,the one calculatedin theInductorSelectionsectionof this applicationreport.(2)VIN(max)= maximuminputvoltageVOUT= desiredoutputvoltageD = duty cyclecalculatedin Equation1fS= minimumswitchingfrequencyof the converterL = selectedinductorvalueIt now has to be determinedif the selectedIC can deliverthe maximumoutputcurrent.

4 (3)ILIM(min)= minimumvalueof the currentlimit of the integratedswitch(givenin the datasheet) IL= inductorripplecurrentcalculatedin Equation2If the calculatedvaluefor the maximumoutputcurrentof the selectedIC, IMAXOUT, is belowthe system'srequiredmaximumoutputcurrent,the switchingfrequencyhas to be increasedto reducethe ripplecurrentor anotherIC with a higherswitchcurrentlimit has to be the calculatedvaluefor 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:(4) IL= inductorripplecurrentcalculatedin Equation2 IOUT(max)= maximumoutputcurrentnecessaryin the applicationThis is the peakcurrent,the inductor,the integratedswitch(es),and the externaldiodehaveto a rangeof this is the case,choosean inductorfromthis higherthe inductorvalue,the higheris the maximumoutputcurrentbecauseof general,the lowerthe inductorvalue,the smalleris the the inductormustalwayshavea highercurrentratingthanthe maximumcurrentgivenin Equation4.

5 This is becausethecurrentincreaseswith partswhereno inductorrangeis given,the followingequationis a goodestimationfor the rightinductor:(5)2 BasicCalculationof a BuckConverter's PowerStageSLVA477B December2011 RevisedAugust2015 SubmitDocumentationFeedbackCopyright 2011 2015,TexasInstrumentsIncorporatedR1/2 FBI100 I R1R2IR1/2 IFBVOUTVFBDFFP = IV (1 )FOUT(max)I = I -DLOUT(max)!I = ( to )I typicalinputvoltageVOUT= desiredoutputvoltagefS= minimumswitchingfrequencyof the Converter IL= estimatedinductorripplecurrent,see the following:The inductorripplecurrentcannotbe calculatedwith Equation1 becausethe inductoris not the inductorripplecurrentis 20%to 40%of the outputcurrent.(6) IL= estimatedinductorripplecurrentIOUT(max)= maximumoutputcurrentnecessaryin the application4 RectifierDiodeSelectionTo reducelosses,use forwardcurrentratingneededis equalto the maximumoutputcurrent:(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)IF= averageforwardcurrentof the receiverdiodeVF= forwardvoltageof the rectifieddiodeD = duty cyclecalculatedin Equation15 OutputVoltageSettingAlmostall convertersset the outputvoltagewith a resistivedividernetwork(whichis integratedif they arefixedoutputvoltageconverters).

6 Withthe givenfeedbackvoltage,VFB, and feedbackbias current,IFB, the voltagedividercan be ResistiveDividerfor Settingthe OutputVoltageThe currentthroughthe resistivedividerneedsto be at least100 timesas big as the feedbackbiascurrent:(9)IR1/2= currentthroughthe resistivedividerto GNDIFB= feedbackbias currentfromdatasheet3 SLVA477B December2011 RevisedAugust2015 BasicCalculationof a BuckConverter's PowerStageSubmitDocumentationFeedbackCop yright 2011 2015,TexasInstrumentsIncorporatedOUT(ESR )L!V= ESR!I LOUT(min )SOUT! IC=8 !V fOUT12 FBVR = R1V - FB2R1/2VR = addsless than1% inaccuracyto the voltagemeasurementand for the calculationof the feedbackdivider,the currentinto the feedbackpin can be currentalso can be a lot onlydisadvantageof smallerresistorvaluesis a higherpowerloss in the resistivedivider,but the accuracyisincreaseda precedingassumption,the resistorsare calculatedas follows.

7 (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) dielectricmaterialmustbe X5 Ror ,the capacitorlosesmuchof its capacitancedue to dc bias valuecan be increasedif the inputvoltageis best practiceis to use low-ESRcapacitorsto minimizethe rippleon the a goodchoiceif the dielectricmaterialis X5 Ror the converterhas externalcompensation,any capacitorvalueabovethe recommendedminimumin thedatasheetcan be used,but the compensationhas to be adjustedfor the ,the recommendedinductorand capacitorvaluesmustbe used,or the recommendationsin the datasheetfor adjustingthe outputcapacitorsto the applicationin the datasheetmustbe followedfor the ratioof L ,the followingequationscan be usedto adjustthe outputcapacitorvaluesfora desiredoutputvoltageripple.

8 (12)COUT(min)= minimumoutputcapacitance IL= estimatedinductorripplecurrentfS= minimumswitchingfrequencyof the Converter VOUT= desiredoutputvoltagerippleThe ESRof the outputcapacitoraddssomemoreripple,givenw ith the equation:(13) VOUT(ESR)= additionaloutputvoltagerippledue to capacitorsESRESR= equivalentseriesresistanceof the usedoutputcapacitor IL= inductorripplecurrentfromEquation2 or Equation6 Oftenthe selectionof the outputcapacitoris not drivenby the steady-stateripple,but by the outputvoltagedeviationis causedby the time it takesthe inductorto catchupwith the increasedor followingformulacan be usedto calculatethe necessaryoutputcapacitancefor a desiredmaximumovershoot:4 BasicCalculationof a BuckConverter's PowerStageSLVA477B December2011 RevisedAugust2015 SubmitDocumentationFeedbackCopyright 2011 2015,TexasInstrumentsIncorporated2 OUTOUT(min),OSO UTOS!

9 ILC=2VV (14)COUT(min),OS= minimumoutputcapacitancefor a desiredovershoot IOUT= maximumoutputcurrentchangein the applicationVOUT= desiredoutputvoltageVOS= desiredoutputvoltagechangedue to the SwitchmodePowerSupplies(SLVA057) Applicationswith the PulseWidthModulatorTL5001(SLVAE05) DC/DCBuckConverters(SLYT293) CurrentModeStep-DownConverters(SLVA352)5 . RobertW. Erickson:Fundamentalsof PowerElectronics, KluwerAcademicPublishers,19976. Mohan/Underland/Robbins:PowerElectronics , JohnWiley& SonsInc., SecondEdition,19957. GeorgeM. Harayda,AkiraOmi,and AxelYamamoto:ImproveYourDesignswith LargeCapacitanceValueMulti-LayerCeramicC hip( MLCC) Capacitors,Panasonic8. JeffreyCain, :Comparisonof MultilayerCeramicand TantalumCapacitors, AVXC orporation5 SLVA477B December2011 RevisedAugust2015 BasicCalculationof a BuckConverter's PowerStageSubmitDocumentationFeedbackCop yright 2011 2015,TexasInstrumentsIncorporatedR1/2 FBCurrent through Resistive Divider Network for Output Voltage Setting: I100 I DFFP ower Dissipation in Rectifier Diode: P = IV (1 )FO UT(max)Av erage Forward Current of Rectifier Diode: I = I -DLOUT(ma x)Inductor ripple Current Estimation: !

10 I =( to )I O UTINOUTLSINV(VV)Inductor Calculation : L=(if no value is rec om m ended in the data s heet)!IV - fLS W(max)O UT(max)!IA pplication specific m axim um switc h current: I=+ I2 LMAXOUTL IM(min)!IMaxim um output current of the selec ted IC: I= I2-()IN (m ax)OU TLSVVDI nductor ripple Current: ! I =L- f(max)O UTINV Maxim um Duty Cyc le: D =V AppendixASLVA477B December2011 RevisedAugust2015 Formulasto Calculatethe PowerStateof a BuckConverter(15)VIN(max)= maximuminputvoltageVOUT= outputvoltage = efficiencyof the Converter , ,estimated85%(16)VIN(max)= maximuminputvoltageVOUT= desiredoutputvoltageD = duty cyclecalculatedin Equation15fS= minimumswitchingfrequencyof the converterL = selectedinductorvalue(17)ILIM(min)= minimumvalueof the currentlimit of the integratedswitch(givenin the datasheet) IL= inductorripplecurrentcalculatedin Equation16(18) IL= inductorripplecurrentcalculatedin Equation16 IOUT(max)= maximumoutputcurrentnecessaryin the application(19)VIN= typicalinputvoltageVOUT= desiredoutputvoltagefS= minimumswitchingfrequencyof the Converter IL= estimatedinductorripplecurrent,see next paragraph(20) IL= estimatedinductorripplecurrentIOUT(max)