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ApplicationReport SLVA317B–February2009–RevisedOctober2012 CreateanInvertingPowerSupplyFromaStep-Down Regulator DavidG.Daniels..............................................................................................SwiftDC/DCConverters ABSTRACT Whengeneratinganegativeoutputvoltagefromapositiveinputvoltage,usethebuck(stepdown) regulatorthatisalreadyavailable.Thisstep-by-stepprocedurehelpsguidetheuserthroughdesigningan invertingpowersupplyusingawideinputvoltagefamilyofSWIFTdc/dcconverters. Applyingdualitytoabuckregulator,allowstheusertoderiveaninverting(buck-boost)regulatorasshown intheReferences(1and2)attheendofthisapplicationreport. TheTPS54060Aisusedtodemonstratethedesignprocedure.Thedesignprocedureisapplicableto otherstepdownpeakcurrentmodecontrolregulatorsandshouldbeusedwiththecomplementaryexcel worksheet(5).Forexample,higherpowerdesignsrequiredeviceswithahighercurrentlimit,suchasthe TPS54360.TheTPS54060Aisa0.5-Aswitchingregulator,withawideswitchingfrequencyrangeof 100kHzto2500kHzandaninputoperatingvoltageof3.5Vto60V. Table1.InvertingPowerSupplyRequirement VI Inputvoltage 24Vnominal18Vto30V Inputvoltageripple 1% VO Outputvoltage –12V dVO Outputvoltageripple 0.5% IO Maximumoutputcurrent 0.3A fsw Switchingfrequency 500kHz Figure1.InvertingPowerSupplySchematic 1 SLVA317B–February2009–RevisedOctober2012 CreateanInvertingPowerSupplyFromaStep-DownRegulator SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com OutputVoltage Thedifferenceinthemaximuminputvoltage,VImax,andtheoutputvoltage,VOshouldnotexceedthe maximumoperatingdevicevoltageoftheregulator.FortheTPS54060A,themaximumoperatingdevice voltage,Vdevmax,is60V. (1) (2) AssumingVOis–12VandusingEquation1,themaximuminputvoltageforthepowersupplycouldbeas highas48V,easilysupportingthe30-VmaximuminputrequirementinTable1.UseEquation2to determineR1fortheoutputdesiredvoltage,setR2equalto1kŸandVrefto0.8VfortheTPS54060A.R1 equals14kŸ. InputVoltageRange Theoperatinginputvoltage,VIminofthepowersupplyshouldbegreaterthantheminimumdevice voltage,Vdevmin.FortheTPS54060A,theVdevminis3.5VTheminimuminputvoltagerequirementforthe powersupplyis18V,thus,satisfyingEquation3. (3) DutyCycle TheidealdutycyclefortheinvertingpowersupplyisshowninEquation4,neglectingthelossesofthe powerswitching,inductoranddiodedrop.Theoutputvoltage,VO,isnegativeandtheinputvoltage,VI,is positiveyieldingapositiveresultforEquation4. (4) Themaximumdutycycle,Dmax,iscalculatedbyusingtheminimuminputvoltage,VIminissubstitutedfor inputvoltage,VIinEquation4.Assuming18VforVIandaVOof–12V,themaximumdutycycle,Dmax, is0.40. OutputCurrent Toestimatewhethertheselectedswitchingregulatorwillbecapableofdeliveringtheoutputcurrent,use Equation5.Theusermustknowthedevice’sminimumcurrentlimit,ICLmin,maximumdutycycle,Dmax, andestimatetheinductorripplecurrentvalue,ILripple. (5) Assumingtheminimumcurrentlimitis0.6AandtheILrippleis25%oftheminimumcurrentlimit,the maximumoutputcurrentthatissupportedbytheTPS54060Aisestimatedtobe315mA. Sincetheinputvoltagerangeandmaximumoutputcurrentissupportedbytheselectedregulator,thenext stepsaretocalculatetheinductorvalue,switchingfrequencyandoutputcapacitorvalue. Themaximumswitchingfrequencyshouldbecalculatedusingtheminimumcontrollableontime, maximuminputvoltageandsomeofthelossesinthesupply.Ifthemaximumfrequencycalculatedis greaterthanthe2500kHzsupportedbytheTPS54060A,limittheƒskipmaxto2500kHz. (6) AconsiderationspecificallyfortheTPS54060Adeviceisthefrequencyshiftthatoccurstoprevent overcurrentrunawayduringanoutputshortcircuit (7) 2 CreateanInvertingPowerSupplyFromaStep-DownRegulator SLVA317B–February2009–RevisedOctober2012 SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com Themaximumswitchingfrequencywillbethelowerfrequencyofƒshiftmaxorƒskipmax.TheVOsctermin Equation7istheoutputvoltageduringtheoutputfault.Theƒdivisthefrequencydivision.ƒdivis8when VOscislessthan25%oftheregulationvoltage.SeetheSelectingtheSwitchingFrequencysectionof TPS54060Adatasheetformoredetailsonthefrequencyshift.Theminimumontime,tOmin,is130nsand themaximumMOSFETonresistance,Rhs,is400mŸfortheTPS54060A.Assumingdiodevoltagedrop, Vfd,is0.5V,inductorresistance,Rdc,is325mŸ,themaximumfrequencycalculatedis2286kHzand 1210kHz,usingEquation6andEquation7,respectively.Themaximumswitchingfrequencyselected shouldnotbegreaterthan1210kHz.Sincethepowersupplyspecificationrequirementfortheswitching frequencyis500kHzandislowerthanthe1210kHz,nodesignchangesarenecessary. Inductor Todeterminetheinductorvalue,calculatetheaverageinductorcurrent,ILavg,atthemaximumoutput currentandmaximuminputvoltage. UsethemaximuminputvoltageasavariableinEquation4tocalculateminimumdutycycle,Dmin. AssumingVImaxis30V,Dminisapproximately0.286andILavgis0.42A. Theinductorvalueiscalculated,Equation9,usingaripplecurrentthatis25%oftheaverageinductor current.UsingtheDmintocalculatetheminimuminductancevaluegivesthelargestinductance. AssumingVImaxof30V,IOof0.3Aandaƒswof500kHz,theLoiscalculatedas163H.Thenearest standardinductorof150Hisusedfortheinductor.Theinductorsaturationcurrentshouldbegreater thanthe0.548AofpeakcurrentcalculatedinEquation10.Theinductorrmscurrentshouldbegreater than0.450AcalculatedinEquation11. (8) (9) (10) (11) OutputCapacitor Theoutputcapacitormustsupplythecurrentwhenthehighsideswitchison.Usetheminimuminput voltagetocalculatetheoutputcapacitanceneeded.Thisiswhenthedutycycleandthepeak-to-peak currentintheoutputcapacitoristhemaximum.Usingthe0.5%voltageripplespecification,dVO,and Equation12,COminis4F.Assumingthe0.5%voltagerippleandmaximumdutycycle,theRc, equivalentseriesresistanceshouldbelessthan109mŸ,usingEquation13.Thermscurrentforthe outputcapacitoris0.245AusingEquation14.Two15F/25VX5Rinparallelareusedfortheoutput capacitorbecauseofthelowESRandsize. (12) (13) (14) DiodeSelection Thediodevoltageneedstobegreaterthanthedifferenceofthemaximuminputvoltageandoutput voltage.Fortheexampledesign,thediodeneedstosupportavoltagegreaterthan42V. 3 SLVA317B–February2009–RevisedOctober2012 CreateanInvertingPowerSupplyFromaStep-DownRegulator SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com UsingEquation15,thepowerdissipationiscalculatedusingthediodeforwardvoltagedrop,Vƒd,atthe maximuminputvoltageandtheaveragediodecurrent.AssumingVƒdof0.5V,Pdiodeis0.150W.The peakcurrentinthediodeisthesameastheinductor,Equation10.Selectadiodewhichhasapower ratinggreaterthan0.107Wandsupportstheinductorcurrent. (15) PowerDissipationinPackage Thepowerdissipationinthepackageisdominatedbytheconductionlossesandswitchinglossesofthe powerswitchandshouldnotexceedthelimitationsofthepackage.Theconductionandswitchinglosses arecalculatedusingEquation16.Theconductionlossesareafunctionofthedutycycle,D,inductorrms current,ILrms,andonresistance,Rhs.Theswitchinglossesareafunctionoftheturnon,tr,andturnoff,tf, times,switchingfrequency,outputcurrent,inputandoutputvoltage. (16) ILrmsiscalculatedtobe0.45Aatnominaldutycycle.Pdeviceis0.2295Wassumingatrandtfof25ns. FrequencyResponseoftheInvertingRegulator Usingabuckregulatortogenerateanegativeoutputdoesnotclosethefeedbackloopaswouldabuck powersupply.So,adifferentdesignmethodisneeded.Theinvertingpowersupplytransferfunctionhas twozeroesandapole.Equation17isasimplifiedtransferfunctionofaninvertingpowersupply,see AppendixAinReferences(3)ortheapplicationreport(4)formoredetailsonthederivation.TheESR zero,ƒz1,isthesameasinaBuckregulator,Equation18,andisafunctionoftheoutputcapacitorandits ESR.Theotherzeroisarighthalfplanezero,ƒz2.Thefrequencyresponseoftheƒz2resultsinan increasinggainandadecreasingphase.Theƒz2frequencyisafunctionofthedutycycle,outputcurrent, andtheinductor.Equation19calculatestheminimumfrequencyoftheƒz2whichisusedtodeterminethe crossoverfrequency.Thedominantpole,ƒp1,isafunctionoftheloadcurrent,outputcapacitorandduty cycle,seeEquation20.Kbbisthedcgainandisusedtocalculatethefrequencycompensation components.Thegmpsvariableisthetransconductanceofthepowerstage,whichis1.9A/Vforthe TPS54060A. Theƒz1isestimatedtobe1516kHz.Theoutputcapacitorisderatedby30%becauseofthedcvoltage andtheESRisassumedtobe5mŸ.Theƒz2isestimatedtobe38.3kHz.Assumingresistanceofthe inductor,Rdcis325mŸ.Theƒp1isestimatedtobe253Hzassuminganominaldutycycle.Kbbis calculatedas38V/Vassumingnominalinputvoltage. (17) (18) (19) (20) (21) 4 CreateanInvertingPowerSupplyFromaStep-DownRegulator SLVA317B–February2009–RevisedOctober2012 SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com Thecrossoverofthepowersupplyshouldbesetbetweentheƒp1and1/3ofƒz2frequencies.Itis recommendedtostartwiththecrossoverfrequency,ƒco,givenbyEquation22.Theƒcoisestimatedto be3.1kHz. (22) Thecompensationresistor,Rcomp,neededtosetthecompensationgainatthefcofrequencyiscalculated usingEquation23.TheVrefis0.8Vandgmeais92A/VfortheTPS54060A. (23) SubstituteƒcointoEquation23,tocalculateRcomp.Rcompisequalto52.8kŸ.Usetheneareststandard valueof52.3kŸ.Thecompensationzeroissetto½ofthedominantpole,ƒp1.Tocalculatethe compensationzerocapacitor,Czero,useEquation24.Equation24gives24nF,usethenextlarger standardvaluewhichis27nF.ThecompensationpoleissettoequaltheRHPzero,ƒz2.Use Equation25,tocalculatethefrequencycompensationpole,Cpolewhichgives79pF.Thenextstandard valueis82pF. (24) (25) InputCapacitors TheTPS54060Aneedsatightlycoupledceramicbypasscapacitor,CdinFigure1,connectedtotheVIN andGNDpinsofthedevice.SincethedeviceGNDisthepowersupplyoutputvoltage,thevoltagerating ofthecapacitormustbegreaterthanthedifferenceinthemaximuminputandoutputvoltageofthepower supply.Itisrecommendedtousea1F/X5R/50V. Equation26toEquation29areusedtoestimatethecapacitance,maximumESR,andcurrentratingfor theinputcapacitor,CI. (26) (27) (28) (29) SlowStartTime PlacingasmallceramiccapacitorontheSS/TRtothechipGND(thatis,systemVO)adjuststheslowstart timeontheTPS54060A.TheslowstartcapacitoriscalculatedusingEquation30.Theequationassumes a2Apullupand10%to90%measurementfortime. (30) 5 SLVA317B–February2009–RevisedOctober2012 CreateanInvertingPowerSupplyFromaStep-DownRegulator SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com FrequencySetResistor Theswitchingfrequencyissetwitharesistor,RT,fromtheRT/CLKpintotheGNDoftheTPS54060A device.UseEquation31toestimatethefrequencysetresistor. (31) SynchronizingtoanExternalClock TheTPS54060AhasaCLKpinthatcanbeusedtosynchronizethepowersupplyswitchingfrequencyto anexternalsystemclock.Butalevelshiftcircuitneedstobeusedtotranslateasystemgroundreference clocksignaltothedevice’sground. StartVoltage Whenusedasastepdownregulator,theTPS54060Ahasanadjustablestartandstopvoltagesetby usingresistorsontheENpin.Thestopvoltageislowerthanthestartvoltage.Whenusedasaninverting powersupplyonlythestartvoltagecanbeuseful.Aftertheinvertingpowersupplystartsup,theeffective inputvoltagetheTPS54060Adeviceexperiencesrisesastheoutputvoltagereachesfullregulation. Therefore,itisrecommendedtousealowervalueresistoronthehighsidetominimizethehysteresis voltage.Theinputvoltagemustdropbytheoutputvoltageandthehysteresisvoltagetoshutdownthe supply.SeetheEnableandAdjustingUndervoltageLockoutsectionoftheTPS54060Adatasheetforthe equation. Figure2.24Vto–12V/0.3APowerSupply ExperimentalResults Figure3toFigure16showtheexperimentaltestresultsoftheFigure2design.Thediscontinuous conductionmode(DCM)tocontinuousconductionmode(CCM)boundaryisatanoutputcurrentof27 mA.Thepulseskipmode(PSM)boundaryisatanoutputcurrentof2.5mA.Theinputcurrentdrawatno loadat24Vinputvoltageis1.77mA. 6 CreateanInvertingPowerSupplyFromaStep-DownRegulator SLVA317B–February2009–RevisedOctober2012 SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com Figure3.EfficiencyVersusLoadCurrent Figure4.LightLoadEfficiencyVersusLoadCurrent Figure5.OutputVoltageVersusLoadCurrent Figure6.OutputVoltageVersusInputVoltage Figure7.OutputVoltageRippleat0.3A Figure8.OutputVoltageRippleatDCM 7 SLVA317B–February2009–RevisedOctober2012 CreateanInvertingPowerSupplyFromaStep-DownRegulator SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com Figure9.OutputVoltageRippleatPSM Figure10.InputRippleCCMATIO=0.3A Figure11.InputRippleDCM Figure12.InputRipplePSM Figure13.VOStartupwithVI Figure14.StartUpwithENandInput 8 CreateanInvertingPowerSupplyFromaStep-DownRegulator SLVA317B–February2009–RevisedOctober2012 SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated www.ti.com Figure15.LoadTransient Figure16.OverallLoopFrequencyResponse References 1.Usingabuckconverterinaninvertingbuck-boosttopology,JohnTucker,LiteratureNumberSLYT286, 4Q2007AnalogApplicationsJournal,TexasInstruments. 2.UsingtheTPS5430asanInvertingBuck-BoostConverter,JohnTucker,LiteraturenumberSLVA257A, ApplicationReport,August20078,TexasInstruments. 3.AchievingHigh-EfficiencywithaMulti-OutputCCMFlybackSupplyUsingSelf-DrivenSynchronous Rectifiers,RobertKollman,LiteratureNumberSLUP204,SEM1500SeminarPaper,Texas Instruments. 4.UnderstandingBuck-BoostPowerStagesinSwitchModePowerSupplies,EverettRogers,Literature NumberSLVA059A-March1999ApplicationReport,TexasInstruments. 5.“TPS54060AINVERTING.xls”excelworksheet(SLVC211A),2009TexasInstrumentsIncorporated. www.ti.com. 9 SLVA317B–February2009–RevisedOctober2012 CreateanInvertingPowerSupplyFromaStep-DownRegulator SubmitDocumentationFeedback Copyright©2009–2012,TexasInstrumentsIncorporated IMPORTANTNOTICE TexasInstrumentsIncorporatedanditssubsidiaries(TI)reservetherighttomakecorrections,enhancements,improvementsandother changestoitssemiconductorproductsandservicesperJESD46,latestissue,andtodiscontinueanyproductorserviceperJESD48,latest issue.Buyersshouldobtainthelatestrelevantinformationbeforeplacingordersandshouldverifythatsuchinformationiscurrentand complete.Allsemiconductorproducts(alsoreferredtohereinas“components”)aresoldsubjecttoTI’stermsandconditionsofsale suppliedatthetimeoforderacknowledgment. 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