DC dc converter.docx
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DC dc converter.docx
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DCdcconverter
DC-DCConverterBasics
ABSTRACT
ADC-to-DCconverterisadevicethatacceptsaDCinputvoltageandproducesaDCoutputvoltage.Typicallytheoutputproducedisatadifferentvoltagelevelthantheinput.Inaddition,DC-to-DCconvertersareusedtoprovidenoiseisolation,powerbusregulation,etc.ThisisasummaryofsomeofthepopularDC-to-DCconvertertopolopgies:
1.BUCKCONVERTERSTEP-DOWNCONVERTER
InthiscircuitthetransistorturningONwillputvoltageVinononeendoftheinductor.Thisvoltagewilltendtocausetheinductorcurrenttorise.WhenthetransistorisOFF,thecurrentwillcontinueflowingthroughtheinductorbutnowflowingthroughthediode.Weinitiallyassumethatthecurrentthroughtheinductordoesnotreachzero,thusthevoltageatVxwillnowbeonlythevoltageacrosstheconductingdiodeduringthefullOFFtime.TheaveragevoltageatVxwilldependontheaverageONtimeofthetransistorprovidedtheinductorcurrentiscontinuous.
Fig.1:
BuckConverter
Fig.2:
Voltageandcurrentchanges
Toanalysethevoltagesofthiscircuitletusconsiderthechangesintheinductorcurrentoveronecycle.Fromtherelation
thechangeofcurrentsatisfies
ForsteadystateoperationthecurrentatthestartandendofaperiodTwillnotchange.TogetasimplerelationbetweenvoltagesweassumenovoltagedropacrosstransistorordiodewhileONandaperfectswitchchange.ThusduringtheONtimeVx=VinandintheOFFVx=0.Thus
whichsimplifiesto
or
anddefining"dutyratio"as
thevoltagerelationshipbecomesVo=DVinSincethecircuitislosslessandtheinputandoutputpowersmustmatchontheaverageVo*Io=Vin*Iin.ThustheaverageinputandoutputcurrentmustsatisfyIin=DIoTheserelationsarebasedontheassumptionthattheinductorcurrentdoesnotreachzero.
1.1Transitionbetweencontinuousanddiscontinuous
WhenthecurrentintheinductorLremainsalwayspositivetheneitherthetransistorT1orthediodeD1mustbeconducting.ForcontinuousconductionthevoltageVxiseitherVinor0.Iftheinductorcurrentevergoestozerothentheoutputvoltagewillnotbeforcedtoeitheroftheseconditions. AtthistransitionpointthecurrentjustreacheszeroasseeninFigure3.DuringtheONtimeVin-Voutisacrosstheinductorthus
(1)
Theaveragecurrentwhichmustmatchtheoutputcurrentsatisfies
(2)
Fig.3:
BuckConverteratBoundary
Iftheinputvoltageisconstanttheoutputcurrentatthetransitionpointsatisfies
(3)
1.2VoltageRatioofBuckConverter(DiscontinuousMode)
AsforthecontinuousconductionanalysisweusethefactthattheintegralofvoltageacrosstheinductoriszerooveracycleofswitchingT.ThetransistorOFFtimeisnowdividedintosegmentsofdiodeconductionddTandzeroconductiondoT. Theinductoraveragevoltagethusgives
(Vin-Vo)DT+(-Vo)dT=0
(4)
Fig.4:
BuckConverter-DiscontinuousConduction
(5)
forthecase
.Toresolvethevalueof
considertheoutputcurrentwhichishalfthepeakwhenaveragedovertheconductiontimes
(6)
Consideringthechangeofcurrentduringthediodeconductiontime
(7)
Thusfrom(6)and(7)wecanget
(8)
usingtherelationshipin(5)
(9)
andsolvingforthediodeconduction
(10)
Theoutputvoltageisthusgivenas
(11)
definingk*=2L/(VinT),wecanseetheeffectofdiscontinuouscurrentonthevoltageratiooftheconverter.
Fig.5:
OutputVoltagevsCurrent
Asseeninthefigure,oncetheoutputcurrentishighenough,thevoltageratiodependsonlyonthedutyratio"d".AtlowcurrentsthediscontinuousoperationtendstoincreasetheoutputvoltageoftheconvertertowardsVin.
2.BOOSTCONVERTERSTEP-UPCONVERTER
TheschematicinFig.6showsthebasicboostconverter.Thiscircuitisusedwhenahigheroutputvoltagethaninputisrequired.
Fig.6:
BoostConverterCircuit
WhilethetransistorisONVx=Vin,andtheOFFstatetheinductorcurrentflowsthroughthediodegivingVx=Vo.Forthisanalysisitisassumedthattheinductorcurrentalwaysremainsflowing(continuousconduction).ThevoltageacrosstheinductorisshowninFig.7andtheaveragemustbezerofortheaveragecurrenttoremaininsteadystate
Thiscanberearrangedas
andforalosslesscircuitthepowerbalanceensures
Fig.7:
Voltageandcurrentwaveforms(BoostConverter)
Sincethedutyratio"D"isbetween0and1theoutputvoltagemustalwaysbehigherthantheinputvoltageinmagnitude.Thenegativesignindicatesareversalofsenseoftheoutputvoltage.
3.BUCK-BOOSTCONVERTER
Fig.8:
schematicforbuck-boostconverter
WithcontinuousconductionfortheBuck-BoostconverterVx=VinwhenthetransistorisONandVx=VowhenthetransistorisOFF.Forzeronetcurrentchangeoveraperiodtheaveragevoltageacrosstheinductoriszero
Fig.9:
Waveformsforbuck-boostconverter
whichgivesthevoltageratio
andthecorrespondingcurrent
Sincethedutyratio"D"isbetween0and1theoutputvoltagecanvarybetweenlowerorhigherthantheinputvoltageinmagnitude.Thenegativesignindicatesareversalofsenseoftheoutputvoltage.
4.CONVERTERCOMPARISON
ThevoltageratiosachievablebytheDC-DCconvertersissummarisedinFig.10.Noticethatonlythebuckconvertershowsalinearrelationshipbetweenthecontrol(dutyratio)andoutputvoltage.Thebuck-boostcanreduceorincreasethevoltageratiowithunitgainforadutyratioof50%.
Fig.10:
ComparisonofVoltageratio
4.CUKCONVERTER
Thebuck,boostandbuck-boostconvertersalltransferredenergybetweeninputandoutputusingtheinductor,analysisisbasedofvoltagebalanceacrosstheinductor.TheCUKconverterusescapacitiveenergytransferandanalysisisbasedoncurrentbalanceofthecapacitor.ThecircuitinFig.11isderivedfromDUALITYprincipleonthebuck-boostconverter.
Fig.11:
CUKConverter
IfweassumethatthecurrentthroughtheinductorsisessentiallyripplefreewecanexaminethechargebalanceforthecapacitorC1.ForthetransistorONthecircuitbecomes
Fig.12:
CUK"ON-STATE"
andthecurrentinC1isIL1.WhenthetransistorisOFF,thediodeconductsandthecurrentinC1becomesIL2.
Fig.13:
CUK"OFF-STATE"
Sincethesteadystateassumesnonetcapacitorvoltagerise,thenetcurrentiszero
whichimplies
Theinductorcurrentsmatchtheinputandoutputcurrents,thususingthepowerconservationrule
Thusthevoltageratioisthesameasthebuck-boostconverter.TheadvantageoftheCUKconverteristhattheinputandoutputinductorscreateasmoothcurrentatbothsidesoftheconverterwhilethebuck,boostandbuck-boosthaveatleastonesidewithpulsedcurrent.
4.IsolatedDC-DCConverters
InmanyDC-DCapplications,multipleoutputsarerequiredandoutputisolationmayneedtobeimplementeddependingontheapplication.Inaddition,inputtooutputisolationmayberequiredtomeetsafteystandardsand/orprovideimpedancematching.
TheabovediscussedDC-DCtopologiescanbeadaptedtoprovideisolationbetweeninputandoutput.
4.1FlybackConverter
TheflybackconvertercanbedevelopedasanextensionoftheBuck-Boostconverter.Fig14ashowsthabasicconverter;Fig14breplacestheinductorbyatransformer.Thebuck-boostconverterworksbystoringenergyintheinductorduringtheONphaseandreleasingittotheoutputduringtheOFFphase.Withthetransformertheenergystorageisinthemagnetisationofthetransformercore.Toincreasethestoredenergyagappedcoreisoftenused.
InFig14ctheisolatedoutputisclarifiedbyremovalofthecommonreferenceoftheinputandoutputcircuits.
Fig.14(a):
Buck-BoostConverter
Fig.14(b):
Replacinginductorbytransformer
Fig.14(c):
Flybackconverterre-configured
4.2ForwardConverter
TheconceptbehindthefowardconverteristhatoftheidealtransformerconvertingtheinputACvoltagetoanisolatedsecondaryoutputvoltage.ForthecircuitinFig.15,whenthetransistorisON,Vinappearsacrosstheprimaryandthengenerates
ThediodeD1onthesecondaryensuresthatonlypositivevoltagesareappliedtotheoutputcircuitwhileD2providesacirculatingpathforinductorcurrentifthetransformervoltageiszeroornegative.
Fig.15:
ForwardConverter
TheproblemwiththeoperationofthecircuitinFig15isthatonlypositivevoltageisappliedacrossthecore,thusfluxcanonlyincreasewiththeapplicationofthesupply.Thefluxwillincreaseuntilthecoresaturateswhenthemagnetisingcurrentincreasessignificantlyandcircuitfailureoccurs.ThetransformercanonlysustainoperationwhenthereisnosignificantDCcomponenttotheinputvoltage.WhiletheswitchisONthereispositivevoltageacrossthecoreandthefluxincreases.WhentheswitchturnsOFFweneedtosupplynegativevoltagetorsetthecoreflux.ThecircuitinFig.16showsatertiarywindingwithadiodeconnectiontopermitreversecurrent.Notethatthe"dot"conventionforthetertiarywindingisoppositethoseoftheotherwindings.WhentheswitchturnsOFFcurrentwasflowingina"dot"terminal.Thecoreinductanceacttocontinuecurrentinadottedterminal,thus
Fig.16:
Forwardconverterwithtertiarywinding
Forfurtherreading:
[1] "PowerElectronics:
Converters,ApplicationsandDesign",Mohan,UndelandandRobbins,Wiley,1989.
Copyright©G.Ledwich1998.
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