SEPIC电路分析

PowerSystemsDesignEuropeNovember200614DESIGNTIPSByDr.RayRidley,RidleyEngineeringTheSepicConverterThemostbasicconverterthatwelookedatlastmonthisthebuckcon-verter.Itissonamedbecauseitalwaysstepsdown,orbucks,theinputvoltage.Theoutputoftheconverterisgivenby:Interchangetheinputandtheoutputofthebuckconverter,andyougetthesecondbasicconverter–theboost.Theboostalwaysstepsup,henceitsname.Theoutputvoltageisalwayshigherthantheinputvoltage,andisgivenby:Whatifyouhaveanapplicationwhereyouneedtobothstepupandstepdown,dependingontheinputandoutputvoltage?Youcouldusetwocas-cadedconverters–abuckandaboost.Unfortunately,thisrequirestwoseparatecontrollersandswitches.Itis,however,agoodsolutioninmanycases.Thebuck-boostconverterhasthede-siredstepupandstepdownfunctions:Theoutputisinverted.Aflybackconvert-er(isolatedbuck-boost)requiresatrans-formerinsteadofjustaninductor,addingtothecomplexityofthedevelopment.Oneconverterthatprovidestheneed-edinput-to-outputgainistheSepic(sin-gle-endedprimaryinductorconverter)converter.ASepicconverterisshowninFig.1.Ithasbecomepopularinrecentyearsinbattery-poweredsystemsthatmuststepupordowndependinguponthechargelevelofthebattery.Fig.2showsthecircuitwhenthepowerswitchisturnedon.Thefirstinductor,L1,ischargedfromtheinputvoltagesourceduringthistime.Thesecondinductortakesenergyfromthefirstcapacitor,andtheoutputcapacitorislefttoprovidetheloadcurrent.ThefactthatbothL1andL2aredisconnect-edfromtheloadwhentheswitchisonleadstocomplexcontrolcharacteristics,aswewillseelater.Whenthepowerswitchisturnedoff,thefirstinductorchargesthecapaci-torC1andalsoprovidescurrenttotheload,asshowninFig.3.Thesecondinductorisalsoconnectedtotheloadduringthistime.Theoutputcapacitorseesapulseofcurrentduringtheofftime,makingitinherentlynoisierthanabuckconverter.Theinputcurrentisnon-pulsating,adis-tinctadvantageinrunningfromabatterysupply.AnalyzingtheSepicConverterInthelastissue,wetalkedaboutthesimplestofallconverters,thebuckconverter,andshowedhowitscontroltransferfunctionscouldbeextraordinarilycomplex.Inthisissue,we’llgototheotherendofthespectrum,andlookataconverterthatisfarmorecomplex,yetisoftenusedbyengineerswhoareunawareofthedifficultiesthatfollow.Figure1.TheSepicconvertercanbothstepupandstepdowntheinputvolt-age,whilemaintainingthesamepolar-ityandthesamegroundreferencefortheinputandoutput.Figure2.Whentheswitchisturnedon,theinputinductorischargedfromthesource,andthesecondinductorischargedfromthefirstcapacitor.Noenergyissuppliedtotheloadcapaci-torduringthistime.Inductorcurrentandcapacitorvoltagepolaritiesaremarkedinthisfigure.Figure3.Withtheswitchoff,bothinductorsprovidecurrenttotheloadcapacitor.PowerSystemsDesignEuropeNovember200616DESIGNTIPSThePWMSwitchModelintheSepicConverterThebestwaytoanalyzeboththeACandDCcharacteristicsoftheSepicconverterisbyusingthePWMswitchmodel,developedbyDr.VatchéVor-périanin1986.Someminorcircuitma-nipulationsarefirstneededtorevealthelocationoftheswitchmodel,andthisisPropersmall-signalanalysisoftheSepicconverterisadifficultanalyticaltask,onlymadepracticalbyadvancedcircuitanalysistechniquesoriginallyde-velopedbyDr.DavidMiddlebrookandcontinuedbyVorpérian.[1]Ifyou’regoingtobuildaSepic,asaminimum,youneedtounderstandthecontrolcharacteristics.Fortunately,Vorpérian’sworkisnowavailableforthisconverter,andyoucandownloadthecompleteanalysisnotes.[2]ThesimplifiedanalysisoftheSepicconverter,derivedindetailin[2],ignoresparasiticresistancesoftheinductorsandcapacitors,andyieldsthefollowingresultforthecontrol-to-outputtransferfunction:WhereshowninFig.4.First,capacitorC1ismovedtothebottombranchoftheconverter.Then,inductorL2ispulledovertotheleft,keepingitsendsconnectedtothesamenodesofthecircuit.ThisrevealsthePWMswitchmodeloftheconverter,withitsactive,passive,andcommonports,allowingustousewell-estab-lishedanalysisresultsforthisconverter.FormorebackgroundonthePWMswitchmodel,thetextbook“FastAnalyticalTechniquesforElectricalandElectronicCircuits”[1]ishighlyrecom-mended.DCAnalysisoftheSepicConverterFig.5showstheequivalentcircuitoftheSepicconverterwiththeDCportionofthePWMswitchmodelinplace.TheDCmodelisjusta1:Dtransformer.Wereplacetheinductorswithshortcircuits,andthecapacitorswithopencircuitsfortheDCanalysis.Youcan,ifyoulike,includeanyparasiticresistancesinthemodel[2],butthat’sbeyondthescopeofthisarticle.Afterthecircuitismanipulatedasshowninthefigure,wecanwritetheKVLequationaroundtheouterloopoftheconverter:Rearranginggives:AndtheDCgainisgivenby:Hereweseetheabilityofthecon-vertertostepupordown,withagainof1whenD=0.5.Unlikethebuck-boostandCukconverters,theoutputisnotinverted.ACAnalysisoftheSepicConverterYouwon’tfindacompleteanalysisoftheSepicconverteranywhereinprintedliterature.Whatyouwillfindareapplica-tionnoteswithcommentslike,“theSepicisnotwell-understood.”Despitethelackofdocumentationfortheconverter,engi-neerscontinuetouseitwhenapplicable.Figure5.ForDCanalysis,thesmallsignalsourcesaresettozero,induc-torsbecomeshortcircuits,andcapaci-torsbecomeopencircuits.Afterthecircuitisredrawn,itisatrivialmattertowriteKVLaroundtheouterloopofthecircuit