AN-1197Selecting Inductors for Buck Converters

1 ApplicationReportSNVA038B May2001 'r'.. r'.. May2001 RevisedApril2013AN-1197 SelectingInductorsforBuckConvertersSubmi tDocumentationFeedbackCopyright 2001 2013, , step-by-stepprocedureis ,allthepreviousstepsareconsolidatedin a singledesigntable,whichanswersthequestio n: Howwilltheselectedinductoractuallyperfor min a specificapplication? Theimportantpointtonotehereis thatthougheveryinductoris designedassumingcertainspecific designconditions', , ,thedesignermustknowhowtobeabletoaccurat elypredict,orextrapolate,theperformanceo ftheinductortoa newsetofconditions,whicharehisspecific applicationconditions'.It willbeshownthat intuition' detailedprocedureis requiredandis presentedin theformoftheDesignTable(Table2) andtheSelectionFlowChart(Figure2).2 Background:TheInductorCurrentWaveformRef ertoFigure1, whichshowsthecurrentthroughaninductorin continuousmodeoperation(boldline). is thegeometricalcenteroftheAC/rampcomponen t is theaveragevalueofthetotalinductorcurrent waveform is thecurrentintotheload,sincetheaveragecur rentthroughtheoutputcapacitor,asforanyca pacitorin steadystate,is IDC+ I/2,andit determinesthepeakenergyin thecore(e= L I2), whichin IDC- I/2anddeterminestheconstantresiduallevel ofcurrent/energyin dependsontheload,eventhoughit is :IAC= I = IPEAK ITROUGH(1) theloadcurrentforthecaseshownin Figure1, IDC= r' is definedastheratiooftheACtoDCcomponents(c urrentrippleratio)evaluatedatmaximumload ,IO.

2 Notethatbydefinition'r' is a constantfora givenconverter/application(asit is calculatedonlyatmaximumload),andit is alsodefinedonlyforcontinuousconductionmo de.(2)A highinductancereduces I andresultsin lower r' (andlowerRMScurrentin theoutputcapacitor),butmayresultin a ,formostbuckregulators, r' is chosentobein (atthemaximumratedload).SeeAppendixA. Oncetheinductanceisselected,aswedecrease theloadontheconverter(keepinginputvoltag econstant), I ,atthepointoftransitiontodiscontinuousmo deofoperation,theDClevelis I/2asshownin Figure1. So: Thecurrentrippleratioatthepointoftransit iontodiscontinuousmodeis ,theupperlimitfor'r' is also2. Theloadatwhichthishappenscanbeshownbysim plegeometrytober/2timesIO. Soforexample,iftheinductanceis chosentobesuchthat r' is loadof2A, ,whichis :If theinductoris a swinging'inductor, May2001 RevisedApril2013 SubmitDocumentationFeedbackCopyright 2001 2013, (Amps)LDC( H)Et(V secs)DCR(nom)m Et100(V secs) = L dl/dt,wegetduringtheONtimeoftheconverter :(3)whereVINis theappliedDCinputvoltage,VSWis thevoltageacrosstheswitchwhenit is ON,D is thedutycycleandf is theswitchingfrequencyin I wecanwrite r' as:(4)Now,fora buckregulator,wecanshowthatthedutycyclei s:(5)whereVDis theforwarddropacrossthecatchdiode( Schottkydiode).

3 R' canbefinallywrittenas:(6)andL is therefore:(7)wheref is in May2001 RevisedApril2013AN-1197 SelectingInductorsforBuckConvertersSubmi tDocumentationFeedbackCopyright 2001 2013, 12 Vata ( 15mV).WeassumeVSW= ,VD= = 150, ,forloopstabilityreasons,weshouldnotusea nyoutputcapacitoroflessthan100m , andsincewedonotwishtouseanLCpostfilter,o ur I mustbe:(8)So r' is:(9)Therequiredinductanceis:(10)L = 127 HTherequiredenergyhandlingcapabilityis ,thepeakcurrentis:(11)IPEAK= (12)Therequiredenergyhandlingcapability e' is:(13)whereL is in :(14)NOTE:Duringa hardpower-up(nosoftstart)orabnormalcondi tionslikea shortcircuitontheoutput,thefeedbackloopi s noteffectivein actuallygoingtohittheinternalcurrentlimi tofthedevice,ICLIMin Figure1, theinductorhassaturated,andif theinputDCvoltageishigherthan40 Vthecurrentcouldslewupata ratesohighthatthecontrollermaynotbeablet olimitthecurrentatall, , ,theinductorshouldbesizedtohandlethewors tcaseenergyeCLIM.

4 (15)whereL is in H andICLIMis theinternallimitoftheregulatorin May2001 RevisedApril2013 SubmitDocumentationFeedbackCopyright 2001 2013, secsor Et'whichis simplythevoltageacrossthewindingoftheind uctortimesthedurationin secsforwhichit is :Currentrampsuptothesamepeakvaluewhether V (theappliedvoltageacrossinductor)islarge butt (thetimeforwhichV is applied)is small,orwhetherV is smallbutt is whatreallycounts.(Theonlyexceptiontothis is theCoreLosstermsincethisdependsdirectlyo ntheabsolutevalueofthefrequencytoo,notju sttheEt).Also,Etcanbecalculatedduringthe ON-time,(V secsgained),orduringtheOFF-time(V secslost).Bothwillgivethesameresultsince thereis nonetchangein V secspercyclein ,rememberthatthoughV secsis relatedtotheenergyin thecore,it secsgivesinformationonlyabouttheACcompon entof r', thatis, , it givenapplicationis completelydefinedbya certainIOandEt(andfrequencyforthecorelos sterm), L (or r')andwefixit accordingtotheguidelinesin = L dl/dt,wecanwritethatV dt= L dtis ,bydefinition:Et= V t = L I V secs(16)whereL is in H.

5 R' canthereforebewrittenas:(17)SolvingforL: (18) :(19)tON= secsSoEtis:Et= (VIN- VSW- VO) tON= (24- 12) secsEt= secsL is therefore:(20)(21)L = 127 Hwhichgivesusthesameresultasin Example1 May2001 RevisedApril2013AN-1197 SelectingInductorsforBuckConvertersSubmi tDocumentationFeedbackCopyright 2001 2013, Aninductanceof127 H (orgreater,basedonmaximum r' ) DCloadof1A(toensureacceptabletemperature rise,specify T)ORsteadystateEnergyhandlingcapabilityo f84 J (toruleoutcoresaturationif DCinputvoltage 40V)ORpeakenergyhandlingcapabilityof1016 J. (MaxCurrentLimitofLM2593 HVis ) Etof38V secs Frequency150kHzThesecanbecommunicateddir ectlytoa vendorfora Figure2, thefirstpassselectionis partfromPulseEngineeringbecauseitsL andIDCareclosetoourrequirements,eventhou ghtherestdoesnotseemtofit ourapplication(seeTable1 andthefollowingbullets).Inparticularthef requencyforwhichtheinductorwasdesignedis 250kHz, , ourcase,andthatis whyit isimportanttofollowthefullprocedureprese ntedbelow.

6 Intuition' : Theinductoris suchthat380mWdissipationcorrespondsto50 C risein temperature. Thecorelossequationforthecoreis 10 18 is in HzandB is in Gauss. Theinductorwasdesignedfora frequencyof250kHz. Et100is theV secsatwhich B'is :Forcorelossequationsit is ,likemostvendors,the B'aboveactuallyrefersto mindin :a)ACComponentofCurrent:Thiscanbeeasilyc alculatedfrom:Et= L I V secswhere:L is in :(22)b) r':Sothisinductorhasbeendesignedforthefo llowing r':(23)r = )PeakCurrent:(24)IPEAK= May2001 RevisedApril2013 SubmitDocumentationFeedbackCopyright 2001 2013, )RMSC urrent:(25)(26)IRMS= )CopperLoss:Thisis:PCU= IRMS2 DCRmWwhere:DCRis in m .Inmostcases,toa closeapproximation,wecansimplyuseIDCinst eadofIRMSin , 387mWPCU= 385mWf) TheACComponentoftheB-Field:Thisis secsproduces100 Gauss(B).Sosincetheinductoris designedforanEt= secs,weget:(27)B = 587 GaussButthisis : B = 2 B = 1174 GaussCHECK:Wecanusethealternativeformfor B asgivenin Table2.

7 Weaskedthevendorformoredetailsthanhehadp rovidedonthedatasheetandwelearnedthatthe effectiveareaofthecore,Ae, N = (28)(29)whichis )TheDCComponentoftheB-Field:Thisis canalwaysbeconsideredproportionaltothein stantaneousvalueofthecurrent(fora giveninductor).Theproportionalityconstan tis knownfromf) above,thatis,a I B :(30)where:IDC= IO= (31)BDC= 2678 Gauss7 SNVA038B May2001 RevisedApril2013AN-1197 SelectingInductorsforBuckConvertersSubmi tDocumentationFeedbackCopyright 2001 2013, )PeakB-Field:SinceB is proportionaltoI, wecanwriteforthepeakB-field:(32)(33)BPEA K= 3265 Gaussi) CoreLoss:Thevendorhasstatedthatcoreloss( inmW)is 10 18 is in HzandB is inGauss.(34)PCORE= 10 18 ) TotalInductorLoss:P = PCU+ PCOREmWP = 385+ = 404mWk)ThermalResistanceofInductor:Theve ndorhasstatedthat380mWdissipationcorresp ondstoa 50 C risein :(35)RTH= C/Wl) EstimatedTemperatureRiseofInductor:(36)( 37) T = 53 CHerethetemperaturerise T' is thetemperatureofthecore, TCORE' minustheworstcaseambienttemperature TAMBIENT'.

8 The ambient'is )EnergyHandlingCapabilityofCore:(38)wher e:L is in H(39)e = 100 JAsbefore,wewarnthattheenergyin thecoreduringhardpower-upora shortcircuitontheoutputs, shouldalsoberememberedthattherearesevera lwaystoimplementthisfeature,andnotalllea dtoa reductionin May2001 RevisedApril2013 SubmitDocumentationFeedbackCopyright 2001 2013, willbeseenthatallinductorsofa family,thatis, thiscoreis foundtobeinadequate,normallytheonlywayou tis Theinductoris designedforabout50 C risein temperatureoverambientata loadof1A. Thecopperlosses(385mW)predominate(asis usualforsuchinductors/corematerials)andt hecorelossesarerelativelysmall. Thepeakfluxdensityis about3200 Gauss,whichoccursata Theratedenergyhandlingcapabilityofthecor eis 100 :Mostvendorsdonotexplicitlyprovidethemat erialused,thoughanastutedesignercanfigur ethisoutbylookingattheexponentsofB andf in thecorelossequationprovided, ferriteandcantypicallyhandlea peakfluxdensityofover3000 4000 Gaussbeforeit startstosaturate.

9 (Caution:notallferritegradesaresimilarin thisregardandalsothatthesaturationfluxde nsityBSAT fallsasthecoreheatsup.) designvalues',andthecorrespondingprimedp arametersaretheextrapolated applicationvalues'.Thefollowingarethedes ignconditions(thesemaybeallowedtochange) : IDC Et f TAMBIENTThe ApplicationConditions'are: I DC Et f T AMBIENTI ngoingfromthe DesignConditions'tothe ApplicationConditions'thefollowingarecon sideredconstant: L DCR Rth ThecorelossequationAnd,finally,to approve'theinductorforthegivenapplicatio nweneedtocertify: r' is acceptable(choiceofL). BPEAKOK. IPEAK< ICLIM. T OK(evaluatePCU+ PCORE). BCLIM< BSAT(ifDCinputvoltageis 40V).9 SNVA038B May2001 RevisedApril2013AN-1197 SelectingInductorsforBuckConvertersSubmi tDocumentationFeedbackCopyright 2001 2013, : Et(V secs) Et100(V secsper100 Gauss) L ( H) IDC(Amps) DCR(m ) f (Hz) Theformforcorelosses(mW)asa *Bb*fc, whereB is in Gauss,f in is halfthepeak-to-peakfluxswing.

10 Thermalresistanceofinductorin freeair( C/W)If anyoftheseareunknown, condensesthestep-by-stepproceduregivenea rlierandalsoshowshowto extrapolate' andFigure2. Wehaveseenthatthe DesignConditions'oftheinductorare: Et= secs f = 250,000Hz IDC= ApplicationConditions'are: Et = 38V secs f = 150,000Hz I DC= 1A(WeassumethatTAMBIENTis unchangedsowecanignoreit above).Weneedtoverifythatusingtheinducto rin thegivenapplication:(a)currentripplerati o r' is closetodesired(b)peakfluxdensity/current arewithinbounds(c)temperatureriseis acceptableUsingTable2:a) r':DesignValue:(40)(41)r = :(42)(43)r = r higherinductancethanwerequired(137 H insteadof127 H).Thisis May2001 RevisedApril2013 SubmitDocumentationFeedbackCopyright 2001 2013, )PeakFluxDensityDesignValue:(44)(45)BPEA K= 3267 GaussExtrapolatedtoourApplication:(46)(4 7)B PEAK= 3084 Gausswhichis )PeakCurrentToensurethattheregulatorwill deliverratedload,weneedtoensurethatthepe akcurrentis :(48)(49)IPEAK= :(50)(51)I PEAK= B-fieldof3084 Gaussascalculatedaboveandis lessthanICLIM.