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1、Pulse-widthmodulationPulse-widthmodulation(PWM)isamodulationtechniquethatconformsthewidthofthepulse,formallythepulseduration,basedonmodulatorsignalinformation.Althoughthismodulationtechniquecanbeusedtoencodeinformationfortransmission,itsmainuseistoallowthecontrolofthepowersuppliedtoelectricaldevices
2、,especiallytoinertialloadssuchasmotors.Inaddition,PWMisoneofthetwoprincipalalgorithmsusedinPhOtOVOltaiCsolarbatterychargers,Theaveragevalueofvoltage(andcurrent)fedtotheIOadiscontrolledbyturningtheswitchbetweensupplyandloadonandoffatafastpace.Thelongertheswitchisoncomparedtotheoffperiods,thehigherthe
3、powersuppliedtotheloadis.ThePWMswitchingfrequencyhastobemuchfasterthanwhatwouldaffecttheload,whichistosaythedevicethatusesthepower.Typicallyswitchingshavetobedoneseveraltimesaminuteinanelectricstove,120Hzinalampdimmer,fromfewkilohertz(kHz)totensofkHzforamotordriveandwellintothetensorhundredsofkHzina
4、udioamplifiersandcomputerpowersupplies.ThetermdutyCyeIedescribestheproportionofontimetotheregularintervalor,period*oftime;alowdutycyclecorrespondstolowpower,becausethepowerisoffformostofthetime.Dutycycleisexpressedinpercent,100%beingfullyon.ThemainadvantageofPwMisthatpowerlossintheswitchingdevicesis
5、verylow.Whenaswitchisoffthereispracticallynocurrent,andwhenitison,thereisalmostnovoltagedropacrosstheswitch.Powerloss,beingtheproductofvoltageandcurrent,isthusinbothcasesclosetozero.PWMalsoworkswellwithdigitalcontrols,which,becauseoftheiron/offnature,caneasilysettheneededdutycycle.PWMhasalsobeenused
6、incertainCommUniCationSyStemSwhereitsdutycyclehasbeenusedtoconveyinformationoveracommunicationschannel.HistoryInthepast,whenonlypartialpowerwasneeded(suchasforaSeWingmachinemotor),arheostat(locatedinthesewingmachine,Sfootpedal)connectedinserieswiththemotoradjustedtheamountofcurrentflowingthroughthem
7、otor,butalsowastedpowerasheatintheresistorelement.Itwasaninefficientscheme,buttolerablebecausethetotalpowerwaslow.Thiswasoneofseveralmethodsofcontrollingpower.Therewereotherssomestillinuse-suchasvariableautotransformers,includingthetrademarkedAutrastatfortheatricallighting;andtheVariac,forgeneralACp
8、oweradjustment.Thesewerequiteefficient,butalsorelativelycostly.Foraboutacentury,somevariable-speedelectricmotorshavehaddecentefficiency,buttheyweresomewhatmorecomplexthanconstant-speedmotors,andsometimesrequiredbulkyexternalelectricalapparatus,suchasabankofvariablepowerresistorsorrotatingconvertersu
9、chasWardLeOnarddrive.However,inadditiontomotordrivesforfans,pumpsandroboticservos,therewasagreatneedforcompactandlowcostmeansforapplyingadjustablepowerformanydevices,suchaselectricstovesandlampdimmers.OneearlyapplicationofPWMwasintheSinCIairX10,a10Waudioamplifieravailableinkitforminthe1960s.Ataround
10、thesametimePWMstartedtobeusedinACmotorcontrol.DTT gDF n QZx)9) Yf OT4D9)Fig. 1: a PUlSe wave, showing the definitions of Vmni UnIZLTand D.s*4Pulse-widthmodulationusesarectangularPUISCWaVCwhosepulsewidthismodulatedresultinginthevariationoftheaveragevalueofthewaveform.Ifweconsiderapulsewaveform/),with
11、periodT,lowvalueUmin,ahighvalueVmandadulyCyCICD(seefigure1),theaveragevalueofthewaveformisgivenby:1ry=f必/JnAs/(t)isapulsewave,itsvalueisVmarfor0fe).TandVminfor力.TVfVT.Theaboveexpressionthenbecomes:=DVnx+(1。)VminThislatterexpressioncanbefairlysimplifiedinmanycaseswhereUmin=OaSQ=DUma.Fromthis,itisobvi
12、ousthattheaveragevalueofthesignal(U)isdirectlydependentonthedutycycleDFig.2:AsimplemethodtogeneratethePWMpulsetraincorrespondingtoagivensignalistheIntersectivePWM:thesignal(heretheredsinewave)iscomparedwithasawtoothwaveform(blue).Whenthelatterislessthantheformer,thePWMsignal(magenta)isinhighstate(1)
13、.Otherwiseitisinthelowstate(0).ThesimplestwaytogenerateaPWMsignalistheintersectivemethod,whichrequiresonlyaSaWtoOthoratrianglewaveform(easilygeneratedusimpleOSCiHatOr)andacomparator.Whenthevalueofthereferencesignal(theredsinewaveinfigure2)ismorethanthemodulationwaveform(blue),thePWMsignal(magenta)is
14、inthehighstate,otherwiseitisinthelowstate.TimeproportioningManydigitalcircuitscangeneratePwMsignals(e.g.,manyIniCroContrOIlCrShavePwMoutputs).TheynormallyuseaCOImterthatincrementsperiodically(itisconnecteddirectlyorindirectlytotheClOCkofthecircuit)andisresetattheendofeveryperiodofthePWM.Whenthecount
15、ervalueismorethanthereferencevalue,thePWMoutputchangesstatefromhightolow(orlowtohigh).3Thistechniqueisreferredtoastimeproportioning,particularlyastime-proportioningcontrol4-whichproportionofafixedCyeIetimeisspentinthehighstate.Theincrementedandperiodicallyresetcounteristhediscreteversionoftheinterse
16、ctingmethod,ssawtooth.Theanalogcomparatoroftheintersectingmethodbecomesasimpleintegercomparisonbetweenthecurrentcountervalueandthedigital(possiblydigitized)referencevalue.Thedutycyclecanonlybevariedindiscretesteps,asafunctionofthecounterresolution.However,ahigh-resolutioncountercanprovidequitesatisf
17、actoryperformance.PWMsamplingtheoremTheprocessofPwMconversionisnon-linearanditisgenerallysupposedthatlowpassfiltersignalrecoveryisimperfectforPWM.ThePWMsamplingtheorem6showsthatPWMconversioncanbeperfect.ThetheoremstatesthatAnybandlimitedbasebandsignalwithin0.637canberepresentedbyapulsewidthmodulatio
18、n(PWM)waveformwithunitamplitude.ThenumberofpulsesinthewaveformisequaltothenumberofNyquistsamplesandthepeakconstraintisindependentofwhetherthewaveformistwo-levelorthree-level.,PowerdeliveryPWMcanbeusedtocontroltheamountofpowerdeliveredtoaloadwithoutincurringthelossesthatwouldresultfromlinearpowerdeli
19、verybyresistivemeans.Potentialdrawbackstothistechniquearethepulsationsdefinedbythedutycycle,switchingfrequencyandpropertiesoftheload.Withasufficientlyhighswitchingfrequencyand,whennecessary,usingadditionalpassiveCICCtroniCfilters,thepulsetraincanbesmoothedandaverageanalogwaveformrecovered.Highfreque
20、ncyPWMpowercontrolsystemsareeasilyrealisablewithsemiconductorswitches.Asexplainedabove,almostnopowerisdissipatedbytheswitchineitheronoroffstate.However,duringthetransitionsbetweenonandoffstates,bothvoltageandcurrentarenonzeroandthuspowerisdissipatedintheswitches.Byquicklychangingthestatebetweenfully
21、onandfullyoff(typicallylessthan100nanoseconds),thepowerdissipationintheswitchescanbequitelowcomparedtothepowerbeingdeliveredtotheload.ModernsemiconductorswitchessuchasMOSFETsorInSUIated-gatebipolartransistors(IGBTs)arewellsuitedcomponentsforhighefficiencycontrollers.FrequencyconvertersusedtocontrolA
22、Cmotorsmayhaveefficienciesexceeding98%.Switchingpowersupplieshavelowerefficiencyduetolowoutputvoltagelevels(oftenevenlessthan2Vformicroprocessorsareneeded)butstillmorethan70-80%efficiencycanbeachieved.Variable-speedfancontrollersforcomputersusuallyusePWM,asitisfarmoreefficientwhencomparedtoaPOtentiO
23、meterorrheostat.(Neitherofthelatterispracticaltooperateelectronically;theywouldrequireasmalldrivemotor.)1.ightdimmersforhomeuseemployaspecifictypeofPWMcontrol.Home-uselightdimmerstypicallyincludeelectroniccircuitrywhichsuppressescurrentflowduringdefinedportionsofeachcycleoftheAClinevoltage.Adjusting
24、thebrightnessoflightemittedbyalightsourceisthenmerelyamatterofsettingatwhatvoltage(orphase)intheAChalfcyclethedimmerbeginstoprovideelectricalcurrenttothelightsource(e.g.byusinganelectronicswitchsuchasatriac).InthiscasethePWMdutycycleistheratiooftheconductiontimetothedurationofthehalfACcycledefinedby
25、thefrequencyoftheAClinevoltage(50Hzor60Hzdependingonthecountry).VoltageregulationMainarticle：SWitchednK)dePoWerSUPpIyPWMisalsousedinefficientVOltageregulators.Byswitchingvoltagetotheloadwiththeappropriatedutycycle,theoutputwillapproximateavoltageatthedesiredlevel.Theswitchingnoiseisusuallyfilteredwi
26、thaninductorandacapacitor.Onemethodmeasurestheoutputvoltage.Whenitislowerthanthedesiredvoltage,itturnsontheswitch.Whentheoutputvoltageisabovethedesiredvoltage,itturnsofftheswitch.AudioeffectsandamplificationPWMissometimesusedinsound(music)synthesis,inparticularSUbtraCtiVeSynthesis,asitgivesasoundeff
27、ectsimilartochorusorslightlydetunedoscillatorsplayedtogether.(Infact,PWMisequivalenttothedifferenceoftwoSaWtOOthWaVeSwithoneoftheminverted.1)TheratiobetweenthehighandlowlevelistypicallymodulatedwithaIOWfrequencyoscillator.Inaddition,varyingthedutycycleofapulsewaveforminasubtractive-synthesisinstrume
28、ntcreatesusefultimbralvariations.Somesynthesizershaveaduty-cycletrimmerfortheirsquarewaveoutputs,andthattrimmercanbesetbyear;the50%point(truesquarewave)wasdistinctive,becauseeven-numberedharmonicsessentiallydisappearat50%.Pulsewaves,usually50%,25%,and12.5%,makeuptheSOUndtraCkSOfCIaSSiCViCIeogames.ne
29、wclassofaudioamplifiersbasedonthePWMprincipleisbecomingpopular.CalledciassT)amplifiers”,theyproduceaPWMequivalentoftheanaloginputsignalwhichisfedtotheIoUdSPeakerviaasuitablefilternetworktoblockthecarrierandrecovertheoriginalaudio.Theseamplifiersarecharacterizedbyverygoodefficiencyfigures(90%)andcomp
30、actsize/lightweightforlargepoweroutputs.Forafewdecades,industrialandmilitaryPWMamplifiershavebeenincommonuse,oftenfordrivingservomotors.Field-gradientcoilsinMRImachinesaredrivenbyrelativelyhigh-powerPWMamplifiers.Historically,acrudeformofPWMhasbeenusedtoplaybackPCMdigitalsoundonthePCspeaker,whichisd
31、rivenbyonlytwovoltagelevels,typically0Vand5V.Bycarefullytimingthedurationofthepulses,andbyrelyingonthespeaker*sphysicalfilteringproperties(limitedfrequencyresponse,self-inductance,etc.)itwaspossibletoobtainanapproximateplaybackofmonoPCMsamples,althoughataverylowquality,andwithgreatlyvaryingresultsbe
32、tweenimplementations.Inmorerecenttimes,theDir。CtStrCamDigitalsoundencodingmethodwasintroduced,whichusesageneralizedformofpulse-widthmodulationcalledPUlSedensitymodulation,atahighenoughsamplingrate(typicallyintheorderofMHz)tocoverthewholeacousticfrequenciesrangewithsufficientfidelity.ThismethodisusedintheSACDformat,andreproductionoftheencodedaudiosignalisessentiallysimilartothemethodusedinclassDamplifiers.
