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Pulse-widthmodulation

Pulse-widthmodulation(PWM)isa

modulation

techniquethatconformsthewidthofthepulse,formallythepulseduration,basedonmodulatorsignalinformation.Althoughthismodulationtechniquecanbeusedtoencodeinformationfortransmission,itsmainuseistoallowthecontrolofthepowersuppliedtoelectricaldevices,especiallytoinertialloadssuchasmotors.Inaddition,PWMisoneofthetwoprincipalalgorithmsusedin

photovoltaic

solarbatterychargers,

[1]

Theaveragevalueofvoltage(andcurrent)fedtothe

load

iscontrolledbyturningtheswitchbetweensupplyandloadonandoffatafastpace.Thelongertheswitchisoncomparedtotheoffperiods,thehigherthepowersuppliedtotheloadis.

ThePWMswitchingfrequencyhastobemuchfasterthanwhatwouldaffecttheload,whichistosaythedevicethatusesthepower.Typicallyswitchingshavetobedoneseveraltimesaminuteinanelectricstove,120

Hz

inalampdimmer,fromfewkilohertz(kHz)totensofkHzforamotordriveandwellintothetensorhundredsofkHzinaudioamplifiersandcomputerpowersupplies.

Theterm

dutycycle

describestheproportionof'on'timetotheregularintervalor'period'oftime;alowdutycyclecorrespondstolowpower,becausethepowerisoffformostofthetime.Dutycycleisexpressedinpercent,100%beingfullyon.

ThemainadvantageofPWMisthatpowerlossintheswitchingdevicesisverylow.Whenaswitchisoffthereispracticallynocurrent,andwhenitison,thereisalmostnovoltagedropacrosstheswitch.Powerloss,beingtheproductofvoltageandcurrent,isthusinbothcasesclosetozero.PWMalsoworkswellwithdigitalcontrols,which,becauseoftheiron/offnature,caneasilysettheneededdutycycle.

PWMhasalsobeenusedincertain

communicationsystems

whereitsdutycyclehasbeenusedtoconveyinformationoveracommunicationschannel.

History

Inthepast,whenonlypartialpowerwasneeded(suchasfora

sewingmachine

motor),a

rheostat

(locatedinthesewingmachine'sfootpedal)connectedinserieswiththemotoradjustedtheamountofcurrentflowingthroughthemotor,butalsowastedpowerasheatintheresistorelement.Itwasaninefficientscheme,buttolerablebecausethetotalpowerwaslow.Thiswasoneofseveralmethodsofcontrollingpower.Therewereothers—somestillinuse—suchasvariable

autotransformers

,includingthe

trademarked

'Autrastat'fortheatricallighting;andthe

Variac

,forgeneralACpoweradjustment.Thesewerequiteefficient,butalsorelativelycostly.

Foraboutacentury,somevariable-speedelectricmotorshavehaddecentefficiency,buttheyweresomewhatmorecomplexthanconstant-speedmotors,andsometimesrequiredbulkyexternalelectricalapparatus,suchasabankofvariablepowerresistorsorrotatingconvertersuchas

WardLeonarddrive

.

However,inadditiontomotordrivesforfans,pumpsand

robotic

servos

,therewasagreatneedforcompactandlowcostmeansforapplyingadjustablepowerformanydevices,suchaselectricstovesandlampdimmers.

OneearlyapplicationofPWMwasinthe

Sinclair

X10,a10Waudioamplifieravailableinkitforminthe1960s.AtaroundthesametimePWMstartedtobeused

inACmotorcontrol.

Fig.1:a

pulsewave

,showingthedefinitionsof,andD.

Pulse-widthmodulationusesa

rectangularpulsewave

whosepulsewidthismodulatedresultinginthevariationofthe

average

valueofthewaveform.Ifweconsiderapulsewaveform,withperiod,lowvalue,ahighvalueanda

dutycycle

D(seefigure1),theaveragevalueofthewaveformisgivenby:

Asisapulsewave,itsvalueisforandfor.Theaboveexpressionthenbecomes:

Thislatterexpressioncanbefairlysimplifiedinmanycaseswhereas.Fromthis,itisobviousthattheaveragevalueofthesignal()isdirectlydependentonthedutycycleD

Fig.2:AsimplemethodtogeneratethePWMpulsetraincorrespondingtoagivensignalistheintersectivePWM:thesignal(heretheredsinewave)iscomparedwithasawtoothwaveform(blue).Whenthelatterislessthantheformer,thePWMsignal(magenta)isinhighstate(1).Otherwiseitisinthelowstate(0).

ThesimplestwaytogenerateaPWMsignalistheintersectivemethod,whichrequiresonlya

sawtooth

ora

triangle

waveform(easilygeneratedusimple

oscillator

)anda

comparator

.Whenthevalueofthe

referencesignal(theredsinewaveinfigure2)ismorethanthemodulationwaveform(blue),thePWM

signal(magenta)isinthehighstate,otherwiseitisinthelowstate.

Timeproportioning

ManydigitalcircuitscangeneratePWMsignals(e.g.,many

microcontrollers

havePWMoutputs).Theynormallyusea

counter

thatincrementsperiodically(itisconnecteddirectlyorindirectlytothe

clock

ofthecircuit)andisresetattheendofeveryperiodofthePWM.Whenthecountervalueismorethanthereferencevalue,thePWMoutputchangesstatefromhightolow(orlowtohigh).

[3]

Thistechniqueisreferredtoastimeproportioning,particularlyastime-proportioningcontrol

[4]

–whichproportionofafixed

cycletime

isspentinthehighstate.

Theincrementedandperiodicallyresetcounteristhediscreteversionoftheintersectingmethod'ssawtooth.Theanalogcomparatoroftheintersectingmethodbecomesasimpleintegercomparisonbetweenthecurrentcountervalueandthedigital(possiblydigitized)referencevalue.Thedutycyclecanonlybevariedindiscretesteps,asafunctionofthecounterresolution.However,ahigh-resolutioncountercanprovidequitesatisfactoryperformance.

PWMsamplingtheorem

TheprocessofPWMconversionisnon-linearanditisgenerallysupposedthatlowpassfiltersignalrecoveryisimperfectforPWM.ThePWMsamplingtheorem

[6]

showsthatPWMconversioncanbeperfect.Thetheoremstatesthat"Anybandlimitedbasebandsignalwithin±0.637canberepresentedbyapulsewidthmodulation(PWM)waveformwithunitamplitude.ThenumberofpulsesinthewaveformisequaltothenumberofNyquistsamplesandthepeakconstraintisindependentofwhetherthewaveformistwo-levelorthree-level."

Powerdelivery

PWMcanbeusedtocontroltheamountofpowerdeliveredtoaloadwithoutincurringthelossesthatwouldresultfromlinearpowerdeliverybyresistivemeans.Potentialdrawbackstothistechniquearethepulsationsdefinedbythedutycycle,switchingfrequencyandpropertiesoftheload.Withasufficientlyhighswitchingfrequencyand,whennecessary,usingadditionalpassive

electronicfilters

,thepulsetraincanbesmoothedandaverageanalogwaveformrecovered.

High

frequency

PWMpowercontrolsystemsareeasilyrealisablewithsemiconductorswitches.Asexplainedabove,almostnopowerisdissipatedbytheswitchineitheronoroffstate.However,duringthetransitionsbetweenonandoffstates,bothvoltageandcurrentarenonzeroandthuspowerisdissipatedintheswitches.Byquicklychangingthestatebetweenfullyonandfullyoff(typicallylessthan100nanoseconds),thepowerdissipationintheswitchescanbequitelowcomparedtothepowerbeingdeliveredtotheload.

Modernsemiconductorswitchessuchas

MOSFETs

or

Insulated-gatebipolartransistors

(IGBTs)arewellsuitedcomponentsforhighefficiencycontrollers.FrequencyconvertersusedtocontrolACmotorsmayhaveefficienciesexceeding98%.Switchingpowersupplieshavelowerefficiencyduetolowoutputvoltagelevels(oftenevenlessthan2Vformicroprocessorsareneeded)butstillmorethan70–80%efficiencycanbeachieved.

Variable-speedfancontrollersforcomputersusuallyusePWM,asitisfarmoreefficientwhencomparedtoa

potentiometer

or

rheostat

.(Neitherofthelatterispracticaltooperateelectronically;theywouldrequireasmalldrivemotor.)

LightdimmersforhomeuseemployaspecifictypeofPWMcontrol.Home-uselightdimmerstypicallyincludeelectroniccircuitrywhichsuppressescurrentflowduringdefinedportionsofeachcycleoftheAClinevoltage.Adjustingthebrightnessoflightemittedbyalightsourceisthenmerelyamatterofsettingatwhatvoltage(orphase)intheAChalfcyclethedimmerbeginstoprovideelectricalcurrenttothelightsource(e.g.byusinganelectronicswitchsuchasa

triac

).InthiscasethePWMdutycycleistheratiooftheconductiontimetothedurationofthehalfACcycledefinedbythefrequencyoftheAClinevoltage(50Hzor60Hzdependingonthecountry).

Voltageregulation

Mainarticle:

Switched-modepowersupply

PWMisalsousedinefficient

voltageregulators

.Byswitchingvoltagetotheloadwiththeappropriatedutycycle,theoutputwillapproximateavoltageatthedesiredlevel.Theswitchingnoiseisusuallyfilteredwithan

inductor

anda

capacitor

.

Onemethodmeasurestheoutputvoltage.Whenitislowerthanthedesiredvoltage,itturnsontheswitch.Whentheoutputvoltageisabovethedesiredvoltage,itturnsofftheswitch.

Audioeffectsandamplification

PWMissometimesusedinsound(music)synthesis,inparticular

subtractivesynthesis

,asitgivesasoundeffectsimilartochorusorslightlydetunedoscillatorsplayedtogether.(Infact,PWMisequivalenttothedifferenceoftwo

sawtoothwaves

withoneoftheminverted.

[1]

)Theratiobetweenthehighandlowlevelistypicallymodulatedwitha

lowfrequencyoscillator

.Inaddition,varyingthedutycycleofapulsewaveforminasubtractive-synthesisinstrumentcreatesusefultimbralvariations.Somesynthesizershaveaduty-cycletrimmerfortheirsquare-waveoutputs,andthattrimmercanbesetbyear;the50%point(truesquarewave)wasdistinctive,becauseeven-numberedharmonicsessentiallydisappearat50%.Pulsewaves,usually50%,25%,and12.5%,makeupthe

soundtracksofclassicvideogames

.

AnewclassofaudioamplifiersbasedonthePWMprincipleisbecomingpopular.Called"

Class-Damplifiers

",theyproduceaPWMequivalentoftheanaloginputsignalwhichisfedtothe

loudspeaker

viaasuitablefilternetworktoblockthecarrierandrecovertheoriginalaudio.Theseamplifiersarecharacterizedbyverygoodefficiencyfigures(≥90%)andcompactsize/lightweightforlargepoweroutputs.Forafew

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