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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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