TypicalElectricalWaveform
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IntroductiontoWaveforms
IntheOscillatorstutorialswesawthatanoscillatorisanelectroniccircuitusedtogenerateacontinuousoutput
signalusuallyintheformofasinusoidatsomepredeterminedfrequencyorwavelengthsetbytheresonantcomponents
ofthecircuit.Wealsosawthattherearemanydifferenttypesofoscillatorcircuitsavailablebutgenerallytheyallconsist
ofanamplifierandeitheranInductor-Capacitor,(LC)orResistor-Capacitor,(RC)tankcircuitusedtoproduceasine
wavetypeoutputsignal.
Butsometimesinelectroniccircuitsweneedtoproducemany
differenttypes,frequenciesandshapesofSignalWaveformsuchas
Square,RectangularTriangularorSawtoothedwaveforms.
Thesetypesofsignalwaveformcanthenbeusedforeithertiming
signals,clocksignalsorastriggerpulses.However,beforewecan
begintolookathowthedifferenttypesofwaveformsareproduced,we
firstlyneedtounderstandthebasiccharacteristicsthatmakeupan
electricalWaveform.
Technicallyspeaking,anElectricalWaveformisbasicallyavisualrepresentationofthevariationofavoltageorcurrent
overtime.InplainEnglishthismeansthatifweplottedthesevoltageorcurrentvariationsonapieceofgraphpaper
againstabase(x-axis)oftime,(t)theresultingplotordrawingwouldrepresenttheshapeofaWaveformasshown.
Therearemanydifferenttypesofwaveformsavailablebuttheycanallbebrokendownintotwodistinctivegroups.
1.Uni-directionalWaveforms-thesewaveformsarealwayspositiveornegativein
natureflowinginoneforwarddirectiononlyastheydonotcrossthezeroaxispoint.Common
uni-directionalwaveformsincludeSquare-wavetimingsignals,ClockpulsesandTrigger
pulses.
2.Bi-directionalWaveforms-thesewaveformsarealsocalledalternatingwaveformsas
theyalternatefromapositivedirectiontoanegativedirectionconstantlycrossingthezeroaxis
point.Bi-directionalwaveformsgothroughperiodicchangesinamplitude,withthemost
commonbyfarbeingtheSine-wave.
Whetherthewaveformisuni-directional,bi-directional,periodic,non-periodic,symmetrical,non-symmetrical,simpleor
complex,allelectricalwaveformsincludethefollowingthreecommoncharacteristics:
1).Period:–Thisisthelengthoftimeinsecondsthatthewaveformtakestorepeatitselffrom
starttofinish.ThisvaluecanalsobecalledthePeriodicTime,(T)ofthewaveformforsine
waves,orthePulseWidthforsquarewaves.
2).Frequency:–Thisisthenumberoftimesthewaveformrepeatsitselfwithinaonesecond
timeperiod.Frequencyisthereciprocalofthetimeperiod,(?=1/T)withthestandardunitof
frequencybeingtheHertz,(Hz).
3).Amplitude:–Thisisthemagnitudeorintensityofthesignalwaveformmeasuredinvolts
oramps.
PeriodicWaveforms
PeriodicwaveformsarethemostcommonofallthewaveformtypesasitincludesSineWaves.TheAC(Alternating
Current)mainswaveforminyourhomeisasinewaveandonewhichconstantlyalternatesbetweenamaximumvalue
andaminimumvalueovertime.Theamountoftimeittakesbetweeneachindividualrepetitionorcycleofasinusoidal
waveformisknownasits"periodictime"orsimplythePeriodofthewaveform.Inotherwords,thetimeittakesforthe
waveformtorepeatitself.
Thenthisperiodcanvarywitheachwaveformfromfractionsofasecondtothousandsofsecondsasitdependsupon
thefrequencyofthewaveform.Forexample,asinusoidalwaveformwhichtakesonesecondtocompleteitscyclewill
haveaperiodictimeofonesecond.Likewiseasinewavewhichtakesfivesecondstocompletewillhaveaperiodictime
offivesecondsandsoon.
So,ifthelengthoftimeittakesforthewaveformtocompleteonefullpatternorcyclebeforeitrepeatsitselfisknownas
the"periodofthewave"andismeasuredinseconds,wecanthenexpressthewaveformasaperiodnumberper
seconddenotedbytheletterTasshownbelow.
ASineWaveWaveform
Unitsofperiodictime,(T)include:Seconds(s),milliseconds(ms)andmicroseconds(μs).
Forsinewavewaveformsonly,wecanalsoexpresstheperiodictimeofthewaveformineitherdegreesorradians,as
onefullcycleisequalto360(T=360)orinradiansas2pi,2π(T=2π),thenwecansaythat2πradians=360-
(Rememberthis!).
Wenowknowthatthetimeittakesforawaveformtorepeatitselfisknownastheperiodictimeorperiodwhich
representsafixedamountoftime.Ifwetakethereciprocaloftheperiod,(1/T)weendupwithavaluethatdenotesthe
numberoftimesaperiodorcyclerepeatsitselfinonesecondorcyclespersecond,andthisiscommonlyknown
asFrequencywithunitsofHertz,(Hz).ThenHertzcanalsobedefinedas"cyclespersecond"(cps)and1Hzisexactly
equalto1cyclepersecond.
Bothperiodandfrequencyaremathematicalreciprocalsofeachotherandastheperiodictimeofthewaveform
decreases,itsfrequencyincreasesandviceversawiththerelationshipbetweenPeriodictimeandFrequencygivenas.
RelationshipbetweenFrequencyandPeriodicTime
Where:?isinHertzandTisinSeconds.
OneHertzisexactlyequaltoonecyclepersecond,butonehertzisaverysmallunitsoprefixesareusedthatdenotethe
orderofmagnitudeofthewaveformsuchaskHz,MHzandevenGHz.
PrefixDefinitionWrittenasTimePeriod
KiloThousandkHz1ms
MegaMillionMHz1us
ooo
GigaBillionGHz1ns
TeraTrillionTHz1ps
SquareWaveWaveforms
Square-waveWaveformsareusedextensivelyinelectronicandmicroelectroniccircuitsforclockandtimingcontrol
signalsastheyaresymmetricalwaveformsofequalandsquaredurationrepresentingeachhalfofacycleandnearlyall
digitallogiccircuitsusesquarewavewaveformsontheirinputandoutputgates.Unlikesinewaveswhichhavea
smoothriseandfallwaveformwithroundedcornersattheirpositiveandnegativepeaks,squarewavesontheother
handhaveverysteepalmostverticalupanddownsideswithaflattopandbottomproducingawaveformwhichmatches
itsdescription,-"Square"asshownbelow.
ASquareWaveWaveform
Weknowthatsquarewavewaveformsaresymmetricalinshapeaseachhalfofthecycleisidentical,sothetimethatthe
pulsewidthispositivemustbeequaltothetimethatthepulsewidthisnegativeorzero.Whensquarewavewaveforms
areusedas"clock"signalsindigitalcircuitsthetimeofthepositivepulsewidthisknownasthe"DutyCycle"ofthe
period.
Thenwecansaythatforasquarewavewaveformthepositiveor"ON"timeisequaltothenegativeor"OFF"timesothe
dutycyclemustbe50%,(halfofitsperiod).Asfrequencyisequaltothereciprocaloftheperiod,(1/T)wecandefinethe
frequencyofasquarewavewaveformas:
ExampleNo1
ASquareWavewaveformhasapulsewidthof10ms,calculateitsfrequency,(?).
Forasquarewaveshapedwaveform,thedutycycleisgivenas50%,thereforetheperiodofthewaveformmustbeequal
to:10ms+10msor20ms
Sotosummarise,SquarewaveWaveformsaresymmetricalinshapeandhaveapositivepulsewidthequaltothe
negativepulsewidthresultingina50%dutycycle.Squarewavewaveformsareusedindigitalsystemstorepresenta
logiclevel"1",highamplitudeandlogiclevel"0",lowamplitude.Ifthedutycycleofthewaveformisanyothervaluethan
50%theresultingwaveformwouldthenbecalledaRectangularWaveformoraPulse.
RectangularWaveforms
RectangularWaveformsaresimilartothesquarewavewaveformabove,thedifferencebeingthatthetwopulsewidths
ofthewaveformareofanunequaltimeperiod.Rectangularwaveformsarethereforeclassedas"Non-symmetrical"
waveformsasshownbelow.
ARectangularWaveform
Theexampleaboveshowsthatthepositivepulsewidthisshorterintimethanthenegativepulsewidth.Equally,the
negativepulsewidthcouldbeshorterthanthepositivepulsewidth,eitherwaytheresultingwaveformshapewouldstill
bethatofarectangularwaveform.
Thesepositiveandnegativepulsewidthsaresometimescalled"Mark"and"Space"respectively,withtheratioofthe
MarktimetotheSpacetimebeingknownasthe"Mark-to-Space"ratiooftheperiodandforaSquarewavewaveformthis
wouldbeequaltoone.
ExampleNo2
ARectangularwaveformhasapositivepulsewidth(Marktime)of10msandadutycycleof25%,calculateitsfrequency.
Thedutycycleisgivenas25%or1/4andthisisequaltothemarktimewhichis10ms,thentheperiodofthewaveform
mustbeequalto:10ms(25%)+30ms(75%)whichequals40ms(100%)intotal.
RectangularWaveformscanbeusedtoregulatetheamountofpowerbeingappliedtoaloadsuchasalampormotor
byvaryingthedutycycleofthewaveform.Thehigherthedutycycle,thegreatertheaverageamountofpowerbeing
appliedtotheloadandthelowerthedutycycle,thelesstheaverageamountofpowerbeingappliedtotheloadandan
excellentexampleofthisisintheuseof"PulseWidthModulation"speedcontrollers.
TriangularWaveforms
TriangularWaveformsaregenerallybi-directionalnon-sinusoidalwaveformsthatoscillatebetweenapositiveanda
negativepeakvalue.Althoughcalledatriangularwaveform,thetriangularwaveisactuallymoreofasymmetricallinear
rampwaveformbecauseitissimplyaslowrisingandfallingvoltagesignalataconstantfrequencyorrate.Therateat
whichthevoltagechangesbetweeneachrampdirectionisequalduringbothhalvesofthecycleasshownbelow.
ATriangularWaveform
Generally,forTriangularWaveformsthepositive-goingramporslope(rise),isofthesametimedurationasthe
negative-goingramp(decay)givingthetriangularwaveforma50%dutycycleandforagivenvoltageamplitudethe
frequencyofthewaveformwilldeterminetheaveragevoltagelevelofthewave,asaslowriseandslowdelaytimeofthe
rampwillgivealowervoltagelevelthanafastriseanddecaytime.However,wecanproducenon-symmetricaltriangular
waveformsbyvaryingeithertherisingordecayingrampvaluestogiveusanothertypeofwaveformknowncommonlyas
aSawtoothWaveform.
SawtoothWaveforms
SawtoothWaveformsareanothertypeofperiodicwaveform.Asitsnamesuggests,theshapeofthewaveform
resemblestheteethofasawblade.Sawtoothedwaveformscanhaveamirrorimageofthemselves,byhavingeithera
slow-risingbutextremelysteepdecay,oranextremelysteepalmostverticalriseandaslow-decayasshownbelow.
SawtoothWaveforms
ThepositiverampSawtoothWaveformisthemorecommonofthetwowaveformtypeswiththerampportionofthe
wavebeingalmostperfectlylinear.TheSawtoothwaveformiscommonlyavailablefrommostfunctiongeneratorsand
consistsofafundamentalfrequency(?)andallitsintegerratiosofevenharmonicsonly,1/2,1/4,1/61/8...1/netc.What
thismeansinpracticaltermsisthattheSawtoothedWaveformisrichinharmonicsandformusicsynthesizersand
musiciansgivesthequalityofthesoundortonalcolourtotheirmusicwithoutanydistortion.
TriggersandPulses
AlthoughtechnicallyTriggersandPulsesaretwoseparatewaveforms,wecancombinethemtogetherhere,asa
"Trigger"isbasicallyaverynarrow"Pulse".Thedifferencebeingisthatatriggercanbeeitherpositiveornegativein
directionwhereasapulseisonlypositiveindirection.
APulseWaveformor"Pulse-train"astheyaremorecommonlycalled,isatypeofnon-sinusoidalwaveformthatis
similartotheRectangularwaveformwelookedatearlier.Thedifferencebeingthattheexactshapeofthepulseis
determinedbythe"Mark-to-Space"ratiooftheperiodandforapulseortriggerwaveformtheMarkportionofthewaveis
veryshortwitharapidriseanddecayshapeasshownbelow.
APulseWaveform
APulseisawaveformorsignalinitsownright.IthasverydifferentMark-to-Spaceratiocomparedtoahighfrequency
squarewaveclocksignalorevenarectangularwaveform.Thepurposeofa"Pulse"andthatofatriggeristoproducea
veryshortsignaltocontrolthetimeatwhichsomethinghappensforexample,tostartaTimer,Counter,Monostableor
Flip-flopetc,orasatriggertoswitch"ON"Thyristors,Triacsandotherpowersemiconductordevices.
FunctionGenerator
AFunctionGeneratororsometimescalledaWaveformGeneratorisadeviceorcircuitthatproducesavarietyof
differentwaveformsatadesiredfrequency.ItcangenerateSinewaves,Squarewaves,TriangularandSawtooth
waveformsaswellasothertypesofoutputwaveforms.Therearemany"off-the-shelf"waveformgeneratorIC''savailable
andallcanbeincorporatedintoacircuittoproducethedifferentperiodicwaveformsrequired.
Onesuchdeviceisthe8038aprecisionwaveformgeneratorICcapableofproducingsine,squareandtriangularoutput
waveforms,withaminimumnumberofexternalcomponentsoradjustments.Itsoperatingfrequencyrangecanbe
selectedovereightdecadesoffrequency,from0.001Hzto300kHz,bythecorrectchoiceoftheexternalR-Ccomponents.
WaveformGeneratorIC
Thefrequencyofoscillationishighlystableoverawiderangeoftemperatureandsupplyvoltagechangesand
frequenciesashighas1MHzispossible.Eachofthethreebasicwaveformoutputs,sinusoidal,triangularandsquare
aresimultaneouslyavailablefromindependentoutputterminals.Thefrequencyrangeofthe8038isvoltagecontrollable
butnotalinearfunction.Thetrianglesymmetryandhencethesinewavedistortionareadjustable.
InthenexttutorialaboutWaveforms,wewilllookatMultivibratorsthatareusedtoproducecontinuousoutput
waveformsorsingleindividualpulses.Onesuchmultivibratorcircuitthatisusedasapulsegeneratoriscalled
aMonostableMultivibrator.
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