1

In this lecture, we will look at how we supply energy to electronic circuits (source) and how such energy is dissipated in circuits.

Wehavehadabrieflookatenergyandpowerinelectricalcircuitsinearlierlecture.Hereisareminderofsomeofthebasicdefinitionofelectricalenergyandelectricalpower.1jouleofelectricalenergyistheenergyrequiredtomove1coulombofchargethroughanelectricalpotentialof1volt.Electricalpowerisenergyusedpersecond,i.e.Energy/time.ThereforeifyouconsiderpowerdissipatedinacircuitonlyusingDCvoltagesourceandthecurrentisessentiallyconstant,thenPower=VxIwhichisprettystraightforward.1wattisusing1Jofenergypersecond.Itisworthputtingsomephysicallymeaningtothese.Atraditionalincandescentlightbulbathomewoulddissipatearound40Wto60W.Therefore1Wisprettysmall.Thei5processorinsideyourlaptopdissipate15W,whichisalreadylowascomparedwiththepowerhungrydesktopversionthatcoulddrawasmuchas50W.HowevertheLEDyouusedinLab4Task1(becauseofthe330W resistoryouusedinseries)hasacurrentofaround7mAfromthe5Vpowersource,thereforeintotaldrawsonly35mW.Yourelectricitybillathomeshowsthattheelectricitycompanyischargingyoufortheenergyyouused(i.e.PowerxTime)andtheunitismeasureinkilowatt-hour.Thecostisaround15porso.That’showmuchyouwouldpayifyouleaveyour40Wlightbulbonforafullday!

WhenitcomestoACsignals,calculatingpowerandenergyismorecomplicated.Takethecircuitabove,v(t)isasimpleACvoltagesourcedrivingaresistorR.v(t)doesnotneedtobesinusoidal,butgoesupanddownasshowninthediagramhere.ToconsiderthepowerdissipatedintheresistorR,weneedtodefinitethequantityinstantaneouspowerp(t),whichisafunctionoftime.Sincepower=voltagexcurrent,orp(t)=v(t)*i(t)(notethatIuselowercasetoindicatethesearetimevaryingquantities),p(t)=v(t)2/R.YoucanusesimpleintegrationtocalculatetheaveragepowerdissipatedinRoveraperiodoftime.TheenergydissipatedbyRintimedurationdt isp(t)dt. Thereforeovertheperiodof0toT,wecanperformthisintegrationtogetthetotalenergyusedanddividethisbyTtogettheaveragepower.Finally,wedefineRMS(rootmeansquare)voltagethesquarerootoftheaverageofv(t)2.RMSvoltageisusefulbecauseittellsushowmuchpowerisconsumedbyjustsquaringthisvalueanddividebyR.ItistheDCvoltagethatwouldcauseRtodissipatethesamepoweraswiththeACsignalv(t).

Nowletusconsiderasinusoidalsignal.Herearethefourimportantmeasuresforacosinesignalwithamplitudeof5V.Rememberthatthefrequencyofthesignaldoesnotaffectthemeansquareorrootmeansquarevoltages.IntheUK,themainspower(i.e.theACpowerlinecomingfromthewallsockets)arequotedas230V+10%and-6%(nominallyitis240Vat50Hz).InfactthisvalueisRMS,notamplitude(peak).Thepeakvalueis√2x230=325V.

5

Thepurposeofthislectureistoconsiderwherethepowerthatdrivesourelectriccircuitscomefrom.Whilemobileelectronicsaredrivenbybatteries,mostotherelectricalequipmentandappliancesaredrivenbyACmains.ItisfarcheapertouseACtodeliver1Wofpowerthantodothesamefromabattery.Ifyouareusingarechargeablebattery,youstillhavetorechargethebatteryusingACmainsasapowersource.Modernpowersupplytakesthe240V50HzmainsandconvertsthistomultipleDCvoltagestodriveourelectroniccircuits.Forexample,atypicalPCpowersupplyunit(insideyourdesktoporyourlaptop)providesfourDCvoltages:12V,5V,3.3Vand1.2V..

6

Howisa240VACsupplyconvertedtoaDCvoltage?Firstlyletusconsidertheideaof“rectification”.WhatthismeanisthatwefirstremovethenegativeportionofthesinusoidalACvoltageusingadiode.Sincethediodecanonlyconductelectricityinonedirection(thedirectionofthe“arrow”inthesymbol),thevoltageacrossRinthecircuitaboveonlyhasthepositivehalfofeachcycle.Onemayuseatransformer(shownastwocoupledinductorinthecircuitdiagram)inordertodotwothings:1)provideisolationbetweentheACmainsandyourcircuitsthroughmagneticcoupling;2)usingdifferentnumberofturnsintheprimary(mains)andthesecond(yourcircuit)sideofthetransformer,youcanreducethetheACamplitudefromtheverylarge325V.

7

Althoughthesimpleonediodecircuitworks,itisnotveryefficientbecauseyouareonlydrawingcurrentthemainssupplyhalfofthetime.Mostpowersupplynowuseafourdiodecircuitknownasabridgerectifier.Tracingthroughthiscircuit,itisclearthatonthepositivecycleofthesinewave,D1andD2conduct.Duringthenegativehalfof thecycle,D3andD3conduct.Inbothcases,the+ve terminalofRLisdrivenhighrelativetothe–ve terminal.Bothhalfcyclesarenowmadepositiveashown here.

8

Wewanttoconvertthishumpyrectifiedsinewave toaDCvoltage.Forthatweuseacapacitor.

ThecapacitordoesagoodjobofsmoothingthepulsesfromtherectifierintoamoreconstantDC.

AsmallvariationoccursintheDCbecausethecapacitordischarges asmallamountbetweenthepositiveandnegativepulses.Thenitrecharges.Thisvariationiscalledripple.

Theripplecanbereducedfurtherbymakingthecapacitorlarger.

Therippleappearstobeasawtooth shapedACvariationridingontheDCoutput.

Asmallamountofripplecanbetoleratedinsomecircuitsbutthelowerthebetteroverall.

9

Evenafterusingthefull-waverectifiercircuitandtheaveragingcapacitor,westillhavetoconvertwhateverDCvoltageattheoutputtothedesirableDCvoltage.ForthatweuseouroldtrustedPWMprincipleagain.By adjustingthedutycycleoftheswitchcontrolsignal,wecanturntheswitchonandoffforexactlythecorrectdurationinordertogetthedesiredDCoutput.Intheplotshere,weshowntwoscenariosforalowandhighoutputvoltage.

10

Theaveragingcircuittypicallyconsistsofaninductorinseries,andacapacitorinparalleltotheloadR.Thewaveformshereshowswhatishappening.WhenSisclosed,theunregulatedvoltageVissuppliedtooneendoftheinductor.AssumingthattheoutputvoltageYismoreorlessconstant,thevoltageacrossLisalsoconstant.ThereforethecurrentIL istheintegralofthevoltageacrossLandittakesatriangularshape.ThisiscurrentwillchargeanddischargethecapacitorCandgivesafurthersmoothedoutputvoltageY.(Rememberthesmoothingeffectofacapacitoronavaryingvoltage.)ThediodeservesthesamepurposeasthediodesyoufoundacrossthesolenoidswitchingtransistororthemotordrivingH-bridgetransistors.Itisoftengivenacolour name– the“fly-wheeling”diode.Don’tworryaboutthename.ItspurposeisthelimitthevoltagespikeinthecircuitwhenSisturnedOFF.Rememberthatcurrentthroughaninductorcannotbechangedsuddenly.SoifSifturnoff,thediodeprovidesapathforthecurrenttoflow– andthislimitthevoltagespike.

Formobileelectronics,weneedbatterytoprovidethepowersource.Herearetwolistsofbatteries:thosethataredisposable,andthosethatarerechargeable.Thedetailsofmaterialsusedandwhytheelectro-chemicalpropertiesofthesebatteriesresultsinthedifferentbatterycharacteristicsisbeyondthescopeofthiscourse.However,itwouldbeusefultoknowabouttheprosandconsofeachbatterytype,andconsiderhowtoselecttherightbatteryforagivenapplication.ThemorepopularbatterytypesarehighlightedinREDhere.

Thisplotshowshowthefourpopulartypesofbatteriesvaryinweightandsizeforagivenbatterycapacity,whichisnormallymeasuredinwatt-hours.(Ifyouhaveafixedvoltage,say5VasinaUSBcompatiblebattery,thecapacitycanalsobequotedinampere-hours.Watt-hourisjustampere-hourxvoltage.

Hereisamoredetailedtablesummarising thekeyparameterrangeforeachtypeofrechargeablebatteries.Itisincludedhereforyourreference.

Thisvideocanbefoundon:https://www.youtube.com/watch?v=saxYilLJ7yw

Supercapacitors arerecenttechnologythatprovidesaviablealternativetobatteries.Seedescriptionofslideabove.Formoreinformationaboutsupercapacitor,see:

https://www.tecategroup.com/ultracapacitors-supercapacitors/ultracapacitor-FAQ.php

Thisdiagramsummariestheadvantages anddisadvantagesofofbatteriesvssupercapactior (shownasdouble-layercapacitors)andnormalcapatiros (Al-Elco fornromal electrolyticcapacitors).

Bestwouldbetoprightcorner.Batteriesaregoodforhighenergydensityapplications,wherewewantsmallpoorofenergyoveralongperiodoftimeSupercapacitorsorUltracapacitors aregoodforapplicationthatrequirehighpowerdensity:fasterflowofenergyovershorterperiodoftime.

Hereisanexcellentvideoaboutsupercapacitor:

https://www.youtube.com/watch?v=XjX3deXDtnQ&feature=youtu.be