ElectronicsOverview
BasicCircuits,PowerSupplies,Transistors,CableImpedance
diodebridge
Lecture 8: Electronics UCSD Physics 122 2
BasicCircuitAnalysis
• Whatwewon’tdo:– commonelectronics-classthings:RLC,filters,detailedanalysis
• Whatwewilldo:– setoutbasicrelaGons– lookatafewexamplesoffundamentalimportance(mostlyresisGvecircuits)
– lookatdiodes,voltageregulaGon,transistors– discussimpedances(cable,output,etc.)
Lecture 8: Electronics UCSD Physics 122 3
TheBasicRelaGons
• Visvoltage(volts:V);Iiscurrent(amps:A);Risresistance(ohms:Ω);Ciscapacitance(farads:F);Lisinductance(henrys:H)
• Ohm’sLaw:V=IR;V=;V=L(dI/dt)• Power:P=IV=V2/R=I2R• Resistorsandinductorsinseriesadd• Capacitorsinparalleladd• Resistorsandinductorsinparallel,andcapacitorsinseriesaddaccordingto:
€
1C
Idt∫
€
1Xtot
=1X1
+1X2
+1X3
+…
Lecture 8: Electronics UCSD Physics 122 4
Example:Voltagedivider• Voltagedividersareaclassicwaytoseta
voltage
• Worksontheprinciplethatallchargeflowingthroughthefirstresistorgoesthroughthesecond– soΔV∝R-value– providedanyloadatoutputisnegligible:
otherwisesomecurrentgoestheretoo
• SoVout=V(R2/(R1+R2))
• R2hereisavariableresistor,orpoten.ometer,or“pot”– typicallythreeterminals:R12isfixed,tap
slidesalongtovaryR13andR23,thoughR13+R23=R12always
1
2
3
R1
R2
V Vout
Lecture 8: Electronics UCSD Physics 122 5
RealBa[eries:OutputImpedance• Apowersupply(ba[ery)ischaracterizedbyavoltage
(V)andanoutputimpedance(R)– someGmescalledsourceimpedance
• Hookinguptoload:Rload,weformavoltagedivider,sothatthevoltageappliedbytheba[eryterminalisactuallyVout=V(Rload/(R+Rload))– thusthesmallerRis,the“sGffer”thepowersupply
– whenVoutsagswithhigherloadcurrent,wecallthis“droop”
• Example:If10.0Vpowersupplydroopsby1%(0.1V)whenloadedto1Amp(10Ωload):– internalresistanceis0.1Ω– calledoutputimpedanceorsourceimpedance
– mayvarywithload,though(notarealresistor)
V
R
Lecture 8: Electronics UCSD Physics 122 6
PowerSuppliesandRegulaGon• Apowersupplytypicallystartswithatransformer
– toknockdownthe340Vpeak-to-peak(120VAC)tosomethingreasonable/manageable
• Wewillbeusingacenter-taptransformer
– (A’-B’)=(windingraGo)×(A-B)• whenA>B,soisA’>B’
– geometryofcentertap(CT)guaranteesitismidwaybetweenA’andB’(frequentlyGethistogroundsothatA’=-B’)
– notethatsecondarysidefloats:nogroundreferencebuilt-in
A
B
A’
CT
B’
ACinput ACoutput
Lecture 8: Electronics UCSD Physics 122 7
Transformerisjustwirecoiledaroundmetal• MagneGcfieldisgeneratedby
currentinprimarycoil• IroncorechannelsmagneGcfield
throughsecondarycoil• SecondaryVoltageis
V2=(N2/N1)V1• SecondaryCurrentis
I2=(N1/N2)I1• ButPowerin=Powerout
– negligiblepowerlostintransformer
• WorksonlyforAC,notDC
Lecture 8: Electronics UCSD Physics 122 8
TypicalTransformers
transformersusuallyheavyduetoironcore
9
= 170 Volts
= -170 Volts
120 VAC is a root-mean-square number: peak-to-peak is 340 Volts!
Lecture 8: Electronics UCSD Physics 122 10
ACReceptacle• Receptacleshavethreeholeseach• Lower(rounded)holeisearthground
– connectedtopipes,usually– greenwire
• Largerslotis“neutral”– forcurrent“return”– neverfarfromground– whitewire– ifwiredcorrectly
• Smallerslotis“hot”– swingsto+170and-170– blackwire– dangerousone
Lecture 8: Electronics UCSD Physics 122 11
Diodes• DiodesareessenGallyone-waycurrentgates• Symbolizedby:• Currentvs.voltagegraphs:
V
I
V
I
V
I
V
I
0.6V
plainresistor diode idealizeddiode WAYidealizeddiode
nocurrentflows currentflows
thedirecGonthearrowpointsinthediodesymbolisthedirecGonthatcurrentwillflow
actsjustlikeawire(willsupportarbitrarycurrent)providedthatvoltageisposiGve
Lecture 8: Electronics UCSD Physics 122 12
DiodeMakeup
• Diodesaremadeofsemiconductors(usuallysilicon)
• EssenGallyastackofp-dopedandn-dopedsilicontoformap-njunc.on– dopingmeansdeliberateimpuriGesthatcontributeextraelectrons(n-doped)or“holes”forelectrons(p-doped)
• Transistorsaren-p-norp-n-parrangementsofsemiconductors
p-type n-type
Lecture 8: Electronics UCSD Physics 122 13
LEDs:Light-EmiingDiodes• MaindifferenceismaterialismoreexoGcthansiliconusedinordinarydiodes/
transistors– typically2-voltdropinsteadof0.6Vdrop
• WhenelectronflowsthroughLED,losesenergybyemiingaphotonoflightratherthanvibraGnglaice(heat)
• LEDefficiencyis30%(comparetoincandescentbulbat10%)
• Mustsupplycurrent-limiGngresistorinseries:– figureon2VdropacrossLED;aimfor1–10mAofcurrent
14
GeingDCbackoutofAC• ACprovidesameansforustodistributeelectrical
power,butmostdevicesactuallywantDC– bulbs,toasters,heaters,fansdon’tcare:plugstraightin– sophisGcateddevicescarebecausetheyhavediodesand
transistorsthatrequireacertainpolarity• ratherthanoscillaGngpolarityderivedfromAC• thisiswhyba[eryorientaGonma[ersinmostelectronics
• Usediodesto“recGfy”ACsignal• Simplest(half-wave)recGfierusesonediode:
ACsource load
inputvoltage
voltageseenbyloaddiodeonlyconductswheninputvoltageisposiGve
Lecture 8: Electronics UCSD Physics 122 15
DoingBe[er:Full-waveDiodeBridge• ThediodeintherecGfyingcircuitsimplypreventedthenegaGveswingofvoltagefromconducGng– butthiswasteshalftheavailablecycle– alsoveryirregular(bumpy):farfroma“good”DCsource
• Byusingfourdiodes,youcanrecoverthenegaGveswing:
A
C
B
D
ACsource
load
inputvoltage
voltageseenbyload
B&Cconduct
A&Dconduct
Lecture 8: Electronics UCSD Physics 122 16
Full-WaveDual-Supply• Bygroundingthecentertap,wehavetwooppositeACsources– thediodebridgenowpresents+and-voltagesrelaGvetoground
– eachcanbeseparatelysmoothed/regulated– cuingoutdiodesAandDmakesahalf-waverecGfier
A
C
B
D
ACsource
+load
-load
voltagesseenbyloads
canbuypre-packageddiodebridges
Lecture 8: Electronics UCSD Physics 122 17
SmoothingouttheBumps• SGllabumpyride,butwecansmooththisoutwithacapacitor– capacitorshavecapacityforstoringcharge– actslikeareservoirtosupplycurrentduringlowspots– voltageregulatorsmoothesoutremainingripple
A
C
B
D
ACsource
load
capacitor
UCSD Physics 122 18
Howsmoothissmooth?
• AnRCcircuithasaGmeconstantτ=RC– becausedV/dt=I/C,andI=V/R→dV/dt=V/RC– soVisV0exp(±t/τ)
• AnyexponenGalfuncGonstartsoutwithslope=Amplitude/τ
• Soifyouwant<10%rippleover120Hz(8.3ms)Gmescale…– musthaveτ=RC>83ms– ifR=100Ω,C>830µF
RC
V
Lecture 8: Electronics UCSD Physics 122 19
RegulaGngtheVoltage• Theunregulated,ripplyvoltagemaynotbeatthe
valueyouwant– dependsontransformer,etc.– supposeyouwant15.0V
• Youcoulduseavoltagedividertosetthevoltage• Butitwoulddroopunderload
– outputimpedance→R1||R2– needtohaveverysmallR1,R2tomake“sGff”– thedividerwilldrawalotofcurrent– perhapsstrainingthesource– powerexpendedindivider>>powerinload
• Nota“real”soluGon• Importantnote:a“bigload”meansasmallresistor
value:1Ωdemandsmorecurrentthan1MΩ
1
2
3
R1
R2
Vin
Vout
Rload
Lecture 8: Electronics UCSD Physics 122 20
TheZenerRegulator• Zenerdiodesbreakdownatsomereverse
voltage– canbuyatspecificbreakdownvoltages– aslongassomecurrentgoesthroughzener,it’ll
work– goodforroughregulaGon
• CondiGonsforworking:– let’smaintainsomeminimalcurrent,Izthrough
zener(sayafewmA)
– then(Vin-Vout)/R1=Iz+Vout/RloadsetstherequirementonR1
– becausepresumablyallelseisknown
– ifloadcurrentincreasestoomuch,zenershutsoff(nodedropsbelowbreakdown)andyoujusthaveavoltagedividerwiththeload
R1
Z
Vin
Vout=Vz
Rload
zenervoltage
highslopeiswhatmakesthezeneradecentvoltageregulator
Lecture 8: Electronics UCSD Physics 122 21
VoltageRegulatorIC• Cantrimdownripplyvoltageto
precise,rock-steadyvalue
• Nowthingsgetcomplicated!– Wearenowintherealmof
integratedcircuits(ICs)
• ICsarewholecircuitsinsmallpackages
• ICscontainresistors,capacitors,diodes,transistors,etc.
notezeners
Lecture 8: Electronics UCSD Physics 122 22
VoltageRegulators• ThemostcommonvoltageregulatorsaretheLM78XX
(+voltages)andLM79XX(-voltages)– XXrepresentsthevoltage
• 7815is+15;7915is-15;7805is+5,etc– typicallyneedsinput>3voltsaboveoutput(reg.)voltage
• AversaGleregulatoristheLM317(+)orLM337(-)– 1.2–37Voutput– Vout=1.25(1+R2/R1)+IadjR2
• Iadjissmall:50µA– Upto1.5A– pictureatrightcangoto25V– datasheetcatalog.comfordetails
bewarethathousingisnotalwaysground
Lecture 8: Electronics UCSD Physics 122 23
Transistors• TransistorsareversaGle,highlynon-linear
devices• TwofrequentmodesofoperaGon:
– amplifiers/buffers– switches
• Twomainflavors:– npn(morecommon)orpnp,describingdoping
structure• AlsomanyvarieGes:
– bipolarjuncGontransistors(BJTs)suchasnpn,pnp– fieldeffecttransistors(FETs):n-channelandp-
channel– metal-oxide-semiconductorFETs(MOSFETs)
• We’lljusthittheessenGalsoftheBJThere– MOSFETinlaterlecture
B
C
E
B
E
C
npn pnp
Lecture 8: Electronics UCSD Physics 122 24
BJTAmplifierMode• Centralideaisthatwhenintherightregime,theBJT
collector-emi[ercurrentisproporGonaltothebasecurrent:– namely,Ice=βIb,whereβ(someGmeshfe)istypically~100– Inthisregime,thebase-emi[ervoltageis~0.6V– below,Ib=(Vin−0.6)/Rb;Ice=βIb=β(Vin−0.6)/Rb– sothatVout=Vcc−IceRc=Vcc−β(Vin−0.6)(Rc/Rb)– ignoringDCbiases,wigglesonVinbecomeβ(Rc/Rb)bigger(and
inverted):thusamplified
out
Rc
Rb
in
Vcc
B
C
E
Lecture 8: Electronics UCSD Physics 122 25
Switching:DrivingtoSaturaGon
• WhatwouldhappenifthebasecurrentissobigthatthecollectorcurrentgotsobigthatthevoltagedropacrossRcwantstoexceedVcc?– wecallthissaturated:Vc−Vecannotdipbelow~0.2V– evenifIbisincreased,Icwon’tbudgeanymore
• Theexamplebelowisagoodlogicinverter– ifVcc=5V;Rc=1kΩ;Ic(sat)≈5mA;needIb>0.05mA– soRb<20kΩwouldputussafelyintosaturaGonifVin=5V– now5Vin→~0.2Vout;<0.6Vin→5Vout
out
Rc
Rb
in
Vcc
Lecture 8: Electronics UCSD Physics 122 26
TransistorBuffer
• Inthehookupabove(emi[erfollower),Vout=Vin−0.6– soundsuseless,right?– thereisnovoltage“gain,”butthereiscurrentgain– ImaginewewiggleVinbyΔV:VoutwigglesbythesameΔV– sothetransistorcurrentchangesbyΔIe=ΔV/R– butthebasecurrentchanges1/βGmesthis(muchless)– sothe“wiggler”thinkstheloadisΔV/ΔIb=β·ΔV/ΔIe=βR– theloadthereforeislessformidable
• The“buffer”isawaytodrivealoadwithoutthedriverfeelingthepain(asmuch):it’simpedanceisolaGon
out
R
in
Vcc
Lecture 8: Electronics UCSD Physics 122 27
ImprovedZenerRegulator• Byaddingatransistortothezenerregulator
frombefore,wenolongerhavetoworryasmuchaboutthecurrentbeingpulledawayfromthezenertotheload– thebasecurrentissmall
– RloadeffecGvelylooksβGmesbigger
– realcurrentsuppliedthroughtransistor• Cano~enfindzenersat5.6V,9.6V,12.6V,
15.6V,etc.becausedropfrombasetoemi[erisabout0.6V– sotransistor-bufferedVregcomesoutto5.0,
9.0,etc.
• Izvarieslessinthisarrangement,sotheregulatedvoltageissteadier
Vreg
Rload
Vz
Vin
Rz
Z
Vin
Lecture 8: Electronics UCSD Physics 122 28
SwitchingPowerSupplies• Powersupplieswithouttransformers
– lightweight;lowcost– canbeelectromagneGcallynoisy
• UseaDC-to-DCconversionprocessthatreliesonflippingaswitchonandoff,storingenergyinaninductorandcapacitor– regulatorswereDC-to-DCconverterstoo,
butlossy:loseΔP=IΔVofpowerforvoltagedropofΔVatcurrentI
– regulatorsonlydown-convert,butswitcherscanalsoup-convert
– switchersarereasonablyefficientatconversion
Lecture 8: Electronics UCSD Physics 122 29
Switchertopologies
from:h[p://www.maxim-ic.com/appnotes.cfm/appnote_number/4087
TheFETswitchisturnedofforoninapulse-width-modulaGon(PWM)scheme,thedutycycleofwhichdeterminestheraGoofVouttoVin
Lecture 8: Electronics UCSD Physics 122 30
Step-DownCalculaGons
• IftheFETisonfordutycycle,D(fracGonofGmeon),andtheperiodisT:– theaverageoutputvoltageisVout=DVin
– theaveragecurrentthroughthecapacitoriszero,theaveragecurrentthroughtheload(andinductor)is1/DGmestheinputcurrent
– undertheseidealizaGons,powerin=powerout
Lecture 8: Electronics UCSD Physics 122 31
Step-downwaveforms• Shownhereisanexampleofthe
step-downwiththeFETdutycyclearound75%
• Theaverageinductorcurrent(dashed)isthecurrentdeliveredtotheload– thebalancegoestothe
capacitor
• Theripple(parabolicsecGons)haspeak-to-peakfracGonalamplitudeofT2(1-D)/(8LC)– sowinbysmallT,largeL&C
– 10kHzat1mH,1000µFyields~0.1%ripple
– means10mVon10V
FET
InductorCurrent
SupplyCurrent
CapacitorCurrent
OutputVoltage
(rippleexag.)
Lecture 8: Electronics UCSD Physics 122 32
CableImpedances
• RG58cableischaracterizedas50Ωcable– RG59is75Ω– someantennacableis300Ω
• Isn’tthecablenearlyzeroresistance?Andshouldn’tthelengthcomeintoplay,somehow?
• ThereisadisGncGonbetweenresistanceandimpedance– thoughsameunits
• Impedancescanbereal,imaginary,orcomplex– resistorsarereal:Z=R– capacitorsandinductorsareimaginary:Z=−i/ωC;Z=iωL– mixturesarecomplex:Z=R−i/ωC+iωL
Lecture 8: Electronics UCSD Physics 122 33
Impedances,cont.
• Notethat:– capacitorsbecomeless“resisGve”athighfrequency– inductorsbecomemore“resisGve”athighfrequency– biggercapacitorsaremoretransparent– biggerinductorsarelesstransparent– i(√-1)indicates90°phaseshi~betweenvoltageandcurrent
• a~erall,V=IZ,soZ=V/I• thusifVissinewave,Iis±cosineforinductor/capacitor• andgiventhatoneisderivaGve,oneisintegral,thismakessense(slide#3)
– addingimpedancesautomaGcallytakescareofsummaGonrules:addZinseries
• capacitanceaddsasinverse,resistors,inductorsstraight-up
Lecture 8: Electronics UCSD Physics 122 34
ImpedancePhasorDiagram• Impedancescanbedrawnona
complexplane,withpureresisGve,inducGve,andcapaciGveimpedancesrepresentedbythethreecardinalarrows
• AnarbitrarycombinaGonofcomponentsmayhaveacompleximpedance,whichcanbebrokenintorealandimaginaryparts
• Notethatasystem’simpedanceisfrequency-dependent
R
ωL
Z
Zi
Zr
1/ωC
realaxis
imag.axis
Lecture 8: Electronics UCSD Physics 122 35
TransmissionLineModel
• Thecablehasafinitecapacitanceperunitlength– propertyofgeometryanddielectricseparaGngconductors– C/l=2πε/ln(b/a),wherebandaareradiiofcylinders
• Alsohasaninductanceperunitlength– L/l=(μ/2π)ln(b/a)
• Whenavoltageisapplied,capacitorschargeup– thusdrawcurrent;propagatesdownthelinenearspeedoflight
• QuesGon:whatistheraGoofvoltagetocurrent?– becausethisisthecharacterisGcimpedance
• Answer:Z0=sqrt(ωL/ωC)=sqrt(L/C)=(1/2π)sqrt(μ/ε)ln(b/a)– notethatZ0isfrequency-independent
CLinput output
Lecture 8: Electronics UCSD Physics 122 36
TypicalTransmissionLines
• RG58coaxisabundant– 30pFperfoot;75nHperfoot;50Ω;v=0.695c;~5ns/m
• RG174isthethinversion– sameparametersasabove,butscaled-downgeometry
• RG59– usedforvideo,cableTV– 21pF/~;118nHperfoot;75Ω;v=0.695c;~5ns/m
• twistedpair– 110Ωat30turns/~,AWG24–28
• PCB(PC-board)trace– get50Ωifthetracewidthis1.84GmestheseparaGonfromthe
groundplane(assumingfiberglassPCBwithε=4.5)
Lecture 8: Electronics UCSD Physics 122 37
Whyimpedancema[ers
• Forfastsignals,getbounces(reflecGons)ateveryimpedancemismatch– reflecGonamplitudeis(Zt−Zs)/(Zt+Zs)
• sandtsubscriptsrepresentsourceandterminaGonimpedances• sourcesintendingtodriveaZ0cablehaveZs=Z0
• Consideralongcableshortedatend:insertpulse– drivingelectronicscan’tknowabouttheterminaGon
immediately:mustchargeupcableasthepulsepropagatesforward,lookinglikeZ0ofthecableatfirst
– surpriseatfarend:it’sashort!retreat!– ineffect,negaGvepulsepropagatesback,nullingoutcapacitors
(reflecGonis−1)– oneround-triplater(10nspermeter,typically),thedriving
electronicsfeelsthepainoftheshort
Lecture 8: Electronics UCSD Physics 122 38
Impedancema[ers,conGnued
• Nowotherextreme:cableun-terminated:open– pulsetravelsmerrilyalongatfirst,thedrivingelectronicsseeing
aZ0cableload– attheend,thecurrenthasnowheretogo,butdrivercan’tknow
thisyet,sokeepsloadingcableasifit’ssGllZ0– effecGvely,aposiGvepulsereflectsback,double-charging
capacitors(reflecGonis+1)– drivergetswordofthisoneround-triplater(10ns/m,typically),
thenmustceasetodelivercurrent(cablefullycharged)• Thegoldilockscase(reflecGon=0)
– iftheendofthecableisterminatedwithresistorwithR=Z0,thencurrentisslurpedupperfectlywithnoreflecGons
– thedriverisnotbeingliedto,andhearsnocomplaints
Lecture 8: Electronics UCSD Physics 122 39
SoBeware!• Iflookingatfast(tensofnsdomain)signalsonscope,be
suretoroutesignaltoscopevia50Ωcoaxandterminatethescopein50Ω– ifthesignalcan’tdrive50Ω,thenuseacGveprobes
• Notethatscopeprobesterminateto1MΩ,eventhoughthecablesareNOT1MΩcables(nosuchthing)– soscopeprobescanbeverymisleadingaboutshapesoffast
signals
Lecture 8: Electronics UCSD Physics 122 40
ReferencesandReading
• References:– ThecanonicalelectronicsreferenceisHorowitzandHill:TheArtofElectronics
– AlsotheaccompanyinglabmanualbyHayesandHorowitzishighlyvaluable(farmorepracGcally-oriented)
• Reading– SecGons6.1.1,6.1.2– Skim6.2.2,6.2.3,6.2.4
– SecGons6.3.1,6.5.1,6.5.2– Skim6.3.2
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