Basic Circuits, Power Supplies, Transistors, Cable Impedance

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.)


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

+…


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


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


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


Transformerisjustwirecoiledaroundmetal•  MagneGcfieldisgeneratedby

currentinprimarycoil•  IroncorechannelsmagneGcfield

throughsecondarycoil•  SecondaryVoltageis

V2=(N2/N1)V1•  SecondaryCurrentis

I2=(N1/N2)I1•  ButPowerin=Powerout

–  negligiblepowerlostintransformer

•  WorksonlyforAC,notDC


TypicalTransformers

transformersusuallyheavyduetoironcore

9

= 170 Volts

= -170 Volts

120 VAC is a root-mean-square number: peak-to-peak is 340 Volts!


ACReceptacle•  Receptacleshavethreeholeseach•  Lower(rounded)holeisearthground

–  connectedtopipes,usually–  greenwire

•  Largerslotis“neutral”–  forcurrent“return”–  neverfarfromground–  whitewire–  ifwiredcorrectly

•  Smallerslotis“hot”–  swingsto+170and-170–  blackwire–  dangerousone


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


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


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


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


Full-WaveDual-Supply•  Bygroundingthecentertap,wehavetwooppositeACsources–  thediodebridgenowpresents+and-voltagesrelaGvetoground

–  eachcanbeseparatelysmoothed/regulated–  cuingoutdiodesAandDmakesahalf-waverecGfier

A

C

B

D

ACsource

+load

-load

voltagesseenbyloads

canbuypre-packageddiodebridges


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


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


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


VoltageRegulatorIC•  Cantrimdownripplyvoltageto

precise,rock-steadyvalue

•  Nowthingsgetcomplicated!–  Wearenowintherealmof

integratedcircuits(ICs)

•  ICsarewholecircuitsinsmallpackages

•  ICscontainresistors,capacitors,diodes,transistors,etc.

notezeners


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


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


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


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


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


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


SwitchingPowerSupplies•  Powersupplieswithouttransformers

–  lightweight;lowcost–  canbeelectromagneGcallynoisy

•  UseaDC-to-DCconversionprocessthatreliesonflippingaswitchonandoff,storingenergyinaninductorandcapacitor–  regulatorswereDC-to-DCconverterstoo,

butlossy:loseΔP=IΔVofpowerforvoltagedropofΔVatcurrentI

–  regulatorsonlydown-convert,butswitcherscanalsoup-convert

–  switchersarereasonablyefficientatconversion


Switchertopologies

from:h[p://www.maxim-ic.com/appnotes.cfm/appnote_number/4087

TheFETswitchisturnedofforoninapulse-width-modulaGon(PWM)scheme,thedutycycleofwhichdeterminestheraGoofVouttoVin


Step-DownCalculaGons

•  IftheFETisonfordutycycle,D(fracGonofGmeon),andtheperiodisT:–  theaverageoutputvoltageisVout=DVin

–  theaveragecurrentthroughthecapacitoriszero,theaveragecurrentthroughtheload(andinductor)is1/DGmestheinputcurrent

–  undertheseidealizaGons,powerin=powerout


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.)


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


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


ImpedancePhasorDiagram•  Impedancescanbedrawnona

complexplane,withpureresisGve,inducGve,andcapaciGveimpedancesrepresentedbythethreecardinalarrows

•  AnarbitrarycombinaGonofcomponentsmayhaveacompleximpedance,whichcanbebrokenintorealandimaginaryparts

•  Notethatasystem’simpedanceisfrequency-dependent

R

ωL

Z

Zi

Zr

1/ωC

realaxis

imag.axis


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


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)


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


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


SoBeware!•  Iflookingatfast(tensofnsdomain)signalsonscope,be

suretoroutesignaltoscopevia50Ωcoaxandterminatethescopein50Ω–  ifthesignalcan’tdrive50Ω,thenuseacGveprobes

•  Notethatscopeprobesterminateto1MΩ,eventhoughthecablesareNOT1MΩcables(nosuchthing)–  soscopeprobescanbeverymisleadingaboutshapesoffast

signals


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

Basic Circuits, Power Supplies, Transistors, Cable Impedance

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