OPERATIONALAMPLIFIERS(OP-AMPS)II
LAB5INTRO:INTRODUCTIONTOINVERTINGAMPLIFIERSANDOTHEROP-AMPCIRCUITS
GOALS
Inthislab,youwillcharacterizethegainandfrequencydependenceofinvertingop-ampcircuits.Youwill
workwithafewapplicationsofnegativefeedbackincludingacircuittosumvoltages.
Proficiencywithnewequipment:
o Invertingop-amps:basic,summing,differentiator,andintegrator
ExperimentalDesign:
o Designing,building,andcharacterizingyourownop-ampcircuit
Modelingthephysicalsystem:
o Frequencydependenceofop-ampcircuits
o Inputandoutputimpedancesofop-ampcircuits
Applications:
o
Buildadigitaltoanalogconverter
DEFINITIONS
Closed-loopgain,G–gainoftheop-ampcircuitatallfrequencieswithfeedbackapplied
Lowfrequencygain,G0–gainoftheop-ampcircuitatDC(f=0Hz)
Open-loopgain,A–gainoftheop-ampitselfatallfrequencieswithnofeedbackapplied
DCgain,A0–gainoftheop-ampitselfatDC(f=0Hz)withnofeedbackapplied
f0–3dBfrequencyforanop-ampitselfwithnofeedback
fB–3dBfrequencyforanop-ampcircuitwithfeedbackapplied
fT–unitygainfrequency,frequencywheretheopenloopgainAisequaltoone
INVERTINGAMPLIFIERS
Figure1.InvertingAmplifier
ThebasicinvertingamplifierisshowninFigure1.WecanusetheGoldenRulestodeterminethelow-frequencygain.
Sincethepositiveinputisgrounded,theop-ampwilldoeverythingitcantokeepthenegativeinputatgroundas
1
well.Inthelimitofinfiniteopenloopgaintheinvertinginputoftheop-ampisavirtualground,acircuitnodethat
willstayatgroundaslongasthecircuitisworking,eventhoughitisnotdirectlyconnectedtoground.WhenAis
infinite,thegainofaninvertingamplifieris
G0 =
R
Vout
=− f Vin
R
Thisisthe“GoldenRule”result.Forthefrequencydependenceofthegainweneedtoconsiderwhathappenswhen
Aisnotinfinite,aswedidforthenon-invertingcase.Weusethesamedefinitionsasforthenon-invertingcase.The
op-ampopenloopgainisA,andthedividerratioBisthesameasbefore:
B=
R
R + Rf
WhenAisfinitethegainforaninvertingamplifierisgivenby
G0 =
A (1− B)
Vout
=− 0
Vin
1+ A0 B
TheaboveformulasarestillcorrectwhenAand/orBdependonfrequency.Bwillbefrequencyindependentifwe
onlyhaveresistors(inothercasesthatusecompleximpedanceitmaynotbe),butAalwaysvarieswithfrequency.
Formostop-amps,includingtheLF356,theopenloopgainvarieswithfrequencylikeanRClow-passfilter:
A0
A=
1+ j
f
f0
The3dBfrequency,f0,isusuallyverylow,around10Hz.Datasheetsdonotusuallygivef0directly;insteadtheygive
thedcgain,A0,andtheunitygainfrequencyfT,whichisthefrequencywherethemagnitudeoftheopenloopgainA
isequaltoone.TherelationbetweenA0,f0,andfTis
𝑓! = 𝐴! 𝑓! ThefrequencydependenceoftheclosedloopgainGisthengivenby
G=
G0
f
1+ j
fB
ThefrequencyresponseoftheamplifierwithfeedbackisthereforealsothesameasforanRClow-passfilter.
InputandOutputImpedancesofInvertingAmplifiers
FormulasfortheinputandoutputimpedanceforaninvertingamplifierarederivedinH&HSection4.26.Whenthe
openloopgainislarge,thenegativeinputoftheop-ampisavirtualgroundandsotheinputimpedanceisjustequal
toR.Thisisverydifferentfromthenon-invertingcasewheretheinputimpedanceisproportionaltoAforlargeA.In
practice,theinputimpedanceofaninvertingamplifierisnotusuallygreaterthanabout100kΩ,whiletheinput
impedanceofanon-invertingamplifiercaneasilybeaslargeas1012Ω.WhenAisnotlargetheformulasforthe
inputimpedanceandoutputimpedanceoftheentirecircuitarederivedinH&HSection4.26.Theresultsare
𝑅!! = 𝑅 +
𝑅!
1+𝐴
𝑅!! = 𝑅! / 1 + 𝐴𝐵 Theoutputimpedanceisthesameforboththeinvertingandnon-invertingamplifiers.
Thegain-bandwidthproductforinvertingamplifierisslightlymodifiedcomparedtonon-invertingamps. 2
𝐴! 𝑓! =
!!! !!
!!!
= 𝑓! Thisisthesame(exceptforthesign)asthenon-invertingresultwhentheclosedloopgainislarge(B<<1,|G0|>>1),
butatunityclosedloopgain(B=1/2,G0=–1)theinvertingamplifierhasonlyhalfasmuchbandwidthasanoninvertingamplifier.
SUMMINGAMPLIFIERS
RF
R1
V1
V2
R2
+
V
3
+15 V
-15 V
Vout
R3
Figure2.SummingAmplifier
TheSummingAmplifier,showninFig.2,isaveryflexiblecircuitbaseduponthestandardinvertingop-amp
configurationthatcanbeusedforcombiningmultipleinputs.Thestandardinvertingamplifierhasasingleinput
voltage,Vin,appliedtotheinvertinginputterminal.Ifweaddmoreinputresistorstotheinput,thecircuitcan
becomeavoltageadderwithdifferentgainforeachinput.Therearemanyapplicationsforsummingamplifiers
includingaudiomixersanddigitaltoanalogconverters.UsingtheGoldenRuleswecandeterminethetransfer
functionlistedbelow.
( "R %
" R %+
"R %
Vout = −*V1 $ F ' +V2 $ F ' +V3 $ F '# R2 &
# R3 &,
) # R1 &
Thiscircuithasmanyapplicationsincludingworkingasanadderinanybasis-setyouspecify.Inclasswegavean
exampleof0-9infixedintegers(decimal).Ifyouonlyrestrictyourselftoinputvoltagesof0or1V(oronandoff),
yougettoabinaryadderandcanconvertbinarysignalstoanalog(e.g.base2tobase10).Digital-to-analog
convertersarefoundineveryresearchlab(orcomputer,orphone,etc.)whereyouwanttocreateanyvalueofa
signalfromjust1’sand0’s.Ifyouwantarefresheronbinaryorcountinginbinary,youmightenjoyvisitingthe
Wikipedia:http://en.wikipedia.org/wiki/Binary_number-Counting_in_binary
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INTEGRATOR
Figure3.Integrator
Thebasicop-ampintegratorisshowninFig.3.AscomparedtotheinvertingamplifierinFig.1,theonlychangeisa
replacementofthefeedbackresistorRfwithacapacitorC.Anintegratoristhesamecircuitasalow-passfilter.If
youareinterestedinwhatfrequenciesgetpassed,youcallitalow-passfilter.Ifyouareinterestedinintegratingthe
inputsignal,youcallitanintegrator.WecanunderstandhowtheintegratorworksbyapplyingtheGoldenRulesand
rememberingthedefiningequationforcapacitors.Justasintheintegratingamplifier,theGoldenRulestellsusthat
V–≈V+=0andthatthecurrentacrossbothcomponentsisthesamebecausenocurrentflowsintotheop-amp.We
labelIRasthecurrentthroughtheresistor,whichisVin/RsinceV–isatground.WelabelICasthecurrentacrossthe
capacitor.ThedefiningequationforcapacitorsisQ=CV.ThecurrentthroughacapacitorisI=dQ/dt=d(CV)/dt=
CdV/dt.Therefore,theequationIR=ICbecomes:
Vin
dV
= −C out
R
dt
SolvingthisequationforVoutgivesthefollowing:
Vout = −
1
∫ Vin dt
RC
Thisiswhyitiscalledanintegrator.Choosingvaluesfortheresistorandcapacitordependsonseveral
considerations.First,oneneedstodeterminethevalueoftheproductRC.Thiswilldependontheexpectedsignal
(sizeandshape),theexpectedintegrationtime,andthedesiredoutput(rememberingtheop-amplimitationson
maximumoutputvoltageandslewrate).OnceRCisdetermined,someconsiderationsforchoosingRandCare:
- Availability:resistorsfrom1Ωto10MΩandcapacitorsfrom2pFto1µFarereadilyavailable.
- Inputimpedance:generallyahighinputimpedance(>1kΩ)isdesiredtoavoidloadingtheinputsignal.
- Avoidingeffectofstraycapacitance:therearemanysourcesofcapacitance,suchascables,whichcan
unintentionallycoupletoyourcircuit.Forthisreason,itisadvisabletoavoidverysmallcapacitorsasthestray
capacitancesmayendupdominating.AfewhundredpFshouldbesufficient.
- DealingwithDCsignal:ADCsignalintheinputresultsinthecapacitoreventuallycharginguptothemaximum
outputvoltageoftheop-amp.ThisDCsignalcanresultfromtheop-ampitself.Onewaytoavoidthisistoadd
anotherresistorinparallelwiththecapacitorsuchthatatlowfrequencies(largeimpedanceincapacitor)the
circuitactslikeaninvertingamplifier.AstheimpedanceofaresistorisproportionaltoRwhiletheimpedance
ofacapacitorisinverselyproportionaltoC,toensurethatthesignalmainlygoesthroughthecapacitor,one
wouldlikelargeresistorand/orlargecapacitorvalues.Ofcourse,theresistorchosenhereincombinationto
themainresistorinthecircuitleadstoaDCgainascalculatedfortheinvertingamplifiersothisshouldbe
consideredinmakingyourchoice.
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USEFULREADINGS
1.
2.
FCSections12.2–12.15.Thebasicrulesofop-ampbehaviorandthemostimportantop-ampcircuits.[Note
whileFCdiscussedbasiccharacteristicsofopampsin12.2itdoesnothavethe“GoldenRule”analysisthat
wewilldiscussinclass.]Donotworryrightnowaboutthetransistorgutsofop-amps.Wewilllearnabout
transistorsinExperiments7-8.
HorowitzandHill,Sections4.04-4.08,4.19-4.20andSections1.13-1.15
LABPREPACTIVITIES
AnswerthefollowingquestionsusingMathematicafortheplots.YoucanuseeitherMathematicafortherestthe
questionsaswellordothembyhandinyourlabbook.Bringanelectroniccopyofyournotebooktolab,preferably
onyourownlaptop.Youwilluseittoplotyourdataduringthelabsession.
Question1
Invertingamplifier
a. CalculatethevaluesoflowfrequencygainG0andthebandwidthfBfortheinvertingamplifier
inFig1forthefollowingcircuityouwillbuildinlabwiththefollowingresistors.
1)RF=100kΩ, R=10kΩ
b. GraphaBodeplotfortheopenloopgainandtheclosedloopgainforthecircuitfrompart(a)
onthesamegraphusingMathematica.
Question2
SummingAmplifier–DigitaltoAnalogConverter
a. Designathreeinputsummingamplifier(Fig.2)thatcancreateananalogvoltageofintegers
from 0 to-7 volts(|Vout|= 0,1,2,3,4,5,6, and 7)usingonlytwopossibleinputstatesoneach
input (Vlow= 0 V and Vhigh = 1). Draw a schematic of your circuit and label all the resistors.
HINT: Write down the binary numbers from 000 binary = 0 in decimal to 111 binary = 7 in
decimal.ThinkabouttherelativevaluesofR1,R2,andR3.
b. Drawatablethatliststheinputvoltagesandcorrespondingoutputvoltagestocreate|Vout|=
0,1,2,3,4,5,6,and7.
Question3
Integrator
Sofaryouhavebeenlookingattheoutputversusfrequency(Bodeplots).Nowyouwillalsoconsider
theoutputversustime.
a.
b.
c.
Question4
5
DesignanintegratorbasedonFig.3andthediscussionabove.Choosevaluesforthe
components(resistorsandcapacitors)anddescribewhyyouchosethosevalues.
Listsomepossibleapplicationsfortheintegrator.
Sketchthetimeresponseofyourcircuit(oryoucoulduseMathematicaifyouwish)forthe
followinginputwaveforms:squarewave,trianglewave,andsinewave.Hint:youcanuse
yourcalculus.
Labactivities
a. Readthroughallofthelabstepsandidentifythestep(orsub-step)thatyouthinkwillbethe
mostchallenging.
b. Listatleastonequestionyouhaveaboutthelabactivity.
LF356PINOUTANDSCHEMATIC
Allop-ampcircuitsstartoutbymakingthebasicpowerconnections.Op-ampsareactivecomponents,whichmeans
theyneedexternalpowertofunctionunlikepassivecomponentssuchasresistors.
Figure4.LF356pin-outandschematic.
GENERALOP-AMPTIPS(SAMEASLAB4)
Theseareremindersofthebasicsstepsyoushouldalwaysfollowwhenworkingwithop-amps.
a. Thisexperimentwilluseboth+15Vand-15VtopowertheLF356op-amp.Turnoffthepowerwhilewiringyour
op-amp.Everyonemakesmistakesinwiring-upcircuits.Thus,it’sagoodideatocheckyourcircuitbefore
applyingpower.Fig.4showsapin-outfortheLF356chip.Familiarizeyourselfwiththelayout.
Thefollowingprocedurewillhelpyouwireupacircuitaccurately:
1.
Draw a complete schematic in your lab book, including all ground and power connections, and all IC pin
numbers.Trytolayoutyourprototypesothepartsarearrangedinthesamewayasontheschematic,asfar
aspossible.
2.
Measureallresistorandcapacitorvaluesbeforeputtingtheminthecircuit.Becarefulwithunitprefixes.Itis
easytomistakea1nFcapacitorfora1µFone.
3.
Adheretoacolorcodeforwires.Forexample:
0V(ground)
Black +15V Red
-15V Blue
b. Theop-ampchipsitsacrossagrooveintheprototypingboard.Beforeinsertingachip,gentlystraightenthe
pins.Afterinsertion,checkvisuallythatnopinisbrokenorbentunderthechip.Toremovethechip,usea
smallscrewdriverinthegroovetopryitout.
c. Youwillhavelesstroublewithspontaneousoscillationsifthecircuitlayoutisneatandcompact,inparticular
thefeedbackpathshouldbeasshortaspossibletoreducedunwantedcapacitivecouplingandlead
inductance.Hint:donotwireoverthechipbutaroundit.
d. Tohelppreventspontaneousoscillationsduetounintendedcouplingviathepowersupplies,usebypass
capacitorstofilterthesupplylines.Abypasscapacitorbetweeneachpowersupplyleadandgroundwill
provideaminiaturecurrent“reservoir”thatcanquicklysupplycurrentwhenneeded.Thiscapacitoris
normallyintherange1µF–10µF.Theexactvalueisusuallyunimportant.Compactcapacitorsinthisrange
areusuallyelectrolytic,tantalum,oraluminumandarepolarized,meaningthatoneterminalmustalways
bepositiverelativetotheother.Thecapacitorsarelabeledwhichsideiswhich,buteachmanufactureuses
differentmarkings.Ifyouputapolarizedcapacitorinbackwards,itwillburnout.Bypasscapacitorsshouldbe
placedascloseaspossibletotheop-amppins.
e. Figure4belowshowsthebasiclayouttotestyourop-ampcircuits.Thetestcircuitfromthepreviouslab(Lab4
Fig.5)(voltagefollowerwithinputgrounded)providesaquickwaytocheckifyourop-ampisbroken.
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DC Power
Supply
+15
0
–15
Vin
Channel 1
Function
Generator
Trig. Sig.
Out
Out
Circuit
Board
Vin
Vout
Channel 2
Channel 4
Trigger
Oscilloscope
Figure5.Testandmeasurementsetupforop-ampcircuits.
Trigger
INVERTINGAMPLIFIER
Step1
7
FrequencyDependentGain
a. BuildtheinvertingamplifiershowninFig.1,withRF=100kΩandR=10kΩ.MeasureR
andRFwiththeDMMbeforeinsertingthemintothecircuitboard.PredictG0andfBfrom
thesemeasuredvaluesandtheop-amp'svalueoffTfromthedatasheet.(Youshouldbe
abletoreviewyourlab-prepworkheretoo!)
b. Usethefunctiongeneratortomeasurethelowfrequencygain.Whatfrequencyshould
youusetotestthelowfrequencygain(i.e.,whatfrequencyshouldthesignalbebelow?)
Considerthegain-bandwidthproductandhowitrelatestoyourcircuit.Whatisthe
predictedgainforthefrequencyyouchose?MeasurethelowfrequencygainG0by
measuringVinandVoutusingthescope.Doyourmeasurementsagreewithyour
predictions?
c. Predictthe3dBfrequencyforyourcircuit.Includeyourcalculationsinyourlabbook.
Now,determinethe3dBfrequencyexperimentally.Describetheprocedure youfollowed
todeterminefB.Doesyourmeasurementagreewithyourprediction?Explicitlyrecord
whatcriteriayouusedtodeterminewhetherornotthemodelandmeasurementsagree.
d. Usingthegain-bandwidthrelationandyourmeasurementsofG0andfBtodeterminefTfor
yourop-amp.DoesyourmeasuredvalueoffTagreewiththeonefromthedatasheet?
e. Measurethefrequencydependenceofyourcircuit.Measurethegainateverydecadein
frequencyfrom10MHzdownto10Hz.Shouldyouusea10Xprobeorcoaxcabletomake
yourmeasurements?Explainyourreasoning.Plotyourmeasurementsandpredictedgain
curveonthesameplot.Where,ifatall,isthesimplemodeloftheop-ampcircuitnot
valid?Suggestpossiblemodelrefinementsand/orphysicalsystemrefinementstoget
betteragreementbetweenthemodelpredictionsandmeasurements.
SUMMINGAMPLIFIER
Step2
Summingamplifier–firsttests
a. Modifyyourbasicinvertingop-ampcircuittomakeitasummingamplifierasshowninFig.
2.Usethecomponentvaluesyoudeterminedinyourlabprepfortheresistors.Check
withaninstructortoseethatthesevaluesmakesense.Drawtheschematicinyourlab
bookandlabelallcomponents.Measuretheresistorsbeforeinsertingthemintoyour
circuitandrecordthevalues.
b. Determinethetransferfunctionforyourexactcomponentvalues.WhatisVoutintermsof
V1,V2,andV3?
c. ConfirmyoursummingamplifierisworkingaccordingtoyourmodelbymeasuringVoutfor
anysetofVinvoltages.Predicttheoutputvoltageforyoursetoftestinputvoltagesand
measureVout.Whatisthebestavailablemeasurementdevicetomakethese
measurements?Whydidyouchoosethatdevice?Doesyourmeasurementagreewith
yourprediction?
Summingamplifier–Digital-to-Analogconversion
a. Useyoursummingamplifierin“digitaltoanalogconversionmode”tocreateinteger
outputvoltagesfrom0to-7Vfromtwoinputvoltages(0Vor1V).Predictwhatsetof
inputvoltagesisrequiredtogeteachdesiredoutputvoltage(HINT:Youdidthisinyour
Labprep.)Doyourmeasurementsagreewithyourpredictionsforalleightvoltages?How
accuratelywereyouabletomakeintegervaluesofvoltage?Describeawaytorefinethe
physicalsystemtomoreaccuratelycreateexactintegervoltages.
Step3
INTEGRATOR
Step4
Integrator
Bynow,youshouldbesomewhatcomfortablewithexperimentaldesignandreportingof
outcomes,especiallywithop-ampsandvoltagedividers.Inthislastsection,youwillgettopractice
designingandcharacterizinganintegrator.Yourstartingpointshouldbethecircuityoudesigned
intheprelab.
Itemsyoulikelywishtoinclude:
Describethecircuityouarebuildingandtesting.
Drawtheschematicofthecircuitwithcomponentvalueslabeled.H&H4.19-4.20isa
usefulresource.
Listyourpredictions/models.Itisfinetostartbyusingidealmodels.
Howdoyouplantotestit?Besuretousesquare,triangle,andsinewavesatvarious
frequencies.
Theresultsofthetestswithvariousinputs.
Dotheresultsmatchyourmodel?Whatdidn’tmatch…?
Howwouldyourefineyourmodelorphysicalsystemtogetbetteragreement?
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