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OPERATIONALAMPLIFIERS(OP-AMPS)ILAB4INTRO:INTRODUCTIONTOONEOFTWOOFTHEMOSTUSEDOP-AMPCIRCUITS:NON-INVERTINGAMPLIFIERS

GOALSInthislab,youwillcharacterizethegainandfrequencydependenceofop-ampcircuits,oneofthemostusefulcomponentsinelectronics(unlessyoulikeusingvacuumtubes).Youwillalsomeasureinputandoutputimpedancesofthesecircuits.Theop-ampisthemostimportantbuildingblockofanalogelectronics.

Proficiencywithnewequipment:

o Op-amps:Non-invertingampswithfinitegainandunitygain(voltagefollower)

Proficiencywithnewanalysisandplottingtechniques:

o Bodeplots

Modelingthephysicalsystem:

o Frequencydependenceofop-ampcircuitso Inputandoutputimpedancesofop-ampcircuits

DEFINITIONSClosed-loopgain,G–gainoftheop-ampcircuitatallfrequencieswithfeedbackappliedLowfrequencygain,G0–gainoftheop-ampcircuitatDC(f=0Hz)Open-loopgain,A–gainoftheop-ampitselfatallfrequencieswithnofeedbackappliedDCgain,A0–gainoftheop-ampitselfatDC(f=0Hz)withnofeedbackappliedf0–3dBfrequencyforanop-ampitselfwithnofeedbackfB–3dBfrequencyforanop-ampcircuitwithfeedbackappliedfT–unitygainfrequency,frequencywheretheopenloopgainAisequaltoone

GENERALPURPOSEOFOP-AMPS Oneofthemainpurposesofanamplifieristoincreasethevoltagelevelofasignalwhilepreservingasaccuratelyaspossibletheoriginalwaveform.Inthephysicalsciences,transducersareusedtoconvertbasicphysicalquantitiesintoelectricsignals,asshowninFigure1.Anamplifierisusuallyneededtoraisethesmalltransducervoltage(µVtomV)toausefullevel(mVtoV).

Figure1:TypicalLaboratoryMeasurementSystem

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Measuringandrecordingequipmenttypicallyrequiresinputsignalsof10mVto10V.Tomeetsuchneeds,atypicallaboratoryamplifiermighthavethefollowingcharacteristics:1. Predictableandstablegain. Themagnitudeofthegain isequaltotheratiooftheoutputsignal

amplitudetotheinputsignalamplitude.2. Linearamplituderesponse,sothattheoutputsignalisdirectlyproportionaltotheinputsignal.3. Accordingtotheapplication,thefrequencydependenceofthegainmightbeaconstant

independentoffrequencyuptothehighestfrequencycomponentintheinputsignal(widebandamplifier),orasharplytunedresonanceresponseifaparticularfrequencymustbepickedout.

4. Highinputimpedanceandlowoutputimpedanceareusuallydesirable.Thesecharacteristicsminimizechangesofgainwhentheamplifierisconnectedtotheinputtransducerandtootherinstrumentsattheoutput.

5. Lownoiseisusuallyimportant.Everyamplifieraddssomerandomnoisetothesignalsitprocesses,andthisnoiseoftenlimitsthesensitivityofanexperiment.

Commerciallaboratoryamplifiersarereadilyavailable,butageneral-purposeamplifierisexpensive(>$1000),andmostofitsfeaturesmightbeunneededinagivenapplication.Often,itispreferabletodesignyourowncircuitusingacheap(<$1)op-ampchip.Op-ampshavemanyothercircuitapplications.Theycanbeusedtomakefilters,limiters,rectifiers,oscillators,integrators,andotherdevices(seeFC12.9–12.15).Wewillbuildsomeofthesecircuitsinthenextlab,Lab5.

OP-AMPBASICSThetwobasicop-ampcircuitconfigurationsareshowninFigs.2(a)and2(b).Bothcircuitsuse

negativefeedback,whichmeansthataportionoftheoutputsignalissentbacktothenegativeinputoftheop-amp.Theop-ampitselfhasveryhighgain,butrelativelypoorgainstabilityandlinearity.Whennegativefeedbackisused,thecircuitgainisgreatlyreduced,butitbecomesverystable.Atthesametime,linearityisimprovedandtheoutputimpedancedecreases.

Bothconfigurationsarewidelyusedbecausetheyhavedifferentadvantages.Besidesthefactthatthesecondcircuitinvertsthesignal,themaindifferencesarethatthefirstcircuithasmuchhigherinputimpedance,whilethesecondhaslowerdistortionbecausebothinputsremainveryclosetoground.Inthislab,wewillbefocusingonthefirst-type,non-inverting.Thegainortransferfunction,A,oftheop-ampaloneisgivenby

−+ −≡

inin

out

VVV

A

3

wherethedenominatoristhedifferencebetweenthevoltagesappliedtothe+and-inputs.WeusethesymbolGforthegainofthecompleteamplifierwithfeedback:G=Vout/Vin.Thisgaindependsontheresistordividerratio

𝐵 =𝑅

𝑅 + 𝑅%

IfweassumeanidealsituationwhereA=∞,thattheop-ampinputimpedanceisinfinite,andthattheoutputimpedanceiszero,thenthebehaviorofthesecircuitscanbeunderstoodusingthesimple“GoldenRules”:

I. Thevoltagedifferencebetweentheinputsiszero.(“voltagerule”)II. Nocurrentflowsinto(oroutof)eachinput.(“currentrule”)

The“GoldenRule”analysisisveryimportantandisalwaysthefirststepisdesigningop-ampcircuits,sobesureyouunderstanditbeforeyoureadthematerialbelow,whereweconsidertheeffectoffinitevaluesofA,mainlysothatthefrequencydependenceoftheclosedloopgainGcanbeunderstood. Non-invertingamplifierThebasicformulaforthelowfrequencygainofnon-invertingamplifiersisderivedinFC,Section12.5.UsingjusttheGoldenrules,whichassumesA>>1,thegainisgivenby

𝐺' =()*+(,-

= 1 + /0/

FormulasfortheinputandoutputimpedanceoftheentirecircuitarederivedinH&HSection4.26.Theresultsare

𝑅23 = 𝑅2 1 + 𝐴𝐵

𝑅53 = 𝑅5/ 1 + 𝐴𝐵

whereRiandRoaretheinputandoutputimpedancesoftheop-ampalone,whiletheprimedsymbolsrefertothewholeamplifierwithfeedback.Theseimpedanceswillbeimprovedfromthevaluesforthebareop-ampifA·Bislarge.TheaboveformulasarestillcorrectwhenAand/orBdependonfrequency.Bwillbefrequencyindependentifwehavearesistivefeedbacknetwork(inothercasesthatusecompleximpedanceitmaynotbe),butAalwaysvarieswithfrequency.Formostop-amps,includingtheLF356,theopenloopgainvarieswithfrequencylikeanRClow-passfilter:

A = A01+ j f

f0

(2)

The3dBfrequency,f0,isusuallyverylow,around10Hz.Datasheetsdonotusuallygivef0directly;

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insteadtheygivethedcgain,A0,andtheunitygainfrequencyfT,whichisthefrequencywherethemagnitudeoftheopenloopgainAisequaltoone.TherelationbetweenA0,f0,andfTis

𝑓8 = 𝐴'𝑓'

ThefrequencydependenceoftheclosedloopgainGisthengivenby

G =G0

1+ j ffB

The frequency response of the amplifier with feedback is therefore also the same as for an RC low-pass filter. We can now derive an example of a very important general rule connecting the gain and bandwidth of feedback amplifiers. Multiplying the low frequency gain G0 by the 3 dB bandwidth fB gives

𝐴'𝑓' = 𝐺'𝑓9 = 𝑓8

In words, this very important formula says that the gain-bandwidth product G0fB equals the unity gain frequency fT. Thus if an op-amp has a unity gain frequency fT of 1 MHz, it can be used to make a non-

inverting amplifier with a gain of one and a bandwidth of 1 MHz, or with a gain of 10 and a bandwidth of 100 kHz, etc. We will consider what this means for the transfer function as a function of frequency on a Bode plot.

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USEFULREADINGS1. FCSections12.2–12.15.Thebasicrulesofop-ampbehaviorandthemostimportantop-ampcircuits.

[NotewhileFCdiscussedbasiccharacteristicsofopampsin12.2itdoesnothavethe“GoldenRule”analysisthatwewilldiscussinclass.]Donotworryrightnowaboutthetransistorgutsofop-amps.WewilllearnabouttransistorsinExperiments7-8.

2. HorowitzandHill,Chapter4.

LABPREPACTIVITIES

AnswerthefollowingquestionsusingMathematicafortheplots.YoucanuseeitherMathematicafortherestthequestionsaswellordothembyhandinyourlabbook.Bringanelectroniccopyofyournotebooktolab,preferablyonyourownlaptop.Youwilluseittoplotyourdataduringthelabsession.

Question1

PropertiesofanOp-ampa. Thefirststepinusinganewcomponentistolookupitsbasiccharacteristics.Findthefollowingspecs

usingthedatasheetfortheop-ampyouwilluseinthelabfortherestofthesemester.DatafortheLF356op-amp(sameasLF156)aregivenattheNationalSemiconductorWebSite.(Thereisaalsoalinkfromthe3330webpageunderUsefulDocs).

a. Unitygainfrequency,fT (sameasGBWintables)b. DCvoltagegain,A0 (sameasAVOLintables)(Note:listedasV/mV,milli=10-3)c. Maximumoutputvoltage (sameasVOintables)d. Maximumoutputcurrent e. Inputresistance,Ri

Question2

Non-invertingamplifiera. Calculate the values of low frequency gain G0 and the bandwidth fB for the non-inverting

amplifierinFig.2(a)forthefollowingtwocircuitsyouwillbuildinlab.1)RF=10kΩ, R=100Ω2)RF=0,R=∞(thisisavoltagefollower)

b. Predicttheoutputvoltage,Vout,forthenon-invertingampwithRF=10kΩ andR=100Ωwhen1) Vin=1mVDC2) Vin=1VDC,Explainyourreasoning.

HINT:seeanswerforQuestion1partc.

c. Plot Bode plots for the open loop gain and the two closed loop gains frompart (a) on thesamegraphusingMathematica.

d. Estimatetheinputimpedanceofthecompleteamplifiercircuit(Ri’)withRF=10kΩandR=100Ωfor1kHzsinewaves.

e. Estimatetheoutput impedanceofthecompleteamplifiercircuit(Ro')withRF=10kOhmandR=100Ohm for1 kHz sinewaves. Thenominaloutput impedanceof the LF356alone is40Ohms.Toobtainthecircuitoutputimpedanceat1kHz,onecanusethisvalueanddetermineRo'usingtheformulagivenabove.Alternatively,onecanreadoffthevaluefromthetopleftplotonpage7ofthedatasheet.Thisshowstheoutputimpedanceforaninvertingamplifier(which has the same output impedance as a non-inverting amplifier) as a function offrequencyforgainsofAV=1,10,100.

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Question3 Labactivitiesa. Readthroughallofthelabstepsandidentifythestep(orsub-step)thatyouthinkwillbethe

mostchallenging.b. Listatleastonequestionyouhaveaboutthelabactivity.

SETTINGUPABASICOP-AMPCIRCUT

Allop-ampcircuitsstartoutbymakingthebasicpowerconnections.Op-ampsareactivecomponents,whichmeanstheyneedexternalpowertofunctionunlikepassivecomponentssuchasresistors.

Figure3.LF356pin-outandschematic.

Figure4.Goodplacementofop-ampandbypasscapacitorsonproto-board.Noteshortwiresareusedforallconnections.Step1 Op-ampTips

a. Thisexperimentwilluseboth+15Vand-15VtopowertheLF356op-amp.Turnoffthepowerwhilewiringyourop-amp.Everyonemakesmistakesinwiring-upcircuits.Thus,it’sagoodideatocheckyourcircuitbeforeapplyingpower.Fig.3showsapin-outfortheLF356chip.Familiarizeyourselfwiththelayout.

Thefollowingprocedurewillhelpyouwireupacircuitaccurately:1. Drawacompleteschematicinyourlabbook,includingallgroundandpowerconnections,

andallICpinnumbers.Trytolayoutyourprototypesothepartsarearrangedinthesamewayasontheschematic,asfaraspossible.

2. Measureallresistorandcapacitorvaluesbeforeputtingtheminthecircuit.Becarewithunitprefixes.Itiseasytomistakea1nFcapacitorfora1µFone.(Youdon’tneedtoknowtheprecisevaluesofthebypasscapacitors,sothereisnoneedtomeasurethem.)

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3. Adheretoacolorcodeforwires.Forexample: 0V(ground) Black +15V Red -15V Blue

b. Theop-ampchipsitsacrossagrooveintheprototypingboard(seeFig4).Beforeinsertingachip,gentlystraightenthepins.Afterinsertion,checkvisuallythatnopinisbrokenorbentunderthechip.Toremovethechip,useasmallscrewdriverinthegroovetopryitout.

c. Youwillhavelesstroublewithspontaneousoscillationsifthecircuitlayoutisneatandcompact,inparticularthefeedbackpathshouldbeasshortaspossibletoreducedunwantedcapacitivecouplingandleadinductance.(seeFig4).Hint:donotwireoverthechipbutaroundit.

d. Tohelppreventspontaneousoscillationsduetounintendedcouplingviathepowersupplies,usebypasscapacitorstofilterthesupplylines.Abypasscapacitorbetweeneachpowersupplyleadandgroundwillprovideaminiaturecurrent“reservoir”thatcanquicklysupplycurrentwhenneeded.Thiscapacitorisnormallyintherange1µF–10µF.Theexactvalueisusuallyunimportant.Compactcapacitorsinthisrangeareusuallyelectrolytic,tantalum,oraluminumandarepolarized,meaningthatoneterminalmustalwaysbepositiverelativetotheother.Thecapacitorsarelabeledwhichsideiswhich,buteachmanufactureusesdifferentmarkings.Ifyouputapolarizedcapacitorinbackwards,itwillburnout.Bypasscapacitorsshouldbeplacedascloseaspossibletotheop-amppins.(seeFig4).

Step2 Testingtheop-ampa. Youcansaveyourselfsomefrustrationbytestingyourop-ampchipstomakesurethey

arenotburnedout.Connecttheop-ampasavoltagefollowerwiththe(positive)inputgrounded(seeFig.5).Whatisthepredictedvoltageonpins2,3,4,6and7usingtheGoldenRulemodel?Measureandrecordthemeasuredvoltagesonthesepins.Ifyourpredictionsdonotmatchyourmeasurementscheckyourconnectionstothechiptofindtheproblem.Makesureyourpredictionsmatchyourmeasurementsbeforegoingon.

b. Ifyoufindyouhaveabadchip,throwitinthetrashtosaveanotherpersonfromhavingtodealwithit.(Incaseyouarewondering,theLF356costs$0.50)

Figure5.Schematicofavoltagefollowerwiththeinputgrounded.

Vin= 0V Vout

_

+

+15 V

-15 V

2

3 6

7

4

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VOLTAGEFOLLOWERAvoltagefolloweristhesimplestversionofanon-invertingamplifier.Thevoltagefollowerhasnovoltagegain(G0=1),butitletsyouconvertasignalwithhighimpedance(i.e.verylittlecurrent)toamuchlowerimpedanceoutputfordrivingloads.Thevoltagefollowerisalsooftencalledaunitygainbuffer.

Figure6.VoltageFollowerStep3 Lowfrequencygainandfrequencydependenceofthegain.

a. Thevoltagefollowercircuitisnearlythesameasthetestcircuit,exceptthatnowasignalentersthepositiveinput(Fig.6).ThebasictestandmeasurementsetupisshowninFig.7.

b. Usethefunctiongeneratortomeasurethelowfrequencygain.Whatfrequencyshouldyouusetotestthelowfrequencygain(i.e.,whatfrequencyshouldthesignalbebelow)?Considerthegain-bandwidthproductforaunitygainamplifier.Whatisgain-bandwidthproductforthiscircuit?Howdidyoufindthevalue?Whatisthepredictedgainforthefrequencyyouchose?MeasurethelowfrequencygainG0bymeasuringVinandVoutusingthescope.Doyourmeasurementsagreewithyourpredictions?

c. Nowvarythefrequencyandlookfordeviationfromtheperformanceofanidealfollowermodel.ThemeasurementathighfrequencywilldependonmanydetailsofyoursetupandyouareunlikelytofindasimpleRCfiltertypefalloff.Usingthe10Xscope-probe,measurethegainateverydecadeinfrequencyfrom10MHzdownto10Hz,with(asusual)afewextrapointsanywherethingsarestartingtochange.Doyoufindanydeviationfromunitygain?HINT:BesurethattheoutputamplitudeisbelowthelevelaffectedbytheslewrateForhelp,seeH&Hp.192.PlotthelowandhighfrequencydataandpredictedbehavioronyourBodeplotfromyourlabprep.Doyoufindasimplefall-offassuggestedbythetheoryfortheidealfollower(fT=fB)?Ifso,findthe3dBfrequency.Howdoesyourmeasured3dBfrequencycomparetowhatisexpectedfromtheop-ampdatasheet?

d. Ifyouobservedidealbehavior,you'relucky!AtfrequenciesaboveafewMHz,thesimplemodelofthefrequencyresponseoftheop-ampisnotaccurate.Onceyouareinthisfrequencyrange,manyphysicaldetailsofyourcircuitandbreadboardcanhavelargeeffectsinthecircuit(seenotesinStep1(d)above).Youcouldmodeltheseeffects,butabetterproceduretofollowistomodifythephysicalsetup.Buildingreliablecircuitsatthesefrequenciestypicallyrequirescarefulattentiontogroundingandminimizationofcapacitiveandinductivecouplingbetweencircuitelementsandtoground.Printedcircuitboardsaremuchbetterforhigh-frequencyapplications.Atlowerfrequencies,ourmodelofthecircuitwillworkmuchbetter.

Vout

_

+

+15 V

-15 V

2

3 6

7

4 Vin

9

Function Generator

Circuit Board

V out V in

V in

Trigger

Trig. Out

Sig. Out

Oscilloscope

Channel 1

Channel 2

Channel 4 Trigger

DC Power Supply

0 +15 –15

Figure7.Testandmeasurementsetupforop-ampcircuits.

NON-INVERTINGAMPLIFIER

Figure8.Non-invertingAmplifier

Step4

FrequencyDependentGain a. ChangethenegativefeedbackloopinyourcircuittotheoneshowninFig.8.,with

RF=10kΩandR=100Ω.MeasureRandRFwiththeDMMbeforeinsertingthemintothecircuitboard.PredictG0andfBfromthesemeasuredvaluesandtheop-amp'svalueoffTfromthedatasheet.(Youshouldbeabletoreviewyourlab-prepworkheretoo!)

b. Usethefunctiongeneratortomeasurethelowfrequencygain.Whatfrequencyshouldyouusetotestthelowfrequencygain(i.e.,whatfrequencyshouldthesignalbebelow)?Considerthegain-bandwidthproductforaunitygainamplifier.Whatisgain-bandwidthproductforthiscircuit?Howdidyoufindthevalue?Whatisthepredictedgainforthefrequencyyouchose?MeasurethelowfrequencygainG0bymeasuringVinandVoutusingthescope.Doyourmeasurementsagreewithyourpredictions?

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c. Measurethevoltagesaturationvaluesforyourcircuit.Varytheinputamplitudeuntilyou

observesaturationintheoutput.Whataretheoutputsaturationlevels,+Vsatand-Vsat?RecordhowyoudeterminedVsat.Cantheop-ampproducevoltagesfromthepositiverail(+15V)tothenegativerail(-15V)?Themodeloftheop-ampyouhavebeenworkingwithdoesnotincludesaturationeffects.Tomakesureyouareworkingwithintherangewhereyourmodelisvalid,alwaysmakesuretheoutputamplitudeisbelowhalfthesaturatedvalue.

e. Predictthe3dBfrequencyforyourcircuit.Includeyourcalculationsinyourlabbook.Now,determinethe3dBfrequencyexperimentally.DescribetheprocedureyoufollowedtodeterminethefB.Doesyourmeasurementagreewithyourprediction?Explicitlyrecordwhatcriteriayouusedtodeterminewhetherornotthemodelandmeasurementsagree.

d. Usingthegain-bandwidthrelationG0fB=fTandyourmeasurementsofG0andfB,determinethefTforyourop-amp.DoesyourmeasuredvalueoffTagreewiththeonefromthedatasheet?

e. Measurethefrequencydependenceofyourcircuit.Measurethegainateverydecadeinfrequencyfrom10MHzdownto10Hz,withextrapointsnearyourcutofffrequency.Shouldyouusea10Xprobeorcoaxcabletomakeyourmeasurements?Explainyourreasoning.Plotyourmeasurementsandpredictedgaincurveonthesameplot.Where,ifatall,isthesimplemodeloftheop-ampcircuitnotvalid?Suggestpossiblemodelrefinementsand/orphysicalsystemrefinementstogetbetteragreementbetweenthemodelpredictionsandmeasurements.

Step5

Input/OutputImpedancesandCurrentLimitoftheCircuit

a. Predicttheinputimpedanceofyournon-invertingamplifiercircuit,Ri’.(HINT:Youfoundtheinputimpedanceoftheop-ampaloneinyourprelab.)Explainhowyoudeterminedthisnumber.Ifyouweretoincreasetheinputimpedancebyplacinga1MΩresistorinserieswiththeinput,predicthowmuchtheoutputvoltagewillchange.HINT:considerthevoltagedropacrossthe1MΩresistortogetthevoltageatPin3.MeasureVoutwithandwithoutthe1MΩresistorinplace.Doyourmeasurementsagreewithyourmodelpredictions?

b. Predicttheoutputimpedanceofyourcircuit,Ro',atafrequencyof1kHz.(HINT:Seeprelab2e.)Predicttheoutputvoltagebasedonyourinputvoltagewhenyourcircuitisusedtodrivealoadof200Ωandaloadof8Ω separatly.(Modelasavoltagedividerwiththeoutputimpedanceandyourloadresistor.)Measuretheoutputvoltagesinallthreeconfigurations(noload,200Ωload,8Ωload).Dothemeasuredvaluesagreewithyourmodelprediction?Ifnot,canyoumakemodificationstoyourmodeltounderstandthediscrepancy? HINT:Considerthemaximumcurrentoutputoftheop-amp.