An Applications Guide for Op Amps - (Natl Semiconductor)

12 Pages·1969·0.193 MB·English

A
An Applications Guide for NationalSemiconductor n
ApplicationNote20 A
Op Amps February1969 p
p
l
i
c
INTRODUCTION a
t
The general utility of the operational amplifier is derived satedsofrequencystabilizationcomponentsarenotshown(cid:59) i
o
fromthefactthatitisintendedforuseinafeedbackloop however(cid:44)otheramplifiersmaybeusedtoachievegreater
n
whose feedback properties determine the feed-forward operatingspeedinmanycircuitsaswillbeshowninthetext(cid:46)
s
characteristicsoftheamplifierandloopcombination(cid:46)Tosuit AmplifierparameterdefinitionsarecontainedinAppendixI(cid:46)
G
itforthisusage(cid:44)theidealoperationalamplifierwouldhave
infinite input impedance(cid:44) zero output impedance(cid:44) infinite THEINVERTINGAMPLIFIER u
gainandanopen-loop3dBpointatinfinitefrequencyrolling ThebasicoperationalamplifiercircuitisshowninFigure1(cid:46) id
offat6dBperoctave(cid:46)Unfortunately(cid:44)theunitcost–inquan- Thiscircuitgivesclosed-loopgainofR2(cid:47)R1whenthisratio e
tity–wouldalsobeinfinite(cid:46) issmallcomparedwiththeamplifieropen-loopgainand(cid:44)as f
thenameimplies(cid:44)isaninvertingcircuit(cid:46)Theinputimped- o
Intensivedevelopmentoftheoperationalamplifier(cid:44)particu-
anceisequaltoR1(cid:46)Theclosed-loopbandwidthisequalto r
larlyinintegratedform(cid:44)hasyieldedcircuitswhicharequite
theunity-gainfrequencydividedbyoneplustheclosed-loop O
goodengineeringapproximationsoftheidealforfinitecost(cid:46)
Quantitypricesforthebestcontemporaryintegratedamplifi- gain(cid:46) p
ers are low compared with transistor prices of five years The only cautions to be observed are that R3 should be A
ago(cid:46)Thelowcostandhighqualityoftheseamplifiersallows chosentobeequaltotheparallelcombinationofR1andR2 m
theimplementationofequipmentandsystemsfunctionsim- tominimizetheoffsetvoltageerrorduetobiascurrentand
practicalwithdiscretecomponents(cid:46)Anexampleisthelow thattherewillbeanoffsetvoltageattheamplifieroutput p
frequencyfunctiongeneratorwhichmayuse15to20opera- equal to closed-loop gain times the offset voltage at the s
tionalamplifiersingeneration(cid:44)waveshaping(cid:44)triggeringand amplifierinput(cid:46)
phase-locking(cid:46)
Theavailabilityofthelow-costintegratedamplifiermakesit
mandatorythatsystemsandequipmentsengineersbefa-
miliarwithoperationalamplifierapplications(cid:46)Thispaperwill
presentamplifierusagesrangingfromthesimpleunity-gain
buffertorelativelycomplexgeneratorandwaveshapingcir-
cuits(cid:46) The general theory of operational amplifiers is not
within the scope of this paper and many excellent refer-
beencsehsaadreedatvoawilaarbdlethinetphreaclittiecraal(cid:44)tuarme(cid:46)p1l(cid:44)i2f(cid:44)ie3(cid:44)r4pTahraemaeptperrosawchillwbiell VOUTeRR21VIN
discussedastheyaffectcircuitperformance(cid:44)andapplica- R3eR1llR2
tionrestrictionswillbeoutlined(cid:46) Forminimumerrordue
toinputbiascurrent
Theapplicationsdiscussedwillbearrangedinorderofin-
TL(cid:47)H(cid:47)6822–1
creasingcomplexityinfivecategories(cid:58)simpleamplifiers(cid:44)op- FIGURE1(cid:46)InvertingAmplifier
erationalcircuits(cid:44)transduceramplifiers(cid:44)waveshapersand
generators(cid:44) and power supplies(cid:46) The integrated amplifiers Offset voltage at the input of an operational amplifier is
showninthefiguresareforthemostpartinternallycompen- comprisedoftwocomponents(cid:44)thesecomponentsareiden-
tifiedinspecifyingtheamplifierasinputoffsetvoltageand
input bias current(cid:46) The input offset voltage is fixed for a
particular amplifier(cid:44) however the contribution due to input
A
N
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2
0
C1995NationalSemiconductorCorporation TL(cid:47)H(cid:47)6822 RRD-B30M115(cid:47)PrintedinU(cid:46)S(cid:46)A(cid:46)
biascurrentisdependentonthecircuitconfigurationused(cid:46) THENON-INVERTINGAMPLIFIER
For minimum offset voltage at the amplifier input without Figure2showsahighinputimpedancenon-invertingcircuit(cid:46)
circuit adjustment the source resistance for both inputs Thiscircuitgivesaclosed-loopgainequaltotheratioofthe
shouldbeequal(cid:46)Inthiscasethemaximumoffsetvoltage sumofR1andR2toR1andaclosed-loop3dBbandwidth
wouldbethealgebraicsumofamplifieroffsetvoltageand equal to the amplifier unity-gain frequency divided by the
thevoltagedropacrossthesourceresistanceduetooffset closed-loopgain(cid:46)
current(cid:46) Amplifier offset voltage is the predominant error
The primary differences between this connection and the
termforlowsourceresistancesandoffsetcurrentcauses
invertingcircuitarethattheoutputisnotinvertedandthat
themainerrorforhighsourceresistances(cid:46)
theinputimpedanceisveryhighandisequaltothedifferen-
Inhighsourceresistanceapplications(cid:44)offsetvoltageatthe tial input impedance multiplied by loop gain(cid:46) (Open loop
amplifieroutputmaybeadjustedbyadjustingthevalueof gain(cid:47)Closed loop gain(cid:46)) In DC coupled applications(cid:44) input
R3andusingthevariationinvoltagedropacrossitasan impedanceisnotasimportantasinputcurrentanditsvolt-
inputoffsetvoltagetrim(cid:46) agedropacrossthesourceresistance(cid:46)
Offsetvoltageattheamplifieroutputisnotasimportantin Applicationscautionsarethesameforthisamplifierasfor
ACcoupledapplications(cid:46)Heretheonlyconsiderationisthat theinvertingamplifierwithoneexception(cid:46)Theamplifierout-
anyoffsetvoltageattheoutputreducesthepeaktopeak putwillgointosaturationiftheinputisallowedtofloat(cid:46)This
linearoutputswingoftheamplifier(cid:46) may be important if the amplifier must be switched from
The gain-frequency characteristic of the amplifier and its sourcetosource(cid:46)Thecompensationtradeoffdiscussedfor
feedback network must be such that oscillation does not theinvertingamplifierisalsovalidforthisconnection(cid:46)
occur(cid:46)Tomeetthiscondition(cid:44)thephaseshiftthroughampli-
fierandfeedbacknetworkmustneverexceed180(cid:167)forany
frequencywherethegainoftheamplifieranditsfeedback
networkisgreaterthanunity(cid:46)Inpracticalapplications(cid:44)the
phaseshiftshouldnotapproach180(cid:167)sincethisisthesitua-
tionofconditionalstability(cid:46)Obviouslythemostcriticalcase
occurs when the attenuation of the feedback network is
zero(cid:46)
Ausmepdliftioersacwhiheivceh ianrcerenaostedintpeernrfaolrlmyacnocmepeinnscairtceuditsmwayhebree VOUTeR1Ra1R2VIN
feedbacknetworkattenuationishigh(cid:46)Asanexample(cid:44)the R1llR2eRSOURCE
LM101maybeoperatedatunitygainintheinvertingamplifi- Forminimumerrordue
toinputbiascurrent
er circuit with a 15 pF compensating capacitor(cid:44) since the
feedbacknetworkhasanattenuationof6dB(cid:44)whileitre- TL(cid:47)H(cid:47)6822–2
quires 30 pF in the non-inverting unity gain connection FIGURE2(cid:46)Non-InvertingAmplifier
where the feedback network has zero attenuation(cid:46) Since
amplifier slew rate is dependent on compensation(cid:44) the THEUNITY-GAINBUFFER
LM101slewrateintheinvertingunitygainconnectionwill Theunity-gainbufferisshowninFigure3(cid:46)Thecircuitgives
be twice that for the non-inverting connection and the in- thehighestinputimpedanceofanyoperationalamplifiercir-
verting gain of ten connection will yield eleven times the cuit(cid:46)Inputimpedanceisequaltothedifferentialinputimped-
slew rate of the non-inverting unity gain connection(cid:46) The ancemultipliedbytheopen-loopgain(cid:44)inparallelwithcom-
compensationtrade-offforaparticularconnectionisstabili- monmodeinputimpedance(cid:46)Thegainerrorofthiscircuitis
tyversusbandwidth(cid:44)largervaluesofcompensationcapaci- equaltothereciprocaloftheamplifieropen-loopgainorto
tor yield greater stability and lower bandwidth and vice thecommonmoderejection(cid:44)whicheverisless(cid:46)
versa(cid:46)
Theprecedingdiscussionofoffsetvoltage(cid:44)biascurrentand
stabilityisapplicabletomostamplifierapplicationsandwill
bereferencedinlatersections(cid:46)Amorecompletetreatment
iscontainedinReference4(cid:46) VOUTeVIN
R1eRSOURCE
Forminimumerrordue
toinputbiascurrent
TL(cid:47)H(cid:47)6822–3
FIGURE3(cid:46)UnityGainBuffer
2
InputimpedanceisamisleadingconceptinaDCcoupled
unity-gainbuffer(cid:46)Biascurrentfortheamplifierwillbesup-
pliedbythesourceresistanceandwillcauseanerroratthe
amplifier input due to its voltage drop across the source
resistance(cid:46)Sincethisisthecase(cid:44)alowbiascurrentamplifi-
er such as the LH1026 should be chosen as a unity-gain
bufferwhenworkingfromhighsourceresistances(cid:46)Biascur- VOUTe(cid:35)RR31aaRR42JRR41V2bRR21V1
rentcompensationtechniquesarediscussedinReference
ForR1eR3andR2eR4
5(cid:46)
The cautions to be observed in applying this circuit are VOUTeRR21(V2bV1)
three(cid:58)theamplifiermustbecompensatedforunitygainop- R1llR2eR3llR4
eration(cid:44)theoutputswingoftheamplifiermaybelimitedby TL(cid:47)H(cid:47)6822–5
Forminimumoffseterror
theamplifiercommonmoderange(cid:44)andsomeamplifiersex-
duetoinputbiascurrent
hibit a latch-up mode when the amplifier common mode
rangeisexceeded(cid:46)TheLM107maybeusedinthiscircuit
with none of these problems(cid:59) or(cid:44) for faster operation(cid:44) the FIGURE5(cid:46)DifferenceAmplifier
LM102maybechosen(cid:46)
Circuitbandwidthmaybecalculatedinthesamemanneras
fortheinvertingamplifier(cid:44)butinputimpedanceissomewhat
morecomplicated(cid:46)Inputimpedanceforthetwoinputsisnot
necessarilyequal(cid:59)invertinginputimpedanceisthesameas
fortheinvertingamplifierofFigure1andthenon-inverting
inputimpedanceisthesumofR3andR4(cid:46)Gainforeither
inputistheratioofR1toR2forthespecialcaseofadiffer-
entialinputsingle-endedoutputwhereR1eR3andR2e
R4(cid:46)Thegeneralexpressionforgainisgiveninthefigure(cid:46)
VOUTebR4(cid:35)RV11aRV22aRV33J Cbaonmdpweidntsha(cid:46)tionshouldbechosenonthebasisofamplifier
R5eR1llR2llR3llR4 Caremustbeexercisedinapplyingthiscircuitsinceinput
Forminimumoffseterrordue impedancesarenotequalforminimumbiascurrenterror(cid:46)
toinputbiascurrent
DIFFERENTIATOR
TL(cid:47)H(cid:47)6822–4
FIGURE4(cid:46)SummingAmplifier The differentiator is shown inFigure6and(cid:44) as the name
implies(cid:44) is used to perform the mathematical operation of
SUMMINGAMPLIFIER differentiation(cid:46)Theformshownisnotthepracticalform(cid:44)itis
Thesummingamplifier(cid:44)aspecialcaseoftheinvertingam- atruedifferentiatorandisextremelysusceptibletohighfre-
plifier(cid:44) is shown inFigure4(cid:46) The circuit gives an inverted quencynoisesinceACgainincreasesattherateof6dB
outputwhichisequaltotheweightedalgebraicsumofall peroctave(cid:46)Inaddition(cid:44)thefeedbacknetworkofthediffer-
threeinputs(cid:46)Thegainofanyinputofthiscircuitisequalto entiator(cid:44)R1C1(cid:44)isanRClowpassfilterwhichcontributes
the ratio of the appropriate input resistor to the feedback 90(cid:167)phaseshifttotheloopandmaycausestabilityproblems
resistor(cid:44) R4(cid:46) Amplifier bandwidth may be calculated as in evenwithanamplifierwhichiscompensatedforunitygain(cid:46)
theinvertingamplifiershowninFigure1byassumingthe
inputresistortobetheparallelcombinationofR1(cid:44)R2(cid:44)and
R3(cid:46)Applicationcautionsarethesameasfortheinverting
amplifier(cid:46)Ifanuncompensatedamplifierisused(cid:44)compensa-
tioniscalculatedonthebasisofthisbandwidthasisdis-
cussedinthesectiondescribingthesimpleinvertingamplifi-
er(cid:46)
Tbehtewaedevnanintapguetsofanthdisocpirecruaittioisnsthastutchhereasissnuomimntienrgacationnd VOUTebR1C1ddt(VIN)
weightedaveragingareimplementedveryeasily(cid:46) R1eR2
Forminimumoffseterror
THEDIFFERENCEAMPLIFIER duetoinputbiascurrent
Thedifferenceamplifieristhecomplementofthesumming TL(cid:47)H(cid:47)6822–6
amplifierandallowsthesubtractionoftwovoltagesor(cid:44)asa FIGURE6(cid:46)Differentiator
special case(cid:44) the cancellation of a signal common to the
twoinputs(cid:46)ThiscircuitisshowninFigure5andisusefulas
acomputationalamplifier(cid:44)inmakingadifferentialtosingle-
endedconversionorinrejectingacommonmodesignal(cid:46)
3
a low-pass filter with a frequency response decreasing at
6dBperoctave(cid:46)Anamplitude-frequencyplotisshownin
Figure10(cid:46)
fce2qR12C1
fhe2qR11C1e2qR12C2
fcmfhmfunitygain TL(cid:47)H(cid:47)6822–7
FIGURE7(cid:46)PracticalDifferentiator
ApracticaldifferentiatorisshowninFigure7(cid:46)Hereboththe
TL(cid:47)H(cid:47)6822–10
stabilityandnoiseproblemsarecorrectedbyadditionoftwo
FIGURE10(cid:46)IntegratorFrequencyResponse
additionalcomponents(cid:44)R1andC2(cid:46)R2andC2forma6dB
peroctavehighfrequencyroll-offinthefeedbacknetwork The circuit must be provided with an external method of
and R1C1 form a 6 dB per octave roll-off network in the establishinginitialconditions(cid:46)Thisisshowninthefigureas
inputnetworkforatotalhighfrequencyroll-offof12dBper S1(cid:46)WhenS1isinposition1(cid:44)theamplifierisconnectedin
octavetoreducetheeffectofhighfrequencyinputandam- unity-gainandcapacitorC1isdischarged(cid:44)settinganinitial
plifiernoise(cid:46)InadditionR1C1andR2C2formleadnetworks conditionofzerovolts(cid:46)WhenS1isinposition2(cid:44)theamplifi-
in the feedback loop which(cid:44) if placed below the amplifier erisconnectedasanintegratoranditsoutputwillchangein
unitygainfrequency(cid:44)provide90(cid:167)phaseleadtocompensate accordancewithaconstanttimesthetimeintegralofthe
the90(cid:167) phaselagofR2C1andpreventloopinstability(cid:46)A inputvoltage(cid:46)
gainfrequencyplotisshowninFigure8forclarity(cid:46) Thecautionstobeobservedwiththiscircuitaretwo(cid:58)the
amplifierusedshouldgenerallybestabilizedforunity-gain
operationandR2mustequalR1forminimumerrordueto
biascurrent(cid:46)
SIMPLELOW-PASSFILTER
Thesimplelow-passfilterisshowninFigure11(cid:46)Thiscircuit
hasa6dBperoctaveroll-offafteraclosed-loop3dBpoint
definedbyfc(cid:46)Gainbelowthiscornerfrequencyisdefinedby
theratioofR3toR1(cid:46)Thecircuitmaybeconsideredasan
AC integrator at frequencies well above fc(cid:59) however(cid:44) the
timedomainresponseisthatofasingleRCratherthanan
integral(cid:46)
TL(cid:47)H(cid:47)6822–8
FIGURE8(cid:46)DifferentiatorFrequencyResponse
INTEGRATOR
TheintegratorisshowninFigure9andperformsthemathe-
matical operation of integration(cid:46) This circuit is essentially
fLe2qR11C1
fce2qR13C1
ALeRR31 TL(cid:47)H(cid:47)6822–11
FIGURE11(cid:46)SimpleLowPassFilter
R2shouldbechosenequaltotheparallelcombinationof
R1andR3tominimizeerrorsduetobiascurrent(cid:46)Theampli-
VOUTeR11C1(cid:35)tt21VINdt fcieormspheonusladtebdeacmopmlipfieenrscaatnedbefoursuendi(cid:46)ty-gain or an internally
fce2qR11C1 TL(cid:47)H(cid:47)6822–9
R1eR2
Forminimumoffseterror
duetoinputbiascurrent
FIGURE9(cid:46)Integrator
4
TL(cid:47)H(cid:47)6822–14
TL(cid:47)H(cid:47)6822–12 FIGURE14(cid:46)AmplifierforPhotoconductiveCell
FIGURE12(cid:46)LowPassFilterResponse
AgainfrequencyplotofcircuitresponseisshowninFigure PHOTOCELLAMPLIFIERS
12toillustratethedifferencebetweenthiscircuitandthe Amplifiersforphotoconductive(cid:44)photodiodeandphotovolta-
trueintegrator(cid:46) iccellsareshowninFigures14(cid:44)15and16respectively(cid:46)
THECURRENT-TO-VOLTAGECONVERTER All photogenerators display some voltage dependence of
both speed and linearity(cid:46) It is obvious that the current
Currentmaybemeasuredintwowayswithanoperational
rhoughaphotoconductivecellwillnotdisplaystrictpropor-
amplifier(cid:46)Thecurrentmaybeconvertedintoavoltagewith
tionalitytoincidentlightifthecellterminalvoltageisallowed
aresistorandthenamplifiedorthecurrentmaybeinjected
tovarywithcellconductance(cid:46)Somewhatlessobviousisthe
directlyintoasummingnode(cid:46)Convertingintovoltageisun-
factthatphotodiodeleakageandphotovoltaiccellinternal
desirable for two reasons(cid:58) first(cid:44) an impedance is inserted
lossesarealsofunctionsofterminalvoltage(cid:46)Thecurrent-to-
intothemeasuringlinecausinganerror(cid:59)second(cid:44)amplifier
voltageconverterneatlysidestepsgrosslinearityproblems
offset voltage is also amplified with a subsequent loss of
by fixing a constant terminal voltage(cid:44) zero in the case of
accuracy(cid:46)Theuseofacurrent-to-voltagetransduceravoids
photovoltaic cells and a fixed bias voltage in the case of
bothoftheseproblems(cid:46)
photoconductorsorphotodiodes(cid:46)
The current-to-voltage transducer is shown inFigure13(cid:46)
Theinputcurrentisfeddirectlyintothesummingnodeand
the amplifier output voltage changes to extract the same
currentfromthesummingnodethroughR1(cid:46)Thescalefac-
torofthiscircuitisR1voltsperamp(cid:46)Theonlyconversion
errorinthiscircuitisIbiaswhichissummedalgebraicallywith
IIN(cid:46)
VOUTeR1ID
TL(cid:47)H(cid:47)6822–15
VOUTeIINR1 FIGURE15(cid:46)PhotodiodeAmplifier
TL(cid:47)H(cid:47)6822–13 Photodetectorspeedisoptimizedbyoperatingintoafixed
FIGURE13(cid:46)CurrenttoVoltageConverter lowloadimpedance(cid:46)Currentlyavailablephotovoltaicdetec-
torsshowresponsetimesinthemicrosecondrangeatzero
Thisbasiccircuitisusefulformanyapplicationsotherthan load impedance and photoconductors(cid:44) even though slow(cid:44)
currentmeasurement(cid:46)Itisshownasaphotocellamplifierin aremateriallyfasteratlowloadresistances(cid:46)
thefollowingsection(cid:46)
Theonlydesignconstraintsarethatscalefactorsmustbe
chosen to minimize errors due to bias current and since
voltagegainandsourceimpedanceareoftenindeterminate
(aswithphotocells)theamplifiermustbecompensatedfor
unity-gain operation(cid:46) Valuable techniques for bias current
compensationarecontainedinReference5(cid:46)
VOUTeICELLR1
TL(cid:47)H(cid:47)6822–16
FIGURE16(cid:46)PhotovoltaicCellAmplifier
5
Thefeedbackresistance(cid:44)R1(cid:44)isdependentoncellsensitivi- The amplifiers used must be compensated for unity-gain
tyandshouldbechosenforeithermaximumdynamicrange andadditionalcompensationmayberequireddependingon
orforadesiredscalefactor(cid:46)R2iselective(cid:58)inthecaseof loadreactanceandexternaltransistorparameters(cid:46)
photovoltaiccellsorofphotodiodes(cid:44)itisnotrequiredinthe
caseofphotoconductivecells(cid:44)itshouldbechosentomini-
mizebiascurrenterrorovertheoperatingrange(cid:46)
PRECISIONCURRENTSOURCE
TheprecisioncurrentsourceisshowninFigures17and18(cid:46)
Theconfigurationsshownwillsinkorsourceconventional
currentrespectively(cid:46)
TL(cid:47)H(cid:47)6822–19
FIGURE19a(cid:46)PositiveVoltageReference
ADJUSTABLEVOLTAGEREFERENCES
AdjustablevoltagereferencecircuitsareshowninFigures
IOeVRI1N 19and20(cid:46)Thetwocircuitsshownhavedifferentareasof
VINt0V applicability(cid:46)Thebasicdifferencebetweenthetwoisthat
Figure19illustratesavoltagesourcewhichprovidesavolt-
agegreaterthanthereferencediodewhileFigure20illus-
TL(cid:47)H(cid:47)6822–17 tratesavoltagesourcewhichprovidesavoltagelowerthan
FIGURE17(cid:46)PrecisionCurrentSink the reference diode(cid:46) The figures show both positive and
Caution must be exercised in applying these circuits(cid:46) The negativevoltagesources(cid:46)
voltagecomplianceofthesourceextendsfromBVCERof
theexternaltransistortoapproximately1voltmorenegative
thanVIN(cid:46)Thecomplianceofthecurrentsinkisthesamein
thepositivedirection(cid:46)
The impedance of these current generators is essentially
infiniteforsmallcurrentsandtheyareaccuratesolongas
VINismuchgreaterthanVOSandIOismuchgreaterthan
Ibias(cid:46)
ThesourceandsinkillustratedinFigures17and18usean
FETtodriveabipolaroutputtransistor(cid:46)Itispossibletouse
aDarlingtonconnectioninplaceoftheFET-bipolarcombi-
nation in cases where the output current is high and the
basecurrentoftheDarlingtoninputwouldnotcauseasig-
nificanterror(cid:46)
TL(cid:47)H(cid:47)6822–20
FIGURE19b(cid:46)NegativeVoltageReference
Highprecisionextendedtemperatureapplicationsofthecir-
cuit ofFigure19require that the range of adjustment of
IOeVRI1N VOUTberestricted(cid:46)Whenthisisdone(cid:44)R1maybechosento
provide optimum zener current for minimum zener T(cid:46)C(cid:46)
VINs0V SinceIZisnotafunctionofVa(cid:44)referenceT(cid:46)C(cid:46)willbeinde-
pendentofVa(cid:46)
TL(cid:47)H(cid:47)6822–18
FIGURE18(cid:46)PrecisionCurrentSource
6
TL(cid:47)H(cid:47)6822–21
FIGURE20a(cid:46)PositiveVoltageReference TL(cid:47)H(cid:47)6822–23
FIGURE21(cid:46)ResetStabilizedAmplifier
Theconnectionisusefulineliminatingerrorsduetooffset
voltageandbiascurrent(cid:46)Theoutputofthiscircuitisapulse
whoseamplitudeisequaltoVIN(cid:46)Operationmaybeunder-
stood by considering the two conditions corresponding to
thepositionofS1(cid:46)WhenS1isinposition2(cid:44)theamplifieris
connectedintheunitygainconnectionandthevoltageat
theoutputwillbeequaltothesumoftheinputoffsetvolt-
ageandthedropacrossR2duetoinputbiascurrent(cid:46)The
voltage at the inverting input will be equal to input offset
voltage(cid:46)CapacitorC1willchargetothesumofinputoffset
voltageandVINthroughR1(cid:46)WhenC1ischarged(cid:44)nocur-
rentflowsthroughthesourceresistanceandR1sothereis
noerrorduetoinputresistance(cid:46)S1isthenchangedtoposi-
tion 1(cid:46) The voltage stored on C1 is inserted between the
outputandinvertinginputoftheamplifierandtheoutputof
theamplifierchangesbyVINtomaintaintheamplifierinput
attheinputoffsetvoltage(cid:46)Theoutputthenchangesfrom
TL(cid:47)H(cid:47)6822–22
FIGURE20b(cid:46)NegativeVoltageReference (VOSaIbiasR2)to(VINaIbiasR2)asS1ischangedfrom
position 2 to position 1(cid:46) Amplifier bias current is supplied
ThecircuitofFigure20issuitedforhighprecisionextended throughR2fromtheoutputoftheamplifierorfromC2when
tdeempepnedraetnutreosneVrvaic(cid:46)eRif1V(cid:44)aR2i(cid:44)sRre3a(cid:44)saonndabRly4caorensctahnotsesinnctoeIpZrois- Sre1diuscientphoesoitfiofsnet2aatnthdepaomsiptiolifnie1roreustppuetcitfivtheely(cid:46)aRm3plsifeierrvemsutsot
videtheproperIZforminimumT(cid:46)C(cid:46)andtominimizeerrors havemaximumlinearrangeorifitisdesiredtoDCcouple
duetoIbias(cid:46) theamplifier(cid:46)
Thecircuitsshownshouldbothbecompensatedforunity- Anadditionaladvantageofthisconnectionisthatinputre-
gain operation or(cid:44) if large capacitive loads are expected(cid:44) sistance approaches infinity as the capacitor C1 ap-
shouldbeovercompensated(cid:46)Outputnoisemaybereduced proachesfullcharge(cid:44)eliminatingerrorsduetoloadingofthe
inbothcircuitsbybypassingtheamplifierinput(cid:46) sourceresistance(cid:46)Thetimespentinposition2shouldbe
Thecircuitsshownemployasinglepowersupply(cid:44)thisre- longwithrespecttothechargingtimeofC1formaximum
quiresthatcommonmoderangebeconsideredinchoosing accuracy(cid:46)
an amplifier for these applications(cid:46) If the common mode Theamplifierusedmustbecompensatedforunitygainop-
range requirements are in excess of the capability of the eration and it may be necessary to overcompensate be-
amplifier(cid:44)twopowersuppliesmaybeused(cid:46)TheLH101may causeofthephaseshiftacrossR2duetoC1andtheampli-
beusedwithasinglepowersupplysincethecommonmode fierinputcapacity(cid:46)Sincethisconnectionisusuallyusedat
rangeisfromVatowithinapproximately2voltsofVb(cid:46) verylowswitchingspeeds(cid:44)slewrateisnotnormallyapracti-
cal consideration and overcompensation does not reduce
THERESETSTABILIZEDAMPLIFIER
accuracy(cid:46)
Theresetstabilizedamplifierisaformofchopper-stabilized
amplifierandisshowninFigure21(cid:46)Asshown(cid:44)theamplifier
isoperatedclosed-loopwithagainofone(cid:46)
7
R5eR1(cid:35)VbJ
10
V1l0
VOUTeV110V2
TL(cid:47)H(cid:47)6822–24
FIGURE22(cid:46)AnalogMultiplier
THEANALOGMULTIPLIER mountthecellsinholesinanaluminumblockandtomount
Asimpleembodimentoftheanalogmultiplierisshownin thelampmidwaybetweenthem(cid:46)Thismountingmethodpro-
Figure22(cid:46) This circuit circumvents many of the problems videscontrolledspacingandalsoprovidesathermalbridge
associated with the log-antilog circuit and provides three betweenthetwocellstoreducedifferencesincelltempera-
quadrantanalogmultiplicationwhichisrelativelytempera- ture(cid:46)ThistechniquemaybeextendedtotheuseofFET’sor
tureinsensitiveandwhichisnotsubjecttothebiascurrent otherdevicestomeetspecialresistanceorenvironmentre-
errorswhichplaguemostmultipliers(cid:46) quirements(cid:46)
CircuitoperationmaybeunderstoodbyconsideringA2asa Thecircuitasshowngivesaninvertingoutputwhosemagni-
controlledgainamplifier(cid:44)amplifyingV2(cid:44)whosegainisde- tude is equal to one-tenth the product of the two analog
pendentontheratiooftheresistanceofPC2toR5andby inputs(cid:46)InputV1isrestrictedtopositivevalues(cid:44)butV2may
consideringA1asacontrolamplifierwhichestablishesthe assume both positive and negative values(cid:46) This circuit is
resistanceofPC2asafunctionofV1(cid:46)Inthiswayitisseen restrictedtolowfrequencyoperationbythelamptimecon-
thatVOUTisafunctionofbothV1andV2(cid:46) stant(cid:46)
A1(cid:44) the control amplifier(cid:44) provides drive for the lamp(cid:44) L1(cid:46) R2andR4arechosentominimizeerrorsduetoinputoffset
Whenaninputvoltage(cid:44)V1(cid:44)ispresent(cid:44)L1isdrivenbyA1 currentasoutlinedinthesectiondescribingthephotocell
untilthecurrenttothesummingjunctionfromthenegative amplifier(cid:46)R3isincludedtoreducein-rushcurrentwhenfirst
supplythroughPC1isequaltothecurrenttothesumming turningonthelamp(cid:44)L1(cid:46)
junctionfromV1throughR1(cid:46)Sincethenegativesupplyvolt- THEFULL-WAVERECTIFIER
age is fixed(cid:44) this forces the resistance of PC1 to a value ANDAVERAGINGFILTER
proportional to R1 and to the ratio of V1 to Vb(cid:46) L1 also ThecircuitshowninFigure23istheheartofanaverage
illuminatesPC2and(cid:44)ifthephotoconductorsarematched(cid:44)
reading(cid:44)rmscalibratedACvoltmeter(cid:46)Asshown(cid:44)itisarecti-
causesPC2tohavearesistanceequaltoPC1(cid:46)
fierandaveragingfilter(cid:46)DeletionofC2removestheaverag-
A2(cid:44)thecontrolledgainamplifier(cid:44)actsasaninvertingamplifi- ingfunctionandprovidesaprecisionfull-waverectifier(cid:44)and
erwhosegainisequaltotheratiooftheresistanceofPC2 deletionofC1providesanabsolutevaluegenerator(cid:46)
toR5(cid:46)IfR5ischosenequaltotheproductofR1andVb(cid:44)
Circuitoperationmaybeunderstoodbyfollowingthesignal
thenVOUTbecomessimplytheproductofV1andV2(cid:46)R5 pathfornegativeandthenforpositiveinputs(cid:46)Fornegative
may be scaled in powers of ten to provide any required signals(cid:44)theoutputofamplifierA1isclampedtoa0(cid:46)7Vby
outputscalefactor(cid:46)
D1anddisconnectedfromthesummingpointofA2byD2(cid:46)
PC1andPC2shouldbematchedforbesttrackingovertem- A2thenfunctionsasasimpleunity-gaininverterwithinput
peraturesincetheT(cid:46)C(cid:46)ofresistanceisrelatedtoresistance resistor(cid:44)R1(cid:44)andfeedbackresistor(cid:44)R2(cid:44)givingapositivego-
match for cells of the same geometry(cid:46) Small mismatches ingoutput(cid:46)
maybecompensatedbyvaryingthevalueofR5asascale
Forpositiveinputs(cid:44)A1operatesasanormalamplifiercon-
factor adjustment(cid:46) The photoconductive cells should re-
nectedtotheA2summingpointthroughresistor(cid:44)R5(cid:46)Ampli-
ceiveequalilluminationfromL1(cid:44)aconvenientmethodisto
fierA1thenactsasasimpleunity-gaininverterwithinput
8
TL(cid:47)H(cid:47)6822–25
FIGURE23(cid:46)Full-WaveRectifierandAveragingFilter
resistor(cid:44)R3(cid:44)andfeedbackresistor(cid:44)R5(cid:46)A1gainaccuracyis with decreasing frequency(cid:46) When this network(cid:208)the Wien
notaffectedbyD2sinceitisinsidethefeedbackloop(cid:46)Posi- Bridge(cid:208)isusedasapositivefeedbackelementaroundan
tivecurrententerstheA2summingpointthroughresistor(cid:44) amplifier(cid:44) oscillation occurs at the frequency at which the
R1(cid:44) and negative current is drawn from the A2 summing phaseshiftiszero(cid:46)Additionalnegativefeedbackisprovided
pointthroughresistor(cid:44)R5(cid:46)SincethevoltagesacrossR1and tosetloopgaintounityattheoscillationfrequency(cid:44)tostabi-
R5areequalandopposite(cid:44)andR5isone-halfthevalueof lize the frequency of oscillation(cid:44) and to reduce harmonic
R1(cid:44)thenetinputcurrentattheA2summingpointisequalto distortion(cid:46)
andoppositefromthecurrentthroughR1andamplifierA2
operatesasasumminginverterwithunitygain(cid:44)againgiving
apositiveoutput(cid:46)
ThecircuitbecomesanaveragingfilterwhenC2isconnect-
edacrossR2(cid:46)OperationofA2thenissimilartotheSimple
Low Pass Filter previously described(cid:46) The time constant
R2C2shouldbechosentobemuchlargerthanthemaxi-
mumperiodoftheinputvoltagewhichistobeaveraged(cid:46)
CapacitorC1maybedeletedifthecircuitistobeusedas
anabsolutevaluegenerator(cid:46)Whenthisisdone(cid:44)thecircuit
outputwillbethepositiveabsolutevalueoftheinputvolt-
age(cid:46)
Theamplifierschosenmustbecompensatedforunity-gain
operationandR6andR7mustbechosentominimizeout-
puterrorsduetoinputoffsetcurrent(cid:46)
SINEWAVEOSCILLATOR
Anamplitude-stabilizedsine-waveoscillatorisshowninFig-
ure24(cid:46) This circuit provides high purity sine-wave output
down to low frequencies with minimum circuit complexity(cid:46)
Animportantadvantageofthiscircuitisthatthetraditional
(cid:42)SeeText
tungsten filament lamp amplitude regulator is eliminated
alongwithitstimeconstantandlinearityproblems(cid:46)
Inaddition(cid:44)thereliabilityproblemsassociatedwithalamp TL(cid:47)H(cid:47)6822–26
FIGURE24(cid:46)WienBridgeSineWaveOscillator
areeliminated(cid:46)
TheWienBridgeoscillatoriswidelyusedandtakesadvan- The circuit presented here differs from the classic usage
tage of the fact that the phase of the voltage across the only in the form of the negative feedback stabilization
parallelbranchofaseriesandaparallelRCnetworkcon- scheme(cid:46)Circuitoperationisasfollows(cid:58)negativepeaksin
nectedinseries(cid:44)isthesameasthephaseoftheapplied excessofb8(cid:46)25VcauseD1andD2toconduct(cid:44)charging
voltageacrossthetwonetworksatoneparticularfrequency
andthatthephaselagswithincreasingfrequencyandleads
9
C4(cid:46) The charge stored in C4 provides bias to Q1(cid:44) which Theintegratorthengeneratesanegative-goingrampwitha
determinesamplifiergain(cid:46)C3isalowfrequencyroll-offca- rateofIa(cid:47)C1voltsperseconduntilitsoutputequalsthe
pacitorinthefeedbacknetworkandpreventsoffsetvoltage negativetrippointofthethresholddetector(cid:46)Thethreshold
andoffsetcurrenterrorsfrombeingmultipliedbyamplifier detectorthenchangestothenegativeoutputstateandsup-
gain(cid:46) pliesanegativecurrent(cid:44)Ib(cid:44)attheintegratorsummingpoint(cid:46)
Distortionisdeterminedbyamplifieropen-loopgainandby Theintegratornowgeneratesapositive-goingrampwitha
theresponsetimeofthenegativefeedbackloopfilter(cid:44)R5 rateofIb(cid:47)C1voltsperseconduntilitsoutputequalsthe
andC4(cid:46)Atrade-offisnecessaryindeterminingamplitude positivetrippointofthethresholddetectorwherethedetec-
stabilization time constant and oscillator distortion(cid:46) R4 is toragainchangesoutputstateandthecyclerepeats(cid:46)
chosen to adjust the negative feedback loop so that the Triangular-wavefrequencyisdeterminedbyR3(cid:44)R4andC1
FETisoperatedatasmallnegativegatebias(cid:46)Thecircuit andthepositiveandnegativesaturationvoltagesoftheam-
shownprovidesoptimumvaluesforageneralpurposeoscil- plifierA1(cid:46)AmplitudeisdeterminedbytheratioofR5tothe
lator(cid:46) combinationofR1andR2andthethresholddetectorsatu-
rationvoltages(cid:46)Positiveandnegativerampratesareequal
TRIANGLE-WAVEGENERATOR
andpositiveandnegativepeaksareequalifthedetector
Aconstantamplitudetriangular-wavegeneratorisshownin has equal positive and negative saturation voltages(cid:46) The
Figure25(cid:46)Thiscircuitprovidesavariablefrequencytriangu- outputwaveformmaybeoffsetwithrespecttogroundifthe
larwavewhoseamplitudeisindependentoffrequency(cid:46) invertinginputofthethresholddetector(cid:44)A1(cid:44)isoffsetwith
respecttoground(cid:46)
The generator may be made independent of temperature
andsupplyvoltageifthedetectorisclampedwithmatched
zenerdiodesasshowninFigure26(cid:46)
The integrator should be compensated for unity-gain and
thedetectormaybecompensatedifpowersupplyimped-
ancecausesoscillationduringitstransitiontime(cid:46)Thecur-
rentintotheintegratorshouldbelargewithrespecttoIbias
formaximumsymmetry(cid:44)andoffsetvoltageshouldbesmall
withrespecttoVOUTpeak(cid:46)
TL(cid:47)H(cid:47)6822–27
FIGURE25(cid:46)Triangular-WaveGenerator
Thegeneratorembodiesanintegratorasarampgenerator
andathresholddetectorwithhysterisisasaresetcircuit(cid:46)
Theintegratorhasbeendescribedinaprevioussectionand
requires no further explanation(cid:46) The threshold detector is
similartoaSchmittTriggerinthatitisalatchcircuitwitha
largedeadzone(cid:46)Thisfunctionisimplementedbyusingpos-
itive feedback around an operational amplifier(cid:46) When the
amplifieroutputisineitherthepositiveornegativesaturated
TL(cid:47)H(cid:47)6822–28
state(cid:44)thepositivefeedbacknetworkprovidesavoltageat FIGURE26(cid:46)ThresholdDetectorwithRegulatedOutput
thenon-invertinginputwhichisdeterminedbytheattenua-
tionofthefeed-backloopandthesaturationvoltageofthe TRACKINGREGULATEDPOWERSUPPLY
amplifier(cid:46)Tocausetheamplifiertochangestates(cid:44)thevolt-
A tracking regulated power supply is shown inFigure27(cid:46)
ageattheinputoftheamplifiermustbecausedtochange
Thissupplyisverysuitableforpoweringanoperationalam-
polaritybyanamountinexcessoftheamplifierinputoffset
plifier system since positive and negative voltages track(cid:44)
voltage(cid:46) When this is done the amplifier saturates in the
eliminatingcommonmodesignalsoriginatinginthesupply
oppositedirectionandremainsinthatstateuntilthevoltage
voltage(cid:46)Inaddition(cid:44)onlyonevoltagereferenceandamini-
atitsinputagainreverses(cid:46)Thecompletecircuitoperation
mumnumberofpassivecomponentsarerequired(cid:46)
maybeunderstoodbyexaminingtheoperationwiththeout-
putofthethresholddetectorinthepositivestate(cid:46)Thede-
tectorpositivesaturationvoltageisappliedtotheintegrator
summingjunctionthroughthecombinationR3andR4caus-
ingacurrentIatoflow(cid:46)
10