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GORESET
TheSummingAmplifier
TheSummingAmplifierisaveryflexiblecircuitbaseduponthestandardInvertingOperationalAmplifierconfiguration
thatcanbeusedforcombiningmultipleinputs.Wesawpreviouslyintheinvertingamplifiertutorialthattheinverting
amplifierhasasingleinputvoltage,(Vin)appliedtotheinvertinginputterminal.Ifweaddmoreinputresistorstothe
input,eachequalinvaluetotheoriginalinputresistor,Rinweendupwithanotheroperationalamplifiercircuitcalled
aSummingAmplifier,"summinginverter"orevena"voltageadder"circuitasshownbelow.
SummingAmplifierCircuit
Theoutputvoltage,(Vout)nowbecomesproportionaltothesumoftheinputvoltages,V1,V2,V3etc.Thenwecan
modifytheoriginalequationfortheinvertingamplifiertotakeaccountofthesenewinputsthus:
However,ifalltheinputimpedances,(Rin)areequalinvalue,wecansimplifytheaboveequationtogiveanoutput
voltageof:
SummingAmplifierEquation
Wenowhaveanoperationalamplifiercircuitthatwillamplifyeachindividualinputvoltageandproduceanoutputvoltage
signalthatisproportionaltothealgebraic"SUM"ofthethreeindividualinputvoltagesV,VandV.Wecanalsoadd
moreinputsifrequiredaseachindividualinput"see''s"theirrespectiveresistance,Rinastheonlyinputimpedance.
Thisisbecausetheinputsignalsareeffectivelyisolatedfromeachotherbythe"virtualearth"nodeattheinvertinginput
oftheop-amp.AdirectvoltageadditioncanalsobeobtainedwhenalltheresistancesareofequalvalueandR?isequal
toRin.
AScalingSummingAmplifiercanbemadeiftheindividualinputresistorsare"NOT"equal.Thentheequationwould
havetobemodifiedto:
Tomakethemath''salittleeasier,wecanrearrangetheaboveformulatomakethefeedbackresistorRthesubjectof
theequationgivingtheoutputvoltageas:
Thisallowstheoutputvoltagetobeeasilycalculatedifmoreinputresistorsareconnectedtotheamplifiersinverting
inputterminal.Theinputimpedanceofeachindividualchannelisthevalueoftheirrespectiveinputresistors,ie,R,R,
R...etc.
TheSummingAmplifierisaveryflexiblecircuitindeed,enablingustoeffectively"Add"or"Sum"(henceitsname)
togetherseveralindividualinputsignals.Iftheinputsresistors,R,R,Retc,areallequalaunitygaininvertingadder
canbemade.However,iftheinputresistorsareofdifferentvaluesa"scalingsummingamplifier"isproducedwhich
givesaweightedsumoftheinputsignals.
ExampleNo1
FindtheoutputvoltageofthefollowingSummingAmplifiercircuit.
SummingAmplifier
Usingthepreviouslyfoundformulaforthegainofthecircuit
123
F
12
3
123
wecannowsubstitutethevaluesoftheresistorsinthecircuitasfollows,
weknowthattheoutputvoltageisthesumofthetwoamplifiedinputsignalsandiscalculatedas:
thentheoutputvoltageoftheSummingAmplifiercircuitaboveisgivenas-45mVandisnegativeasitsaninverting
amplifier.
SummingAmplifierApplications
Iftheinputresistancesofasummingamplifierareconnectedtopotentiometerstheindividualinputsignalscanbe
mixedtogetherbyvaryingamounts.Forexample,measuringtemperature,youcouldaddanegativeoffsetvoltageto
makethedisplayread"0"atthefreezingpointorproduceanaudiomixerforaddingormixingtogetherindividual
waveforms(sounds)fromdifferentsourcechannels(vocals,instruments,etc)beforesendingthemcombinedtoan
audioamplifier.
SummingAmplifierAudioMixer
AnotherusefulapplicationofaSummingAmplifierisasaweightedsumdigital-to-analogueconverter.Iftheinput
resistors,Rinofthesummingamplifierdoubleinvalueforeachinput,forexample,1kΩ,2kΩ,4kΩ,8kΩ,16kΩ,etc,thena
digitallogicalvoltage,eitheralogiclevel"0"oralogiclevel"1"ontheseinputswillproduceanoutputwhichisthe
weightedsumofthedigitalinputs.Considerthecircuitbelow.
DigitaltoAnalogueConverter
Ofcoursethisisasimpleexample.InthisDACsummingamplifiercircuit,thenumberofindividualbitsthatmakeupthe
inputdataword,andinthisexample4-bits,willultimatelydeterminetheoutputstepvoltageasapercentageofthefull-
scaleanalogueoutputvoltage.Also,theaccuracyofthisfull-scaleanalogueoutputdependsonvoltagelevelsofthe
inputbitsbeingconsistently0Vfor"0"andconsistently5Vfor"1"aswellastheaccuracyoftheresistancevaluesused
fortheinputresistors,Rin.Fortunatelytoovercometheseerrors,commercialavailableDigital-toAnalogueand
Analogue-toDigitaldevicesareavailable.
InthenexttutorialaboutOperationalAmplifiers,wewillexaminetheeffectoftheoutputvoltage,Voutwhenasignal
voltageisconnectedtotheinvertinginputandthenon-invertinginputatthesametimetoproduceanothercommontype
ofoperationalamplifiercircuitcalledaDifferentialAmplifierwhichcanbeusedto"subtract"thevoltagespresenton
itsinputs.
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