13SignalConditioningforResistiveSensorsSensorsandSignalConditioning2Therearemanymechanismsthatcanmodifytheelectricresistanceofamaterialandalsomanysignalconditionersforresistivesensors.Thusthisgroupofsensorsisthelargest.Thischapterpresentsseveralmethodstoobtainfromresistivesensorsoutputvoltagesinarangesuitedtoanalog-to-digitalconverters(ADCs)orotherelectricmeasuringequipment.Italsopresentsseveralmethodsofinterferencecompensationandsensorlinearizationinthesignalconditionerfollowingthesensor.3ThegeneralequationforasensorwhoseresistancechangesbyafractionxinresponsetoameasurandisR=R0f(x),assumingf(0)=1.Forlinearsensorswehave3.1MeasurementofResistanceTherangeofvaluesforxdependsstronglyonthetypeofsensorandonthemeasurandspan.4Therearetworequirementsforallconditionersforresistivesensors.First,theymustdrivethesensorwithanelectricvoltageorcurrentinordertoobtainanoutputsignal.Second,thissupply,whosemagnitudeaffectsthatoftheoutputsignal,islimitedbysensorself-heating,whichmustbeavoidedunlessthesensingprincipleusessensorself-heating,asinsomeflowmetersandliquidlevelmeters.5ThepowerdissipatedbythesensorisTheTheveninequivalentcircuit67IfthesensorresistancenevermeetstheconditionR=Ro,themaximaldissipationhappensfortheresistancevalueclosesttoRo.Ifthesensorisdrivenatconstantcurrent,thedissipationismaximalforthehighestsensorresistance.8Methodsforresistancemeasurementcanbeclassifiedintodeflectionmethodsornullmethods.Deflectionmethodssensethedropinvoltageacrosstheresistancetobemeasuredorthecurrentthroughitorboth.Nullmethodsarebasedonmeasurementbridges.93.2(3.3)WheatstoneBridge:BalanceMeasurementsTheWheatstonebridgemeasurementmethodwasfirstproposedbyS.H.Christiein1833andreportedbySirCharlesWheatstonetotheRoyalSociety(London)in1858asamethodtomeasuresmallresistances.Itisbasedonafeedbacksystem,eitherelectricormanual,inordertoadjustthevalueofastandardresistoruntilthecurrentthroughthegalvanometerorothernullindicatoriszero(Figure3.16).1011OncethebalanceconditionhasbeenachievedwehaveThatis,changesinR3aredirectlyproportionaltothecorrespondingchangeswehavetoproduceinR4inordertobalancethebridge.Thismeasurementmethodcanbealsousedasapolaritydetectorbecausetheoutputispositiveornegative,dependingonwhetherxisgreaterorlessthanagiventhreshold.12Figure3.16bshowsanarrangementforeliminatingtheinfluencethatthecontactresistanceintheadjustablearmhasonthemeasurement.Itworksbyincludingthatresistanceinserieswiththecentralarm(``bridge''),throughwhichthereisnocurrentwhenreachingthebalance.13Forremotesensorswemustconsiderlongleadswhoseresistanceaddstothesensorresistance.Temperaturechangescanresultinimportanterrors,thisshouldalsobeconsidered.TheSiemensorthree-wiremethod(Figure3.17a)solvesthisproblem.1415Figure3.17(a):Wires1and3mustbeequalandundergothesametemperaturechanges.Thecharacteristicsofwire2areirrelevantbecauseinthebalanceconditionthereisnocurrentthroughthebridgecentralarm.163.3(3.4)WheatstoneBridge:DeflectionMeasurementszSensitivityandLinearityWheatstonebridgesareoftenusedinthedeflectionmode.Insteadofmeasuringtheactionneededtorestorebalanceonthebridge,thismethodmeasuresthevoltagedifferencebetweenbothvoltagedividersorthecurrentthroughadetectorbridgingthem.1718UsingthenotationofFigure3.19a,ifthebridgeisbalancedwhenx=0,whichistheusualsituation,wedefineaparameterk,Thevoltagedifferencebetweenbothbranchesis19ThustheoutputvoltageisproportionaltothechangesinR3onlywhenxk+1;thatis,thesensitivitydependsonx(andkandVr).Forx=0,thesensitivityisThemaximalsensitivityasafunctionofkisobtainedbysettingdS0/dk=0,whichyieldsk=1.Ontheotherhand,from(3.45)weinferthatk=1yieldsanonlinearoutputunlessx2.Figure3.19bshowshowtheactualoutputdepartsfromastraightlinethroughtheoriginfork=1.20Figure3.19(b)itsidealandrealtransfercharacteristicswhenk=1.(Wheatstonebridgeusingthedeflectionmethod)21Formetalstraingages,xseldomexceeds0.02.Therefore,usuallyk=1toimprovesensitivityand,unlessaveryhighlinearityisdesired,thepresenceofxinthedenominatorof(3.45)isignored.Alternatively,theactualxcanbecalculatedfromtheoutputvoltageorcurrentbysolvingforxinthoseequations[5].Forexample,forabridgesuppliedbyconstantvoltageandk=1,from(3.45)weobtain22Thesecondfactorontheright-sidemembercorrectsthe``uncorrected''output4vo/Vr.23Forresistancethermometers,xcanbecloseto1andevenhigher,sothatdesigningabridgewithk=1wouldresultinastronglynonlineartransfercharacteristic.ForaPt100-basedthermometer,forexample,at100ºCtheresistancehaschangedfrom100Ωat0ºCto140Ω.Forthesecaseswecanlinearizethebridgebyanalogordigitaltechniquesorworkwithareducedsensitivitybymakingk=10,orevenhigher,andcompensatingpartofthesensitivitylossbyincreasingthesupplyvoltage.Thisoptionislimitedbysensorself-heating.Nevertheless,supplyingshortdutycyclerectangularvoltagesgiveshighpeakoutputvoltageswithlowrmsvalue.24zAnalogLinearizationofResistiveSensorBridgesToobtainavoltageproportionaltoanysizechangeinoneoftheresistancesinaWheatstonebridge,wecanmodifythestructureofthebridgetokeepconstantthecurrentthroughit.Figure3.2025Foranidealopamp,theoutputisThismethod,howe