16Self-GeneratingSensorsSensorsandSignalConditioning2Self-generatingsensorsyieldanelectricsignalfromameasurandwithoutrequiringanyelectricsupply.Theyofferalternativemethodsformeasuringmanycommonquantities-inparticular,temperature,force,pressure,andacceleration.Thischapterdescribesthermoelectricsensors,piezoelectricSensors,photovoltaicsensorsandelectrochemicalsensors(relatedtocomposition).3zReversibleThermoelectricEffectsThermoelectricsensorsarebasedontwoeffectsthatarereversibleascontrastedwiththeirreversibleJouleeffect.TheyarethePeltiereffectandtheThomsoneffect.6.1ThermoelectricSensors:Thermocouples4DemoofthermocoupleworkingprinciplethermoelectrodeAreferencejunctionConclusion:Whenthetwojunctionsareatdifferenttemperatures,emfexistsintheloop.measurementjunctionthermoelectrodeBthermoelectricelectromotiveforce(emf)AB5Historically,itwasThomasJ.Seebeckwhofirstdiscoveredin1822thatinacircuitwithtwodissimilarhomogeneousmetalsAandB,havingtwojunctionsatdifferenttemperatures,anelectriccurrentarises(Figure6.1).Thatis,thereisaconversionfromthermaltoelectricenergy.Ifthecircuitisopened,athermoelectricelectromotiveforce(emf)appearsthatdependsonlyonthemetalsandonthejunctiontemperatures.Apairofdifferentmetalswithafixedjunctionatapointorzoneconstitutesathermocouple.6Figure6.1Seebeckeffectinathermocouple:(a)acurrentor(b)apotentialdifferenceappearwhentherearetwometaljunctionsatdifferenttemperatures.7TherelationshipbetweentheemfEABandthedifferenceintemperaturebetweenbothjunctionsTdefinestheSeebeckcoefficientSAB,whereSAandSBare,respectively,theabsolutethermoelectricpowerforAandB.SABisnotingeneralconstantbutdependsonT,usuallyincreasingwithT.8Itisimportanttorealizethattheemfdoesnotdependontheresistivity,ontheconductors‘crosssections,orontemperaturedistributionorgradient.Itdependsonlyonthedifferenceintemperaturebetweenbothjunctionsandonthemetals,providedthattheyarehomogeneous.ThisemfisduetothePeltierandThomsoneffects.9ThePeltiereffectistheheatingorcoolingofajunctionoftwodifferentmetalswhenanelectriccurrentflowsthroughit(Figure6.2).Whenthecurrentdirectionreverses,sodoestheheatflow.Figure6.2Peltiereffect:Whenthereisacurrentalongathermocouplecircuit,onejunctioncoolsandtheotherwarms.10T,(K)11ThePeltiereffectisreversibleanddoesnotdependonthecontact,namely,ontheshapeordimensionsoftheconductors.Itdependsonlyonthejunctioncompositionandtemperature.Furthermore,thisdependenceislinearandisdescribedbythePeltiercoefficientπAB,sometimescalledPeltiervoltagebecauseitsunitisvolts.πABisdefinedastheheatgeneratedatthejunctionbetweenAandBforeachunitof(positivecharge)flowingfromBtoA;thatis,12ItcanbeshownthatforajunctionatabsolutetemperatureTwehaveThePeltiereffectisalsoindependentoftheoriginofthecurrent,whichcanthusevenbethermoelectricasinFigure6.1a.Inthiscasethejunctionsreachatemperaturedifferentfromthatoftheambient,andthiscanbeanerrorsourceaswewilldiscusslater.13TheThomsoneffectconsistsofheatabsorptionorliberationinahomogeneousconductorwithanonhomogeneoustemperaturewhenthereisacurrentalongit,asshowninFigure6.3.Figure6.3Thomsoneffect:Whenthereisacurrentalongaconductorwithnonhomogeneoustemperature,heatisabsorbedorliberated.14151617ThisequationconstitutesthebasictheoremforthermoelectricityandshowsthattheSeebeckeffectresultsfromthePeltierandThomsoneffects.181920Equations(6.1)and(6.6)allowustoapplythermocouplestotemperaturemeasurement.Athermocouplecircuitwithajunctionatconstanttemperature(referencejunction)yieldsanemfthatisafunctionofthetemperatureattheotherjunction,whichwecallthemeasuringjunction.21Theapplicationofthermocouplestotemperaturemeasurementissubjecttoseverallimitations.First,wemustselectthetypeofthermocouplesothatitdoesnotmeltinourapplication.Wemustalsobesurethattheenvironmentitisplacedindoesnotattackanyofthejunctionmetals.22Second,wemustkeepthecurrentalongthethermocouplecircuitverysmall.Otherwise,becausethePeltierandThomsoneffectsarereversible,thetemperaturesoftheconductorsandparticularlythoseofthejunctionswoulddifferfromthatoftheenvironmentbecauseoftheheatflowtoandfromthecircuit.Dependingontheintensityofthecurrent,eventheJouleeffectcouldbeconsiderable.Inaddition,conductorsmustbehomogeneous,sothatcautionisneededtopreventanymechanicalorthermalstressduringinstallationoroperation-forexample,becauseofagingcausedbylongexposuretolargetemperaturegradients.23Anotherlimitationisthatoneofthejunctionsmustbekeptatafixedtemperatureifthetemperatureattheotherjunctionistobemeasured.Anychangeinthatreferencejunctionwouldresultinaseriouserrorbecausetheoutputvoltageisverysmall.Furthermore,ifthereferencetemperatureisnotclosetothemeasuredtemperature,theoutputsignalwillhavearelativelyhighconstantvalueundergoingonlyverysmallchangesduetothetemperaturechangesweareinterestedin.24Whenhighaccuracyisdesired,thenonlinearityoftherelationshipbetweentheemfandthetemperaturemaybecomeimportant.Anapproximateformulavalidforallthermocouplesis2526Inspiteoftheabovelimitations,thermocoupleshavemanyadvantagesandarebyfarthemostfrequentlyusedsensorsfortemperaturemeasurement.–broadmeasurementra