传感器英文课件第2章-resistive-sensors

12ResistiveSensorsSensorsandSignalConditioning2Sensorsbasedonthevariationoftheelectricresistanceofadeviceareverycommon.Thatisbecausemanyphysicalquantitiesaffecttheelectricresistanceofamaterial.Thischapterdiscussessensorsbasedonavariationinresistance.Itdescribestheirfundamentals(sensingprinciple,dynamicmodel,limitations,advantages),technology,equivalentelectriccircuit,andapplications.Thedifferentresistivesensorsareclassifiedbythephysicalquantitybeingmeasuredasmechanical,thermal,magnetic,optical,andchemicalvariables.3Apotentiometerisaresistivedevicewithalinearorrotaryslidingcontact(Figure2.1).2.1PotentiometersFigure2.1(a)Ideal(linear)potentiometerconnectedasavoltagedividerand(b)itssymbol;thearrowindicatesthattheresistancevariationrespondstoamechanicalaction.(c)Thewipercanalsobeconnectedtoanendterminaltoobtainavariableresistor(rheostat).4Theresistancebetweenthatcontactandthebottomterminaliswherepistheresistivity,Aisthecrosssection,listhelength,xisthedistancetraveledfromthebottomterminal,andaisthecorrespondinglengthfraction.5Apotentiometerisazero-ordersystem.Equation(2.1)meansthattheresistanceisproportionaltothetravelofthewiper.Thisimpliestheacceptanceofseveralsimplificationsthatmaynotnecessarilybetrue.First,weassumethattheresistanceisuniformalongthelengthl.Second,weassumethattheslidingcontactgivesasmoothresistancevariation,notasteppedone,andthereforethattheresolutionisinfinite.Furthermore,themechanicaltravelisusuallylargerthantheelectricaltravel.6For(2.1)tobevalid,ifthepotentiometerissuppliedbyanalternatingvoltage,itsinductanceandcapacitanceshouldbeinsignificant.ForlowvaluesofthetotalresistanceRT,theinductancemaybesignificant,particularlyinmodelswithwoundresistiveelements.ForhighvaluesofRT,theparasiticcapacitancemaybeimportant.Furthermore,resistorsdriftwithtemperature.Temperaturechangescanarisenotonlyfromfluctuationsinambienttemperaturebutalsofromselfheatingduetothefinitepowerthatthepotentiometerdissipates.Frictionandinertiaofthewiperalsolimitthemodelvalidity.Finally,noiseassociatedwiththewipercontactlimitsresolution.7Mostoftheselimitationsareoutweighedbytheadvantagesofthisdevice.Itissimpleandrobustandyieldsahigh-levelvoltagewithhighaccuracyrelativetoitscost.Potentiometerscomprisearesistiveelement,awiper,anactuatingordrivingrod,bearings,andhousing.linearandrotary82.2StrainGageszFundamentals:PiezoresistiveEffectStraingagesarebasedonthevariationofresistanceofaconductororsemiconductorwhensubjectedtoamechanicalstress.Theelectricresistanceofawirehavinglengthl,crosssectionA,andresistivitypis9Whenthewireisstressedlongitudinally,eachofthethreequantitiesthataffectRchangeandthereforeRundergoesachangegivenbyThechangeinlengththatresultswhenaforceFisappliedtoawire,withintheelasticlimit(Figure2.6a),isgivenbyHooke'slaw,10Considerawirethatinadditiontoalengthlhasatransversedimensiont(Figure2.6b).Alongitudinalstresschangesbothlandt.AccordingtoPoisson'slaw,wehave11ForawireofcircularcrosssectionofdiameterD,wehaveThechangeinresistivityasaresultofamechanicalstressiscalledthepiezoresistiveeffect.P.W.Bridgmanshowedthat,inmetals,thepercentchangesofresistivityandvolumeareproportional:12whereCistheBridgman‘sconstant.Fortheusualalloysfromwhichstraingagesaremade,1.13C1.15.Forplatinum,C=4.4.Byapplying(2.10),thechangeinvolumecanbeexpressedasThereforeifthematerialisisotropic,withintheelasticlimit,(2.7)leadsto13whereGisthegagefactor,definedasthefactorinsidethesquarebrackets.Thereforeforsmallvariations,theresistanceofthemetallicwireis1415Whenasemiconductorisstressed,inadditiontoitsdimensionalchange,boththenumberofcarriersandtheiraveragemobilitychange.Unlikemetals,theresistivitychangeunderstressdominatesoverthedimensionalchange.Gisfromabout40toabout200.16Semiconductorswitharelativelylownumberofcarriersyieldlargegagefactors,buttheyaretemperature-sensitiveanddependonthestress;thatis,theyarenonlinear.Semiconductorswitharelativelyhighnumberofcarriershavesmallergagefactors,butthesearelesstemperatureandstress-dependent.17Thusthechangeintheelectricresistanceofametalorasemiconductorisrelatedtoitsstrain.Iftherelationshipbetweenthatstrainandtheforcecausingitisknown,fromthemeasurementofresistancechangesitispossibletoinfertheappliedforcesandthequantitiesthatproducethoseforcesinaprimarysensor.Aresistorarrangedtosenseastrainconstitutesastraingage.Thismethodhasprovedtobeveryusefulformanyyears.However,therearemanylimitationswemustconsiderconcerningthismeasurementprincipletoobtainvalidinformation.18First,theappliedstressshouldnotexceedtheelasticlimitofthegage.Second,themeasurementwillbecorrectonlyifallthestressistransmittedtothegage.Thisisachievedbycarefullybondingthegagewithanelasticadhesivethatmustbealsostablewithtimeandtemperature.Atthesametime,thegagemustbeelectricallyinsulatedfromtheobjectitadherestoandbeprotectedfromtheenvironment.19Figure2.8Installationofafoilstraingage(fromBLHelectronics):1,substratematerial;2,adhesive;3,straingage;4,solderterminals;5,solder;6,leadwires;7,environmentalbarrier.20Temperatureinterferesthroughseveralmechanisms.Itaffectsth