4-REACTANCE-VARIATION-AND-ELECTROMAGNETIC-SENSORS-

4REACTANCEVARIATIONANDELECTROMAGNETICSENSORS4.1CAPACITIVESENSORS4.1.1VariableCapacitorManyreactancevariationmeasurementmethodsdonotrequireanyphysicalcontactwiththesystemtobemeasured.TherelationshipbetweenthechargeQandthedifferenceinvoltageVbetweenthetwoelectricconductorsisdescribedbyVQC4.1CAPACITIVESENSORSThecapacitancedependsonthegeometricalarrangementoftheconductorsandonthedielectricmaterialbetweenthem.ForacapacitorformedbynequalparallelplaneplateshavinganareaA,withadistancedbetweeneachpair,andaninterposedmaterialwitharelativedielectricconstant,thecapacitanceisAnymeasurandproducingavariationinεr,AordwillresultinachangeinthecapacitanceCandcanbeinprinciplesensedbydevice.r10ndACr4.1CAPACITIVESENSORSThechangeofdielectricresultsinthevariationofrelativepermittivity.Thiscanbeappliedtolevelmeasurementforwaterintankorhumiditymeasurement.ThecapacitanceoftheHC1000humiditysensorisThedielectricconstantforferroelectricmaterialsabovetheCurietemperatureisproportionaltothereciprocalofthetemperatureaccordingto7617676RHCCCTTk4.1CAPACITIVESENSORSThelimitationsofvariablecapacitorsensor:•FringeeffectsareusuallyneglectedbutmaynotalwaysbeacceptableTheouterguardringinacapacitivesensoriskeptatthesamevoltageasoneofthetwoelectrodestoreducefringingfields.4.1CAPACITIVESENSORS•Theinsulationbetweenplatesmustbehighandconstant•Becauseonlyoneofthetwoconductivesurfacescanbegrounded,thereisariskofcapacitiveinterference.•Connectingwiresarepossibleerrorsource.Shieldingthemtopreventcapactiveinterferenceaddsacapacityinparallelwiththesensor.Thisresultsinalossofsensitivity.4.1CAPACITIVESENSORSCapacitivesensorsarelinearornonlinear,dependingontheparameterthatchangesandwhetherwemeasurethecapacitiveimpedanceoradmittance(导纳).Inparallelplatecapacitor,forexample,theoutputvoltageislinearwhenwemeasuretheadmittance,butitisnonlinearifthemeasurandchangestheseparationbetweenplates:xdAC14.1CAPACITIVESENSORSThesensitivity:ForasensorofthekindThesensitivity3202022432111xxxdCxdCxdAdzdCzAC2zA4.1CAPACITIVESENSORSAddingadielectricasshowninFigure4.2,wehaveThetotalcapacitancewillbetheseriescombinationofbothpartsThesensitivityisnowdACzACrz000zzCCCCC002022022032111xxdCdzdAzdAdzdCrrrrrrrrFigure4.24.1CAPACITIVESENSORSAnothermethodtoobtainalinearvoltagefromasensorwhenthedistancebetweenplatesvariesistomeasure,insteadofitsadmittance,itsimpedance.Capacitivesensorshavehighoutputimpedance.Itdecreaseswhenthesupplyfrequencyincreases.Possiblesolutionsaretoplacesignalconditioningcircuitsclosetothesensorandtouseanimpedancetransformer.4.1CAPACITIVESENSORSAdvantages•Theloadingerrorisminimal•Nodirectmechanicalcontact,friction,orhysteresisForaparallelplatecapacitortheforceneededtomoveaplateisaboutForA=10cm2,d=1cm,andV=10V2221VdAdEFnNVcmcmmpFF45.410110285.8224.1CAPACITIVESENSORSHighlystableandreproduciblebecausethecapacitanceCisindependenttotheelectricalconductivityoftheplates.Ifthedielectricmaterialisair,changesonlyslightlywithtemperatureaccordingtoand0039.0135281TppRHTpairw78.23.3827345.7lgTTpw4.1CAPACITIVESENSORSThehighresolutionavailableforcapacitancemeasurementsmakesahighresolutionalsoavailableforcapacitivesensors.Thecapacitorsthemselvesdonotproducelargemagneticorelectricfields.Figure4.3showssomesensorconfigurationsforcapacitivedisplacementsensorsbasedonachangeofarea(a-e),electrodeseparation(f),orthedielectric(g,h).4.1CAPACITIVESENSORSFigure4.34.1CAPACITIVESENSORSFigure4.4CapacitancestraingageHightemperature,lowtemperaturecoefficientandlargedimension(1cm-2cm)4.1CAPACITIVESENSORSApplicationsCapacitiveproximitysensorHavearangetwicethatofinductivesensorsDetectnotonlymetalobjectsbutalsodielectricssuchaspaper,glass,wood,andplastics.Usedforhumantremormeasurementandinintrusionalarms.Variationsindielectricconstantareusedforhumiditymeasurementusingpolymerfilmasdielectricmaterial.4.1CAPACITIVESENSORSChemicalanalysisofbinarymixturesofnonconductingfluidshavingratherdifferentdielectricconstants.LevelgagesforconductiveandnonconductiveliquidsFigure4.512ln2ddhC122211ln2ddhhC4.1CAPACITIVESENSORSForthelevelsensorinFigure4.5b,theresultingcapacitivevoltagedivideryieldsanoutputvoltagewhereC1isconstantandC2changesinverselywiththeliquidheighth.2110CCCvvr4.1CAPACITIVESENSORSExample4.1IfinFigure4.5cwecallh2=handh1=H-h,thenIfd2=40mm,d1=8mm,H=1.2m,andεr=2.1,wehavehHddhhHddCrr1ln2ln200120012pFpFHCpFmmpFHCr07.871.246.415ln246.415ln2.185.825ln20max0min4.1CAPACITIVESENSORSThevolumeofthestoragetankisHence,thesensitivityisLmmHdV5.2352.145.0422LpFLpFpFVCCS19.06.23546.4107.87minmax4.1CAPACITIVESENSORS4.1.2DifferentialCapacitorAdifferentialcapacitorconsistsoftwovariablecapacitorssoarrangedthattheyundergothesamechangebutinoppositedirections.Figure4.64.1CAPACITIVESENSORSTherespectivedropinvoltageacrosseachcapacitorisThenzdACzdAC2121122122121211111111CCCVCjCjCjVVCCCVCjCjCjVVrrrrdzdVzdzdzdVVdzdVzdzdzdVVrrr