Capacitance Sensing Theory.docx
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Capacitance Sensing Theory.docx
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CapacitanceSensingTheory
CapacitanceSensingTheory
1)Introduction
Capacitivesensorscanbedividedintotwocategoriesbasedupontheirperformanceandintendeduse.Highresolutionsensorsaretypicallyusedindisplacementandpositionmonitoringapplicationswherehighaccuracy,stabilityandlowtemperaturedriftarerequired.Quitefrequentlythesesensorsareusedinprocessmonitoringandclosed-loopfeedbackcontrolsystems.Proximitytypecapacitivesensorsaremuchlessexpensiveandaretypicallyusedtodetectthepresenceofapartorusedincountingapplications.Thefollowingpaperdescribescharacteristicsofhighresolutionsystems,theiroperatingprincipleandapplication.
Figure1:
TypicalCapacitanceSensor
Thesesensorsareusedthroughoutavarietyofindustriestoprovidehighlystable,accuratemeasurementsofdisplacement,vibration,position,thicknessandrunout.Mostprobesarepassivebydesign,allowingthemtobeoperatedinhighshockandvibrationenvironments,andatextremetemperatures.Capacitanceprobesaretypicallymodeledasaparallelplatecapacitor.Iftwoconductivesurfacesareseparatedbyadistanceandavoltageisappliedtooneofthesurfaces,anelectricfieldiscreated.Thisoccursduetothedifferentchargesstoredoneachofthesurfaces.Capacitancereferstotheabilityofthesurfacestoholdacharge.Inatypicalsensorsystemtheprobeisoneoftheplatesandthetargetbeingmeasuredistheotherplate.Ifaconstantcurrentisapplied,thecapacitancechangecanbemonitoredasalinearvoltagechargerelatedtothedistancebetweentheplates.Thisdistance,orgap,isafunctionoftheareaofthecapacitancesensoraccordingtothefollowingformula:
Capacitance=AreaXDielectric/Gap
Fromthisrelationship,youcanseethatcapacitanceisdirectlyproportionaltotheareaofthesensorandthedielectricpropertyofthematerialbetweenthesensorandtarget(typicallyair).Thegreatertheareaofthecapacitancesensorthelargerthemeasurementrange,orgap.Ifweassumetheareaandthedielectricbetweentheplatesremainconstantforaspecificprobe,anychangeincapacitanceisinverselyproportionaltothechangeindistancebetweentheprobeandtargetbeingmeasured.ThischangeisprocessedwithinMTII’sAccumeasure™capacitanceamplifierandconvertedtoavoltageformonitoring.Theamountofvoltageoutputchangeforagivendistancechangeiscommonlyreferredtoasthesensitivityofthesystem.Forexample,ifadistancechangeof1mmcorrespondstoavoltageoutputchangeof10voltsthesensitivitywouldbe1mm/10volts,or0.1mm/volt.
i.CapacitanceSensorsElectricField
Atypicalhighperformancecapacitancesensorconsistsofthreebasicelements:
thesensortip,theguardandthegroundshell.Figure1illustratesatypicalcapacitanceprobemanufacturedbyMTIInstruments.Whenavoltageisappliedtothesensortip,anelectricfieldisestablishedbetweenitandanyotherlocalconductivematerial.Tomaintainaccuracyandlinearityitisessentialthattheelectricfieldinthemeasurementareabelinear,directedtowardthetargetandnotdistorted.Toprotectthisfield,eachcapacitivesensorhaswhatiscalledaguard.Thisisanadditionalfieldcreatedaroundtheprobesensingtipthatisdrivenatthesamephaseandvoltagepotentialasthesensor.Bybeingequal,theauxiliaryfieldprotectstheareafrombecomingwarpedandcancelsanystraycapacitancebetweenthetwoelements.
Becausethegroundshellisatadifferentpotentialthantheguardadistortionoftheguardfieldtothegroundshell(seeFigure2)occurs.Althoughundesirable,thedistortionoftheguardisacceptableaslongasthesensortipfieldremainslinear.Forbestperformance,thewidthoftheguardshouldbeatleast2Xthesystemmeasurementrange.
Figure2:
CapacitanceSensorField
AllofMTII’scapacitanceprobesaredesignedwithsufficientguardstoprotectthesensingareaundernormaloperatingconditions.However,theflexibilityofMTII’sAccumeasureseriesallowsthesystemmeasurementrangetobeincreasedby50timesormore.Thisrangeextension,or“Push”,shouldnotbegreaterthanthewidthoftheguardorpoorlinearitywillresult.ContactMTII’sApplicationsEngineersforassistancewhen“pushing”capacitiveprobes.
Inadditiontoimprovinglinearityandaccuracy,theguardisalsousedtoreducenoiseandexternalinterference.Eachcapacitanceprobeisdrivenbyalownoisecoaxialcable.Theshieldofthecableisusedtodeliverthevoltagetotheguard,andyoumayrecallatthesamevoltagepotentialandphase.Thiseliminatesanystraycapacitancethatmightbecreatedbetweenthecenterconductorandtheshieldofthecable,oranyotherpartthatmaybeclosetothecable.Bydesign,thisprotectionsignificantlyreducesexternalinfluencesfromRFIandEMI.Itisimportanttonotethatordinarycoaxialcableusuallydoesnotprovideadequateprotectionorshieldingforthesystemandspecialcableisgenerallyrequired.
2)CharacteristicsofCapacitiveSensors
i.NonContact
Capacitivedisplacementsensorsarenoncontactbydesign.Thatis,theyareabletopreciselymeasurethepositionordisplacementofanobjectwithouttouchingit.Becauseofthistheobjectbeingmeasuredwillnotbedistortedordamagedandtargetmotionswillnotbedampened.Additionally,theycanmeasurehighfrequencymotionsbecausenopartofthesensorneedstostayincontactwiththeobject,makingthemidealforvibrationmeasurementsorhighspeedproductionlineapplications.
ii.Range/StandoffDistance
Asmentionedabove,therangeofacapacitancesensorisdictatedbythediameter,orarea,ofthesensor.Thelargerthearea,thelargerthemeasurementrange.Measurementrangeistypicallyspecifiedstartingwhentheprobeistouchingthetarget.Atthispointtheoutputfromtheamplifieriszerovolts.Whenthegapisincreasedtoequalthefullscalemeasurementrangeofthecapacitivesystemtheamplifieroutputis10volts(Vdc).Intheory,theprobecanoperateanywherebetweenthesetwoextremes,however,itisnotrecommendedtooperatebelow10%ofthegap.Withthissaid,theidealoperatingorstandoffdistanceissomewherebetween5Vdcto7Vdcwhichwillallowthetargettomoveclosertoorfurtherawayfromtheprobewithoutgoingoutofrange.Figure3(below)isasimplifieddiagramshowingrange,outputvoltageandrecommendedstandoffforatypicalcapacitancesensor.
Figure3:
CapacitanceProbeOperatingRange
AllofMTII’sAccumeasuremeasurementsensorshaveabuilt-indcvoltageoffset.Onceengaged,theoutputvoltagecanbechangedbyasmuchas10voltsbysimplyadjustingapotentiometer.Thisisidealifyourdataacquisitionormonitoringsystemrequiresa-5Vdcto+5Vdcinputorifitisdesiredtotakerelativemeasurementsfromsomefixedvoltagepoint.
iii.Resolution
Theresolutionofadisplacementsensorisdefinedasthesmallestamountofdistancechangethatcanbereliablymeasuredbyaspecificsystem.Capacitancesensorsofferextremelyhighresolutionandstabilityoftenexceedingthatofexpensiveandcomplexlaserinterferometersystems.Becauseoftheirabilitytodetectsuchsmallmotions,theyhavebeensuccessfullyusedinmanydemandingmeasurementapplicationsincludingcomputerdiskdriverunout,microscopefocusingandnano-positioningwithinhighlycomplexphotolithographytools.
Theprimaryfactorindeterminingresolutionisthesystem’selectricalnoise.Ifthedistancebetweenthesensorandtargetisconstant,thevoltageoutputwillstillfluctuateslightlyduetothe“white”noiseofthesystem.Itisassumedthat,withoutexternalsignalprocessing,onecannotdetectashiftinthevoltageoutputoflessthantherandomnoiseoftheinstrument.Becauseofthismostresolutionvaluesarepresentedbasedonthepeak-to-peakvalueofnoiseandcanberepresentedbythefollowingformula:
Resolution=SensitivityXNoise
Sensitivityissimplythemeasurementrangedividedbythevoltageoutputswingofthecapacitanceamplifier.Fromtheformula,youcanseethatforafixedsensitivitytheresolutionissolelydependentuponthenoiseofthesystem.Thelowerthenoise,thebettertheresolution!
Itisimportanttonotethatsomemanufacturersspecifyresolutionbasedonpeakorrmsnoise,resultinginclaimsthatare2xand6xrespectivelybetterthanpeak-to-peak.Althoughanacceptablemethod,itissomewhatmisleadingasmostusersdonothavetheabilitytodeciphervoltageschangeslessthanthepeak-to-peaknoisevalue.
Theamountofnoisedependsonthesystembandwidth.Thisisbecausenoiseisgenerallyrandomlydistributedoverawiderangeoffrequenciesandlimitingthebandwidthwithfilteringwillremovesomeoftheunwantedhigherfrequencyfluctuations.Figures4and5showthedifferenceintheoutputoftwoidenticalsystemswithdifferentlowpassfilters.AllofMTII’sAccumeasurecapacitancesystemshaveplug-inlowpassfiltersthatallowforeasyadjustmentinthefield.
Figure4:
AmplifierOutputNoisewith20kHzLowPassFilter
Figure5:
AmplifierOutputNoisewith100HzLowPassFilter
iv.Bandwidth
Thebandwidth,orcutofffrequency,ofasystemistypicallydefinedasthepointwheretheoutputisdampenedby-3dB.Thisisapproximatelyequaltoanoutputvoltagedropof30%oftheactualvalue.Inotherwords,ifatargetisvibratingwithanamplitudeof1mmat5kHzandthebandwidthofthecapacitancesensoris5kHztheactualsensoroutputwouldbe1mmX70%=0.70mm.BandwidthcurvesareprovidedwithallofMTII’ssystemsandcanbeusedtocorrectforthisdampeninginhighfrequencyapplications.MTII’sapplicationsengineerstypicallyselectafilterthathasacutof
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