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/ALow-Cost,SmartCapacitivePositionSensorAbstractAnewhigh-performance,low-cost,capacitiveposition-measuringsystemisdescribed.Byusingahighlylinearoscillator,shieldingandathree-signalapproach,mostoftheerrorsareeliminated.Theaccuracyamountsto1μmovera1mmrange.Sincetheoutputoftheoscillatorcandirectlybeconnectedtoamicrocontroller,anA/Dconverterisnotneeded.I.INTRODUCTIONThispaperdescribesanovelhigh-performance,low-cost,capacitivedisplacementmeasuringsystemfeaturing:1mmmeasuringrange,1μmaccuracy,0.1stotalmeasuringtime.Translatedtothecapacitivedomain,thespecificationscorrespondto:apossiblerangeof1pF;only50fFofthisrangeisusedforthedisplacementtransducer;50aFabsolutecapacitance-measuringinaccuracy.MeijerandSchrier[l]andmorerecentlyVanDrecht,Meijer,andDeJong[2]haveproposedadisplacement-measuringsystem,usingaPSD(PositionSensitiveDetector)assensingelement.SomedisadvantagesofusingaPSDarethehighercostsandthehigherpowerconsumptionofthePSDandLED(Light-EmittingDiode)ascomparedtothecapacitivesensorelementsdescribedinthispaper.Thesignalprocessorusestheconceptspresentedin[2],butisadoptedfortheuseofcapacitiveelements.Bytheextensiveuseofshielding,guardingandsmartA/Dconversion,thesystemisabletocombineahighaccuracywithaverylowcost-price.Thetransducerproducesthree-period-modulatedsignalswhichcanbeselectedanddirectlyreadoutbyamicrocontroller.Themicrocontroller,inreturn,calculatesthedisplacementandcansendthisvaluetoahostcomputer(Fig.1)oradisplayordriveanactuator.ElectronicCircuitPElectronicCircuitPersonalComputer ActuatorDisplayFig.1.BlockdiagramofthesystemFig.2.PerspectiveanddimensionsoftheelectrodestructureⅡ.THEELECTRODESTRUCTUREThebasicsensingelementconsistsoftwosimpleelectrodeswithcapacitanceCx,(Fig.2).Thesmallerone(E2)issurroundedbyaguardelectrode.Thankstotheuseoftheguardelectrode,thecapacitanceCxbetweenthetwoelectrodesisindependentofmovements(lateraldisplacementsaswellasrotations)paralleltotheelectrodesurface.TheinfluenceoftheparasiticcapacitancesCpwillbeeliminatedaswillbediscussedinSectionⅢ.AccordingtoHeerens[3],therelativedeviationinthecapacitanceCxbetweenthetwoelectrodescausedbythefiniteguardelectrodesizeissmallerthan:δ<e-π(x/d)(1)wherexisthewidthoftheguardanddthedistancebetweentheelectrodes.Thisdeviationintroducesanonlinearity.Thereforewerequirethatδislessthan100ppm.Alsothegapbetweenthesmallelectrodeandthesurroundingguardcausesadeviation:δ<e-π(d/s)(2)withsthewidthofthegap.Thisdeviationisnegligiblecomparedto(l),whenthegapwidthislessthan1/3ofthedistancebetweentheelectrodes.Anothercauseoferrorsoriginatesfromapossiblefiniteskewangleαbetweenthetwoelectrodes(Fig.3).Assumingthefollowingconditions:thepotentialsonthesmallelectrodeandtheguardelectrodeareequalto0V,thepotentialonthelargeelectrodeisequaltoVvolt,theguardelectrodeislargeenough,itcanbeseenthattheelectricfieldwillbeconcentric.dl/2dl/2l/2Fig.3.Electrodeswithangleα.Tokeepthecalculationssimple,wewillassumetheelectrodestobeinfinitelylargeinonedirection.Nowtheproblemisatwo-dimensionalonethatcanbesolvedbyusingpolar-coordinates(r,φ).Inthiscasetheelectricalfieldcanbedescribedby:(3)Tocalculatethechargeonthesmallelectrode,wesetφto0andintegrateoverr:(4)withBltheleftborderofthesmallelectrode:(5)andBrtherightborder:(6)Solving(4)resultsin:(7)Forsmallα'sthiscanbeapproximatedby:(8)Itappearstobedesirabletochooselsmallerthand,sotheerrorwilldependonlyontheangleα.Inourcase,achangeintheangleof0.6°willcauseanerrorlessthan100ppm.Withaproperdesigntheparametersεoandlareconstant,andthenthecapacitancebetweenthetwoelectrodeswilldependonlyonthedistancedbetweentheelectrodes.Ⅲ.ELIMINATIONOFPARASITICCAPACITANCESBesidesthedesiredsensorcapacitanceC,therearealsomanyparasiticcapacitancesintheactualstructure(Fig.2).ThesecapacitancescanbemodeledasshowninFig.4.HereCplrepresentstheparasiticcapacitancesfromtheelectrodeE1andCp2fromtheelectrodeE2totheguardelectrodesandtheshielding.ParasiticcapacitanceCp3resultsfromimperfectshieldingandformsanoffsetcapacitance.WhenthetransducercapacitanceCxisconnectedtoanACvoltagesourceandthecurrentthroughtheelectrodeismeasured,CplandCp2willbeeliminated.Cp3canbeeliminatedbyperforminganoffsetmeasurement.Fig.4.EliminationofparasiticcapacitancesThecurrentismeasuredbytheamplifierwithshuntfeedback,whichhasaverylowinputimpedance.Toobtaintherequiredlinearity,theunity-gainbandwidthfToftheamplifierhastosatisfythefollowingcondition:(9)whereTistheperiodoftheinputsignal.SinceCp2consistsofcablecapacitancesandtheinputcapacitanceoftheopamp,itmayindeedbelargerthanCfandcannotbeneglected.IV.THECONCEPTOFTHESYSTEMThesystemusesthethree-signalconceptpresentedin[2],whichisbasedonthefollowingprinciples.WhenwemeasureacapacitorCxwithalinearsystem,weobtainavalue:(10)wheremistheunknowngainandMoff,theunknownoffset.ByperformingthemeasurementofareferencequantityCref,inanidenticalwayandbymeasuringtheoffset,Moff,bymakingm=0,theparametersmandMoffareeliminated.ThefinalmeasurementresultPisdefinedas:(11)Inourcase,forthesensorcapacitanceC,itholdsthat:(12)whereAxistheareaoftheelectrode,doistheinitialdistancebetweenthem,εisthedielectricconstantand△disthedisplacementtobemeasured.Forthereferenceelectrodesitholdsthat:(13)withAreftheareaanddrefthedistance.Substitutionof(12)and(13)into(10)andtheninto(11)yields:(14)Here,Pisavaluerepresentingthepositionwhilea1anda0areunknown,butstableconstants.Theconstanta1=Aref/Axisastableconstantprovidedthereisagoodmechanicalmatchingbetweentheelectrodeareas.Theconstantao=(Arefd0/(Axdref)willalsobeastableconstantprovidedthatdoanddrefareconstant.Theseconstantscanbedeterminedbyaone-timecalibration.Inmanyapplicationsthiscalibrationcanbeomitted;whenthedisplacementsensorispartofalargersystem,anoverallcalibrationisrequiredanyway.Thisoverallcalibrationeliminatestherequirementforaseparatedeterminationofa1anda0.V.THECAPACITANCE-TO-PERIODCONVERSIONThesignalswhichareproportionaltothecapacitorvaluesareconvertedintoaperiod,usingamodifiedMartinoscillator[4](Fig.5j.WhenthevoltageswingacrossthecapacitorisequaltothatacrosstheresistorandtheNANDgatesareswitchedoff,thisoscillatorhasaperiodToff:Toff=4RCoff.(15)Sincethevalueoftheresistoriskeptconstant,theperiodvariesonlywiththecapacitorvalue.Now,byswitchingontherightNANDport,thecapacitanceCXcanbeconnectedinparalleltoCoff.Thentheperiodbecomes:Tx=4R(Coff+Cx)=4RCx+Toff(16)TheconstantsRandToffareeliminatedinthewaydescribedinSectionIV.In[2]itisshownthatthesystemisimmuneformostofthenonidealitiesoftheopampandthecomparator,likeslewing,limitationsofbandwidthandgain,offsetvoltages,andinputbiascurrents.Thesenonidealitiesonlycauseadditiveormultiplicativeerrorswhichareeliminatedbythethree-signalapproach.VI.PERIODMEASUREMENTWITHAMICROCONTROLLERPerformingperiodmeasurementwithamicrocontrollerisaneasytask.Inourcase,anINTEL87C51FAisused,whichhas8kByteROM,256ByteRAM,andUARTforserialcommunication,andthecapabilitytomeasureperiodswitha333nsresolution.Eventhoughthecountersare16bwide,theycaneasilybeextendedinthesoftwareto24bormore.Theperiodmeasurementtakesplacemostlyinthehardwareofthemicrocontroller.Therefore,itispossibletolettheCPUofthemicrocontrollerperformothertasksatthesametime(Fig.6).Forinstance,simultaneouslywiththemeasurementofperiodTx,periodTrefandperiodToff,therelativecapacitancewithrespecttoCrefiscalculatedaccordingto(11),andtheresultistransferredthroughtheUARTtoapersonalcomputer.Fig.5.ModifiedMartinoscillatorwithmicrocontrollerandelectrodes.Fig.6.Periodmeasurementasbackgroundprocess.Fig.7.Positionerrorasfunctionofthepositionandestimateofthenonlinearity.VII.EXPERIMENTALRESULTSThesensorisnotsensitivetofabricationtolerancesoftheelectrodes.Thereforeinourexperimentalsetupweusedsimpleprintedcircuitboardtechnologytofabricatetheelectrodes,whichhaveaneffectiveareaof12mm×12mm.Theguardelectrodehasawidthof15mm,whilethedistancebetweentheelectrodesisabout5mm.Whenthedistancebetweentheelectrodesisvariedovera1mmrange,thecapacitancechangesfrom0.25pFto0.3pF.Thankstothechosenconcept,evenasimpledualopamp(TLC272AC)andCMOSNAND’scouldbeused,allowingasingle5Vsupplyvoltage.Thetotalmeasurementtimeamountstoonly100ms,wheretheoscillatorwasrunningatabout10kHz.Thesystemwastestedinafullyautomatedsetup,usinganelectricalXYtable,thedescribedsensorandapersonalcomputer.Toachievetherequiredmeasurementaccuracythesetupwasautozeroedeveryminute.Inthiswaythenonlinearity,long-termstabilityandrepeatabilityhavebeenfoundtobetterthan1μmoverarangeof1mm(Fig.7).ThisiscomparabletotheaccuracyandrangeofthesystembasedonaPSDasdescribedin[2].Asaresultoftheseexperiments,itwasfoundthattheresolutionamountstoapproximately20aF.Thisresultwasachievedbyaveragingover256oscillatorperiods.Afurtherincreaseoftheresolutionbylengtheningthemeasurementtimeisnotpossibleduetothel/fnoiseproducedbythefirststagesinboththeintegratorandtheComparator.Theabsoluteaccuracycanbederivedfromthepositionaccuracy.Sincea1mmdisplacementcorrespondstoachangeincapacitanceof50fF,theabsoluteaccuracyof1μminthepositionamountstoanabsoluteaccuracyof50aF.CONCLUSIONAlow-cost,high-performancedisplacementsensorhasbeenpresented.Thesystemisimplementedwithsimpleelectrodes,aninexpensivemicrocontrollerandalinearcapacitance-to-periodconverter.Whenthecircuitryisprovidedwithanaccuratereferencecapacitor,thecircuitcanalsobeusedtoreplaceexpensivecapacity-measuringsystems.REFERENCES[1]G.C.M.MeijerandR.Schner,“Alinearhigh-performancePSDdisplacementtransducerwithamicrocontrollerinterfacing,”SensorsandActuators,A21-A23,pp.538-543,1990.[2]J.vanDrecht,G.C.M.Meijer,andP.C.deJong,“ConceptsforthedesignofsmartsensorsandsmartsignalprocessorsandtheirapplicationtoPSDdisplacementtransducers,”DigesrofTechnicalPapers,Transducers’91.[3]W.C.Heerens,“Applicationofcapacitancetechniquesinsensordesign,”Phys.E:Sci.Insfrum.,vol.19,pp.897-906,1986.[4]K.Martin,‘‘Avoltage-controlledswitched-capacitorrelaxationoscillator,”IEEEJ.,vol.SC-16,pp.412-413,1981.一種低成本智能式電容位置傳感器摘要本文描述了一種新的高性能,低成本電容位置測量系統(tǒng)。通過運用高線性振蕩器,屏蔽和三信號通道,大部分誤差被消退。其精確度在1毫米范圍內(nèi)達1微米。由于振蕩器的輸出可干脆連接到微限制器,所以無需用A/D轉(zhuǎn)換器。Ⅰ.導言本文介紹了一種新型高性能,低成本的電容位移測量系統(tǒng),特點如下:1毫米測量范圍1微米精確度0.1s總測量時間對應到電容域,規(guī)格相當于:1皮法的變更范圍;只有這個范圍的50fF(fF是法拉乘以10的負15次方。f是femto的縮寫)用于位移傳感器。50aF確定電容測量誤差。梅耶爾和施里爾[1]以及最近的范德雷赫特河,梅耶爾,和德容[2]提出了位移測量系統(tǒng),接受一個PSD(位置敏感探測器)作為傳感元件。和本文描述的電容傳感器元件相比,運用PSD的缺點是,PSD和LED(發(fā)光二極管)有更高的成本和功率消耗。運用[2]中所提概念的信號處理器,被接受到電容元件的運用中。通過廣泛運用屏蔽,智能A/D轉(zhuǎn)換,該系統(tǒng)能夠?qū)⒏呔_度和低成本結(jié)合。換能器產(chǎn)生可以選擇和干脆由微限制器讀出的三段調(diào)制信號。微限制器,相應的,計算位移及發(fā)送此值到主機電腦(圖1)或顯示或驅(qū)動執(zhí)行器。電子電路上位機 電子電路上位機 執(zhí)行器演示圖1該系統(tǒng)的框圖金屬屏蔽電極屏蔽金屬屏蔽電極屏蔽圖2電極結(jié)構(gòu)的尺寸和透視圖Ⅱ.電極結(jié)構(gòu)基本傳感元件包含電容為Cx的兩個簡潔電極(圖2)。較小的一個(E2)是由屏蔽電極包圍。由于運用屏蔽電極,兩電極間的電容Cx可平行于電極表面獨立運動(橫向平移以及旋轉(zhuǎn))。寄生電容Cp的影響可被消退,將在第3節(jié)探討。據(jù)Heerens[3],由有限屏蔽電極大小造成的兩個電極之間電容Cx的相對偏差小于:δ<e-π(x/d)(1)其中x是屏蔽的寬度,d是電極之間的距離。這種偏差引入了非線性。因此,我們規(guī)定δ小于100ppm。此外小電極和四周屏蔽之間的間距產(chǎn)生一個偏差:δ<e-π(d/s)(2)S是間距的寬度。當間距寬度小于電極之間距離的1/3時,這偏差和(1)相比是微乎其微的。另一個誤差的緣由可能源自兩個電極之間的有限傾斜角α(圖3)。假設(shè)符合下列條件:小電極和屏蔽電極上的電勢等于0V大型電極電勢等于V伏屏蔽電極足夠大可以看出,電場將同心。dl/2dl/2l/2圖3傾斜角度α的電極為了使計算簡潔,我們將假設(shè)電極在一個方向無限大。問題就成為一個二維問題,可以用極坐標(Υ,φ)方法解決。在這種狀況下,電場可以表述為:(3)為了計算小電極的損耗,我們設(shè)定φ為0,整定Υ:(4)Bl是小電極的左側(cè)邊界:(5)Br是右邊界:(6)求解(4)結(jié)果:(7)對小α的近似:(8)選擇比d小的l似乎是可行的,因此該誤差將只確定于角度α。在這種狀況下,0.6°的角度變更,將產(chǎn)生小于100ppm的誤差。對參數(shù)εo和l是常數(shù)的設(shè)計,兩個電極之間的電容將僅僅取決于電極之間的距離d。Ⅲ.寄生電容的消退除了志向傳感器電容Cx,在實際結(jié)構(gòu)中還有許多寄生電容(圖2)。這些電容可以建模,如圖4所示。這里Cpl代表電極El的寄生電容,Cp2是從電極E2到屏蔽電極和屏蔽層的。寄生電容Cp3造成不完善屏蔽,形成一個偏移電容。當傳感器電容Cx連接到AC電壓源,通過電極的電流可測,Cpl和Cp2,將被消退。Cp3可通過偏移測量消退。圖4消退寄生電容電流通過并聯(lián)反饋放大器測量,它具有特殊低的輸入阻抗。要獲得所需的線性度,放大器的單位增益帶寬fT必需符合下列條件:(9)T是在此期間的輸入信號。由于Cp2包括電纜電容和運算放大器的輸入電容,它很可能大于Cf而不行忽視。Ⅳ.本系統(tǒng)的概念該系統(tǒng)接受了[2]提出的三信號的概念,它是基于以下原則。當我們用線性系統(tǒng)測量電容Cx,得到一個值:(10)其中m是未知的增益,Moff是未知偏移。以相同的方式,通過測量參考量Cref,測量偏移Moff,使m=0,參數(shù)m和Moff被抵消。最終的測量結(jié)果P定義為:(11)在我們的例子中,傳感器的電容Cx為:(12)其中Ax,是電極面積,do是它們之間最初的距離,ε是介電常數(shù),△d是要測量的位移。對于參考電極,它為:
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