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1、A Low-Cost, Smart Capacitive Position SensorAbstractA new high-performance,low-cost, capacitiveposition-measuringsystemis described. By using a highly linear oscillator, shielding and a three-signal approach, most of the errors are eliminated. The accuracy amounts to 1 mover a 1 mm range. Since the
2、output of the oscillator candirectly be connectedto a microcontroller, an A/D converter is not needed.I. INTRODUCTIONThis paper describes a novel high-performance, low-cost, capacitive displacementmeasuringsystemfeaturing:1 mm measuringrange,1 maccuracy,0.1 stotal measuringtime.Translatedto the capa
3、citivedomain, the specificationscorrespondto:a possiblerangeof 1 pF;only 50 fF of this rangeis usedfor the displacementtransducer;50 aF absolutecapacitance-measuringinaccuracy.Meijer and Schrier l and more recently Van Drecht,Meijer, and De Jong 2 haveproposeda displacement-measuringsystem,using a P
4、SD (Position Sensitive Detector)as sensing element. Some disadvantagesof using a PSD are the higher costs and thehigher power consumptionof the PSD and LED (Light-Emitting Diode) ascomparedtothe capacitivesensorelementsdescribedin this paper.The signal processorusesthe conceptspresentedin 2,but is a
5、dopted for the use ofcapacitive elements. Bythe extensive use of shielding, guarding and smart A/Dconversion,the system is able to combine a high accuracy with a very low cost-price. The transducer produces three-period-modulated signals which can be selected and directly read out by a microcontroll
6、er. The microcontroller,in return, calculates thedisplacementandcan sendthis value to a host computer(Fig. 1) or a display or drive anactuator.PersonalComputerElectronicCCxCircuitDisplayActuatorC refFig. 1. Block diagram of the systemFig. 2. Perspectiveanddimensionsof the electrodestructure . THE EL
7、ECTRODE STRUCTUREThe basicsensingelementconsistsof two simple electrodeswith capacitanceCx, (Fig.2). The smaller one (E2) is surroundedby a guard electrode. Thanks to the use of theguard electrode, the capacitance Cx between the two electrodes is independent of movements (lateral displacements as we
8、ll as rotations) parallel to the electrode surface.The influence of the parasitic capacitancesCp will be eliminated as will be discussedin Section .According to Heerens3, the relative deviation in the capacitanceCx betweenthetwo electrodescausedby the finite guardelectrodesize is smaller than: e- (x
9、/d)(1)where x is the width of the guard and d the distance between the electrodes. Thisdeviation introducesa nonlinearity.Thereforewe require that is lessthan 100 ppm.Alsothe gap betweenthe small electrodeand the surroundingguardcausesa deviation: e- (d/s)(2)with s the width of the gap. This deviati
10、on is negligible comparedto (l), when the gapwidth is lessthan 1/3 of the distancebetweenthe electrodes.Another causeof errorsoriginates from apossiblefinite skew angle betweenthe two electrodes(Fig. 3). Assuming the following conditions:the potentialson the small electrodeand the guardelectrodearee
11、qualto 0 V,the potential on the largeelectrodeis equalto V volt,the guard electrodeis largeenough,it canbeseenthat the electric field will be concentric.dl/2l/2Fig. 3. Electrodeswith angle .To keepthe calculations simple, we will assumethe electrodesto be infinitely large inone direction. Now the pr
12、oblem is a two-dimensional one that can be solved by usingpolar-coordinates(r, ).In this casethe electrical field canbe describedby:V sinEr(3)V cosrTo calculatethe chargeon thesmall electrode,we set to 0 andintegrateover r:Q0Br VdrBlrwith Bl the left borderof the small electrode:Bldltan2and Br the r
13、ight border:Brdltan2Solving (4) resultsin:Q V0ln2d cosl sina2d cosl sinFor small sthis canbeapproximatedby:(4)(5)(6)(7)C0l1 4d 2l 22(8)d12d 2It appearsto be desirableto choosel smaller than d, so the error will dependonly onthe angle .In our case,a changein the angle of 0.6 will causean error lessth
14、an 100ppm.With a proper design the parametersoand l are constant,andthen the capacitancebetweenthe two electrodeswill dependonly on the distanced betweenthe electrodes.ELIMINATIONOF PARASITIC CAPACITANCESBesidesthe desiredsensorcapacitanceC, thereare alsomany parasitic capacitancesinthe actual struc
15、ture (Fig.2). Thesecapacitancescan be modeled as shown in Fig.4. HereCpl representsthe parasitic capacitances from the electrode E1 and Cp2 from theelectrodeE2 to the guardelectrodesand the shielding. ParasiticcapacitanceCp3 results from imperfect shielding and forms an offset capacitance. When the
16、transducer capacitance Cx is connected to an AC voltage source and the current through the electrode is measured,Cpl and Cp2 will be eliminated. Cp3 can be eliminated byperforming anoffset measurement.Fig. 4. Elimination of parasitic capacitancesThe current is measuredby the amplifier with shunt fee
17、dback,which has a very low input impedance. To obtain the required linearity, the unity-gain bandwidth fT of theamplifier hasto satisfy the following condition:12(9)fTC fTC p2C fwhereT is the period of the input signal.Since Cp2 consistsof cable capacitancesand the input capacitanceof the op amp, it
18、may indeedbe larger than Cf andcannot be neglected.IV. THE CONCEPT OF THE SYSTEMThe system uses the three-signal concept presentedin 2, which is based on thefollowing principles. When we measurea capacitorCx with a linear system,we obtain avalue:M xmCxM off(10)where m is the unknown gain and Moff,th
19、e unknown offset.By performing themeasurementof a referencequantity Cref, in an identical way and by measuring theoffset, Moff,by making m = 0, the parametersm and Moff are eliminated.The finalmeasurementresult P is defined as:M refM off(11)PM offM xIn our case,for the sensorcapacitanceC, it holds t
20、hat:CxAx(12)dd0where Ax is the areaof the electrode,do is the initialdistance between them, is thedielectric constant andd is the displacement tobe measured. For the referenceelectrodesit holds that:CrefAref(13)d refwith Aref the areaand dref the distance.Substitution of (12) and (13) into (10) and
21、theninto (11) yields:Aref d0da1d(14)Pa0d refAx drefHere, P is a value representingthe position while a1 and a0 are unknown, but stableconstants. The constant a1 =Aref/Axis a stable constant provided there is a goodmechanical matching between the electrode areas.The constant ao = (Arefd0/(Axdref)will
22、 alsobe a stableconstantprovided that do anddref are constant.Theseconstantscanbe determined by a one-time calibration. In many applications this calibration can beomitted; when the displacementsensoris part of a larger system,an overall calibration is required anyway. This overall calibration elimi
23、nates the requirement for a separate determinationof a1 anda0.V . THE CAPACITANCE-TO-PERIOD CONVERSIONThe signals which areproportional to the capacitor valuesare convertedinto a period,using a modified Martin oscillator 4 (Fig. 5j.When the voltage swing acrossthe capacitoris equalto that acrossthe
24、resistorandtheNAND gatesareswitchedoff, this oscillator hasa period Toff:Toff = 4RCoff.(15)Since the value of the resistor is kept constant, the period varies only with thecapacitor value. Now, by switching on the right NAND port, the capacitanceCX can beconnectedin parallel to Coff. Then the period
25、 becomes:Tx=4R(Coff+Cx)=4RCx+Toff(16)The constantsR andToff are eliminated in the way describedin SectionIV.In 2 it is shown that the systemis immune for mostof the nonidealities of the op ampand the comparator,like slewing, limitations of bandwidth and gain, offset voltages,andinput bias currents.
26、These nonidealities only cause additive or multiplicative errors which areeliminated by the three-signalapproach.VI. PERIOD MEASUREMENT WITH A MICROCONTROLLERPerforming period measurementwith a microcontroller is an easytask. In our case,anINTEL 87C51FA is used,which has 8 kByte ROM, 256 Byte RAM, a
27、nd UART for serial communication, and the capability to measureperiods with a 333 ns resolution. Even though the countersare 16 b wide, they can easily be extendedin the software to 24 b or more.The period measurementtakes place mostly in the hardware of the microcontroller.Therefore,it is possiblet
28、o let the CPU of the microcontroller perform other tasksat thesame time (Fig. 6). For instance, simultaneously with the measurementof period Tx,period Tref and period Toff,the relative capacitancewith respect to Cref is calculatedaccordingto (11), andthe resultis transferredthrough the UART to a per
29、sonalcomputer.Fig. 5. Modified Martin oscillator with microcontroller andelectrodes.Fig. 6. Periodmeasurementasbackgroundprocess.Fig. 7. Position error asfunction of the position and estimateof thenonlinearity.VII. EXPERIMENTAL RESULTSThe sensoris not sensitive to fabrication tolerancesof the electr
30、odes.Therefore in ourexperimental setup we used simple printed circuit board technology to fabricate theelectrodes,which have an effective area of 12 mm 12 mm. The guard electrodehasawidth of 15 mm, while the distancebetween the electrodesis about 5 mm. When thedistancebetween the electrodesis varie
31、d over a 1 mm range, the capacitancechangesfrom 0.25 pF to 0.3 pF.Thanks to the chosen concept, even a simple dual op amp(TLC272AC) andCMOS NANDscould be used,allowing a single 5 V supply voltage.The total measurementtime amountsto only 100 ms, wherethe oscillator wasrunning atabout10 kHz.The system
32、 was tested in a fully automated setup, using an electrical XY table, thedescribed sensor and a personal computer. To achieve the required measurementaccuracythe setupwas autozeroedevery minute. In this way the nonlinearity, long-termstability and repeatability have been found to better than 1 mover
33、 a range of 1 mm(Fig.7). This is comparableto the accuracyand rangeof the system basedon a PSD asdescribedin 2.As a result of these experiments, it was found that the resolution amounts toapproximately 20 aF. This result was achievedby averagingover 256 oscillator periods.A further increaseof the re
34、solution by lengthening the measurementtime is not possible due to the l/f noiseproducedby the first stagesin both the integrator and theComparator.The absolute accuracy can be derived from the position accuracy. Since a 1 mm displacementcorrespondsto a changein capacitanceof 50 fF, the absoluteaccu
35、racyof 1min the position amountsto an absoluteaccuracyof 50 aF.CONCLUSIONA low-cost, high-performance displacementsensorhasbeenpresented.The systemis implementedwith simple electrodes,aninexpensivemicrocontroller and a linearcapacitance-to-period converter. When the circuitry is provided with an acc
36、urate referencecapacitor,the circuit can alsobe usedto replaceexpensivecapacity-measuring systems.REFERENCES1 G. C. M. Meijer andR. Schner,“Alinear high-performancePSD displacementtransducerwith a microcontroller interfacing, Sensors”and Actuators, A21-A23, pp. 538-543,1990.2J. van Drecht, G. C. M.
37、Meijer, andP.C. deJong, “ Conceptsfor thedesignof smartsensorsand smartsignal processorsandtheir applicationto PSD displacementtransducers, Digesr” of Technical Papers,Transducers 91.3W. C. Heerens,“ Applicationof capacitancetechniquesin sensordesign, Phys. E: Sci. Insfrum., vol. 19, pp. 897-906, 19
38、86.”4K. Martin, Avoltage-controlled switched-capacitorrelaxation oscillator, 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(cè)量系統(tǒng)。通過(guò)使用高線(xiàn)性振蕩器,屏蔽和三信號(hào)通道,大部分誤差被消除。其精確度在1 毫米范圍內(nèi)達(dá) 1 微米。由于振蕩器的輸出可直接連接到微控制器,所以無(wú)需用A/D 轉(zhuǎn)換器。 .導(dǎo)言本文介紹了一種新型高性能,低成本的電容位移測(cè)量系統(tǒng),特點(diǎn)如下:1 毫米測(cè)量范圍1 微米精確度0.1 s 總測(cè)量時(shí)間對(duì)應(yīng)到
39、電容域,規(guī)格相當(dāng)于:1 皮法的變化范圍;只有這個(gè)范圍的50fF(fF 是法拉乘以 10 的負(fù) 15 次方。 f是 femto 的縮寫(xiě))用于位移傳感器。50aF 絕對(duì)電容測(cè)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(cè)量系統(tǒng),采用一個(gè)PSD(位置敏感探測(cè)器)作為傳感元件。和本文描述的電容傳感器元件相比,使用PSD 的缺點(diǎn)是, PSD 和 LED (發(fā)光二極管)有更高的成本和功率消耗。使用 2 中所提概念的信號(hào)處理器,被采用到電容元件的使用中。通過(guò)廣泛使用屏蔽,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)生可以選擇和直接由微控制器讀出的三段調(diào)制
40、信號(hào)。微控制器,相應(yīng)的,計(jì)算位移及發(fā)送此值到主機(jī)電腦(圖1)或顯示或驅(qū)動(dòng)執(zhí)行器。上位機(jī)Cx電子電路C演示執(zhí)行器C ref圖 1 該系統(tǒng)的框圖屏蔽金屬屏蔽電極圖 2 電極結(jié)構(gòu)的尺寸和透視圖 .電極結(jié)構(gòu)基本傳感元件包含電容為Cx 的兩個(gè)簡(jiǎn)單電極 (圖 2)。較小的一個(gè)(E2)是由屏蔽電極包圍。由于使用屏蔽電極,兩電極間的電容Cx 可平行于電極表面獨(dú)立運(yùn)動(dòng)(橫向平移以及旋轉(zhuǎn))。寄生電容 Cp 的影響可被消除,將在第3 節(jié)討論。據(jù) Heerens3 ,由有限屏蔽電極大小造成的兩個(gè)電極之間電容Cx 的相對(duì)偏差小于:e-(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(xiàn)性。
41、因此,我們規(guī)定 小于 100ppm。此外小電極和周?chē)帘沃g的間距產(chǎn)生一個(gè)偏差: e- (d/s)(2)S 是間距的寬度。當(dāng)間距寬度小于電極之間距離的1/3 時(shí),這偏差和( 1)相比是微不足道的。另一個(gè)誤差的原因可能源自?xún)蓚€(gè)電極之間的有限傾斜角(圖 3)。假設(shè)符合下列條件:小電極和屏蔽電極上的電勢(shì)等于0V大型電極電勢(shì)等于V 伏屏蔽電極足夠大可以看出,電場(chǎng)將同心。dl/2l/2圖 3 傾斜角度 的電極為了使計(jì)算簡(jiǎn)單,我們將假設(shè)電極在一個(gè)方向無(wú)限大。問(wèn)題就成為一個(gè)二維問(wèn)題,可以用極坐標(biāo)( ,)方法解決。在這種情況下,電場(chǎng)可以表述為:V sinErV cos r為了計(jì)算小電極的損耗,我們?cè)O(shè)定 為 0
42、,整定 :Q 0Br VdrBlrBl 是小電極的左側(cè)邊界:ldlBtan2Br 是右邊界:Brdltan2求解( 4)結(jié)果:Q V 0 ln2d cosl sina2d cosl sin對(duì)小 的近似:C0l1 4d 2l 22d12d 2(3)(4)(5)(6)(7)(8)選擇比 d 小的 l 似乎是可行的,因此該誤差將只決定于角度 。在這種情況下, 0.6的角度變化,將產(chǎn)生小于 100 ppm 的誤差。對(duì)參數(shù) o 和 l 是常數(shù)的設(shè)計(jì),兩個(gè)電極之間的電容將僅僅取決于電極之間的距離 d。 .寄生電容的消除除了理想傳感器電容 Cx,在實(shí)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
43、 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(gè)偏移電容。當(dāng)傳感器電容 Cx 連接到 AC 電壓源,通過(guò)電極的電流可測(cè), Cpl 和 Cp2,將被消除。 Cp3 可通過(guò)偏移測(cè)量消除。圖 4 消除寄生電容電流通過(guò)并聯(lián)反饋放大器測(cè)量,它具有非常低的輸入阻抗。要獲取所需的線(xiàn)性度,放大器的單位增益帶寬fT 必須符合下列條件:12(9)fTC fTC p2C fT 是在此期間的輸入信號(hào)。由于 Cp2 包括電纜電容和運(yùn)算放大器的輸入電容,它很可能大于Cf 而不可忽略。.本系統(tǒng)的概念該系統(tǒng)采用了 2 提出的三信號(hào)
44、的概念,它是基于以下原則。當(dāng)我們用線(xiàn)性系統(tǒng)測(cè)量電容 Cx,得到一個(gè)值:M x mCxM off(10)其中 m 是未知的增益 ,Moff 是未知偏移。以相同的方式,通過(guò)測(cè)量參考量Cref,測(cè)量偏移 Moff ,使 m= 0,參數(shù) m 和 Moff 被抵消。最后的測(cè)量結(jié)果 P 定義為:M refM off(11)PM offM x在我們的例子中,傳感器的電容Cx 為:Ax(12)Cxdd0其中 Ax ,是電極面積, do 是它們之間最初的距離, 是介電常數(shù),d 是要測(cè)量的位移。對(duì)于參考電極,它為:Aref(13)CrefdrefAref 為面積, dref 為距離。將( 12)(13)式代入( 10)式,然后代入( 11)得:Aref d0dd(14)Pa1a0d r
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