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1、A Low-Cost, Smart Capacitive Position SensorAbstractA new high-performance, low-cost, capacitive position-measuring system is described.By using a highly linear oscillator, shielding and a three-signal approach, most of theerrors are eliminated. The accuracy amounts to 1 mover a 1 mm range. Since th

2、e output of the oscillator can directly be connected to a microcontroller, an A/D converter is not needed.I. INTRODUCTIONThis paper describes a novel high-performance, low-cost, capacitive displacementmeasuring system featuring:1 mm measuring range,1 m accuracy,0.1 s total measuring time.Translated

3、to the capacitive domain, the specifications correspond to:a possible range of 1 pF。only 50 fF of this range is used for the displacement transducer。50 aF absolute capacitance-measuring inaccuracy.Meijer and Schrier l and more recently Van Drecht,Meijer, and De Jong 2 haveproposed a displacement-mea

4、suring system, using a PSD (Position Sensitive Detector)assensing element. Some disadvantages of using a PSD are the higher costs and the higherpower consumption of the PSD and LED (Light-EmittingDiode) as compared to thecapacitive sensor elements described in this paper.The signal processor uses th

5、e concepts presented in 2,but is adopted for the use ofcapacitive elements. Bythe extensive use of shielding, guarding and smart A/D1/19conversion,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

6、directly read out by a microcontroller. The microcontroller,in return, calculates thedisplacement and can send this value to a host computer (Fig. 1) or a display or drive anactuator.PersonalComputerElectronicCCxCircuitDisplayActuatorC refFig. 1. Block diagram of the systemFig. 2. Perspective and di

7、mensions of the electrode structure . THE ELECTRODE STRUCTUREThe basic sensing element consists of two simple electrodes with capacitance Cx, (Fig. 2/192). The smaller one (E2) is surrounded by a guard electrode. Thanks to the use of theguard electrode, the capacitance Cx between the two electrodes

8、is independent ofmovements (lateral displacements as wellas rotations) parallel to the electrodesurface.The influence of the parasitic capacitances Cp willbe eliminated as willbediscussed in Section.According to Heerens 3, the relative deviation in the capacitance Cx between the two electrodes cause

9、d by the finite guard electrode size is smaller than: <e- (x/d) (1)where x is the width of the guard and d the distance between the electrodes. Thisdeviation introduces a nonlinearity.Therefore we require thatis less than 100 ppm.Alsothe gap between the small electrode and the surrounding guard c

10、auses a deviation: <e- (d/s)(2)with s the width of the gap. This deviation is negligible compared to (l), when the gapwidth is less than 1/3 of the distance between the electrodes.Another cause of errors originates from a possible finite skew angle betwelectrodes (Fig. 3). Assuming the following

11、conditions:the potentials on the small electrode and the guard electrode are equal to 0 V,the potential on the large electrode is equal to V volt,the guard electrode is large enough,it can be seen that the electric field will be concentric.3/19dl/2l/2Fig. 3. Electrodes with angle .To keep the calcul

12、ations simple, we will assume the electrodes to be infinitely large inone direction. Now the problem is a two-dimensional one that can be solved byusingpolar-coordinates (r, ). In this case the electrifieldcanl be described by:V sinEr(3)V cosrTo calculate the charge on the small electrode, we set to

13、 0 and integrate overBrQVdr(4)rwith Bl the left border of the small electrode:Bldl(5)tan2and Br the right border:Brdl(6)tan2Solving (4) results in:Q V 0 ln2d cosl sin(7)a2d cosl sinFor small 's this can be approximated by:4/19C0l4d 2l 22(8)112d 2dIt appears to be desirable to choose l smaller th

14、an d, so the error will depend only onthe angle . In our case, a change in the angle of 0.6° will cause an error less thppm.With a proper design the parameters oand l are constant,and then the capacitancebetween the two electrodes will depend only on the distance d between the electrodes.ELIMIN

15、ATION OF PARASITIC CAPACITANCESBesides the desired sensor capacitance C, there are also many parasitic capacitances in the actual structure (Fig.2). These capacitances can be modeled as shown in Fig.4. Here Cpl represents the parasitic capacitances from the electrode E1 and Cp2 from the electrode E2

16、 to the guard electrodes and the shielding. Parasitic capacitance Cp3 resultsfromimperfect shielding and forms an offset capacitance. When the transducercapacitance Cx is connected to an AC voltage source and the current through theelectrode is measured,Cpl and Cp2 willbe eliminated. Cp3 can be elim

17、inated byperforming an offset measurement.Fig. 4. Elimination of parasitic capacitancesThe current is measured by the amplifier with shunt feedback, which has a very lowinput impedance. To obtain the required linearity, the unity-gain bandwidth fT ofthe5/19amplifier has to satisfy the following cond

18、ition:12fT(9)TC fC p 2C fwhere T is the period of the input signal.Since Cp2 consists of cable capacitances and the input capacitance of the op amp, itmay indeed be larger than Cf and can not be neglected.IV. THE CONCEPT OF THE SYSTEMThe system uses the three-signal concept presented in 2, which is

19、based on the following principles. When we measure a capacitor Cx with a linear system, we obtain a value:M xmCxM off(10)where m is the unknown gain and Moff,the unknown offset.By performing themeasurement of a reference quantity Cref, in an identical way and by measuring the offset, Moff,by making

20、m = 0, the parameters m and Moff are eliminated.The final measurement result P is defined as:M refM off(11)PM offM xIn our case, for the sensor capacitance C, it holds that:CxAx(12)d0dwhere Ax is the area of the electrode, do is the initial distance between them, dielectric constant and d is the dis

21、placement to be measured. For the reference electrodes it holds that:ArefCref(13)d refwith Aref the area and dref the distance. Substitution of (12) and (13) into (10) and then6/19into (11) yields:Arefd 0ddPAx d refa1 drefa0 (14)Here, P is a value representing the position while a1 and a0 are unknow

22、n, 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 also be a stable constant provided that do and dref are constant. These constants canbe determined by a one-time calibr

23、ation. In many applications this calibration can beomitted。 when the displacement sensor is part of a larger system, an overall calibration is required anyway. This overall calibration eliminates the requirement for a separate determination of a1 and a0.V . THE CAPACITANCE-TO-PERIOD CONVERSIONThe si

24、gnals which are proportional to the capacitor values are converted into a period,using a modified Martin oscillator 4 (Fig. 5j.When the voltage swing across the capacitor is equal to that across the resistor and theNAND gates are switched off, this oscillator has a period Toff:Toff = 4RCoff.(15)Sinc

25、e the value of the resistor is kept constant, the period varies only with the capacitor value. Now, by switching on the right NAND port, the capacitance CX can be connected in parallel to Coff. Then the period becomes:Tx=4R(Coff+Cx)=4RCx+Toff (16)The constants R and Toff are eliminated in the way de

26、scribed in Section IV.In 2 it is shown that the system is immune for most of the nonidealities of the op ampand the comparator, like slewing, limitations of bandwidth and gain, offset voltages,and7/19input bias currents. These nonidealities only cause additive or multiplicativeerrorswhich are elimin

27、ated by the three-signal approach.VI. PERIOD MEASUREMENT WITH A MICROCONTROLLERPerforming period measurement with a microcontroller is an easy task. In our case, anINTEL 87C51FA is used,which has 8 kByte ROM, 256 Byte RAM, and UART for serialcommunication, and the capability to measure periods with

28、a 333 ns resolution. Even though the counters are 16 b wide, they can easily be extended in the softwareto 24 b ormore.The period measurement takes place mostly in the hardware of the microcontroller.Therefore, it is possible to let the CPU of the microcontroller perform other tasks at thesame time

29、(Fig. 6). For instance, simultaneously with the measurement of period Tx,period Tref and period Toff,the relative capacitance with respect to Cref is calculatedaccording to (11), and the result is transferred through the UART to a personal computer.Fig. 5. Modified Martin oscillator with microcontro

30、ller and electrodes.8/19Fig. 6. Period measurement as background process.Fig. 7. Position error as function of the position and estimate of the nonlinearity.VII. EXPERIMENTAL RESULTSThe sensor is not sensitive to fabrication tolerances of the electrodes. Therefore in ourexperimental setup we used si

31、mple printed circuit board technology to fabricate the electrodes, which have an effective area of 12 mm 12 mm. The×guard electrode has a width of 15 mm, while the distance between the electrodes is about 5 mm. When the distance between the electrodesis varied over a 1 mm range, the capacitance

32、 changesfrom 0.25 pF to 0.3 pF.Thanks to the chosen concept, even a simple dual op amp(TLC272AC) and CMOS NANDs could be used, allowing a single 5 V supply voltage.The total measurement time amounts to only 100 ms, where the oscillator was running atabout 10 kHz.9/19The system was tested in a fully

33、automated setup, using an electrical XY table, thedescribed sensor and a personal computer. To achieve the required measurementaccuracy the setup was autozeroed every minute. In this way the nonlinearity, long-termstability and repeatability have been found to better than 1overa mrange of 1 mm(Fig.7

34、). This is comparable to the accuracy and range of the system based on a PSD asdescribed in 2.As a result of these experiments, it was found that the resolution amounts toapproximately 20 aF. This result was achieved by averaging over 256 oscillator periods. A further increase of the resolution by l

35、engthening the measurement time is not possibledue to the l/f noise produced by the first stages in both the integrator and the Comparator.The absolute accuracy can be derived from the position accuracy. Since a 1 mmdisplacement corresponds to a change in capacitance of 50 fF, the absolute accuracy

36、of 1 m in the position amounts to an absolute accuracy of 50 aF.CONCLUSIONA low-cost, high-performance displacement sensor has been presented. The system isimplemented with simple electrodes, an inexpensive microcontroller and a linearcapacitance-to-period converter. When the circuitryis provided wi

37、th an accuratereference capacitor, the circuit can also be used to replace expensive capacity-measuringsystems.REFERENCES1 G. C. M. Meijer and R. Schner,“ A lin-performancearhigh PSDdisplacement transducer with a microcontroller interfacing,”Sensorsand Actuators, A21-A23, pp. 538-543, 1990.2J. van D

38、recht, G. C. M. Meijer, and P. C. de Jong, 10/19“theConcepts fordesign of smart sensors and smart signal processors and their applicationto PSD displacement transducers,” Digesr of Technical Papers,Transducers 91.3W. C. Heerens,“ Application of capacitance techniques in sensor design,Phys. E: Sci. I

39、nsfrum., vol. 19, pp. 897-906, 1986.4K. Martin, A-vcoltagentrolled switched-capacitor relaxation 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 M范圍內(nèi)達(dá) 1微M 。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

40、點(diǎn)如下:1毫 M 測(cè)量范圍1微 M 精確度0.1 s總測(cè)量時(shí)間對(duì)應(yīng)到電容域,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)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11/19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)

41、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)電子電路CCx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)12/19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) Heerens 3,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:

42、 <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性。因此,我們規(guī)定 小于 100ppm。此外小電極和周圍屏蔽之間的間距產(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兩個(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/213/19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

43、極坐標(biāo)( , )方法解決。在這種情況下,電場(chǎng)可以表述為:V sinEr(3)V cosr為了計(jì)算小電極的損耗,我們?cè)O(shè)定為 0,整定 :BrQV dr (4)rBl 是小電極的左側(cè)邊界:Bldl (5)tan2Br 是右邊界:Brdl (6)tan2求解( 4)結(jié)果:Q V0 ln2d cosl sin(7)a2d cosl sin對(duì)小 的近似:C0 l14d 2l 22 (8)d12d 2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

44、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14/19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(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 p 2C fT 是在此期間的輸入信

45、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)的概念,它是基于以下原則。當(dāng)我們用線性系統(tǒng)測(cè)量電容 Cx,得到一個(gè)值:M xmCxM 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:15/19PM refM off (11)M xM off在我們的例子中,傳感器的電容Cx 為:AxCx(12)d0d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:ArefCref(13)drefAref 為面積, dref 為距離。將( 12)( 13)式代入( 10)式,然后代入(11)得:Arefd 0ddPAx d

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