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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 the errors are elim in ated. The accuracy amounts to 1 卩 mover a 1 mm ran ge. S

2、i nee the 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 displacement measuring system featuring:1 mm measuring range,1 卩 m accuracy,0.1 s total measuring time.

3、Translated 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 have proposed a disp

4、lacement-measuring system, using a PSD (Position Sensitive Detector) as sensing element. Some disadvantagesof using a PSD are the higher costs and the higher power consumption of the PSD and LED (Light-Emitting Diode) as compared to the capacitive sensor elements described in this paper.The signal p

5、rocessor uses the concepts presented in 2,but is adopted for the use of capacitive elements. By the 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

6、be selected and directly read out by a microcontroller. The microcontroller,in return, calculates the displaceme nt and can send this value to a host computer (Fig. 1) or a display or drive anactuator.Electro nicCrCxtCircuitm4Pers onalComputerDisplayActuatorrefFig. 1. Block diagram of the systemShie

7、ldingFig. 2. Perspective and dimensions of the electrode structureII . THE ELECTRODE STRUCTUREThe basic sensing eleme nt con sists of two simple electrodes with capacita nee Cx, (Fig.2). The smaller one (E2) is surro un ded by a guard electrode. Thanks to the use of the guard electrode, the capacita

8、nee Cx between the two electrodes is independent of movements (lateral displacements as well as rotations) parallel to the electrode surface.The in flue nce of the parasitic capacita ncesCp will be elimi nated as will be discussed in SectionE .Accord ing to Heere ns 3, the relative deviati on in the

9、 capacita nce Cx betwee n the two electrodes caused by the finite guard electrode size is smaller tha n:S <e冗(x/d)(1)where x is the width of the guard and d the distance between the electrodes. This deviation introduces a nonlinearity.Therefore we require thatSis less than 100 ppm.Also the gap be

10、twee n the small electrode and the surrounding guard causes a deviati on:S <e (d/s)(2)a betswith s the width of the gap. This deviatio n is n egligible compared to (l), whe n the gap width is less than 1/3 of the distance between the electrodes.Ano ther cause of errors origi nates from a possible

11、 finite skew an gleelectrodes (Fig. 3). Assu ming the follow ing con diti ons:the pote ntials on the small electrode and the guard electrode are equal to 0 V,the pote ntial on the large electrode is equal to V volt,the guard electrode is large eno ugh, it can be seen that the electric field will be

12、concentric.Fig. 3. Electrodes with angle . aTo keep the calculati ons simple, we will assume the electrodes to be infini tely large in one directi on. Now the problem is a two-dime nsional one that can be solved by usingpolar-coordi nates (r,© ).1 n this case the electrical field can be describ

13、ed by:V sin r© to 0 and integrate overV cos rTo calculate the charge on the small electrode, we setBr VQ 0 B drbi rwith Bl the left border of the small electrode:BldItan2and Br the right border:Brd丄tan2Solving (4) results in:02d cosI sinQ VIn a2d cosI sinFor small a's this can be approximat

14、ed by:卫 1 4d2 I2 2d12d2will cause an error less th;It appears to be desirable to choose I smaller tha n d, so the error will depe nd only on the angle a .In our case, a change in the angle of 0.6 ppm.With a proper design the parameters £ cand l are constant,and then the capacitaneebetween the t

15、wo electrodes will depend only on the distanee d between the electrodes.川.ELIMINATION OF PARASITIC CAPACITANCESBesides the desired sen sor capacita nee C, there are also many parasitic capacita nces in the actual structure (Fig.2). These capacitances can be modeled as shown in Fig.4. Here Cpl repres

16、ents the parasitic capacitances from the electrode E1 and Cp2 from the electrode E2 to the guard electrodes and the shielding. Parasitic capacitance Cp3 results from imperfect shielding and forms an offset capacitance. When the transducer capacitance Cx is connected to an AC voltage source and the c

17、urrent through the electrode is measured,Cpl and Cp2 will be eliminated. Cp3 can be eliminated by perform ing an offset measureme nt.Fig. 4. Elimination of parasitic capacitancesThe current is measured by the amplifier with shunt feedback, which has a very low in put impeda nce. To obta in the requi

18、red lin earity, the uni ty-ga in ban dwidth fT of theamplifier has to satisfy the following condition:12T -CfCfCp2where T is the period of the in put sig nal.Since Cp2 con sists of cable capacita nces and the in put capacita nee of the op amp, itmay in deed be larger tha n Cf and can not be n eglect

19、ed.IV. THE CONCEPT OF THE SYSTEMThe system uses the three-signal concept presented in 2, which is based on the following principles. When we measure a capacitor Cx with a linear system, we obtain a value:M x mCx MOff(10)where m is the unknown gain and Moff, the unknown offset.By performing the measu

20、rementof a referenee quantity Cref, in an identical way and by measuring the offset, Moff,by making m = 0, the parameters m and Moff are eliminated.The finalmeasurement result P is defined as:M refM offM x M off(11)In our case, for the sen sor capacita nee C, it holds that:Axdo d(12)where Ax is the

21、area of the electrode, do is the initial distance between them,dielectric constant and d is the displacement to be measured. For the referenceelectrodes it holds that:refArefdref(13)with Aref the area and dref the distance. Substitution of (12) and (13) into (10) and theninto (11) yields:Aefd。 dAxda

22、irefd refHere, P is a value representing the position while ai and a0 are unknown, but stable constants. The constant ai =Aref/Ax is a stable constant provided there is a good mecha ni cal matchi ng betwee n the electrode areas. The con sta nt ao = (Arefd0/(Axdref) will also be a stable con sta nt p

23、rovided that do and dref are con sta nt. These con sta nts can be determ ined by a on e-time calibrati on. In many applicati ons this calibrati on can be omitted; when the displacement sensor is part of a larger system, an overall calibration is required any way. This overall calibrati on elimi nate

24、s the requireme nt for a separate determ in ati on of ai and a0.V . THE CAPACITANCE-TO-PERIOD CONVERSIONThe sig nals which are proporti onal to the capacitor values are con verted in to a period, using a modified Martin oscillator 4 (Fig. 5j.When the voltage swing across the capacitor is equal to th

25、at across the resistor and theNAND gates are switched off, this oscillator has a period Toff:Toff = 4RCoff.(15)Since 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

26、to Coff. Then the period becomes:Tx=4R(Coff+Cx)=4RCx+Toff(16)The constants R and Toff are eliminated in the way described in Section IV.In 2 it is shown that the system is immune for most of the nonidealities of the op amp and the comparator, like slew in g, limitati ons of ban dwidth and gain, offs

27、et voltages,a ndin put bias curre nts. These noni dealities only cause additive or multiplicative errors which are elimi nated by the three-sig nal approach.VI. PERIOD MEASUREMENT WITH A MICROCONTROLLERPerformi ng period measureme nt with a microc on troller is an easy task. In our case, anINTEL 87C

28、51FA is used,which has 8 kByte ROM, 256 Byte RAM, and UART for serial com muni cati on, and the capability to measure periods with a 333 ns resolutio n. Eve n though the counters are 16 b wide, they can easily be extended in the software to 24 b or more.The period measureme nttakes place mostly in t

29、he hardware of the microco ntroller. Therefore, it is possible to let the CPU of the microc on troller perform other tasks at the same time (Fig. 6). For instanee, simultaneously with the measurementof period Tx, period Tref and period Toff,the relative capacitancewith respect to Cref is calculated

30、according to (11), and the result is transferred through the UART to a personal computer.Fig. 5. Modified Martin oscillator with microcontroller and electrodes.Fig. 6. Period measureme nt as backgro und process.Fig. 7. Position error as function of the position and estimate of the nonlinearity.VII.

31、EXPERIMENTAL RESULTSThe sensor is not sensitive to fabrication tolerances of the electrodes. Therefore in our experime ntal setup we used simple prin ted circuit board tech no logy to fabricate the electrodes, which have an effective area of 12 mm 12 mm. Theguard electrode has a width of 15 mm, whil

32、e the distance between the electrodesis about 5 mm. When the dista nce betwee n the electrodesis varied over a 1 mm ran ge, the capacita nce cha nges from 0.25 pF to 0.3 pF.Thanks to the chosen concept, even a simple dual op amp (TLC272AC) and CMOS NAND s could be used, allowing a single 5 V supply

33、voltage. The total measurement time amounts to only 100 ms, where the oscillator was running at about 10 kHz.The system was tested in a fully automated setup, using an electrical XY table, the described sensor and a personal computer. To achieve the required measurement accuracy the setup was autoze

34、roed every minute. In this way the nonlinearity, long-term stability and repeatability have been found to better than 1 over 困 mange of 1 mm (Fig.7). This is comparable to the accuracy and range of the system based on a PSD as described in 2.As a result of these experiments, it was found that the re

35、solution amounts to approximately 20 aF. This result was achieved by averaging over 256 oscillator periods. A further increase of the resolution by lengthening the measurement time is not possible due to the l/f noise produced by the first stages in both the integrator and the Comparator.The absolut

36、e accuracy can be derived from the position accuracy. Since a 1 mm displacement corresponds to a change in capacitance of 50 fF, the absolute accuracy of 1 卩 m in the position amounts to an absolute accuracy of 50 aF.CONCLUSIONA low-cost, high-performance displacement sensor has been presented. The

37、system is implemented with simple electrodes, an inexpensive microcontroller and a linear capacitance-to-period converter. When the circuitry is provided with an accurate reference capacitor, the circuit can also be used to replace expensive capacity-measuring systems.REFERENCES1 G. C. M. Meijer and

38、 R. Schner,ar“higAhl-ipnerformance PSDdisplacement transducer with a microcontroller interfacing,” Sensorsand Actuators, A21-A23, pp. 538-543, 1990.2 J. van Drecht, G C. M. Meijer, and P. C. de Jon g,“ Co ncepts for thedesig n of smart sen sors and smart sig nal processors and their applicatio nto P

39、SD displaceme nt tran sducers,” Digesr of Tech ni cal Papers,Transducers' 91.3 W. C. Heere ns,“ Applicati on of capacita nee tech niq ues in sen sor desig n,Phys. E: Sci. I nsfrum., vol. 19, pp. 897-906, 1986.4 K. Marti n,''gAs-cdtarolled switched-capacitor relaxati on oscillator,IEEEJ.,

40、 vol. SC-16, pp. 412-413, 1981.一种低成本智能式电容位置传感器摘要本文描述了一种新的高性能,低成本电容位置测量系统。通过使用高线性振荡器,屏蔽和三信号通道,大部分误差被消除。其精确度在1毫米范围内达1微米。由于振荡器的输出可直接连接到微控制器,所以无需用A/D转换器。I .导言本文介绍了一种新型高性能,低成本的电容位移测量系统,特点如下:1毫米测量范围1微米精确度0.1 s总测量时间对应到电容域,规格相当于:1皮法的变化范围;只有这个范围的 50fF (fF是法拉乘以10的负15次方。f 是femto的缩写)用于位移传感器。50aF绝对电容测量误差。梅耶尔和施里尔

41、1以及最近的范德雷赫特河,梅耶尔,和德容2提出了位移 测量系统,采用一个PSD(位置敏感探测器)作为传感元件。和本文描述的电容传 感器元件相比,使用PSD的缺点是,PSD和LED (发光二极管)有更高的成本和 功率消耗。使用2中所提概念的信号处理器,被采用到电容元件的使用中。通过广泛使用 屏蔽,智能A/D转换,该系统能够将高精确度和低成本结合。换能器产生可以选 择和直接由微控制器读出的三段调制信号。微控制器,相应的,计算位移及发送此 值到主机电脑(图1)或显示或驱动执行器。C ref图1该系统的框图图2电极结构的尺寸和透视图n.电极结构基本传感元件包含电容为 Cx的两个简单电极(图2)。较小的

42、一个(E2)是由 屏蔽电极包围。由于使用屏蔽电极,两电极间的电容 Cx可平行于电极表面独立运 动(横向平移以及旋转)。寄生电容Cp的影响可被消除,将在第3节讨论。据Heerens 3,由有限屏蔽电极大小造成的两个电极之间电容Cx的相对偏差小于:S <e- n (x/d)其中x是屏蔽的宽度,d是电极之间的距离。这种偏差引入了非线性。因此,我们 规定S小于100ppm。此外小电极和周围屏蔽之间的间距产生一个偏差:S <e-n (d/s)(2)S是间距的宽度。当间距宽度小于电极之间距离的1/3时,这偏差和(1)相比是微不足道的。另一个误差的原因可能源自两个电极之间的有限倾斜角a (图3)

43、。假设符合下列条件:小电极和屏蔽电极上的电势等于 0V大型电极电势等于V伏屏蔽电极足够大 可以看出,电场将同心图3倾斜角度a的电极为了使计算简单,我们将假设电极在一个方向无限大。 问题就成为一个二维问题,可以用极坐标(Y,© )方法解决。在这种情况下,电场可以表述为:V sinE Vcos为了计算小电极的损耗,我们设定©为0,整定Y:BrQ 0 Bl drrBl是小电极的左侧边界:Bidtan|_2Br是右边界:Brdtan求解(4)结果:V ina2d cosi sin2d cosl sin对小a的近似:4d2 i2212d2选择比d小的I似乎是可行的,因此该误差将只决定

44、于角度a。在这种情况下, 0.6°的角度变化,将产生小于100 ppm的误差。对参数& o和I是常数的设计,两个电极之间的电容将仅仅取决于电极之间的 距离do川寄生电容的消除除了理想传感器电容Cx,在实际结构中还有许多寄生电容(图 2)o这些电容 可以建模,如图4所示。这里CpI代表电极EI的寄生电容,Cp2是从电极E2到屏 蔽电极和屏蔽层的。寄生电容Cp3造成不完善屏蔽,形成一个偏移电容。当传感器 电容Cx连接到AC电压源,通过电极的电流可测,CpI和Cp2,将被消除。Cp3 可通过偏移测量消除。电流通过并联反馈放大器测量,它具有非常低的输入阻抗。要获取所需的线性度,放大器

45、的单位增益带宽fT必须符合下列条件:fT12Cf(9)CfC p2T是在此期间的输入信号由于Cp2包括电缆电容和运算放大器的输入电容,它很可能大于Cf而不可忽IV.本系统的概念该系统采用了 2提出的三信号的概念,它是基于以下原则。当我们用线性系统 测量电容Cx,得到一个值:Mx mCx M°ff(10)其中m是未知的增益,Moff是未知偏移。以相同的方式,通过测量参考量Cref,测量偏移Moff,使m= 0,参数m和Moff被抵消。最后的测量结果 P定义为:p M ref M offM x M off(11)在我们的例子中,传感器的电容 Cx为:Axdo d(12)其中Ax,是电极面积,do是它们之

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