resistive capacitive sensors

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768 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 44,NO. 3, JUNE 1995

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A Novel Smart Resistive-Capacitive Position Sensor

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Xiujun Li and Gerard C. M. Meijer

Abstract- A novel smart resistive-capacitive angular positionsensor is presented. The main advantagesof this ow-cost systemare its simplicity,high stability and high reliability.A very hearoscillator is used in the processing circuit to convert the positionquantity to a period-modulated signal which c n directly be readout by a microcontroller. The system does not need an A Dconverter. The nonlinearityof the smart angular position sensorsystem is less than f03 (f0.9) ver the range of 270.

I. INTRODUCTIONONSISTING of a single wire with a sliding contact, theC esistive potentiometer is one of the simplest and mostefficient position sensors. Its disadvantages are low accuracyand linearity. Moreover, the long-term stability of this systemis bad since the sliding contact is directly in contact with theresistive element of the potentiometer. The position-sensitive

detector (PSD) which is an optical potentiometer [1]-[3] isan interesting alternative which is suited to be implementedas an integrated circuit. But this system can only measuredisplacement over a small range (3 mm), and the cost andenergy consumption of the PSD and the LED are ratherhigh. These drawbacks are overcome in the novel resistive-capacitive potentiometer which is described in this paper.This potentiometer is used as a sensing element for a smartresistive-capacitive position sensor.The smart resistive-capacitive position sensor is suited toreplace both linear and circular potentiometers. In this paper,we limit ourselves to the discussion of an angular encoder forthe measurement range of 270.

11. BASIC PRINCIPLEFig. 1 shows the entire resistive-capacitive position sensorsystem. The resistive-capacitive sensing element is a modifiedpotentiometer with a sliding contact which is not directlyin contact with the resistive layer of the potentiometer. Theslide forms an electrode which is capacitively coupled to theresistive layer. The advantages are low cost, high long-termstability and a wide measuring range.The 3-signal approach presented in [l] and [5] is used to

obtain a simple and accurate signal processor. In this proces-sor, an oscillator is used of which the period of oscillation islinearly related to the position. This period-modulated signalcan directly be read out by a microcontroller. There is no needfor an additional A/D converter or for other analog processingcircuits.The resistive-capacitive sensing element consists mainly oftwo parts: a rotating electrode and a resistive layer. A simple

Manuscript received May 10, 1994; revised anuary 31, 1995.The authors are with the Department of Electrical Engineering, DelftIEEE Log Number 941 1490.University of Technology, 2628 CD Delft, The Netherlands.

sensing elementig. 1. An overview of the smart resistive-capacitive angul ar position sensorfor a linear potentiometer.

SelectorI .

i ./7?7

Fig. 2. A simple equivalent model of the resistivecapacitive sensing ele-ment.equivalent model of the resistive-capacitive position sensor isshown in Fig. 2.The capacitor C represents the equivalent capacitancebetween the sliding electrode and the resistive layer. The sumof the resistances R1 and R2 is the resistance R p s ~f theresistive layer. When I1 and 1 2 represent the currents throughC n the position 1 and 2 of the switches respectively andwe denote the relative position by a number 2 which variesfrom 1 for the bottom position to 1 for the top position,then we can find that

The position is only the function of the resistances R1and R2 and is not related to capacitance C . This is animportant property because it means that the measurement isimmune to the electrode distance and the mechanical toler-ances which result from deviations or nonuniformity of theelectrode distance.111. SIGNALROCESSING

According to the 3-signal method presented in [l], [5], wemeasure successively a variable quantity M and two referencequantities M I and M2 in an identical way, using the samesystem. The measuring result is the ratio

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LI AND MELTER A NOVEL SMART RESISTIVECCAPACITIVE POSITION SENSOR 769

When the system is linear, then in this ratio the influence ofthe unknown offset and the unknown gain of the measurementsystem is eliminated.In order to obtain the position x , the three currents 11,12,and IO have to be measured. The current IO is permitted tobe zero. The three currents can be converted into period-modulated signals, using a capacitance-controlled oscillatorwhich generates square-wave output signals where periods Tpiare related to the current by the linear equationTp;= uI b i = 0 , 1 , 2 ) . (3)

When IO = 0, we find4)

Fig. 3shows the electronic circuitry for the smart resistive-capacitive position sensor system.The modified Martin oscillator [4], [5] is composed of anoperational amplifier A I , a comparator CP, an inverter, thecapacitancesC1 C2 and a resistance Ro. The microcontrollercan directly read out the period-modulated signals from V4and control the selector (two NAND gates). A buffer is usedbetween the oscillator and the selector to eliminate undesiredinteractions.

Iv. THE INFLUENCEOF SYSTEMATIC ERRORSIn [l] it is shown that the system is immune to most ofthe nonidealities of the opamp and the comparator, such asslewing, limitations of bandwidth and gain, offset voltages andinput bias currents. These nonidealities only cause additiveor multiplicative errors which are eliminated by the 3-signalmethod. But some effects cannot be eliminated by the 3-signalmethod in this system, as will be discussed now:

A. The Effect of Two NAND G ates WhichHave Different ON Resistances RON

The output stages of two NAND gates shown in Fig. 3will cause influence on the measured position. It is assumedrespectively the ON resistances of the output stages of twoNAND gates under the high and low output levels. A straight-forward calculation of the offset of RON or the measuredposition can be approximated by:

the resistances R p o ~ l , N O N ~nd R p o ~ 2 , N O N ~epresent

x2 RPON1 RPONP R N O N ~RNONl)/zRPSD RPONP RPONlRNON2 R N O N ~ ) / ~ R P S D .5 )

Formula (5) shows that the ON resistances of the NANDgates not only cause an offset and a gain error but also thenonlinearity. Usually, the offset and gain error can easily beeliminated during the installation and calibration of the angularposition sensor in its final setup. The maximum influenceof RONoccurs at x = f l . When, for example, RNON=R p s ~ 100kR hen both the maximum nonlinearity and theoffset amount to 0.0045 (which corresponds to 21.1 arcsec).40 R , ARNON 4 R, RPON= 50 R , ARPON= 5 R and

IFig. 3.sensor system.The electronic Circuitry of the smart resistive-capacitive position

pdjg mp 1c p JcPzFig. 4. The parasitic capacitances of the sensor.

B. The Effect of the Parasitic CapacitorsThe parasitic capacitors of the smart angular position sensorare shown in Fig. 4.The effects of the parasitic capacitors Cpl ,CLl,Cp, can

be neglected, where the Cpl ,CL , and Cp, include the cablecapacitances. The parasitic capacitances Cp2and CLz are alsocomposed of two parts: the parasitic capacitances between thesliding electrode and the terminals of the resistive layer, andthe parasitic capacitances between the outputs of the selectorand the inverting input of the integrator in the measuringcircuit.The influence of the parasitic capacitances on the measuredposition can be expressed by the following equation:

6)Equation (6) shows that the measured position is relatedto the capacitance Cc due to the effect of the parasiticcapacitances.Since the value of capacitorCc s very small (about 2.2 pF),the parasitic capacitors Cp2 and CL2 can cause a large errorin the position measurement. This error will change with theposition x since the capacitor C and the parasitic capacitors

Cp2and CL2depend on the position x . Therefore, the parasiticcapacitances Cp2and CL2have to be minimized in the designof the sensing element and measuring system.

Tpl Tp2Tpl Tp2 Tpo

+ V P 2 c;21/cc1 Cp2 c;,/cc

v. EXPERIMENTESULTSThe system has been built and tested using a resistive-capacitive angular sensor, a signal-processing circuit and amicrocontroller of the type INTEL D87C51FA. The signal-processing circuit uses a modified Martin oscillator [4], [5]


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770 IEEE TRANSACTIONS ON I N S T R U ~ E N T A T I O NAND MEASUREMENT, VOL. 4 O. 3, JUNE 1995

electrode 1 i r a t euarding The measured angular posit ion (degree)coupling electrode resistive ayer Fig. 7.fixed electr ode sensor. The experimental results for the nonlinearity of the complete smartFig. 5. The physical structure of the sensing element.I s T

parasitic capacitors in the sensing element and the nonlinearityof the resistive layer.2.g 103 ACKNOWLEDGMENTg g 03 8CIO h The authors would like to thank G . W. de Jong, F. N. Toth,H. M. M. Kerkvliet, R. J. H. Janse, and A. F. P. van Schiefor their painstaking help.g -5-10

100 200 300 400 500 6 700 800The serial number REFERENCES

Fig. 6. The noise of the signal processor. The result of a series of 800measurements performed under identical conditions. Each measurement takesabout 100 ms. [ MeiJer van Drecht p c de Jong and HNew conce pts for smart signal processors and their application to PSDdisplacement transducers, Sensors and Actuators, vol. A35, pp. 23-30,1992.which has been implemented with a simple dual opamp(TLC272AC) and two CMOS NAND gates according to thecircuit shown in Fig. 3.The structure of the sensing elementis shown in Fig. 5. The resistive potentiometer R p s ~s about100 k 0 .The electrodes were made using printed circuit board tech-nology. The sliding electrode has an effective area of 61 mm2.The distance between the sliding electrode and the resistivelayer is about 0.2 mm, and the equivalent capacitance C isabout 2.2 pF. In order to eliminate the influence of the parasiticcapacitors and the electromagnetic interference, a guardingelectrode was made all around the sliding electrode, and theshielding is used.The measuring system is powered by a single 5 V supplyvoltage. The frequency of the oscillator is about 7.0 kHz,and the applied range of the oscillator frequency is about 3.3kHz-7.0 kHz. The three periods TPo,T p l , p2 are measured ina total measurement time of about 100 ms. The noise of thesignal processor, which includes the sampling noise, is shownin Fig. 6.The measured nonlinearity of the entire smart sensor systemover the measurement range of -135 to f13.5 is less than410.3 (see Fig. 7). This nonlinearity is mainly due to thenonlinearity of the resistive layer and the effect of the parasiticcapacitors.

VI. CONCLUSIONA novel resistive-capacitive position sensor has been pre-sented. The signal-processing circuit is simple and can be

[2] G. C. M. Meijer and R. Schrier, A linear high-performance PSDdisplacement transducer with microcontroller interfacing, Sensors andActuators, vol. A21-A23, pp. 538-543, 1990.[3] Y. Z. Xing and W. J. Lian, A novel integrated optical potentiometer,in Proc. 4th Int. Con8 Solid-State Sensors and Actuators Transducers87 . Tokyo, Japan, June 2-5, 1987, pp. 427 43 0.[4] K. Martin, A voltage-controlled switched-capacitor relaxation oscilla-tor, IEEE J Solid-State Circuits, vol. SC-16, pp. 412414, 1981.[ 5 ] F. N. Toth and G. C. M. Meijer, A low-cost, smart capacitive positionsensor, IEEE Trans. Instrum. M eas., vol. 41, no. 6, Dec. 1992.

Xiujun Li was bom in Tianjin, China, on February19, 1963. He received the B.S. degree in physicsand the M.S. degree in electrical engineering fromNankai University, Tianjin, China, in 1983 and1986.He joined the Department of Electronic Science,Nankai University in 1986. He is now workingtoward the Ph.D. degree at Delft University of Tech-nology, Department of Electrical Engineering, TheNetherlands. His research interests are in the area ofthe smart capacitive sensor and signal processing.

Gerard C. M. Meijer was bom in Wateringen,The Netherlands, on June 28, 1945. He receivedthe ingenieurs (M.S.) and Ph.D. degrees in electricalengineering from the Delft University of Technol-ogy, Delft, The Netherlands, in 1972 and 1982,respectively.

Since 1972 he has been part of Laboratory ofElectronics, Delft University of Technology, wherehe is an associate professor, engaged in researchand teaching on analog IC s. In 1984 and part-timeduring 1985-1987 he was seconde d to the Delftimplemented as a single-chipCMOS integrated circuit. A pro-totype Of the System has been built and tested. The nonlinearityamounts to 0.3 . The main causes of this nonlinearity are the

Instruments Company in Delft, where he was involved in the developmentof industrial level gauges and temperature transducers.Dr, Meijer is a member of the Netherlands Society for Radio and Elec-tronics.

resistive capacitive sensors

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