640 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997

A Novel AC Current Source forCapacitance-Based Displacement Measurements

Roberto Nerino, Andrea Sosso, and Gian Bartolo Picotto

Abstract—A 100 kHz bandwidth ac current source suitableto be used with capacitive sensors in displacement measurementapplications has been designed and constructed. The high-outputimpedance of the source is obtained by sensing the load voltagewith a buffer stage having very low input capacitance. Thesensing-buffer power supply, its shield, and the input shieldingconnections are driven at the buffer input potential in such away that the effect of all input parasitic admittances, includingthe buffer common-mode impedance, are almost suppressed.The load impedance variations, which are directly proportionalto displacements, are monitored by the output voltage of thesensing buffer. Measurements made at different frequencies withcalibrated capacitance loads ranging from (1 to 20) pF haveshown that the load-impedance values are proportional to theoutput voltage of the sensing buffer with a linearity better than4�10

�4 and resolution of about3�10�5 over a 1 kHz bandwidth

of load variation signal. The features of the current source andits performance in a displacement measurement application aredescribed.

I. INTRODUCTION

I N STANDARDS laboratories, the highest accuracy level inimpedance measurements is achieved typically by means

of transformer-bridge techniques [1]. However, in industrialmeasurements, accuracy is affected by a tradeoff with otherrequirements, such as cost and measurement speed. Often,the impedance to be measured must be known for the de-termination of another quantity, as in capacitive displacementtransducers [2]–[4]. The plane-parallel-type capacitive trans-ducer is widely used due to its manufacturing simplicity andsensitivity, and several techniques are available to measure itsadmittance (see [3] for a review). The most accurate techniquesmake use of the two-port representation for the sensor and theparasitic capacitances, applying an ac voltage source to oneport and measuring the output current from the other port,driven to a virtual ground. The effect of parasitic capacitancesis almost canceled out, but the measured current is directlyproportional to the sensor admittance and inversely to displace-ment. Furthermore, the technique is not applicable when oneof the sensor electrodes is grounded. The direct measurementof displacement is more convenient because it avoids real-time signal conversion and simplifies the feedback control loopdesign of servoed displacement actuators. Moreover, lineardisplacement transducers are simpler to calibrate comparedwith inherently nonlinear ones.

Manuscript received June 20, 1996; revised October 1, 1996.R. Nerino and A. Sosso are with the Istituto Elettrotecnico Nazionale “G.

Ferraris,” Torino, Italy.G. B. Picotto is with the CNR–Istituto di Metrologia “G. Colonnetti,”

Torino, Italy.Publisher Item Identifier S 0018-9456(97)01648-3.

Several methods that apply the parasitic capacitance-suppression technique described above give a direct displace-ment measurement. In auto balancing bridge methods [5], [6],a linear transducer is obtained by varying automatically theamplitude of the voltage source across the sensor to maintainits current constant. The voltage amplitude is then directlyproportional to the displacement. The accuracy of thesemethods is good at the expense of cost and/or measurementspeed. In another method, the current in the sensor capacitancecontrols the period of an oscillator, whose frequency is directlyproportional to the displacement [7]. In [8], a constant amountof charge is injected into the sensor capacitance. In this case,it is the sensor voltage that is directly related to displacement.

We propose a solution in which the displacement is directlyrelated to the voltage across the impedance of a parallel-plate capacitive sensor when it is driven by an ac cur-rent source of constant amplitude. The effectiveness of themethod is guaranteed by an active guard technique basedon a novel buffer circuit that senses the voltage across theload and ensures that the current source output impedanceis much greater than that of the sensor [4]. Another benefitof the current source approach is the possibility to drivemultiterminal capacitive sensors having one of the electrodesgrounded. When displacements are to be monitored along twoor three axes, the multiterminal capacitive sensor [9] becomescompetitive compared with assemblies of single ones. In [4],the currents from each electrode can sum in a unique groundedcounterelectrode; hence, displacements can be measured bythe voltages of the independent electrodes. The complicationof different frequency sources or of separate counterelectrodeswith related connection wires can be thus avoided, and theshielding of the mobile counterelectrode is simplified. Thevery high output impedance obtained with feedback makesthis low-cost current source useful for every application inwhich a constant-amplitude ac current has to be fed to a veryhigh impedance load. Other possible applications of the accurrent source are to be found in bioelectric measurementsas, for example, in the analysis of the electrical impedanceof biological tissue. The following sections deal with the cur-rent source circuit description and analysis. Limits on outputimpedance, linearity, and stability are discussed together withcalibration results and the dynamic performance of the sourcein displacement monitoring applications.

II. CIRCUIT DESCRIPTION

The ac current source circuit, which is based on a modifiedversion of the Howland voltage-controlled current source [10],

0018–9456/97$10.00 1997 IEEE

NERINO et al.: AC CURRENT SOURCE FOR CAPACITANCE-BASED DISPLACEMENT MEASUREMENTS 641

is shown in Fig. 1. As the working principle of this circuitrelies on the equality of the ratio of the feedback imped-ances ( ), we use four matched impedances

, and coupled to a sinusoidal voltage sourceby means of a high-quality transformer that ensures that theoutput impedance of loads and symmetrically. Hence,impedance matching in the and branch is maintained,preserving the high output impedance of the current source.The high input impedance buffer circuit comprises a FET-inputoperational amplifier , whose power supplies are driven bythe output voltage of a wide-bandwidth operational amplifier

. is fully shielded, and both its shield and biasing circuitare driven by the wide-bandwidth operational amplifier.The stability of the buffer circuit is obtained through a suitablepassive compensation network (COMP. CIRC.). The wholebuffer circuit behaves like a voltage follower with an inputcapacitance to ground of approximately 1 fF and an inputresistance that is greater than 10 Gfrom dc to 100 kHz. Thevery low phase shift and gain error of the buffer circuit in theoperating bandwidth does not affect the accurate impedancematching of the feedback network of . In the measurementof displacements to hundreds of microns, a typical sensorcapacitance varies from (1 to 20) pF. Any residual parasiticcapacitance shunting represents a source of nonlinear-ity when using the voltage across the sensor impedance tomonitor displacements; therefore, it should be reduced to anegligible value to maintain the linearity of voltage changewith displacement. The common mode input capacitance ofvoltage followers based on operational amplifiers, togetherwith the sensor shielding, imposes a lower bound of a fewpicofarards to parasitic capacitances so that the linearity wouldbe heavily compromised. Due to the high impedance of thebuffer circuit, the ac current, which is set by and , flowsalmost completely into the load , and the linearity is notaffected by more than a few parts in . The voltage acrossthe sensor is measured after synchronous demodulation andlowpass filtering of the output voltage of . The phase ofthe synchronous demodulator reference signal can be set sothat operation with resistive sensors is possible without anycircuit modification. The precise tracking of the sensor voltage(output of ) by the buffer circuit drives a guard that greatlyreduces currents to the wiring and shielding of the input node,thus avoiding the reduction of the very high input impedanceof the buffer alone.

III. A NALYSIS OF CIRCUIT PERFORMANCE

Circuit features of interest in capacitive sensor applicationsare

a) the bandwidth of the impedance variation signal,b) linearity of versus ,c) resolution,d) stability against variations in sensor impedance,e) linearity of versus ,f) the operating range of impedance changes.

a) The actual bandwidth of the output signal is con-strained by two factors: the maximum frequency of thesource at which the output impedance of the current source

Fig. 1. Circuit diagram.

is still negligible compared with the load and the requirementson the lowpass filter design after the demodulation. A second-order lowpass filter and a value of about 100 kHzare used; this allows one to obtain easily, with a signalbandwidth of several kilohertz, a good linearity and a lowsignal distortion.

b) A high linearity of output voltage versus impedance isa desirable feature in displacement measurement applications.Factors affecting the linearity are the mismatch of the feedbacknetwork, the common mode gain, and the limited differentialgain of and the departure from the ideal behavior ofphase, gain, and input impedance of the sensing buffer. Theeffect of all these on the linearity can be represented ascontributions to the output impedance of the current sourcegiven by (1) below. The nonideal gain of the buffer can beinterpreted as being equivalent to a mismatch of the feedbacknetwork. Measurements and accuracy specifications of theprecise matched resistor network (Vishay) and on the buffergain enable these contributions to be evaluated to a relativemismatch of the order of few parts of . The contributionto the output impedance due to the finite gain ofcombinesin (1) with the contributions due to network mismatch andbuffer gain. For the component values we used, this givesrise to a reduction by 20–30 in the magnitude of the outputimpedance with respect to its maximum theoretical value of[ ]. The contribution to the nonlinearity dueto the common mode gain of is generally negligible.The output impedance is given by

(1)

where (see Fig. 1) are the differential and commonmode gain of , and

. From (1), it follows that higher and lower nonlinear-ity values are obtained by increasing and/or decreasing .The input impedance of the buffer was measured by connectingits input to a stable ac voltage source through a calibrated

642 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 46, NO. 2, APRIL 1997

Fig. 2. Residual of linear fits of the measured dependence ofUouton 1/Cx for different frequencies.

three-terminal reference capacitor having a capacitance valueof 2 fF. The complex ratio between the output voltage of thebuffer and the voltage source measured at different frequenciesallows the input impedance to be evaluated as an arm ofthe voltage divider formed with the reference capacitor. Theresistive component of the buffer input impedance was foundto be greater than 10 Gand the capacitive component lessthan 1.5 fF in the frequency range from 0.01–100 kHz.

c) Resolution depends on the noise level after the lowpassfilter, and it was better evaluated experimentally. A white noiselevel of 300 Vrms was measured in a 1 kHz bandwidth ofthe output signal . The load was varied from (1 to 30) pF,with a corresponding variation of from (10 to 0.33) V.In this particular operating condition, the estimated resolutionin the impedance measurements was about .

d) Instability arising in Howland-type current source appli-cations is generally due to inductive loads [10]. Such problemsdo not arise here where the reference and the loadare capacitances, and the phase lag of the buffer circuit isnegligible.

e) The nonlinearity of versus was measured byvarying for various load values and was found to benegligible compared with those described in b).

f) Very small impedance values are tolerated by the circuit.We experimented with normal operation (zero output voltage)with a short circuit as a load. The maximum load impedancethat still produced a nonlinearity of a few parts in wasfound to be that given by a capacitance of about 1 pFat 100 kHz. An advantage of the voltage-controlled currentsource is the compliance to different load variation ranges. Indisplacement measurement, proper regulation of the amplitudeof allows the circuit to be easily adapted to a particularsensor and to different displacement ranges. In this way, themaximum operating output voltage (10 V) corresponding to

Fig. 3. Comparison between the interferometric signal and the circuit output.

the maximum impedance value is maintained, thus obtainingthe best resolution over the whole impedance range.

IV. CALIBRATION RESULTS

The circuit linearity was evaluated by measuring the bufferoutput voltage ( ) produced by stable three-terminal capac-itors of known values (see Fig. 2). The measurement wasperformed at three different frequencies of the reference source

(30, 50, and 100 kHz), and the voltage was measured by apreviously calibrated true rms digital voltmeter (Fluke 8506A).The relative deviation from linearity of the output volt-age versus (normalized by the full-range voltage) waswithin . An evaluation of the dynamic performanceand the resolution of the impedance-to-voltage converter wasexperimentally obtained in a displacement measurement ap-plication. Prototypes of the converter circuit coupled withcapacitive sensors have been used to monitor tip displacementalong three axes in a scanning tunneling microscope (STM)scanner [4]. The capacitive sensors were made by fixed

NERINO et al.: AC CURRENT SOURCE FOR CAPACITANCE-BASED DISPLACEMENT MEASUREMENTS 643

guarded electrodes and movable counterelectrodes mountedon a piezo-actuator. The operating frequency of thesourcewas 100 kHz, and the displacement signal bandwidth aftersynchronous demodulation was limited to 1 kHz by a lowpassfilter. The output signals of the current source-based transducerand of an interferometer, while monitoring the same electrodedisplacement, are shown in Fig. 3. The displacement resolutionwas about of the full range (30 m). This valuecorresponds to an absolute capacitance resolution of 60 aFwith a sensor capacitance value of about 2 pF.

V. CONCLUSIONS

A low-cost ac current source is described. Thanks to a novelwideband high-impedance input buffer circuit, this sourceis suitable for use in monitoring high value impedances asgiven by capacitive sensors in displacement measurementapplications. The circuit performance could be further im-proved both by reduction of the sensing buffer noise andby a better linear demodulation technique. Nevertheless, thegood linearity, bandwidth, and resolution of the circuit suggestthat by these techniques, an even better performance can beobtained, with possible applications in extending the normalload range of ac current sources to higher value impedances.

REFERENCES

[1] B. Hague (revised by Foord),Alternating Current Bridge Methods,6thed. London, U.K.: Pitman, 1971.

[2] W. Heerens, “Application of capacitance techniques in sensor design,”J. Phys. E: Sci. Instrum.,vol. 19, pp. 897–906, 1986.

[3] S. M. Huangh, A. L. Stott, R. G. Green, and M. S. Beck, “Electronictransducer for industrial measurement of low value capacitances,”J.Phys. E: Sci. Instrum.,vol. 21, pp. 242–250, 1988.

[4] G. B. Picotto, S. Desogus, S. L´anyi, R. Nerino, and A. Sosso, “Scanningtunneling microscopy head having integrated capacitive sensors forcalibration of scanner displacements,”J. Vac. Sci. Technol.,vol. B.14,no. 2, p. 897, 1996.

[5] X. Zhao, G. Wilkening, H. Marth, and K. Horn, “High-accuracy capac-itance sensor for positioning of piezoelectric displacement actuator,” inDig. ACTUATOR 94 Conf.,Bremen, Germany, June 15–17, 1994.

[6] W. C. Kabele, “A fast microcomputer-controlled admittance bridge,”IEEE Trans. Instrum. Meas.,vol. IM-25, pp. 541–544, Dec. 1976.

[7] F. N. Toth and G. Meyer, “A low-cost, smart capacitive position sensor,”IEEE Trans. Instrum. Meas.,vol. 41, pp. 1041–1044, Dec. 1992.

[8] P. D. Chapman, “A capacitance-based ultra-precision spindle erroranalyzer,”Precision Eng.,vol. 7, no. 3, July 1985.

[9] W. Heerens, “Multi-terminal capacitor sensors,”J. Phys. E: Sci. In-strum., vol. 15, pp. 137–141, 1982.

[10] J. Steel and T. Green, “Tame those versatile current source circuits,”Elec. Des.,pp. 61–72, Oct. 15, 1992.

Roberto Nerino was born in Rivoli, Italy, in 1956.He graduated in electronic engineering from thePolitecnico di Torino, Torino, Italy in 1981, andreceived the doctoral degree in metrology fromPolitecnico di Torino in 1992.

Since 1988, he has been working on precisioncapacitance measurements and capacitive sensor de-sign at the Electrical Metrology Department of theIstituto Elettrotecnico Nazionale “Galileo Ferraris,”Torino. He is currently with the Computer VisionDepartment of the same institute. His present ac-

tivity concerns image and signal processing applications to dimensionalmeasurements and robotics.

Andrea Sossowas born in 1964 and received thedegree in electronic engineering in 1990. He re-ceived the doctoral degree in metrology in 1994from the Electrical Metrology Department of theIstituto Elettrotecnico “G. Ferraris” (IEN).

While at IEN, he has been involved in the com-parison between electrical and mechanical power.Since 1994, he has been a researcher at IEN, wherehe has worked on ac quantum Hall effect mea-surements and capacitive sensors. At present, heis working at the National Institute of Standards

and Technology, Gaithersburg, MD, as a guest researcher. His main interestsconcern dc voltage standards and the design of electronic circuits for precisionmeasurements.

Gian Bartolo Picotto received the degree in physicsfrom the University of Torino, Torino, Italy, in 1987.

He is currently a researcher at the CNR–Istitutodi Metrologia, where he has been involved inthe field of optical frequency standards andlaser spectroscopy. Since 1990, he has beenresponsible for the research on submicron surfacemetrology. His main interests are in scanningprobe microscopy, stylus profilometry, laserinterferometry, and capacitance-based displacementtransducers.