3006 ac feedback esvm

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Trek Application Note Number 3006

AC-Feedback Electrostatic Voltmeter Operation

Dr. Maciej A. Noras

Abstract An AC-feedback electrostatic voltmeter (ESVM) is an inexpensive tool which providesgood measurement accuracy of surface voltage and charge. It provides precision similar to DC-

feedback voltmeter along with the convenience and low price of a fieldmeter. This paper describes

the principle of the Trek AC-feedback technology.

1 Introduction

Measuring electrostatic quantities poses ratherspecial problems because electrostatic systemsare generally characterized by high resistancesand small amounts of electrical charge. As a re-

sult, conventional electronic instrumentation can-not normally be used for surface charge and volt-age measurements, especially in those applica-tions where the measured surface cannot be con-tacted.

One of the most versatile and least expensivetools for electric voltage and charge measure-ments is a fieldmeter. A fieldmeter is a ground ref-erenced measuring device in which readings areinversely related to the distance from the probeto the surface or object under test. This is oneof the limiting factors of all fieldmeters and if ac-curate readings are to be obtained, the distance

from the field-meter probe to the surface undertest must be precisely known and maintained, or,

alternately, the fieldmeter calibration must be per-formed before every measurement at the speci-fied spacing. The measurement geometry is ex-tremely important, because the presence of themeasuring instrument and nearby grounded ob- jects alters the electrostatic field. Another limit-ing factor is the voltage difference between thefieldmeters sensor and the tested surface. If thedistance between the surface and the meter istoo close, an electrical discharge between the two

may occur.DC-feedback electrostatic voltmeters (ESVM) usea DC voltage feedback to their sensor probe hous-ings to null the electric field between the chargedsurface and the probe. Compared with fieldme-ters, this method minimizes capacitive loading

of the charged surface and more accurately re-ports the electric potential of the tested object.DC-feedback voltmeters supply voltages equalto measured voltage levels back to the sensor.These voltages can be as high as 10 [kV] or more.The DC ESVM also has to be capable of followingsudden changes in measured voltages, utilizing

high speed amplifier circuitry for that purpose. Allthese requirements influence the cost of the DC-feedback ESVM.An AC-feedback electrostatic voltmeter [1–3] isan instrument that combines the low cost of theelectrostatic fieldmeter with the accuracy of DC-feedback electrostatic voltmeter. Its constructionallows for elimination of high voltage circuitry thatis a major cost driver for DC-feedback ESVMs.At the same time AC-feedback voltmeter offers

spacing-independent measurements with betteraccuracy and repeatability than fieldmeters.

2 Theory of AC-feedback

A parallel-plate capacitance model is very fre-

quently used for description of operation of theDC-feedback ESVM [4–7], (Figure 1). The sensor(a.k.a. Kelvin probe) vibrates sinusoidally in thedirection perpendicular to the tested surface andthe current flowing to and from the probe changesproportionally to the amplitude and frequency ofthat vibration:

I = U · dC dt

=

= U ·d

dt

0A

D 0 + D 1 · sin(ωt )

=

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= -U · 0A ·

D 1ω cos(ωt )

[D 0

+ D 1

sin(ωt )]2

(1)

U is the voltage between the plate and the sen-sor,

A is the surface area of the capacitive sensor-to-plate coupling,

is the relative electric permittivity of the materialbetween the plate and the sensor, ≈ 1 forair,

0 is the electric permittivity of vacuum, = 8.85 ·

10- 12 [F/m],

D 0 is the average distance between the plate andthe sensor,

D 1 is the amplitude of vibrations [m],

ω is the circular frequency of vibrations, ω = 2πf [rad/s], where f is a frequency in [Hz].

Figure 1: Parallel-plate capacitor.

In the DC ESVM this current is nullified bybringing the value of the voltage U to zero. It is

done by increasing the voltage on the sensor (U 1in Figure 1) to the voltage level of the surface un-der test (U 2). If the current I equals zero, it meansthat U 1 = U 2, voltage U 2 is then measured andconsidered a true representation of the voltage on

the tested surface.AC-feedback voltmeter uses a different method forthe current I cancellation. An additional currentsignal I is fed to the probe sensor in order to ob-tain that effect:

I = -U · 0A ·

D 1ω cos(ωt )

[D 0 + D 1 sin(ωt )]2

+ I =

= 0 (2)

The current I is produced by an internal gen-erator circuit:

I = C ·dU t

dt , (3)

where C is expressed as:

C = 0A

D 0 + D 1 · sin(ωt )

The internal generator supplies current signalnot only to the sensor but also to the body of theprobe:

I = C probe ·dU t dt

, (4)

For the round body probe, the capacitanceC probe , formed between the probe and the surfaceunder test is equal to:

C probe

= 2π · L

cosh- 1

D 0+R R

, (5)

where L is the length of the probe, R is theradius of the probe. All other capacitive cou-plings between the probe and surroundings are








assumed to be negligible. The current I is notused for nullification of the current I at the sensor.I is a current with constant amplitude which de-pends only on the distance D 0 between the probeand the tested surface and presents an additional,

fixed load to the internal signal generator. Thecurrent I , detected on the sensor, is being zeroedby the current I delivered directly to the sensor.Thus, combining equations 2 and 3:

0A

D 0 + D 1 · sin(ωt ) ·

dU t dt

=

= U · 0A ·

D 1ω cos(ωt )

[D 0 + D 1 sin(ω

t )]

2 (6)

dU t

dt = U ·

D 1ω cos(ωt )

D 0 + D 1 sin(ωt ) (7)

If the voltage U t is sinusoidal, i.e.:

U t = U t 0 · sin(ω1t ) (8)

dU t dt

= U t 0 · ω1 · cos(ω1t ) (9)

Assume that voltage U t and vibration of thesensor have the same circular frequencies, ω1 =ω, and compare equations 7 and 9.

U t 0 · ω · cos(ωt ) = U ·D 1ω cos(ωt )

D 0 + D 1 sin(ωt )

U t 0

U =

D 1

D 0 + D 1 sin(ωt ) (10)

If the amplitude of sensor vibration D 1 is smallcompared to the distance between the plate andthe sensor D 0, the equation 10 becomes:

U t 0

U =

D 1

D 0≈ const,

within a certain range of distances D 0 (Figure2). Notice that this semi-linear region is extended

if the amplitude of vibrations D 1 is being reduced.Use of D 1 /D 0 scaling factor allows for a voltageof relatively low amplitude U t 0 to represent muchhigher voltage U present on the plate. There is noneed for high voltage circuitry. It is extremely im-

portant to remember that this relationship is validonly within the certain, specified range of sensor-to-plate distances. If D 0 is comparable to the am-plitude of vibrations of the sensor D 1, the aboveD 1D 0

≈ const statement becomes invalid.

0 10 20 30 40 500

0.5

1

1.5

D0

D 1

/ D 0

r a t i o

D1

=1

D1

=0.5

D1=2

Figure 2: Influence of the sensor-to-plate distanceD 0 on the current cancellation condition for vari-

ous amplitudes of vibrations of the sensor D 1.

3 Conclusions

The distance D 0, for which AC-feedback voltmeterachieves its maximum accuracy, is limited by sev-eral factors. First factor is the D 1

D 0ratio which deter-

mines the minimum plate-to-sensor spacing. An-other element limiting that minimum is the voltagedifference between the plate and the sensor. No-tice that, unlike in the DC-feedback ESVM, AC-feedback technique does not bring the potentialon the sensor to that of the surface under test.








There is a possibility of an electric discharge be-tween the sensor and the plate, which can lead todamage of the voltmeter.There is also a limit regarding the maximum dis-tance D 0. It depends on the size of the sensor,

if an influence of environmental conditions can beconsidered negligible. If the sensor is too far fromthe tested surface, it becomes capacitively cou-pled to the surrounding, i.e. test equipment, furni-ture, etc. An additional constraint for AC-feedbackESVMs pertains to the type of surfaces that canbe examined with accuracy specified by the man-ufacturer. If capacitance between the tested object and the earth ground is comparable to or less

than the probe-to-ground capacitance, the AC-feedback voltmeter readings become inaccurate[8]. The AC signal generated by the AC feedbackis being induced on the surface due to the capac-itive coupling between the probe and the surfaceunder test. The AC component present on thetested object creates an error offset voltage.

References

[1] B. T. Williams. High voltage electrostatic sur-face potential monitoring system using low

voltage a.c. feedback. U. S. patent no.4797620, 1989.

[2] D. M. Zacher. Feedback-based field metereliminates need for HV source. EE Eval. Eng.,pages S43–S45, November 1995.

[3] D. Pritchard. Electrostatic voltmeter andfieldmeter measurements on GMR recordingheads. In EO/ESD Symposium Proceedings ,volume EOS-22, pages 499–504, Ananheim,

CA, September 2000. EOS/ESD.

[4] W. A. Zisman. Rev. Sci. Instrum., 3:367–368,1932.

[5] Foord T. R. Measurement of the distribution ofsurface electric charge by use of a capacitive

probe. J. Sci. Instrum. (J. Phys. E), 2(2):411– 413, 1969.

[6] F Rossi, G. I. Opat, and A. Cimmino. Mod-

ified Kelvin technique for measuring strain-induced contact potentials. Rev. Sci. Instrum.,63(7):3736–3743, 1992.

[7] M. Wolff, A. E. Guile, and D. J. Bell. Mea-surement of localized surface potential differ-ences. J. Sci. Instrum. (J. Phys. E), 2(2):921– 924, 1969.

[8] M. A. Noras. AC-feedback electrostatic volt-

meter measurements. Optimal measurement conditions . Trek, Inc., 2002.




3006 ac feedback esvm

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