M E A S U R E M E N T S OF E L E C T R I C A L A N D M A G N E T I C Q U A N T I T I E S

E L E C T R I C F I E L D - S T R E N G T H M E T E R W I T H A C E R A M I C

E L E C T R E T T R A N S D U C E R

V. Y u . L a z a u s k a s UDC621.317.328

Electrodynamic meters in which the measured field is modulated with an a l ternat ing field are used increasing- ly for measuring e lec t r ic field strength. Instruments of this type are provided with various e lec t rodynamic trans- ducers (vibrating capaci tors with a var iable linear capaci tance and capaci t ive measuring oscillators). However, the use of moving parts in the e lectrometers , their compl ica ted manufacture, sensitivity to vibrations, as wel l as the use in them of transducers with re la t ive ly large dimension, or of electrodes with large surfaces, make it inconve- nient or impossible to use these instruments for measuring e lec t r i c field strength in a confined space.

In order to raise the current generated by e lec t rodynamic transducers in electrometers , it becomes necessary to increase the working surface S of electrodes, e lec t r ic induction Dt, and the frequency of surface S oscil lations, or the value of e lec t r ic induction D.

The current of exist ing e lec t rodynamic transducers [ 1] is not raised by increasing induction D t, since the e lec t rodynamic transducers' e lectrodes are normally in a gas medium (air or inert gas) and the value of D in this case is min imal :

D = eeo E ~ eoE.

Below we examine the possibili ty of raising the sensitivity of e lec t rodynamic modulated transducers by rais- ing e lec t r ic induction D. This problem becomes par t icular ly important in designing instruments for measuring con-

stant e lec t r ic fields in a confined space. In such a case surface S of the operat ing electrodes must be as smal l as possible, and the raising of the instrument's sensitivity by increasing the oscil lations frequency of surface S or of the value of D t is l imited by design possibilities.

It is possible to raise the e lec t r ic induction by fi l l ing the working space of the converter modulators with a d ie lec t r ic which has a high re la t ive permit t iv i ty ~, for instance, with a nonIinear ferroelectr ic ma te r i a l (e = 10,000- 100,000). However, the sensitivity of such a transducer, owing to depolar izat ion, wil l not rise proportionately to s [2]. The use of electrets in e lec t rodynamic transducers is also expedient, because mechan ica l modulat ion of capaci tance is then substituted by e lec t r i ca l modulat ion, i .e . , such a transducer has no moving parts.

Research has shown [3] that the largest sensitivity is possessed by different ial (balanced) transducers (Fig. 1).

In this circui t depolar iza t ion is decreased by using two e lec t re t plates which have a much larger extension in the direct ion of the measured e lec t r ic f ie ld 's lines of force than in the transverse direction. Owing to the special positioning of the transducer's electrodes, the measured field is superposed upon the exci ta t ion field longitudinally along the entire length of the electrets .

Figure 2a shows curves of the relationship of the electrets ' polar izat ion and dynamic permit t iv i ty ~ = d D ~ /

dE ~ to the exci ta t ion field strength E ~. When an e lec t re t is exci ted by a field of E = Emsinut (Fig. 2b), its dynam- ic permit t iv i ty varies with t ime at a double frequency 2:o (Fig. 2c).

L

r

Relationship ~ (t) can be represented in the form

Fig. 1

Go

= ~av+ ~ e~n cos ~n~t, (1) r t=[

where n are integers.

When the above balanced transducer's circuit is symmetr i - ca l and the measured constant field is not applied, an even

Translated from Izmer i t e l ' naya Tekhnika, No. t0, pp. 46-48, October, 1967. Original ar t ic le submitted August 12, 1966.

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Em] I-7"--

/ OC

&r

_ I ! u ! , i v t , _ ] 6 EL- O~ ~ Zr~t

C

~at

Fig. 2

harmonics' current in the circuit of load r is not induced. How-

ever, as soon as the measured field E 0 appears, the polarization of the electrets along their asymmetrical polarization curve pro-

duces in the load circuit current izn, which comprises the even harmonic frequencies of the excitat ion field. The amplitude of the measured field. Any even harmonic can be used for measur- ing electr ical field E 0 and, therefore, let us write a general ex-

pression for the load current comprising all the even harmonics.

Assuming E 0 << E m, we find that in a differential modula- tor circuit (see Fig. 1) the current generated by the transducer is equal to

dD de i = S --~- = 2SEo �9 (2)

By substituting in (2) for e its value from (1) we obtain

co

i2n =- - - 4So~Eo E neon sin 2no~t. (3) t l = 1

It will be seen that the current consists only of even har- monics. For any even harmonic (n = k) the amplitude value of the current is

I2k := 4kSo)Eoe2k. (4)

In the theory of modulators with a nonlinear capaci tance the polarization curve DN (EN) can be approxi-

mated by a broken line. Then the variations of e with t ime can be represented by a rectangular pulses of height Sm and width 2 a (See Fig. 2c):

Es cz = arc sin - - (5)

Em

where E s is the strength of the saturation field.

o u r c a s e

90

e = e m (o~ @ ~ ~ - sin 2mz cos2not .

n ~ I

By comparing (6) with (1) we obtain

Having applied this value to (5) we find

(6)

~Ern e2n = - - �9 sin 2na. (7)

g n

8 12k = - - Coem SEo sin 7k~x. (8)

It will be seen from (8) that the current of any even harmonics depends essentially on angle a which is deter-

mined by the relationship of the saturated field strength E s to the amplitude of the excitat ion field strength Em.

The sensitivity of a transducer modulator with a nonlinear capacitance is determined by relationship

dI2k (9) G i - dEo

By substituting in (9) for I~k its value from (8) we obtain

G2k = 8~(oSemsin 2ko~. (10)

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Fig. 3

Hence the opt imum exci ta t ion field strength for any even harmonic is equal to

Es Em~ t - sin r~14~

(11)

and the maximum sensitivity is

8 (oSem. 0 2 ) G~kma x = - ~

A model of a device for measuring e lec t r ic field strength by means of a transducer with an e lect re t was made and tested out in the e lec t r i c field measurements ' trade laboratory of the Kaunas Polytechnical Institute. The in- strument's b lock-schemat ic (Fig. 3) contains a different ia l e lec t re t transducer 1 (see Fig. 1) which is excited by sin- usoidal oscil lator 4. In measuring a constant e lec t r ic f ield, the transducer provides at its output a signal comprising even harmonics of the exci ta t ion field, whose second harmonic is picked out and amplif ied by band-pass amplif ier 2. The direct ion of the f ield is found by phase detector 3. The value of the measured field is registered by measur-

ing instrument 5.

The plates transducer's e lee t re t are made of a temperature-s table ferroelectr ic ma te r i a l which is used in type VK4-3 varicaps. The la te ra l surfaces of the plates carry at a minimum distance from each other the exci ta t ion electrodes. The transducer's exci ta t ion frequency is 1000 Hz.

The transducer is screened from external e lec t r ic fields by placing it inside a meta l tube and connecting it

through a screened cable to its amplif ier . The instrument can measure the value and determine the direct ion of a field in the range of i (1-10) k V / c m . The instrument's sensitivity in the range of i 1 k V / c m amounts to :~40 V / cm/d iv . The area of the transducer's measuring surface is S ~ 0.3 cm 2.

Investigations of the transducer 's s tabi l i ty have shown that, as in similar magnet ic modulators, there is a zero- signal drift mainly due to the d ie lec t r ic lag. The zero drift decreases gradually and in 15 sec it returns to normal. The residual zero drift expressed by a quantity measured in field strength units E k can be reduced considerably by using a compensat ion measuring method, and by select ing plates of appropriate dimensions with a smal ler coercive force, as wel l as a suitable exci ta t ion voltage.

The above-ment ioned investigation of a laboratory model has shown that i t is possible, by ut i l iz ing the non-

l inear capaci tance of electrets in transducer modulators, to produce very sensitive and fairly stable instruments for measuring constant e lec t r ic field strength in a confined space. The sensitivity of such an instrument is on a par with vibrat ing capaci tor instruments. However, the stabil i ty and precision of the above instrument (zero drift) were found to be unsatisfactory, thus making further study necessary.

1.

2. 3.

L I T E R A T U R E C I T E D

I. M. Imyanitov, Instruments and Methods for Measuring Atmospheric Electrici ty [in Russian] (1957).

H. W. Katz, Sol id-State Magnetic and Dielect r ic Devices, New York (1959). R. V. Khomskis, In coll . : Works of the Higher Educational Institutions of the Lithuanian SSR, Electronics and Mechanics (1963).

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