Toward the Study of Dielectrics Using a Q Meter

M. D. Lavrov

(Presented by Corresponding Member of the Academy of Sciences of the USSR V. D. Kuznetsov)

The Q meter is widely used for quality control of dielectrics. Owing to its ease of operation and the comparatively rapid obtaining of final results, the Q meter is rightly regarded as a shop-floor instrument. However, a number of shortcomings limit the laboratory use of the Q meter [1, 2].

Instability of the power sources, a high harmonic coefficient of the generator, instability of the generator frequency, scatter in the parameters of the voltmeter tubes, inaccuracy of calibration, and the presence of parallax in readings lead to a rather high error of the instrument, which increases noticeably at high frequencies. All this limits the use of the Q meter for measuring small angles of dielectric loss on the order of \(10^{-4}\) radians.

In this connection, the task was set of improving the possibility of using a production-model Q meter of type KV-1 for measuring the frequency and temperature dependences of \(\operatorname{tg}\delta\) and \(\varepsilon\) of dielectrics.

Proceeding from an analysis of the sources of error of the Q meter given by a number of authors [1, 2, 3], improvements were made to a type KV-1 Q meter that made it possible to carry out sufficiently reliable measurements of \(\operatorname{tg}\delta \simeq 10^{-4}\) in the frequency range from \(10^5\) to \(2 \cdot 10^7\) Hz; the possibility was obtained of recording temperature dependences up to \(300^\circ\text{C}\); and conditions were established under which the smallest scatter in the readings of the instrument is obtained.

A major role in increasing the accuracy of measurements is played by the stability of the Q meter supply. Since the KV-1 instrument lacks any voltage stabilization, the instrument must be powered from an external stabilizer; this requirement is mandatory. Good results are obtained by using an electronic alternating-voltage stabilizer of the “PR” type from the “Orekh” installation, which provides a sufficiently well stabilized alternating voltage when the mains voltage varies by \(\pm 10\%\). The use of ferroresonant stabilizers does not give satisfactory results.

The microammeter of the tube voltmeter used in the KV-1 instrument is very coarse. Suffice it to say that its calibration in \(Q\) has a scale division value of 5 units. This means that with the instrument one can reliably measure specimens giving a change in the Q of the measuring—

of the circuit by five times or more. If the capacitance of the specimen is chosen to be on the order of 25 pF and the measurement frequency such that the initial capacitance does not exceed 100 pF (optimal measurement conditions), and if it is assumed that the quality factor of the circuit is then on the order of 200, it turns out that \(\operatorname{tg}\delta \simeq 5 \cdot 10^{-4}\). The random error of the measurements [4] will be about 75%, with the error in reading \(\Delta Q\) amounting to 68%.

To increase the accuracy of reading \(\Delta Q\), a microammeter of the LM type for 75 \(\mu\)A was introduced into the circuit (Fig. 1). Structurally, the instrument was made as a remote unit. A toggle switch \(b\) and terminals \(B\) were brought out to the front panel of the Q meter; the remote instrument \(A\) was connected to these terminals. The scale of the instrument was graduated in \(Q\) with an upper limit of 250, as in the existing instrument. Owing to the larger scale dimensions, the scale division of the remote instrument was one unit (instead of 5), and the mirrored scale plate made it possible to eliminate parallax in reading and to increase the reading accuracy to 0.25 of a scale division. If the preceding data are now used, the measurement error will be \(\sim 15\%\).

Fig. 1. Circuit for connecting the remote instrument. The additional circuits and components are shown by the heavy line.

If, however, it is assumed that in the example we have chosen the difference \(Q_1 - Q_2 = 1\), which corresponds to the sensitivity of the setup, it turns out that

\[ \operatorname{tg}\delta = 10^{-4} \quad \text{and} \quad \frac{\Delta(\operatorname{tg}\delta)}{\operatorname{tg}\delta} = 55\%. \]

To obtain frequency and temperature characteristics, a special holder was made, consisting of two symmetrical capacitors fastened to a quartz tube (Fig. 2). Before measurement the holders were balanced, i.e., the initial capacitances \(C'_d\) and \(C''_d\) of the left and right holders were equalized by relative displacement of the supporting clips (3) and (2).

After balancing, the specimen under measurement is inserted into the right-hand capacitor, and a gap \(d\), equal to the thickness of the specimen, is established between the plates of the left-hand capacitor. The electrode diameters of both capacitors are equal. The electrodes of the right-hand capacitor were made cup-shaped and were filled with mercury for operation at room temperature, or with Wood’s alloy for operation at elevated temperatures. \(Q_1\) was measured with the left-hand capacitor connected (air), and \(Q_2\) with the right-hand capacitor connected (with the specimen). Taking the geometrical capacitances of the right- and left-hand capacitors to be equal, one can find the capacitance of the specimen \(C_x\) as the difference in the capacitance readings on the Q meter, and calculate \(\operatorname{tg}\delta\) of the specimen. Since this operation is repeated at each frequency point, the frequency dependence of the holder is eliminated. At the very least, the error due to the influence of the holder is considerably smaller than the error of the instrument.

When measuring the temperature dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\), a quartz cup with an electric heater sealed into its bottom was placed over the capacitor with the specimen. To account for the influence of the holders, the dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\) of the right-hand capacitor with an air dielectric was measured. This dependence was taken into account in studying the dielectric.

Fig. 2. Construction of the holder.

1. Front post. 2. Measuring capacitor with the dielectric under study, \(C_d''\). 3. Standard air capacitor, \(C_d'\). 4. Rear post with micrometer heads. 5. Thick-walled quartz tube.

Analysis of the frequency dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\), obtained for micalex, steatite ceramic M-4, and mica (Fig. 3), showed that the accuracy of the instrument is not the same as the frequency changes. At the beginning of each range, when the capacitance of the Q meter is large (400–200 pF) and \(\Delta Q\) is small (\(\sim 1 \div 2\)), the scatter of the values of \(\operatorname{tg}\delta\) is greatest. As the capacitance of the Q meter decreases (\(C \le 150 \div 100\) pF), \(\Delta Q\) increases to several units and the scatter of the values of \(\operatorname{tg}\delta\) becomes small.

Fig. 3. Frequency dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\).
\(o\)—micalex, \(x\)—ceramic M-4, \(\Delta\)—muscovite mica.

It is seen from Fig. 3 that, if at the beginning of each frequency range the scatter of measurements reaches 10% for \(\varepsilon\) and 30–50% for \(\operatorname{tg}\delta\), then at the end of the range the scatter does not exceed 3% for \(\varepsilon\) and 10% for \(\operatorname{tg}\delta\). This is apparently explained by two causes. First, by the high harmonic coefficient of the generator at the beginning of the range [2]. Second, by the fact that \(\Delta Q\) is measured as the difference of two large quantities (\(Q \simeq 200\), \(\Delta Q \simeq 2\)). Therefore the relative error in reading \(\Delta Q\) decreases toward the end of the range.

The same may be said about the error in measuring \(\varepsilon\). Since \(\varepsilon\) is proportional to the capacitance of the specimen \(\Delta C = C_1 - C_2\), then at the beginning of the range, with large capacitances \(C_1\) and \(C_2\) and small \(\Delta C\), the relative error in measuring \(\varepsilon\) is greater than at the end, where \(C_1\) becomes comparable with \(\Delta C\). In addition, in the calculation an error of the order of 1% is introduced owing to measurement of the geometrical dimensions of the specimen. From above, the frequency range is limited by the fact that, beginning with a frequency of \(10\) MHz, the Q meter begins to operate unstably, and when working with a sensitive external instrument the tuning of the resonance is extremely difficult. The limiting frequency of measurement is the lower, the smaller the losses in the specimen.

Specimens with \(\operatorname{tg}\delta \simeq 5 \cdot 10^{-3}\) were successfully measured at a frequency of \(2 \cdot 10^{7}\) Hz. Proceeding from all that has been set forth, in measuring the temperature dependences of \(\operatorname{tg}\delta\) and \(\varepsilon\), the dimensions of the specimen and the generator frequency were chosen so that the initial capacitance \(C_1\) would be as small as possible. The capacitance of different specimens was chosen within the limits \(15 \div 80\) pF; therefore it was possible to choose \(C_1 \simeq 100\) pF at a frequency of \(10^{6}\) Hz. This frequency was, moreover, also chosen for the convenience of comparison with measurement results obtained on other installations.

Figure 4 presents the temperature dependence for fused quartz. Curve 1 was obtained on a resonance installation by the method

substitution [5]. Curve 2 was obtained on a Q meter. Since the losses in quartz are small, it is necessary to take into account the losses in the holder [3].

Figure 5 gives the dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\) on temperature for micalex. The results obtained on the Q meter (curve 2) agree well with the data of Bogoroditskii and Fridberg [6] (curve 1). Similar results were obtained for mica and ceramics. The discrepancy between the absolute values obtained by different methods is evidently explained by systematic errors of the setups.

On the basis of the data presented, it may be concluded that the results obtained on the Q meter after the improvements made coincide with the results of measurements by other methods. The measurement error at a value \(\operatorname{tg}\delta \sim 10^{-4}\) does not exceed the error of other methods, and with the proper choice of the specimen capacitance \(\Delta C\), the initial capacitance of the Q meter \(C_1\), and the frequency, it can be considerably smaller.

Fig. 4. Temperature dependence for fused quartz.
1. Substitution method. 2. Q meter with allowance for the holder correction.

In conclusion it should be noted that the low-resistance energy injection into the measuring circuit used in the KV-1 Q meter does not make it possible to obtain a higher accuracy of measurements. This is due to the fact that the assumed proportionality of the injected voltage to the current flowing through the small injection resistance \(r\) will hold only if \(r\) is completely nonreactive. In reality, the reactance of the injection resistance leads to a dependence of \(r\) on frequency.

Fig. 5. Temperature dependence for micalex.
1. According to Bogoroditskii and Fridberg. 2. Measured on the improved Q meter.

With an increase in the frequency and in the harmonic coefficient of the generator, the injection voltage at unchanged current does not remain unchanged and, consequently, the accuracy of calibration of the \(Q\) scale is impaired.

This is one of the principal sources of errors. It can be eliminated only by switching to other injection methods and by directly measuring the injection voltage with a tube voltmeter. To reduce the harmonic coefficient and increase stability, it is advisable to construct the generator with a powerful buffer stage and a low-power master oscillator.

In addition, it is necessary to eliminate parallax when taking readings from the Q-meter scales and to improve the accuracy of calibration.

REFERENCES

1. Bigs A. J., Hovldin J. E. Measurement of total resistances with a Q-meter. P.I.R.E., vol. 3, No. 12, 1949.

2. Trokhal’skii A. A. Development of a method and apparatus for testing a Q-meter. Technical report. State Institute of Measures and Measuring Instruments, Novosibirsk, 1956.

3. Shelyubskii V. I., Indenbom V. L. Use of a Q-meter for measuring capacitance, dielectric permittivity, and dielectric losses at high frequency. Zavodskaia Laboratoriia, No. 6, p. 713, 1954.

4. Skanavi G. I. Dielectric losses and polarization in glasses and ceramic materials with high dielectric permittivity. Gosenergoizdat, 1952.

5. Vodop’ianov K. A. and Ivlev V. F. Improvement of the substitution method for measuring small dielectric-loss angles, ZhTF 8, 1521, 1938.

6. Bogoroditskii N. P. and Fridberg I. D. High-frequency inorganic dielectrics. Sov. Radio, 1948.