Proceedings
of the Tomsk Order of the Red Banner of Labor Polytechnic
Institute named after S. M. Kirov

Volume 171 1969

REFERENCE SOURCE OF CALIBRATED AC VOLTAGE GK-4

M. S. Roitman, Yu. M. Fomichev, E. I. Tsimbalist

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

The absence in the country of highly necessary alternating-current apparatus*) prompted the authors of the present article to attempt to develop an installation for checking AC-voltage meters. As a result, the GK-3 generator-calibrator was created [1, 2]. Further studies carried out by the authors made it possible to simplify the GK-3 generator and, at the same time, substantially improve its metrological characteristics.

The functional and schematic diagrams of the improved model of the GK-4 generator-calibrator are shown in Fig. 1 and Fig. 2.

The purpose of modifying the generator was to improve the following technical and operational characteristics:

1. Reduction of the magnitude of the low-frequency error in setting the output voltage to \(\pm 0.05\%\) at the lower boundary of the frequency range \((20\ \text{Hz})\).

2. Obtaining the output-voltage level in the form of an integer value \((9\ \text{V})\) instead of the previously used fractional-rational value \((9.2860\ \text{V})\), which created certain inconveniences in operation.

3. Reduction of the nonlinear-distortion coefficient of the output voltage while sharply simplifying the power-amplifier circuit.

4. Introduction of a simplified DC potentiometer, which made it possible to operate the instrument without an external DC potentiometric installation.

In addition to the above, the feedback system for setting and calibrating the output-voltage level, a number of other functional units of the instrument, and its mechanical design were modernized (Fig. 3).

The GK-4 generator-calibrator is a system for automatic regulation of the output-voltage level \(U_2\), the measuring element of which is a differential comparator based on photoelectric converters \((FP_3\) and \(FP_4)\). The value \(U_2\) is determined by the voltage of a reference DC source (ORDS) \((D_1, R_{108} \div R_{110}, R_{117}, R_{118})\), which is periodically checked and set equal to \(9\ \text{V}\) by means of the built-in DC potentiometer (DCP) and a standard cell (SC).

*) At the All-Union Scientific Research Institute of Metrology and Measurement Engineering there is an installation suitable for checking class 0.2 voltmeters. However, it is unique and exists in a single specimen.

Fig. 1.

Fig. 2.

Visible labels in the schematic:

• \(+300\ \mathrm{V}\)
• \(Л_3,\ Л_4\)
• \(Л_2\)
• \(Л_1\)
• Set \(\sim 98\)
• Coarse
• Medium
• Fine
• Coarse
• Fine
• \(-9\ \mathrm{V}\)
• \(-1\ \mathrm{V}\)
• \(-0.18\ \mathrm{V}\)
• \(\sim 6.3\ \mathrm{V}\)
• \(Л_1,\ Л_2,\ Л_3,\ Л_4\)
• Galvanometer
• Standard cell
• \(+\)
• \(-\)

The AC voltage from the setting generator ($L_1$ and $L_2$), stabilized by the thermistor $R_{\mathrm{t}}$, is applied to the power amplifier $K_1(L_3, L_4)$ through a controlled divider assembled on FP$_1$ and FP$_2$, whose transmission coefficient is determined by the amplified mismatch signal of the comparator. The use in the setting generator, as a nonlinear inertial element, of a TP 6/2 thermistor instead of low-power incandescent lamps is due to the desire to reduce nonlinear distortion of the generator in the low-frequency region.

Fig. 3.

A detailed study of various power amplifiers showed that a push-pull amplifier with series anode supply, while very simple, at the same time has very high metrological characteristics. The zero indicator of the GK-4 is an M26 microammeter connected at the output of the phase detector of the mismatch amplifier $K_2(\mathrm{PT}_1 \div \mathrm{PT}_8)$; it makes it possible to set the required value of the output voltage and to monitor its instability.

The GK-3 and GK-4 generators are, as already indicated, static automatic-control systems $I_2$. The static error is determined by the instabilities of the links and by the loop gain (the gain coefficient along the feedback loop). Obtaining large feedback depths presents great difficulties, since it is associated with a possible loss of stability. Therefore, a small static error must be achieved by taking measures to stabilize the generator links and by using two or more local feedback loops. It is precisely this approach that is used in the GK-4. The potential stability of the generator and its other characteristics in this case are determined by the metrological characteristics of the comparator based on FP and by the standard voltage measure [1].

In this connection it is of interest to estimate the possibilities for reducing the error in setting the output voltage at the lower frequencies.

It is known that for any electrothermal converter that is the main component of the comparator, including FP$_1$, which integrates the instantaneous values of the measured voltage, the comparison error increases as the frequency decreases because of the finite values of the time constants of the FP elements. A decrease in the voltage frequency leads to a change in the output quantity of the measuring transducer—the resistance of the photoresistor $R_{\phi\text{-sr}}$—relative to its value at direct current. This change occurs as a result of a change in the average temperature of the filament of the incandescent lamp,

and, consequently, also of the luminous flux, as well as due to the influence of pulsations of the luminous flux on the photoresistor.

Earlier, in [3], approximate relationships were derived for calculating the comparison error in the low-frequency region, under the condition that the photoresistor of the FP is inertia-free. A more detailed consideration of this error makes it possible to express it in the following form:

\[ \gamma_{f\mathrm{n}}= \frac{d_2(2\beta-1)}{d_1(n+1)} \left(\delta_0-\frac{\delta_1}{2}\cos\varphi_{\mathrm{l}}\right) + \frac{d_2}{d_1}\cdot \frac{K_1/(n+1)^2} {4[1+(2\omega\tau_{\mathrm{l}})^2]\,[1+(2\omega\tau_{\mathrm{f}})^2]} \tag{1} \]

where

\[ \delta_0=\frac{\alpha^2(2\beta-1)} {8\varkappa[1+(2\omega\tau_{\mathrm{l}})^2]}; \qquad \delta_1=\frac{\alpha} {4\varkappa\sqrt{1+(2\omega\tau_{\mathrm{l}})^2}}, \]

\[ \alpha=1,\,2 \]

is the nonlinearity exponent of the function \(R_{\mathrm{l}}=AT^\alpha\);

\[ n=1.8 \]

is the degree of nonlinearity of the current-voltage characteristic of the incandescent lamp;

\[ \beta=\frac{R_{\mathrm{l}}}{R+R_{\mathrm{l}}}; \qquad \varkappa=1+\frac{\alpha}{4}(2\beta-1); \qquad d_1=1+\frac{R}{R_{\mathrm{l}}}; \qquad d_2=n+\frac{R}{R_{\mathrm{l}}} \]

are coefficients determined by the mode of connecting the lamp into the circuit;

\(K_1\) is the relative current transfer coefficient of the FP;

\(\tau_{\mathrm{l}}, \tau_{\mathrm{f}}\) are, respectively, the time constants of the incandescent lamp and of the photoresistor;

\(R\) is the added resistance in the lamp circuit.

The first term of expression (1) gives the component of the error caused by the influence of the nonlinearity of the characteristic of the incandescent lamp; the second gives the component of the error introduced by the photoresistor. Consideration of (1) shows that, for \(\beta \ne 1/2\), the most effective way of reducing the low-frequency error is to increase the time constants of the FP elements, especially of the incandescent lamp. The latter is increased by using lamps with increased values of the rated current (with an increase in the mass of the lamp filament) and by reducing the operating current relative to the rated value.

These requirements made it necessary to abandon the NSM6, 3×20 VN-2 lamps used in the GK-3 and to use lamps with an operating current

\[ I=20\ \mathrm{mA}\ll I_{\mathrm{nom}}^{*}). \]

Calculation of the low-frequency error and its subsequent experimental determination showed that, when such lamps are used, the problem of reducing the error at low frequencies is solved completely.

The circuit for obtaining the OIN voltage, equal to 9 V, and the circuit of the simplified potentiometer are implemented in the usual manner (Fig. 2) and require no explanation.

Verification of the principal quality indicators of the GK-4 generator-calibrator was carried out using standard instruments of the D. I. Mendeleev VNIIM.

The following technical characteristics of the generator were subjected to experimental investigation:

1. Instability of the generator’s constant OIN voltage.
2. Time instability of the generator’s output alternating voltage in the operating frequency range.

\[ \overline{\phantom{xxxxxxxx}} \]

*) In (3) it was shown that the use of NSM 9.0×60 VN-2 lamps makes it possible to obtain a low-frequency comparison error on the order of 0.05%, beginning with frequencies greater than 20 Hz. However, the presence of a supporting traverse in the lamps sharply increases the instability of their resistance under vibration; therefore experimental lamps without traverses were used, with characteristics approximately analogous to those of the NSM 9.0×60 VN-2.

1. Sensitivity of the zero indicator of the GK-4 comparator.
2. Error in comparing the output voltage of the generator with the voltage of the RVS.
3. Coefficient of nonlinear distortion of the generator.

The temporal instability of the GK-4 output voltage was determined with the mode selector switch in the “Output” position, using the VNIIM thermoelectric comparator. The effect of instability of the comparator itself and of the auxiliary equipment was reduced by preheating them for 3–4 hours.

The magnitude of the generator-voltage instability was determined from the deviation of the emf of the thermoelectric comparator. The block diagram of the experiment is shown in Fig. 4, a; the results are given in the Appendix.

The experimental determination of the sensitivity of the GK-4 zero indicator was carried out on alternating current. In this case the source of stable alternating voltage was the GK-4 generator itself, and the magnitude of the alternating-voltage deviation corresponding to $\alpha$ divisions of the indicator was determined by measuring this voltage with a thermoelectric comparator (the block diagram of the measurements is shown in Fig. 4, b).

In addition to the above, the sensitivity of the GK-4 zero indicator was determined on direct current (a direct voltage from an auxiliary source was applied to the lamp circuit).

The measurements performed showed that the scale value of the indicator was identical on direct and alternating currents.

The error in setting the generator output voltage ($\sim 9$ V) was determined using a measuring setup,

Fig. 4.

T — VNIIM thermal unit
R309 — direct-current potentiometer, No. 000001, class 0.005.
F305 — photoamplifier, No. 000217.
R35 — divider, No. 000035, class 0.005.
P136 — No. 73.

the block diagram of which is shown in Fig. 4, b. The measurement procedure consisted of the following:

1. The output voltage was set according to the generator zero indicator with the thermal unit connected.
2. The value of the converter thermoelectric emf was recorded.
3. A direct voltage from an auxiliary source was applied to the thermoelectric converter, and by changing it the previous value of the thermoelectric emf was restored.
4. The voltage magnitude was measured with a direct-current potentiometer.

The magnitude of the error in setting voltage \(U_2\) was calculated from the formula

\[ \delta=\frac{U_{01}-U_{02}}{U_{01}}, \]

where \(U_{01}\) is the voltage of the ZIN of the GK-4 generator,
\(U_{02}\) is the voltage of the auxiliary source.

It should be noted that the error obtained somewhat exceeds the error in setting the value of voltage \(U_2\) of the GK-4 comparator, since it includes the error of the standard comparator.

Results of Verification

1. The error in setting the dc voltage of the reference source, equal to 9 V, by means of the simplified potentiometer does not exceed \(\pm 0.01\%\). The instability of the reference source is \(\pm 0.02\%\) per day.

2. The instability of the generator ac voltage, when it is loaded with a current of 10 mA in the frequency range 20 Hz–100 kHz, is less than \(\pm 0.01\%\) per minute and not more than \(\pm(0.02\text{–}0.03)\%\) over 10–15 min.

3. The sensitivity threshold of the generator null indicator is 0.005%.

4. The value of the generator output voltage (at the terminals \(\sim 9\) V) differs from the value of the dc voltage of the reference source (9 V) by not more than \(\pm 0.03\%\) in the frequency range 55 Hz–100 kHz and by not more than \(-0.05\%\) at a frequency of 20 Hz.

5. The value of the generator output voltage (at the terminals \(\sim 1\) V), when a load with an output resistance of not less than 500 kΩ and an input capacitance of not more than 100 pF is connected, differs from the indicated value by not more than \(\pm 0.2\%\) in the frequency range 20 Hz–100 kHz.

6. The values of the generator output voltage (at the terminals \(\sim 0.1\) V), when a load with an output resistance of not less than 100 kΩ and an input capacitance of not more than 200 pF is connected, differ from the indicated value by not more than \(\pm 0.2\%\) in the frequency range 20 Hz–100 kHz.

7. The coefficient of nonlinear distortion of the output signal does not exceed the values given in the table.

Table

GK-4 Standard Source of Calibrated AC Voltage

The coefficient of nonlinear distortion of the generator is determined from the formula:

\[ K_\Gamma=\sqrt{K_{\Gamma 2}^{2}+K_{\Gamma 3}^{2}}, \]

where \(K_{\Gamma 2} = \dfrac{U_2}{U_1}\); \(K_{\Gamma 3} = \dfrac{U_3}{U_1}\) are the coefficients of the 2nd and 3rd harmonics;

\(U_1\); \(U_2\); \(U_3\) are the voltages of the first, second, and third harmonics of the generator output signal.

The results of verification of the GK-4 generator show that the latter can be used for the certification of electronic voltmeters of accuracy class 0.1–0.2 (\(U_2 = 9\ \text{V}\)) in the frequency range from 20 Hz to 100 kHz.

The authors thank Doctor of Technical Sciences T. B. Rozhdestvenskaya and the staff of the electrical-measurements laboratory of the D. I. Mendeleev All-Union Scientific Research Institute of Metrology for the opportunity provided to verify the characteristics of the GK-4 and for their assistance in the work.

REFERENCES

1. M. S. Roitman, E. I. Tsimbalist, Yu. M. Fomichev. A reference source of alternating voltage. Proceedings of the VIII All-Union Conference on Automatic Monitoring and Methods of Electrical Measurements, Novosibirsk, (in press).

2. M. S. Roitman, E. I. Tsimbalist, Yu. M. Fomichev. Device for obtaining a stable sinusoidal voltage calibrated by rms value. Decision on granting an inventor’s certificate for application 1048212/26-9 of 4/I-1966, (in press).

3. B. A. Perminov, M. S. Roitman, E. I. Tsimbalist. An alternating-current comparator using photoelectric converters. Avtometriya, No. 5, 1965.