High-Frequency Reference Generator-Calibrator
Abstract Generated abstract
The paper describes the design and evaluation of a GK-5 high-frequency standard generator-calibrator intended for verification of digital AC measuring instruments requiring higher accuracy than existing calibrators provided. Its main technical approach is to combine amplitude stabilization and voltage calibration in a single automatic system, using a differential comparator to compare the generator’s effective AC output voltage with a DC reference and to correct deviations through a controlled divider. The authors analyze output-voltage instability, setting error, frequency error, and comparator asymmetry, and derive stabilization coefficients for the principal circuit elements. Tests report ten fixed frequencies from 100 kHz to 10 MHz, nonlinear distortion of about 0.10 percent, short-term voltage instability not exceeding 0.01 percent per minute, and 9 V rms setting errors of ±0.05 percent up to 1 MHz and no more than ±0.5 percent at higher frequencies.
Full Text
HIGH-FREQUENCY STANDARD GENERATOR-CALIBRATOR
M. S. ROITMAN, E. I. TSIMBALIST, Yu. M. FOMICHEV
(Presented by the scientific-technical seminar of the Department of Radio Engineering)
Verification of digital measuring instruments, whose measurement error on alternating current is \(0.2 \div 0.5\%\), requires verification equipment with a basic error of no more than \(0.05\%\). The equipment in use, intended for the verification and calibration of electronic voltmeters, such as V 1-2—V 1-4 and others, has in a number of cases already exhausted its capabilities and does not provide the required accuracy.
When creating a new verification installation, it is necessary to solve the following tasks:
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To ensure an increase in the accuracy of measuring alternating voltage in the frequency range \(100\ \text{kHz} \div 10\ \text{MHz}\) and up to \(5 \cdot 10^{-4}—5 \cdot 10^{-3}\%\).
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To develop amplitude-stable generators with short-term instability of about \(\pm 0.01\%\) over \(1—3\ \text{min}\) and a resolution of output-voltage setting of about \(0.05\%\).
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To ensure a reduction in the coefficient of nonlinear distortion of the generator output voltage \((K_2 \leqslant 0.1 \div 0.2\%\) in the indicated frequency range).
The standard source of alternating voltage described in the present work satisfies the stated tasks to a significant degree.
Usually the problem of obtaining a stable generator output voltage and its calibration is separated. In the generator, various circuit solutions are used to increase the stability of the output voltage (linear and nonlinear feedback, automatic gain control, etc.), and then, with the aid of a comparator, this voltage is calibrated. Such a solution of the problem increases the instability of the calibrated voltage, since it includes both the instability of the comparator and the instability of the generator. These shortcomings are eliminated if the functions of stabilization and calibration of the generator voltage are combined. The functional diagram of such a generator-calibrator is shown in Fig. 1.
The output voltage from the master generator 1, the controlled divider 2, through the selective amplifier 3 and the power amplifier 4, is fed to the input of the differential comparator 5, to which are also applied a direct voltage from the reference source 6 and an alternating voltage from the auxiliary source 7. With the aid of the differential comparator, an accurate comparison is made of the effective value of the generator output voltage with the standard direct voltage.
Fig. 1
Fig. 2
In the event of a deviation of the output voltage from the set value (the value of the deviation is recorded by indicator 9), a mismatch signal will appear at the output of the comparator; through amplifier 8 this signal acts on controlled divider 2 and selects the deviation that has arisen.
The value of the reference voltage is set by means of precision potentiometer 10.
Evaluation of the quality characteristics of the generator
1. Instability of the output voltage. The magnitude of the instability of the output voltage of the GK-5 generator was evaluated on the basis of consideration of its expanded functional diagram (Fig. 1). The total instability of the amplitude of voltage \(U_2\) is equal to
\[ \frac{\Delta U_2}{U_2}=\sum_{i=1}^{k}\frac{1}{C_i}\left(\frac{\Delta H}{H}\right)_i, \]
\[ \left(\frac{\Delta H}{H}\right)_i \]
are the relative instabilities of the nodes and elements of the circuit,
\(C_i\) are the coefficients of amplitude stabilization, showing how many times smaller the relative changes of the amplitude of the stabilized voltage are than the relative instabilities causing them.
Let us determine the value of the stabilization coefficients of voltage \(U_2\), first opening the automatic-control system at points 1—1, and assigning an arbitrary value \(\dfrac{dU_2}{U_2}\) at the input of the photoelectric converter \((\mathrm{FP}_3)\), included in the alternating-current circuit. Then, going around the system along the contour, we obtain
\[ \frac{dR_{\phi3}}{R_{\phi3}}=-K_{i3}\cdot\frac{di_{i3}}{i_{i3}}, \tag{1} \]
\[ \frac{di_{i3}}{i_{i3}}=\frac{d_1}{d_2}\frac{dU_2}{U_2}, \tag{2} \]
\[ \frac{dU_6}{U_6}=\frac{U_8}{U_6}\cdot\frac{d_1\cdot d_3\cdot K_{i3}\cdot K_2}{d_2}\cdot\frac{dU_2}{U_2}, \tag{3} \]
\[ \frac{dR_{\phi1,2}}{R_{\phi1,2}}=\pm\frac{U_8}{U_6}\cdot\frac{d_1\cdot d_3\cdot d_4\cdot K_{i3}\cdot K_{i1,2}\cdot K_2}{d_2}\cdot\frac{dU_2}{U_2}, \tag{4} \]
\[ \frac{dK_q}{K_q}=(1-K_q)\left(\frac{dR_{\phi2}}{R_{\phi2}}-\frac{dR_{\phi1}}{R_{\phi1}}\right), \tag{5} \]
\[ \frac{dU_1}{U_1}=\frac{dK_q}{K_q}, \tag{6} \]
\[ C_{\mathrm{st}}=\frac{dU_1/U_1}{dU_2/U_2}=\frac{dK_q/K_q}{dU_2/U_2}= \]
\[ =(1-K_q)\frac{d_1\cdot d_3\cdot K_{i3}\cdot K_2}{d_2}\left[(\pm d_4K_{i2})-(\pm d_4K_{i1})\right]\cdot\frac{U_8}{U_6}. \tag{7} \]
In expressions (1)—(7) the following notation has been introduced:
Fig. 3.
\(K_{i1}, K_{i2}, K_{i3}\) are the relative current transfer coefficients of the photomultipliers PM\(_1\), PM\(_2\), PM\(_3\), respectively:
\[ d_1 = 1 + \frac{R_3}{R_{\mathrm{l}3}}; \qquad d_2 = n_3 + \frac{R_3}{R_{\mathrm{l}3}}; \]
\[ d_3 = \frac{R_{\phi 3}\cdot R_{\phi 4}}{(R_{\phi 3}+R_{\phi 4})^2}; \qquad d_4 = \frac{1}{n_{1,2}} \text{ are constant} \]
coefficients characterizing the operating modes of the PM;
\(R_{\mathrm{l}3}\) is the static resistance of the PM incandescent lamp at the operating point;
\(n_1, n_2, n_3\) are constant coefficients characterizing the degree of nonlinearity of the characteristics of the PM lamps;
\(K_2\) is the transfer coefficient of the feedback-circuit amplifier.
Using expressions (1)—(6), or analogous ones, together with (7), we determine the amplitude-stabilization coefficients \(C_i\) (Table).
Table
| No. | Stabilization coeff. | Formulas | Numerical values of the components | Magnitude |
|---|---|---|---|---|
| 1 | \(C_1\) | \(-\dfrac{d_1^2}{d_2}\) | \(d_1 = 3,\quad d_2 = 4\) | \(-\dfrac{9}{4}\) |
| 2 | \(C_2\) | \(-\dfrac{K_{i3}\cdot d_1\cdot d_5}{d_2\cdot K_{i4}}\) | \(d_1 = 3,\quad d_2 = 4,\quad d_5 = 3\) \(K_{i3}=5,\quad K_{i4}=5\) |
\(-\dfrac{9}{4}\) |
| 3 | \(C_3\) | \(\pm\dfrac{d_1}{d_2}\cdot K_{i3}\) | \(\pm\dfrac{15}{4}\) | |
| 4 | \(C_4\) | \(-\dfrac{K_{i3}\cdot d_1\cdot d_5}{d_2\cdot d_5\cdot K_{i4}}\) | \(d_5 = 4\) | \(-1\) |
Fig. 4.
Textual labels visible in the schematic:
- Frequency, MHz
- Instrument: coarse–fine
- coarse
- fine
- Output
- Table
- Switch
- \(U = 9\text{ V}\)
- \(U_{\mathrm{st}} = 0\)
- \(+300\text{ V}\)
- \(-300\text{ V}\)
- \(\sim 6.3\text{ V}\)
Component and terminal designations visible in the schematic include:
\(P_1, P_2, P_3, P_4, P_5, P_6\);
\(R_1\)–\(R_{45}\);
\(C_1, C_{10}, C_{11}, C_{20}, C_{21}, C_{22}, C_{24}, C_{25}, C_{26}, C_{27}, C_{28}, C_{29}, C_{30}, C_{31}, C_{32}\);
\(L_1, L'_1, L_{10}, L'_{10}, L_{11}, L_{20}, L'_{20}\);
\(\mathrm{Rp}_1, \mathrm{Rp}_2\);
\(\Pi_1, \Pi_2, \Pi_3, \Pi_4, \Pi_5, \Pi_6\).
Continuation of the table
| 1 | 2 | 3 | 5 | 4 |
|---|---|---|---|---|
| 5 | $C_5$ | $\dfrac{U_8}{U_3}\dfrac{d_1\cdot d_3\cdot K_{i3}}{d_2}$ | $U_8=10\ \mathrm{V},\ U'_3=1\ \mathrm{mV},\ d_3=\dfrac14$ | $10^3$ |
| 6 | $C_6$ | $\dfrac{U_8}{U_3}\dfrac{d_1\ d_3\cdot K_{i3}}{d_2}$ | $10^3$ | |
| 7 | $C_7$ | $\dfrac{U_8}{U'_8}\dfrac{K_2\cdot K_{i3}\cdot d_1\cdot d_3}{d_2}$ | $K_2=12,\quad U'_8=4$ | 28 |
| 8 | $C_8$ | $\pm\dfrac{U_8}{U_6}\dfrac{K_2\cdot K_{i3}\cdot d_1\cdot d_3\cdot d_4}{d_2}$ | $d_4=\dfrac12,\quad U_6=2$ | 28 |
| 9 | $C_9$ | $\pm\dfrac{U_8}{U_6}\dfrac{d_1\cdot d_3\cdot d_4\cdot K_{i3}\cdot K_{i1,2}\cdot K_2}{d_2}(1-K_q)$ | $K_{i1,2}=5,\quad K_{i3}=5$ | 60 |
| 10 | $C_{10}$ | $C_{10}=C_{\mathrm{st}}=(1-K_q)\dfrac{d_1\cdot d_3\cdot K_{i3}\cdot K_2}{d_2}\times$ $\times\dfrac{U_8}{U_6}\left[(\pm d_4K_{i2})-(\mp d_4K_{i1})\right]$ |
$K_q=\dfrac9{11},\quad U_6=2,\quad U_8=10$ $K_{i1}=5,\quad K_{i2}=5,\quad d_4=\dfrac12$ $d_1=3,\quad d_2=4,\quad d_3=\dfrac14$ |
60 |
| 11 | $C_{11}$ | $\dfrac{dU_7}{U_7}=-\dfrac14\alpha_{\mathrm{T}}$ | $\alpha_{\mathrm{T}}=\pm 2.5\%/10^\circ\mathrm{C}$ | $0.6\%$ |
| 12 | $C_{\mathrm{st}}$ | $C_{\mathrm{st}}=\dfrac{dU_1/U_1}{dU_2/U_{2(\mathrm{t.u.})}}$ | $\dfrac{dU_2}{U_{2(\mathrm{t.u.})}}=0.01\%$ | 60 |
An analysis of the stabilization coefficients shows that the principal instability of the output voltage will consist of the following components:
\[ \frac{dU_2}{U_2} = \frac{1}{C_1}\cdot\frac{dR_{\lambda3}}{R_{\lambda3}} - \frac{1}{C_2}\cdot\frac{dR_{\lambda4}}{R_{\lambda4}} + \frac{1}{C_3} \left( \frac{dR_{\phi3}}{R_{\phi3}} - \frac{dR_{\phi4}}{R_{\phi4}} \right) + \frac{1}{C_4}\cdot\frac{dU_0}{U_0}. \]
Using the data of the table, we obtain
\[ \frac{dU_2}{U_2} = \frac{4}{9} \left( \frac{dR_{\lambda4}}{R_{\lambda4}} - \frac{dR_{\lambda3}}{R_{\lambda3}} \right) + \frac{4}{15} \left( \frac{dR_{\phi3}}{R_{\phi3}} - \frac{dR_{\phi4}}{R_{\phi4}} \right) - \frac{dU_0}{U_0}. \]
From the last equation it is not difficult to see that, with completely identical characteristics of the instabilities of the elements FP$_3$ and FP$_4$ of the differential comparator, the instability of the output voltage is equal to the instability of the reference DC source. In this connection, constant-current filament lamps and photoresistors are selected. In the reference source a silicon stabilitron D 818 E with TKN $10^{-3}\%/\mathrm{deg}$ is used.
2. Error in setting the nominal value of the output voltage. The error in setting the value of the variable voltage by means of the comparator may be represented by the expression
where
\[ \gamma_u=\gamma_{0u}+\gamma_{fu}+\gamma_a, \]
$\gamma_{0u}$ is the error of changing the constant voltage, caused by the error of the compensator and by the insensitivity of the zero indicator of the compensator,
\(\gamma_{f u}\)—frequency error of comparison,
\(\gamma_a\)—error due to asymmetry.
A decrease in accuracy may also occur because of instability of the comparator elements and other factors. The appearance of a frequency error at high frequencies is caused by the presence of reactance in the comparator elements. The magnitude of the generator frequency error, without taking into account the error due to skin effect (lamp filament diameter \(\leq 5\,\mu\)), is determined by the expression
\[ \gamma_{f u}=1-\frac{U_2}{U_0} =1-\frac{Z'_{l3}\left(1+\frac{Z_3}{Z_{l3}}\right)}{R_3+R_{l3}}, \]
where
\(Z_3\)—modulus of the additional resistance in the lamp circuit, taking into account the shunting capacitance determined by the sum of the parasitic capacitances with respect to ground;
\(R_3\)—value of this resistance at direct current;
\(Z_{l3}\)—total resistance of the lamp filament, taking into account the parasitic capacitances shunting the filament;
\(Z'_{l3}\)—resistance of the filament to alternating current, without taking into account the shunting capacitances;
\(R_{l3}\)—resistance of the lamp filament to direct current.
In the limiting case when the photodiode amplifier operates without additional resistance in the lamp circuit \((R_3=0)\), the upper operating frequency of the converter will be determined from
\[ \omega_{\mathrm{v}}=\frac{R_l}{L}\sqrt{2(\gamma_{f u})_{\mathrm{adm}}}, \]
\(L\)—inductance of the lamp filament, which is calculated from the structural data of the lamp.
The error due to asymmetry [4] is difficult to estimate theoretically; however, it has been determined experimentally that this error can be less than \(0.01\%\). To obtain high accuracy in setting the generator output voltage, the generator provides for balancing of the comparator at direct current. This eliminates the influence of long-term instability of the comparator elements.
Test results of the GK-5 generator-calibrator
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The generator has 10 fixed frequencies: 100, 200, 500 kHz; 1, 2, 3, 5, 7, 8, 10 MHz.
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The coefficient of nonlinear distortion of the output voltage over the frequency range is \(0.10\%\).
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The instability of the generator alternating voltage (when loaded by a current of 10 mA) over the frequency range 100 kHz–10 MHz is no more than \(0.01\%\) per min and \(0.03\)–\(0.05\%\) over 5–10 min.
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The value of the generator output voltage, 9 V (rms value), is set with an error of \(\pm 0.05\%\) in the frequency range 100 kHz–1 MHz and no more than \(\pm 0.5\%\) in the remaining frequency range.
References
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M. S. Roitman, V. K. Zhukov. Application of photoresistors for voltage stabilization. Automatic Control and Methods of Electrical Measurements (Proceedings of the 2nd Conference). Publishing House of the Siberian Branch of the USSR Academy of Sciences, 1962.
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“New Scientific Research Works on Metrology,” No. 4. (Electrical Measurements). Standards Publishing House, Moscow, 1964.
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A. A. Lvovich. Amplitude-stable generators with automatic gain control. Radio Engineering, vol. 15, No. 4, 1960.
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T. B. Rozhdestvenskaya. Electrical Comparators for Precise Measurements of Current, Voltage, and Power. Standards Publishing House, 1964.
Fig. 1. Basic circuit diagram of the phase indicator.
ERRATA NOTED
| Page | Line | Printed | Should read |
|---|---|---|---|
| 3* | 18 from top | $10$ MHz and up to $5 \cdot 10^{-4}$ — $5 \cdot 10^{-3}\%$ | $10$ MHz up to $5 \cdot 10^{-4}$ — $5 \cdot 10^{-3}$ |
| 3 | 7 from bottom | $2$ | $3$ |
| 3 | 7 from bottom | $3$ | $2$ |
| 16 | 4 from bottom | Collection of papers of TIRiETa (in press) | Izvestiya TPI, vol. 171, 1968 |
| 30 | 5 from top | $T$ | $\mathrm{PT}_2$ |
| 31 | 5 from top | $r_{\Sigma}+$ | $r_{\Sigma}=$ |
| 34—35 | in all cases | $\Delta_f$ | $\Delta_{\varphi}$ |