REGULATING DEVICES BASED ON PHOTOELECTRIC CONVERTERS

Yu. M. FOMICHEV

(Presented by the scientific seminar of the Department of Radio Engineering)

One of the key elements in automatic control systems for calibrated-voltage sources is the regulating device (RD), which changes the amplitude of the output oscillations in accordance with the law of the control signal.

Devices suitable for carrying out this operation may be divided, according to the time required to perform it, into inertial and non-inertial devices, and, according to the connection between the input and control signals, into RDs with galvanic coupling and without galvanic coupling.

Among the modern arsenal of inertial electrically controlled elements, photoelectric converters (PCs) possess the best characteristics. PCs are characterized by a large transmission coefficient, the absence of galvanic coupling between the controlled and controlling circuits, the ability to operate in direct- and alternating-current circuits, good short-term and acceptable long-term stability, and comparatively low inertia.

The principal characteristics of light sources and photoresistors produced by domestic industry and suitable for constructing PCs are given in Tables 1 and 2.

Regulating devices based on PCs are constructed in the form of an electrically controlled divider. A light source is included in the control circuit, and a photoresistance in the controlled circuit (Fig. 1).

Fig. 1.

The principal characteristics that determine the possibility of using an RD in calibrated-voltage sources are the steepness of regulation and the distortions introduced by it into the fundamental signal. The characteristics of PCs on which the steepness of regulation depends have been considered in sufficient detail in [1, 2]. Here we shall dwell on the second, no less important, parameter of the RD. When an RD is constructed in the form of a controlled divider (Fig. 1), the appearance in the circuit of higher harmonic components and their amplitude will be determined by the properties of the pho-

Table 1

Continuation of Table 1

Table 2

The ratio \(R_T/R_{\mathrm{sv}}\) for photoresistors OS-4-681-010 was determined for an illumination of 100 lx.

thermoelectric transducer. The equation relating the photocurrent to the voltage and the luminous flux has the form [3]

\[ I_{\phi}=D\cdot U_{\phi}^{\gamma}\cdot \Phi^{\alpha}, \tag{1} \]

where \(D\) is a constant determined by the properties of the material and by the construction of the photoresistor, and \(\gamma\) and \(\alpha\) are the nonlinearity coefficients of the current-voltage and light characteristics.

Let us consider this expression in more detail. First assume \(\alpha=\gamma=1\); then the appearance of higher components in the photocurrent is possible only under the condition that the luminous flux is modulated with a frequency \(\Omega\) that is a multiple of the frequency of the applied voltage \((\omega)\). For example, if \(U_{\phi}=U\cos\omega t\), and \(\Phi=\Phi_{0}+\Phi_{m}\cos\Omega t\), then for \(\Omega=\omega\)

\[ I_{\phi}=\frac{1}{2}DU\Phi_{m}+DU\Phi_{0}\cos\omega t+\frac{1}{2}DU\Phi_{m}\cos 2\omega t, \]

i.e., a component with frequency \(2\omega\) appears in the photocurrent; for \(\Omega=2\omega\), one with frequency \(3\omega\), etc. Indeed, in broadband SIC this phenomenon is observed in the low-frequency region, when the operation of the filters in the control-signal circuit becomes less effective and the time constant of the converters is comparable with the period of the fundamental signal. In more detail, although taking into account only the nonlinearity of the light characteristic of the photoresistance, this question is considered in [2, 4].

At higher frequencies, modulation of the luminous flux will practically be absent, and one may take \(\Phi=\mathrm{const}\); then expression (1) is transformed into the equation of the current-voltage characteristic of the photoresistor:

\[ I_{\phi}=B\cdot U_{\phi}^{\gamma}, \]

where \(B=D\Phi^{\alpha}\).

The distortions introduced will then be determined by the nonlinearity exponent \(\gamma\).

Deviation of the current-voltage characteristic from linearity is observed in photoresistances in two regions: in the voltage region significantly below the operating voltage, because of non-ohmic contacts. In this region the greatest value, \(\gamma-2\), is reached for pressed cadmium-sulfide and cadmium-selenide resistances of the FSK, FSD type. The second case of deviation occurs at very high voltages, because of changes in the concentration or mobility of the current carriers. Here \(\gamma\) may take values \(0.2—0.4\) [4]. In film photoresistances, especially for types SF 2-2, SF 2-3, SF-2-5, this phenomenon is observed to a significantly lesser extent; nevertheless, with stringent requirements on the nonlinear distortions of the regulating device (in precision sources \(K_{\mathrm{g}}\leq 0.01 \div 0.03\%\)), the nonlinearity of the current-voltage characteristic of these photoresistors has to be taken into account, and in a number of cases special linearization measures must be adopted.

To analyze the nonlinear distortions of the regulating device on the phototransducer, we shall use a method based on investigating the degree of change of the instantaneous transmission coefficient under the action of the instantaneous voltage of the signal [5].

Using this method, let us find an expression for the coefficients of the harmonics of the output voltage of the regulating device constructed according to the circuit of Fig. 1.

In the analysis it is assumed that the luminous flux remains constant, \(\Phi=\mathrm{const}\), and that the fundamental-signal transmission circuit is inertia-free. The instantaneous transmission coefficient of the regulating device (Fig. 1) is determined by the following expression:

\[ K_{g}(U)=\frac{R_{2}R_{3}+R_{\phi}(U)(R_{2}+R_{3})}{R_{2}(R_{1}+R_{3})+R_{\phi}(U)(R_{1}+R_{2}+R_{3})}. \tag{2} \]

From expression (2) it is seen that the nonconstancy of the instantaneous transfer coefficient \(K_g(U)\) is due to the dependence, on the signal voltage, of the parameter \(R_\phi(U)\). At small voltages on the photoresistor, the dependence \(R_\phi(U)\) can be expanded in a Taylor series in powers of \(U_\phi\):

\[ R_\phi(U) = R_{\phi 0} + R'_\phi U_\phi + \frac{1}{2} R''_\phi U_\phi^2, \tag{3} \]

where \(R_{\phi 0}\) is the value of the photoresistance determined by the light flux;

\[ R'_\phi \]

is the first derivative at the point \(U_\phi = 0\);

\[ R''_\phi \]

is the second derivative at the same point.

Denoting the ratio of the voltage on the photoresistor \((U_\phi)\) to the output voltage \((U_2)\) by the insertion coefficient,

\[ K_{\mathrm{ins}} = \frac{U_\phi}{U_2} = \frac{R_{\phi 0}\cdot R_2}{R_2\cdot R_3 + R_{\phi 0}(R_2 + R_3)} \tag{4} \]

and carrying out transformations according to [5], we obtain

\[ K_{r2} = \frac{1}{4}(a - K_g b)\frac{R'_\phi}{R_{\phi 0}}\cdot \frac{1}{K_g}\cdot U_\phi; \tag{5} \]

\[ K_{r3} = \frac{1}{12} \left[ \frac{1}{2}(a - K_g b)\frac{R''_\phi}{R_{\phi 0}} + a(K_g a - b)\left(\frac{R'_\phi}{R_{\phi 0}}\right)^2 \right] \frac{1}{K_g} U_\phi^2, \tag{6} \]

where \(K_g\) is the transfer coefficient of the regulating device when \(R_\phi(U)=R_{\phi 0}\);

\[ a = \frac{R_{\phi 0}(R_2 + R_3)} {R_2(R_1 + R_3) + R_{\phi 0}(R_1 + R_2 + R_3)}; \]

\[ b = \frac{R_{\phi 0}(R_1 + R_2 + R_3)} {R_2(R_1 + R_3) + R_{\phi 0}(R_1 + R_2 + R_3)}. \]

The obtained expressions (5, 6) show that the amplitude of the harmonic components of the output voltage of the regulating device increases as the voltage applied to the photoresistor increases. In this case, the third harmonic increases considerably faster, since it depends on the square of the voltage applied to the photoresistor. The term included in both expressions,

\[ \left(1 - K_g \frac{b}{a}\right), \]

shows the dependence of nonlinear distortions on the operating mode of the photoresistor.

Let us consider the possibilities for reducing the nonlinear distortions of the regulating device on the phototransducer. Obviously, this can be achieved by reducing the voltage on the photoresistor, with an unchanged transfer coefficient, or by changing the operating mode of the photoresistor. A reduction of \(U_\phi\) at a constant input and output signal is achieved by introducing an additional resistance \((R_3)\) into the photoresistor circuit. In this case the reduction will occur both through a change in \(U_\phi\) and through the insertion coefficient \((K_{\mathrm{ins}})\).

Indeed, for \(R_2 \to \infty\) we obtain that \(a=b=K_{\mathrm{ins}}\cdot K_g\); taking this into account, expressions (5, 6) are reduced to the form

\[ K_{r2} \approx \frac{1}{4}(1-K_g)\frac{R'_\phi}{R_{\phi 0}}\cdot K_{\mathrm{ins}}\cdot U_\phi; \]

\[ K_{r3} \approx \frac{1}{24}(1-K_g)\frac{R''_\phi}{R_{\phi 0}}\cdot K_{\mathrm{ins}}\cdot U_\phi^2, \]

where

\[ K_{\mathrm{sw}}=\frac{R_{\phi0}}{R_3+R_{\phi0}}<1. \]

The nonlinear distortions of the control device, under the same conditions, i.e., \(U_{\mathrm{in}}\) and \(U_{\mathrm{out}}=\mathrm{const}\) and an unchanged value of \(R_{\phi}\), can be reduced by shunting it with an active resistance \((R_2)\). For \(R_3=0\), \(a=K_g\),

\[ b=K_g\left(1+\frac{R_1}{R_2}\right), \]

and expressions (5, 6) take the form:

\[ K_{r2}^{\prime}=\frac{1}{4}\left(1-K_g-K_g\frac{R_1}{R_2}\right)\frac{R_{\phi}^{\prime}}{R_{\phi0}}\cdot U_{\phi}; \]

\[ K_{r3}^{\prime}=\frac{1}{24}\left(1-K_g-K_g\frac{R_1}{R_2}\right)\frac{R_{\phi}^{\prime\prime}}{R_{\phi0}}\cdot U_{\phi}^{2}. \]

In the case when \(R_{\phi}\) is not shunted, i.e., \(R_2\to\infty\), the terms \(K_g\cdot \frac{R_1}{R_2}\) will be absent from the expressions given above; having established this, we determine how much \(K_r\) changes upon introducing \(R_2\):

\[ n=\frac{K_{r2}}{K_{r2}^{\prime}}=\frac{K_{r3}}{K_{r3}^{\prime}}= \frac{1-K_g}{1-K_g-K_g\frac{R_1}{R_2}}, \]

where \(n\) is the number showing by how many times the nonlinear distortions of the control device decrease when the photoresistance is shunted. Since the introduction of either \(R_2\) or \(R_3\) separately leads to a change in the input and output resistances of the control device, combined connections are often used, as shown in Fig. 1; in this case

\[ n=\frac{1-K_g} {\left(1+\frac{R_3}{R_2}\right)-K_g\left(1+\frac{R_3}{R_2}+\frac{R_1}{R_2}\right)} \cdot \frac{1}{K_{\mathrm{sw}}}. \]

The switching coefficient is determined by expression (4).

The indicated methods of linearization lead to changes in other important characteristics of the control device, such as the dynamic range and the steepness of regulation.

If the dynamic range of the control device is taken as

\[ D=\left.\frac{U_{\mathrm{out}\,max}}{U_{\mathrm{out}\,min}} =\frac{K_{g\,max}}{K_{g\,min}}\right|_{U_{\mathrm{in}}=\mathrm{const}}, \]

then in the limit, for \(R_{\phi}\) varying from 0 to \(\infty\), we obtain:

1) Introducing \(R_3\) limits the minimum transmission coefficient to the value

\[ K_{g\,min}=\frac{R_3}{R_1+R_3}. \]

2) Introducing \(R_2\)—the maximum

\[ K_{g\,max}=\frac{R_2}{R_1+R_2}. \]

3) When \(R_2\) and \(R_3\) are inserted, the limitation will occur from both sides, and

\[ D_{\mathrm{lim}}=\frac{(R_2+R_3)(R_1+R_3)} {R_3(R_1+R_2+R_3)}. \]

To clarify the change in the magnitude of the steepness of regulation, let us find the relative transmission coefficients \(dK_g/K_g\) of the circuits with linearization and without it, and then take their ratio.

For \(R_2 \to \infty\) and \(R_3=0\)

\[ \frac{dK_g}{K_g}=\frac{R_1}{R_1+R_\phi}\cdot\frac{dR_\phi}{R_\phi}. \]

Let us consider the 3 cases given earlier:

a) an additional resistance \(R_3\) is introduced.

\[ \frac{dK'_g}{K'_g}=K_{\mathrm{in}}\cdot \frac{R'_1}{R'_1+R_3+R_\phi}\cdot \frac{dR_\phi}{R_\phi}; \]

\[ m'=\frac{dK_g/K_g}{dK'_g/K'_g}=\frac{1}{K_{\mathrm{in}}}; \]

b) the photoresistance is shunted by \(R_2\).

\[ \frac{dK''_g}{K''_g}= \frac{R''_1\cdot R_2}{R''_1\cdot R_2+R_\phi\left(R''_1+R_2\right)} \cdot \frac{dR_\phi}{R_\phi}; \]

\[ m''=\frac{dK_g/K_g}{dK''_g/K''_g} =\frac{1-K_g}{K_g}\cdot\frac{R_\phi}{R''_1}\to n; \]

c) \(R_2\) and \(R_3\) are installed.

\[ m'''=\frac{dK_g/K_g}{dK'''_g/K'''_g} =\frac{1}{K_g}\cdot\frac{1}{K_{\mathrm{in}}^2}\cdot \frac{R_\phi}{R_1+R_\phi}. \]

Thus, if the transfer coefficient after the introduction of the linearizing resistances remains unchanged, i.e. \(K_g=K'_g=K''_g=K'''_g\), and the voltage across the photoresistance is the same, then by however many times we gain in nonlinear distortions, by almost the same amount we lose in the steepness of regulation. Since reference literature for photoresistors gives a linear current–voltage characteristic and, accordingly, assumes that the value of \(R_\phi\) does not depend on the voltage applied to it, a quantitative calculation of nonlinear distortions by means of the expressions obtained is difficult.* Recording the current–voltage characteristics themselves, or the dependence \(R_\phi(U_\phi)\), especially for such photoresistors as SF 2-2, SF 2-3, SF 2-5, SF 2-8, etc., which have small deviations of \(\gamma\) from unity, is a very labor-intensive process requiring the use of precision apparatus, which is not always possible or desirable. Moreover, these characteristics are not identical for different photoresistances even from one batch and depend on the degree of illumination of the photoresistor.

Fig. 2.
Figure labels: \(G\)—GZ-33; SV—S5-2; \(R_1\); \(R_\phi\).

In this connection, we carried out investigations directly of the nonlinear distortions arising in the circuit with a photoresistance. The experimental circuit is shown in Fig. 2. An inductive divider with a transfer coefficient of \(1/2\), a photoresistor, and a series-connected

\[ \text{*) The qualitative picture of the process described is quite reliable; this is also evidenced by the course of the experimental curves (Fig. 5).} \]

together with it form a bridge. A sinusoidal-voltage generator (G) is connected in one diagonal of it, and a selective millivoltmeter (SV) in the other. By varying the value of the PS, the bridge is balanced at the 1st harmonic. In this case, if there are no phase shifts, the higher harmonics of the generator will also be compensated. The harmonic components that arise due to the nonlinearity of the PS will be separated in the diagonal of the bridge and can be measured by the selective voltmeter.

Fig. 3.

By changing the output voltage of the generator, one can obtain the dependence \(K_{\mathrm{g}}=f(U_{\phi})\), and by setting different values of \(R_1\) (with balance \(R_1 \simeq R_{\phi}\)), the dependence \(K_{\mathrm{g}}=f(R_{\phi}, U_{\phi})\).

The coefficients of the second and third harmonics in the output voltage of the RU with photoresistances of type SF 2-5, obtained in this way, are given in Figs. 3, 4, 5.

It follows from the graphs presented that:

1) in circuits with PS, odd harmonics predominate;

2) at voltages not exceeding the working \(U\), the third harmonic depends on the square of the applied voltage.

3) the 2nd harmonic depends on \(U_{\phi}\) linearly up to \(U_{\phi}=U_{\mathrm{rab}}\), and at higher voltages, for some specimens, even a decreasing portion \(K_{\mathrm{g}2}(U_{\phi})\) is observed;

4) there is a rather strong dependence of \(K_{\mathrm{g}}\) on the selected value of \(R_{\phi 0}\), and this dependence becomes more pronounced as \(U_{\phi}\) increases;

5) a scatter of the values of \(K_{\mathrm{g}}\) is observed for different PS specimens even from the same batch.

To determine the limits of scatter of \(K_{\mathrm{g}}\), we investigated 10 specimens of photoresistances from three different batches of SF 2-5 produced in 1968–1969. The results are presented in the histograms of Fig. 6 for the second and third harmonics at \(U_{\phi}=U_{\mathrm{rab}}\).

Fig. 4.

Fig. 5.

From this it may be concluded that the majority of photoresistors of the SF 2-5 type have nonlinear distortions within the range \(0.1 \div 0.2\%\) at voltages not exceeding \(U_{\mathrm{op}}\).

Several circuit variants of a regulating device (RD) using photoelectric transducers were considered earlier. Of the other possible configurations, the most interesting is the differential connection of PTs (Fig. 7).

In Fig. 6:
— distribution by \(K_{g2}\);
— distribution by \(K_{g3}\);
\(U_{\phi}=U_{\mathrm{op}}=2\text{ V}\).

Fig. 6.

Fig. 7.

Let us consider this circuit in somewhat greater detail. The regulation slope, which, as noted above, is equivalent to the relative transmission coefficient,

\[ S_p:\frac{dK_g}{K_g} = \frac{R_{\phi1}}{R_{\phi1}+R_{\phi2}} \left[ \frac{dR_{\phi2}}{R_{\phi2}}+ \frac{dR_{\phi1}}{R_{\phi1}} \right], \]

and for such a circuit, with identical transducers and \(R_{\phi1}=R_{\phi2}\), is twice as large as for an RD with a single PT.

The harmonic coefficients determined for this circuit by the method proposed earlier are equal to

\[ K_{g2}\simeq \frac{1}{4} \left[ (1-K_g)K_g \frac{R'_{\phi2}}{R_{\phi2}}U_{\phi2} - \frac{R_{\phi1}}{R_{\phi2}}K_g^2 \frac{R'_{\phi1}}{R_{\phi1}}U_{\phi1} \right]; \]

\[ K_{g3}\simeq \frac{1}{24} \left[ (1-K_g)K_g \frac{R''_{\phi2}}{R_{\phi2}}U_{\phi2}^{2} - K_g\frac{R_{\phi1}}{R_{\phi2}}\cdot \frac{R''_{\phi1}}{R_{\phi1}}U_{\phi1}^{2} \right]. \]

It follows from the last expressions that, with identical transducers, the same operating mode \((R_{\phi1}=R_{\phi2})\), and a transmission coefficient equal to 0.5, complete compensation of the distortions introduced by the photoresistors is possible.

This proposition was verified experimentally: in the circuit of Fig. 2, the linear resistance was replaced by a PT; otherwise the procedure remained the same. The results obtained are shown in the graph of Fig. 8, where curves 1 and 2 reflect the behavior of \(K_{g3}\) for \(R_{\phi1}\) and \(R_{\phi2}\), obtained by the method described earlier.

Curve 3 shows the dependence of \(K_{g3}\) on \(U_{\mathrm{out}}=U_{\phi}\) for the differential connection of these same photoresistors.

Under real conditions, it is of course impossible to achieve complete compensation of nonlinear distortions, all the more so because during operation of the RD the changes in \(R_{\phi}\) will occur in different directions. However, it is quite obvious that such a connection, while providing a substantial gain in regulation slope, will not lead to an increase in \(K_g\); moreover, in this case broader possibilities are opened for linearizing the RD by the methods described above, if \(S_p\) is left as for a single transducer.

The frequency properties of the regulating device are determined by the reactances of its constituent elements and, in particular, by the reactances of the photoresistor. At elevated frequencies the PS can be represented as a series-connected lead inductance \((L_{\phi})\) with an active resistance \((R_{\phi})\), shunted by a capacitance \((C_{\phi})\).

The value \(L_{\phi}\) is determined by the geometrical dimensions and material of the leads and can be calculated from known expressions [6].

Fig. 8.

The calculation of the capacitance \(C_{\phi}\) is much more difficult, since many necessary dimensions of PS are not given in the reference literature, and measuring them is practically impossible.

We measured the capacitances of several batches of different photoresistors using an E12-1 capacitance meter; as the investigations showed, the scatter for PS of the same type was 0.1–0.3 pF, and therefore for calculations one may quite well use the average data given in Table 3.

The reactances \(L_{\phi}\) and \(C_{\phi}\) will give rise to the frequency dependence of two parameters of the RD—the transfer coefficient \((K_g)\) and the regulating slope \((S_r)\). The calculation of the frequency characteristic, i.e. \(K_g(\omega)\), must be carried out in each particular case; here, however, we shall consider the change in the relative sensitivity of the photoresistor \(S_{\phi}\). Let us denote, for direct current,

\[ \frac{dR_{\phi}}{R_{\phi}} = S_{\phi 0}. \]

According to the equivalent circuit,

\[ Z_{\phi} = Z_L + \frac{Z_c \cdot R_{\phi}}{Z_c + R_{\phi}} . \]

and

\[ \frac{dZ_\phi}{Z_\phi}=S_{\phi\omega}= \frac{Z_c^2\cdot R_\phi}{[Z_L(R_\phi+Z_c)+R_\phi Z_c](R_\phi+Z_c)} \cdot \frac{dR_\phi}{R_\phi}. \]

Using these expressions, we find how much lower the sensitivity of the photoresistance is at frequency \(\omega\) in comparison with direct current:

\[ A=\frac{S_{\phi 0}}{S_{\phi\omega}}\approx \sqrt{1+\omega^2\left(C_\phi R_\phi+\frac{L_\phi}{R_\phi}\right)^2}. \]

From this expression, for specified values of \(A\) and \(\omega\), with known \(C_\phi\) (Table 3) and \(L_\phi\), the required value of \(R_\phi\) can be determined.

Table 3

* The limiting frequency was calculated from expression 7 for the level \(\sqrt{2}\); \(R_\phi\) was taken at an illumination of 200 lx, and \(L_\phi=0\).

The investigations carried out on regulating devices based on photoelectric transducers allow the following conclusions to be drawn:

1) RUs based on FTs are constructed in the form of an electrically controlled divider. The control circuit consists of a light source, for which either incandescent lamps or semiconductor diodes with a luminous \(pn\)-junction may be used. The controlled circuit includes a photoresistor. At present, photoresistances of type SF 2-5 are the most suitable for RUs.

2) The maximum dynamic range of an RU with one transducer reaches \((40—50)\) dB, and with differential connection of FTs it can reach 100 dB.

3) The real control steepness for an RU with one FT is equal to \(2\div5\), and with differential connection of two transducers—\(4\)-\(10\).

4) The nonlinearity of the volt-ampere characteristic of the photoresistor leads to the appearance of higher components in the output signal of the RU. In this case the 3rd harmonic predominates, which depends on the square of the voltage applied to the FS.

5) There is a sharp dependence of \(K_r\) on the magnitude of the resistance of the photoresistor. Moreover, the greater \(R_\phi\), the greater the distortion.

6) Possible methods of linearization lead to a narrowing of the dynamic range and of the control steepness. The most effective way of reducing \(K_r\) is to reduce the voltage on the photoresistor.

7) Differential connection of FTs with identical transducers and equal \(R_\phi\) can provide complete compensation of the higher components.

8) The frequency applicability of the control device with a photoconverter is determined by the reactances of the photoresistor and by the value \(R_{\phi 0}\). At present, the most wideband are photoconverters of the SF 2-5 type.

REFERENCES

1. M. S. Roitman, E. I. Tsimbalist, A. I. Lysov. A photoelectric converter as a controlled element of an electrical circuit. Izv. vuzov—Priborostroenie, No. 6, 1966.

2. V. F. Anikin. Development and investigation of stabilizing devices for alternating voltage with photoelectric converters. Dissertation, Tomsk, 1970.

3. S. V. Svechnikov. Photoresistances as elements of an electrical circuit. Avtomatika i telemekhanika, No. 4, 1959.

4. S. F. Korndorf et al. Calculation of photoelectric circuits. Energiya Publishing House, Moscow, 1967.

5. V. D. Ivanchenko. Nonlinear distortions in transistor amplifiers. Semiconductor Devices in Electrical Communication Engineering. Collection of articles edited by I. F. Nikolaevskii, issue 2, Svyaz’ Publishing House, Moscow, 1968.

6. L. A. Tseitlin. Inductances of Wires and Circuits. Gosenergoizdat, Moscow—Leningrad, 1950.