UDC 62-555.41

CONTROL DEVICES WITH LOW NONLINEAR DISTORTION

Yu. M. Fomichev, Yu. N. Varakuta

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

The possibilities of constructing control devices with low nonlinear distortion using electron-beam-deflection tubes and field-effect transistors are considered.

An analysis is given of the operation of control devices using beam-deflection tubes with negative feedback and a compensation circuit. The results of experimental studies are shown in graphs.

Expressions have been obtained for the harmonic coefficients of an attenuator based on field-effect transistors; the possibility of reducing nonlinear distortions is shown, and calculation results and experimental results with controlled attenuators are presented.

Illustrations 8, tables 2, references 4.

One of the key elements in systems for the automatic regulation of calibrated-voltage sources is the regulating (control) device (RU), which changes the amplitude of the output oscillations in accordance with the law of the control signal. To construct an RU with parameters approaching ideal ones, an electrically controlled element is needed with a linear current–voltage characteristic in the controlled-signal circuit and maximum regulation steepness in the control circuit. The article considers various possibilities for constructing linear (with respect to the main-signal circuit) RUs using electron tubes and semiconductor devices.

Among electron tubes suitable for constructing RUs, the beam-deflection tubes of types N-41 and N-37 developed in recent years are of greatest interest [1].

The presence in the tube of three control electrodes in combination with a push-pull output makes it possible to build various circuits of control devices with them.

It is known that introducing negative feedback into an RU is undesirable, since it leads to deterioration of the regulating properties.

In this respect, RUs using a beam-deflection tube are favorably distinguished. The presence of a push-pull output for the control signal makes it possible to encompass the stage with negative feedback for the main signal and, at the same time, with positive feedback for the control signal. This leads to a reduction of the nonlinear distortions of the stage while preserving and even somewhat improving its regulating properties.

Let us consider the operation of such an RU (Fig. 1). The voltage acting between the control grid and the cathode is equal to

\[ U_1=\frac{U_{\mathrm{in}}\cdot R_3}{R_1+R_2\parallel R_3} -\frac{U_2''R_3}{R_2+R_1\parallel R_3}. \tag{1} \]

A change in the control voltage will lead to changes in the output voltages \((U_2'',\, U_2')\); moreover, as \(U_p\) increases, \(U_2'\) will increase, while \(U_2''\) will decrease. According to (1), this will lead to an increase in \(U_1\) and, correspondingly, in \(U_2^1\), and thus to an increase in the slope of the control characteristic.

To clarify how the harmonic composition of the output signal changes when the RU is encompassed by the indicated feedback, let us find the solution of the graph constructed for this circuit (Fig. 2) with respect to the additional product \(\Delta U_2'\) in the output voltage of the RU \((U_2')\). In Fig. 2 the following are denoted:

Fig. 1

Fig. 2

\(\gamma\) — the transfer coefficient from point 1 to point 2 (Fig. 1);

\(\beta\) — the transfer coefficient from point 3 to point 2 (i.e., the feedback coefficient);

\(K_{24}\) — the gain coefficient without feedback (transfer from point 2 to point 4);

\(K_{23}\) — the transfer coefficient from point 2 to point 3;

\(\Delta U_2''\) — the additional product in the output voltage \(U_2''\) without feedback.

The transfer coefficients of the additional products into the output signal \((U_2')\) will be equal to

\[ T_{\Delta 4}=1,\qquad T_{\Delta 34}=-\frac{K_{24}\beta}{1+K_{23}\beta}, \]

then

\[ \Delta U_{2\mathrm{fb}}' =\Delta U_2'\cdot T_{\Delta 4} +\Delta U_2''\cdot T_{\Delta 34} = \]

\[ =\Delta U_2' -\Delta U_2''\cdot \frac{K_{24}\cdot \beta}{1+K_{23}\cdot \beta}. \tag{2} \]

It follows from the expression obtained that, with equal anode loads and \(K_{23}=K_{24}\), and with \(K\beta\gg 1\), very small nonlinear distortions can be obtained.

A disadvantage of such a circuit, in addition to the disadvantages generally known for parallel negative feedback, is that when \(U_p\) is varied (in either direction), nonlinear distortions will increase. This is especially clearly seen if one assumes \(\Delta U_2''=\Delta U_2'\); then (2) takes the form

\[ \Delta U_{2\mathrm{fb}}' \approx \Delta U_2' \left( 1-\frac{K_{24}\beta}{1+K_{23}\beta} \right). \]

During control, \(K_{24}\) and \(K_{23}\) change in opposite directions, and \(\Delta U_{2\mathrm{fb}}'\) increases, tending in the limit to \(\Delta U_2'\). Thus, if there is no need for a wide dynamic range, one can choose

a definite control region in which the nonlinear distortions will be sufficiently small.

All of the above is well confirmed by the experimental data shown in Fig. 3, where curves 1 and 3 show the dependence of nonlinear distortions on the control voltage at different feedback coefficients \((\beta)\), while curves 2 and 4 represent the control characteristics of the control device for the same \(\beta\). As can be seen from the graphs, the control slope increases with increasing depth of feedback and is, for

\[ \beta = \frac{1}{2}, \quad S_p = 3.4, \]

and for

\[ \beta = \frac{1}{5}, \quad S_p = 1.6. \]

It is also necessary to note that control devices with feedback have good linearity of the control characteristic. Their maximum dynamic range is \(30\)—\(35\) dB, while the linear region amounts to \(15\)—\(20\) dB.

Fig. 3

The possibility of obtaining output voltages shifted in phase by \(180^\circ\) opens up yet another interesting possibility for linearizing control devices using beam-deflection tubes. Let us consider the circuit of Fig. 4: here the main signal is fed to one of the deflecting electrodes, and the second—so far as its alternating component is concerned—is grounded*). The same control voltage may be fed either to the control grid or to the screen grid. With such a connection, and with good identity between the two anodes, two antiphase voltages of equal amplitude are obtained at the output, as in an ordinary push-pull stage.

Let us see what happens if the resultant signal taken at point \(C\) is fed to the control grid, as shown in Fig. 4.

The alternating components of the voltages acting on the anodes are equal to:

\[ \left. \begin{aligned} e_a &= -\frac{1}{2} R_a S_1 e_1 + R_a S_3 e_2 + K_{\mathrm{dv}} R_a e_1 e_2; \\ e_{\mathrm{v}} &= -\frac{1}{2} R_a S_1 e_1 - R_a S_3 e_2 - K_{\mathrm{dv}} R_a e_1 e_2; \end{aligned} \right\} \tag{3} \]

where \(S_1\) is the slope of the characteristic with respect to the first grid;

\(S_3\) is the slope with respect to the deflecting electrode;

\[ K_{\mathrm{dv}} = \frac{\partial I_a}{\partial U_{c1}\partial U_{c3}} = \frac{\partial S_1}{\partial U_{c3}} = \frac{\partial S_3}{\partial U_{c1}} \]
\[ \text{—} \]

* In beam-deflection tubes this is equivalent to applying to the deflecting electrodes two antiphase voltages of half the amplitude.

— the coefficient of double control, which shows how the slope of the anode-current characteristic with respect to one of the control electrodes changes when the voltage on the other is changed.

Since the total signal \(l_1\) is small, in the first approximation the slope \(S_1\) may be regarded as constant; then the harmonic components in the output signal will appear owing to the nonlinearity of \(S_3\). Expanding the latter in a Taylor series in powers of \(l_2\) and carrying out the corresponding transformations, we find the harmonic composition of the output voltage for the RU under consideration:

\[ e_a = R_a S_3 e_2 + \frac{S'_3 R_a e_2^2}{1+K} + \frac{1}{2} S''_3 R_a e_2^3 + \frac{K_{\mathrm{dv}} R_a^2 e_2^3}{1+K}. \]

It follows from this that the term giving the second harmonic is reduced by a factor of \((1+K)\), where \(K=\frac{1}{2}R_aS_1\) is the gain factor for one of the anodes. At the same time, however, the content of the third harmonic is increased by an amount equal to

\[ \frac{K_{\mathrm{dv}}R_a^2e_2^3}{1+K}. \]

Since in beam-deflection tubes \(K_{\mathrm{dv}}\) is small, while \(K\) can be made large in real stages, the increase in the third harmonic will be insignificant. At the same time, the predominant second harmonic can be reduced to a very small value. During adjustment, the gain factor \((K)\) will change, and the nonlinear distortions will change accordingly.

A model assembled according to the schematic diagram of Fig. 4 was tested. Adjustment of the gain factor was carried out by changing the bias voltage on the control grid. The effectiveness of reducing the intrinsic distortions of the RU was determined by measuring the second-harmonic coefficient at the output of the RU with the compensation circuit open and closed (at point \(b\)). The test results are given in the graphs of Fig. 5 for the RU with the compensation circuit open and closed, respectively. It follows from this that the content of the second harmonic in the output signal can be reduced by one to two orders of magnitude, while the third harmonic increases, in the worst case, by only a factor of two.

Fig. 4

Fig. 5

The adjustment of the stage for the smallest nonlinear distortion can be carried out in two ways:

1. By directly comparing the input and output signals, and by selecting the position of the mean point \(C\), obtain the smallest value of the 2nd harmonic.

2. With the aid of an oscilloscope, connecting it at point \(C\), and also by selecting its position, ensure that only the second harmonic is present in the signal \(l_1\). In this case the adjustment can be performed with the compensation circuit open.

It should be noted that the magnitude of the change in \(K_{\Gamma_2}\) during adjustments depends on the bias voltage on the first grid \((-E_{c0})\) at which the adjustment was carried out. Evidently, this is due to the incomplete identity of the tube at the two anodes.

Investigations carried out on the breadboard showed that the smallest changes in \(K_{\Gamma_2}\) occur if the adjustment is performed at \(E_{c0}=-2\) V. In general, if the adjustment is to be carried out over a small range, it is better to perform the adjustment at the point relative to which it will be made.

The maximum dynamic control range of such a stage is 30--33 dB with nonlinear distortion not exceeding 0.01--0.02%, while the linear portion of the control characteristic is 15--20 dB and \(K_{\Gamma}\le 0.03\%\).

Control devices using semiconductor elements

Recently, in automatic control systems for calibrated-voltage sources, inertialess semiconductor control devices using field-effect transistors have been finding increasing application. The use of field-effect transistors as controlled resistances in circuits of controlled attenuators is based on the property of their characteristics. At small drain--source voltages

\[ |U_c|<|U_z|-|U_0|, \]

where
\(U_c\) is the voltage at the drain;
\(U_z\) is the voltage at the gate;
\(U_0\) is the cutoff voltage,

the field-effect transistor behaves as a variable resistor, the value of which (the resistance between drain and source) depends on the control voltage at the gate.

This is valid for drain voltages of both signs, provided that the drain--gate junction is not biased in the forward direction,

\[ |U_{mc}|\le |U_z|+|U_\phi|, \]

where
\(U_{mc}\) is the amplitude value of the voltage at the drain;
\(U_z\) is the voltage at the gate;
\(U_\phi\) is the contact potential.

A family of characteristics of a field-effect transistor with a \(p\)-\(n\) junction in the “ohmic” region is shown in Fig. 6. The dependence of the drain--source resistance on the gate voltage relative to the source is expressed approximately by the formula

\[ R_{ci}=R_0 \exp(\eta U_z), \]

where \(R_0\) and \(\eta\) are constants for the given transistor. The transmission coefficient of the controlled divider (Fig. 7) is expressed by the formula

\[ K_1=\frac{U_{\text{out }a}}{U_{\text{in }a}}=\frac{R_{\text{si}}}{R+R_{\text{si}}}. \]

The range of variation of the attenuation coefficient of the attenuator can be

Fig. 6

Fig. 7

Fig. 8

significant and depends on the value of \(R\), \(m=\dfrac{R_{\text{si max}}}{R_{\text{si min}}}\), and on the permissible nonlinear distortions.

Nonlinear distortions of an attenuator with a field-effect transistor

When the drain current \(i_c\) is specified, the transfer characteristic of the field-effect transistor will be expressed by the function \(U_c=f(i_c)\). Expanding it in a Taylor series in powers of the argument and assigning a sinusoidal value of the current through the transistor \((i_c=I_c\cos\omega t)\), we find the coefficients of the higher harmonic components of the voltage on the field-effect transistor:

\[ K_{\Gamma_2}= \frac{\dfrac{\alpha_2}{4} I_{mc}^{2}+\dfrac{\alpha_4}{48} I_{mc}^{4}} {\alpha_1 I_{mc}+\dfrac{\alpha_3}{8} I_{mc}^{3}} \approx \frac{\alpha_2 I_{mc}}{4\alpha_1}; \tag{4,а} \]

\[ K_{\Gamma_3}= \frac{\dfrac{\alpha_3}{24} I_{mc}^{3}} {\alpha_1 I_{mc}+\dfrac{\alpha_3}{8} I_{mc}^{3}} \approx \frac{\alpha_3 I_{mc}^{2}}{24\alpha_1}, \tag{4,б} \]

where \(\alpha_1;\ \alpha_2;\ \alpha_3;\ldots \alpha_n=\dfrac{d^n U}{di^n}\).

For a quantitative and qualitative analysis of the nonlinear distortions of the attenuator, it is necessary to determine the coefficients \(\alpha_1;\ \alpha_2;\ \alpha_3\). The transfer characteristics of channel transistors whose channel is obtained using diffusion technology (KP103, KP303) are described rather well by the Shockley equation (abrupt junction, homogeneous carrier distribution)

\[ i_c=I_{\max}\left[ \frac{U_3+U_c+U_\varphi}{U_0} \left(3-2\sqrt{\frac{U_3+U_c+U_\varphi}{U_0}}\right) -\frac{U_3+U_\varphi}{U_0} \left(3-2\sqrt{\frac{U_3+U_\varphi}{U_0}}\right) \right], \tag{5} \]

where \(I_{\max}\) is the drain current for \(U_3=0\) and \(|U_c|>|U_0|\). For \(i_c=f(U_c)\) it is impossible to find the inverse function \(U_c=f(i_c)\). To find the derivatives

\[ \frac{d^n U_c}{d i_c^n}, \]

we shall use the rule for differentiating an implicit function.

Differentiate both sides of the equation \(i_c=f(U_c)\) with respect to \(i_c\):

\[ 1=\frac{df(U_c)}{dU_c}\cdot\frac{dU_c}{di_c}; \]

hence

\[ \frac{dU_c}{di_c}=\alpha_1=\left[\frac{df(U_c)}{dU_c}\right]^{-1}; \tag{6,a} \]

\[ \alpha_2=\frac{d^2 f(U_c)}{d i_c^2} = \frac{d}{dU_c}\left[\frac{df(U_c)}{dU_c}\right]^{-1} \cdot \frac{dU_c}{di_c} = -\frac{d^2 f(U_c)}{dU_c^2} \left[\frac{df(U_c)}{dU_c}\right]^{-3}; \tag{6,b} \]

\[ \alpha_3=\frac{d^3 f(U_c)}{d i_c^3} = \left\{ -\frac{d^3 f(U_c)}{dU_c^3}\cdot\frac{df(U_c)}{dU_c} + 3\left[\frac{d^2 f(U_c)}{dU_c^2}\right]^2 \right\} \left[\frac{df(U_c)}{dU_c}\right]^{-5}. \tag{6,c} \]

Let us find the derivatives \(\dfrac{df(U_c)}{dU_c}\) from (5) and, substituting their values into (6a–6c), obtain:

\[ \alpha_1= \frac{1}{ 3\dfrac{I_{\max}}{U_0} \left[ 1-\left(\dfrac{U_3+U_c+U_\varphi}{U_0}\right)^{1/2} \right] }; \]

\[ \alpha_2= \frac{3}{2}\, \frac{I_{\max}}{U_0^{3/2}}\, (U_3+U_c+U_\varphi)^{-1/2}\cdot \alpha_1^3; \]

\[ \alpha_3= \left[ \frac{ -\dfrac{3}{4}\dfrac{I_{\max}}{U_0^{3/2}} (U_3+U_c+U_\varphi)^{-3/2} }{\alpha_1} + \frac{27}{4}\frac{I_{\max}^2}{U_0^3} (U_3+U_c+U_\varphi)^{-1} \right]\alpha_1^5. \]

Substituting the values of \(\alpha_1\), \(\alpha_2\), \(\alpha_3\) into (4,a, b) and taking into account that \(I_{mc}=\dfrac{U_{mc}}{\alpha_1}\), we obtain the expressions for the harmonic coefficients:

\[ K_{\Gamma_2}= \frac{U_{mc}}{ 8U_0 \left[ \left(\dfrac{U_3+U_c+U_\varphi}{U_0}\right)^{1/2} + \dfrac{U_3+U_c+U_\varphi}{U_0} \right] }; \tag{7,a} \]

\[ K_{\Gamma_3}= \frac{U_{mc}^2}{96U_0^2}\cdot \frac{ 3\left(\dfrac{U_3+U_c+U_\varphi}{U_0}\right)^{1/2}-1 }{ \left(\dfrac{U_3+U_c+U_\varphi}{U_0}\right)^{3/2} - \left(\dfrac{U_3+U_c+U_\varphi}{U_0}\right)^2 }. \tag{7,b} \]

The most favorable operating mode of the controlled attenuator is when there is no dc voltage at the drain. For \(U_c=0\), expressions (7) take the form:

\[ K_{\Gamma_2}= \frac{U_{mc}} {8U_0\left[\left(\frac{U_3+U_\varphi}{U_0}\right)^{1/2} -\frac{U_3+U_\varphi}{U_0}\right]}; \tag{8,a} \]

\[ K_{\Gamma_3}= \frac{U_{mc}^2}{96U_0^2}\cdot \frac{3\left(\frac{U_3+U_\varphi}{U_0}\right)^{1/2}-1} {\left(\frac{U_3+U_\varphi}{U_0}\right)^{3/2} -\left(\frac{U_3+U_\varphi}{U_0}\right)^2}. \tag{8,b} \]

The expressions obtained describe the nonlinear distortions of a field-effect transistor fed from a current generator. Distortions in a real attenuator will depend on the value of the channel resistance and the value of the resistance in the upper arm (Fig. 7)

\[ K_{\Gamma_n a}= \frac{K_{\Gamma_n \text{ FET}}\cdot R}{R+\alpha_1}, \]

where \(K_{\Gamma_n a}\) is the coefficient of the \(n\)-th harmonic of the attenuator;
\(K_{\Gamma_n \text{ FET}}\) is the coefficient of the \(n\)-th harmonic of the field-effect transistor fed from a current generator (8);
\(\alpha_1=R_{\text{si}}\) is the drain–source resistance.

Table 1 gives the values of \(K_{\Gamma_2}\), obtained by calculation and as a result of an experiment with an attenuator using a KP103M transistor with \(I_{\max}=11\) mA, \(U_\varphi=450\) mV, \(U_0=6.4\) V. Good agreement between the theoretical and experimental data is found. The discrepancy in the region of small and large gate voltages, where the characteri-

Table 1

the characteristics of real devices differ from the characteristics of an “ideal” Shockley device.

As is clear from the analysis of expressions (8), the second harmonic predominates in the distortion. The smallest nonlinear distortions will be obtained in attenuators in which transistors with a high cutoff voltage are used. The nonlinear distortions introduced by the regulating element of the automatic-control system of precision AC voltage sources must not exceed 0.01–0.03%. Such nonlinear distortions can be obtained in controlled attenuators with field-effect transistors at drain voltages of several millivolts. This is a significant drawback of regulating devices with field-effect transistors, since, in order to obtain calibrated output voltages of 10 V and higher at the source output, amplifiers with a very large gain and low nonlinear distortion must be used. It is possible to obtain low nonlinear distortion at drain voltages of several hundred millivolts if special measures are taken to linearize the characteristics of the field-effect transistor.

Method for Reducing Nonlinear Distortion

The main problem associated with the use of field-effect transistors in the circuit of a controlled attenuator is the elimination of the nonlinear and asymmetric character of their current–voltage characteristics.

A known method for linearizing and symmetrizing the dependence \(i_c = f(U_c)\) (5) is one in which part of the drain voltage is applied to the gate (Fig. 8). The characteristic of a field-effect transistor with a \(p\)–\(n\) junction will in this case be described by the equation

\[ i_c = \frac{3 I_{\max}\left[U_3 + U_c(1-\kappa)+U_\varphi\right]}{U_0} - 2 I_{\max} \left[ \frac{U_3+U_c(1-\kappa)+U_\varphi}{U_0} \right]^{3/2} - \]

\[ - \frac{3 I_{\max}(U_3+U_\varphi-\kappa U_c)}{U_0} + 2 I_{\max} \left[ \frac{U_3+U_\varphi-\kappa U_c}{U_0} \right]^{3/2}, \]

where \(\kappa\) is the transfer coefficient of the divider formed by resistors \(R1, R2\).

As was already mentioned, the nonlinear distortions of an attenuator with a field-effect transistor are determined by the level of the second harmonic. Therefore, the condition for linearity of the characteristics will be \(K_{\Gamma_2}=0\), or \(\alpha_2=0\)

\[ \alpha_2 = - \frac{ \frac{3}{2}\frac{I_{\max}}{U_0^{3/2}}\kappa_0^2 \left(U_3+U_\varphi-\kappa_0 U_c\right)^{-1/2} - \frac{3}{2}\frac{I_{\max}}{U_0^{3/2}} }{ \left\{ 3\frac{I_{\max}}{U_0} + 3\frac{I_{\max}}{U_0^{3/2}} \left[\kappa_0\left(U_3+U_\varphi-\kappa_0 U_c\right) - (1-\kappa_0)\right. } \right. \]

\[ \left. \left. \cdot \frac{ \left[U_3+U_\varphi+(1-\kappa_0)U_c\right]^{-1/2}(1-\kappa_0)^3 }{ \left[U_3+U_\varphi+(1-\kappa_0)U_c\right]^{-1/2} } \right] \right\}^{2} } =0; \]

\[ \kappa_0^2\left(U_3+U_\varphi-\kappa_0 U_c\right)^{-1/2} - (1-\kappa_0)^2 \left[U_3+U_\varphi+(1-\kappa_0)U_c\right]^{-1/2} =0. \tag{9} \]

In the absence of a DC voltage at the drain, expression (9) takes the form
\[ \left[\kappa_0^2-(1-\kappa_0)^2\right](U_3+U_\varphi)^{-1/2}=0, \]
whence \(\kappa_0=\frac{1}{2}\),

\(\kappa_0\) is the value of the transfer coefficient of the feedback divider for which \(K_{\Gamma_2}=0\).

Experimentally, for transistors KP103I, KP103M, KP303V, the value \(\kappa_0=0.53\) was obtained for the range of drain-voltage values ...

Table 2

at the gate \(0.1 \leq \dfrac{U_3}{U_0} \leq 0.6\); outside this region \(K_0\) is a nonlinear function of \(\dfrac{U_3}{U_0}\).

The results of investigations of attenuators according to Fig. 8 are summarized in Table 2.

Regulating properties of attenuators with field-effect transistors

As follows from (5), the characteristic of the attenuator with respect to the control input is nonlinear. The differential transmission coefficient is expressed by the relation:

\[ K_{\mathrm{reg}}= \frac{\dfrac{dU_c}{U_c}}{\dfrac{dU_3}{U_3}} = \frac{dU_c}{dU_3}\cdot \frac{U_3}{U_c}; \]

\[ \frac{dU_c}{dU_3} = \frac{dU_c}{dR_{\mathrm{ci}}}\cdot \frac{dR_{\mathrm{ci}}}{dU_3}; \qquad U_c=\frac{R_{\mathrm{ci}}U_{\mathrm{in}}}{R+R_{\mathrm{ci}}}; \]

\[ \frac{dU_c}{dR_{\mathrm{ci}}} = \frac{U_{\mathrm{in}}\cdot R}{(R+R_{\mathrm{ci}})^2}; \qquad K_a=\frac{R_{\mathrm{ci}}}{R+R_{\mathrm{ci}}}; \qquad R=\frac{R_{\mathrm{ci}}(1-K_a)}{K_a}. \]

Here \(K_a\) is the transmission coefficient of the attenuator at the signal input,

\[ \frac{dU_c}{dR_{\mathrm{ci}}} = \frac{U_c(1-K_a)}{R_{\mathrm{ci}}}. \]

The value \(R_{\mathrm{ci}}\) was determined earlier \((R_{\mathrm{ci}}=a_1)\)

\[ \frac{dR_{\mathrm{ci}}}{dU_3} = \frac{1}{ 3\dfrac{I_{\max}}{U_0} \left(1-\sqrt{\dfrac{U_3}{U_0}}\right)^2 \cdot 2\sqrt{U_3U_0} }; \]

\[ K_{\mathrm{reg}} = -\frac{U_3(1-K_a)} {2\left(\sqrt{\dfrac{U_3}{U_0}}-\dfrac{U_3}{U_0}\right)U_0}. \tag{10} \]

Expression (10) was obtained under the assumption that regulation takes place within small deviations from the established state.

The results of experiments and theoretical studies show that control devices using beam-deflection tubes and field-effect transistors can be successfully applied in designing calibrated alternating-voltage sources; they make it possible to obtain small nonlinear distortions with high regulating properties. The fact that these control devices are inertia-free gives the designer a certain freedom in implementing a stabilization system with a high stabilization coefficient.

REFERENCES

1. New receiving-amplifying radio tubes. Prospekt, Ministry of the Electronics Industry of the USSR, 1967.
2. L. Sevin. Field-Effect Transistors. “Sovetskoe radio,” 1968.
3. V. V. Malin, M. S. Sonin. Parameters and Properties of Field-Effect Transistors. “Energiya,” 1967.
4. Bilotti A. Operation of a MOS Transistor a Variable Resistor. Proc. IEEE, v. 54 Aug. 1966.