Video Amplifier with a Common Filter

I. A. Suslov

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

Introduction

For undistorted amplification of long-duration pulses, it is necessary in each stage of a video amplifier to use capacitors of large capacitance in the cathode circuits, in the screen-grid circuit, and in the anode filter. This leads to an increase in the size and cost of the amplifier. One of the most economical solutions is to combine the functions of the cathode, anode, and screen filters. Such a problem can be solved by means of the circuit in Fig. 1. Here the capacitor $C_{\phi}$ shorts the alternating component of the screen current to the cathode, thereby performing the function of the capacitor of the screen filter. At the same time it is included in the anode filter and makes it possible to filter the anode-supply voltage, decouple the stages, and correct the low frequencies. The alternating component of the anode current passes in the circuit of Fig. 1 through the capacitor $C_{\phi}$ directly to the anode load, bypassing the resistance $R_k$. Owing to this, current feedback is eliminated, for which in the usual circuit a capacitor in the cathode serves. Taking into account the indicated combination of the functions of the cathode, anode, and screen capacitors, we shall call the circuit of Fig. 1 an amplifier with a common filter.

Fig. 1.

The circuit of Fig. 1 was first described by G. M. Cheydler and J. D. Noe [1]. The authors called it a “pentriode” amplifier on the grounds that at high frequencies the tube operates here as an ordinary pentode, while at low frequencies—because of the finite resistance of the capacitor $C_{\phi}$—an alternating potential appears on the screen grid, as in triode connection. However, a similar phenomenon also occurs in an ordinary rheostat stage. Therefore “pentriode” operation is not a characteristic feature of the circuit under consideration.

In [1] only the particular case is investigated in which the negative feedback due to the variable potential on the screen grid is compensated by a corresponding increase in the anode load, and the frequency characteristic becomes uniform down to the frequency \(\omega=0\)¹. In this, the action of the transient network \(C_gR_g\) is not taken into account. However, for video amplifiers the case of correction of all low-frequency distortions, including those caused by the \(C_gR_g\) circuit, is of greatest interest.

Fig. 2.

The equivalent circuit of the amplifier under consideration is shown in Fig. 2. Here \(\dot U_n\) is the voltage of the parasitic feedback developed by the output stages at the terminals of the anode-supply source; \(C_2\) includes the stray capacitance to ground and the input capacitance of the following stage.

Omitting the elements that determine the amplifier characteristics in the low-frequency region, we write the equations of the nodal potentials of the circuit of Fig. 2 for high frequencies:

\[ \dot U_1 j\omega C_{gk}-\dot U_k j\omega C_{gk}=\dot I_1, \]

\[ -(S+j\omega C_{gk})\dot U_1+\dot U_k\left[S+\frac{1}{R_k}+\frac{1}{Z_a}+j\omega(C_k+C_{gk})\right]-\dot U_2\frac{1}{Z_a}=0, \tag{1} \]

\[ -S\dot U_1-\dot U_k\left(S+\frac{1}{Z_a}\right)+\dot U_2\left(\frac{1}{Z_a}+j\omega C_2\right)=0, \]

where

\[ \frac{1}{Z_a}=j\omega C_1+\frac{1}{R_a+j\omega L_a}. \]

The gain factor of the circuit can be found from the last two equations (1). They can be simplified by neglecting the admittance \(j\omega C_{gk}\) in comparison with the term containing \(S\). Then these equations are rewritten in the form:

\[ \dot U_k\left(S+\frac{1}{R_k}+\frac{1}{Z_a}+j\omega C_k\right)-\dot U_2\frac{1}{Z_a}=S\dot U_1, \]

¹ In exactly the same way one can compensate the distortions produced by the screen-grid circuit in a rheostat stage.

\[ -\dot U_k\left(S+\frac{1}{Z_a}\right)+\dot U_2\left(\frac{1}{Z_a}+j\omega C_2\right)=-S\dot U_1 . \tag{2} \]

From system (2) we obtain

\[ \dot K=-SR_a\cdot \frac{1+j(k+q)\Omega+j^2kq\Omega^2} {1+j[q+(1-x)m+1+(1-x)(\gamma-1)]\Omega+\cdots} \]

\[ \cdots \frac{}{+j^2[k+q+(1-x)xm+k(1-x)(\gamma-1)]\Omega^2+j^3k[q+(1-x)xm]\Omega^3}. \tag{3} \]

Here the following notation has been introduced:

\[ C_1+C_2=C_0,\qquad \Omega=\omega C_0R_a,\qquad x=\frac{C_1}{C_0}, \]

\[ q=\frac{C_kR_k}{C_0R_a},\qquad m=\frac{R_k}{R_a},\qquad k=\frac{L_a}{C_0R_a^2},\qquad \gamma=1+SR_k. \]

It follows from (3) that at midrange frequencies (since we are not taking into account the circuit elements that determine the characteristics in the low-frequency region, and therefore also at \(\Omega=0\)) the gain coefficient is equal to \(K_0=-SR_a\). Thus, the gain at midrange frequencies will be the same as the gain of an ordinary grounded-cathode stage, i.e., there is no current feedback at midrange frequencies. However, it appears at high frequencies owing to the fact that the current charging the parasitic capacitance \(C_2\) will flow through the resistance \(R_k\).

For simplicity, let us put \(k=0\) in expression (3) and assume that \(C_k\) is formed only by parasitic capacitance, i.e. \(q\simeq 0\).

Then

\[ \dot K=-\frac{SR_a}{1+j\Omega[m+x+(1-x)\gamma]} =-\frac{SR_a}{1+j\omega C_0R_a[m+x+(1-x)\gamma]} \]

and the complex gain coefficient will be the same as that of an ordinary rheostat stage, but with a parasitic capacitance increased by a factor of \(m+x+(1-x)\gamma\). As a result, the passband of the amplifier is appreciably reduced. To eliminate this drawback, two approaches may be taken: 1) increase the correcting inductance and use the capacitor \(C_k\) as an additional correcting element; 2) use \(C_k\) as a bypass capacitance. In the first case, an alternating potential will be present across the resistance \(R_k\), affecting the dynamic input capacitance of the stage.

Input capacitance of the amplifier in Fig. 1

The flow of high-frequency components of the signal through the resistance \(R_k\) may lead to the dynamic input capacitance of the amplifier in Fig. 1 differing from the input capacitance of the tube, and an appropriate refinement of formula (3) for \(\dot K\), obtained under the assumption that this capacitance is constant, will be required.

From the system of equations (1), the input conductance of the amplifier under consideration is found to be:

\[ Y_{\mathrm{in}}=\frac{\dot I_1}{\dot U_1}=j\omega C_{gk}\cdot \frac{ \begin{vmatrix} \dfrac{1}{R_k}+j\omega(C_k+C_{gk}), & j\omega C_2 \\[6pt] -\left(\dfrac{1}{Z'_a}+j\omega C_1\right), & \dfrac{1}{Z'_a}+j\omega(C_1+C_2) \end{vmatrix} }{ \begin{vmatrix} \dfrac{1}{R_k}+j\omega(C_k+C_{gk}), & j\omega C_2 \\[6pt] -\left(S+\dfrac{1}{Z'_a}+j\omega C_1\right), & \dfrac{1}{Z'_a}+j\omega(C_1+C_2) \end{vmatrix} }. \tag{4} \]

Here \(Z'_a=R_a+j\omega L_a\).

It follows from (4) that both at low \((\omega\to 0)\) and at very high \((\omega\to\infty)\) frequencies the input conductance of the stage is equal to \(j\omega C_{gk}\), and the dynamic capacitance is equal to the input capacitance of the tube. Between these limiting values there must be a decrease in the input capacitance owing to the appearance of a variable potential at the cathode.

Let us rewrite (4) in the form

\[ Y_{\mathrm{in}}=j\omega C_{gk}\, \frac{1}{ 1+ \dfrac{S j\omega C_2}{ \left[\dfrac{1}{R_k}+j\omega(C_k+C_{gk})\right] \left[\dfrac{1}{Z'_a}+j\omega(C_1+C_2)\right] +j\omega C_2\left(\dfrac{1}{Z'_a}+j\omega C_1\right) } }. \tag{5} \]

The second term of the denominator of the fraction entering (5) is considerably smaller than the first, since

\[ \frac{1}{R_k}\gg \omega C_2. \]

Therefore we shall not make a large error if we supplement \(j\omega C_2\left(\dfrac{1}{Z'_a}+j\omega C_1\right)\) to \(j\omega C_2\left[\dfrac{1}{Z'_a}+j\omega(C_1+C_2)\right]\).

Then (5) will be rewritten in the form

\[ Y_{\mathrm{in}}=j\omega C_{gk}\, \frac{1}{ 1+ \dfrac{S j\omega C_2}{ \left[\dfrac{1}{R_k}+j\omega(C_{gk}+C_2+C_k)\right] \left[\dfrac{1}{Z'_a}+j\omega(C_1+C_2)\right] } } = \frac{1}{1+Ae^{j\varphi}}. \tag{5′} \]

If complete rigor were observed in the derivations, it would be necessary in expression (5′) to separate the real and imaginary parts and then find the dynamic input capacitance and the active conductance. However, such a procedure leads to cumbersome expressions¹. Therefore we shall confine ourselves to an approximate estimate.

The quantity \(A\) tends to zero both for \(\omega\to 0\) and for \(\omega\to\infty\). The influence of the fraction \(Ae^{j\varphi}\) will be greatest at the maximum of \(A\). Let us find

maximum \(A\), neglecting, for simplicity, the presence of inductive correction in the anode circuit, i.e., assuming \(L_a=0\). For \(L_a=0\)

\[ A^2=\frac{S^2 R_k^2(1-x)^2\Omega^2}{\left[1+q^2(1+n)^2\Omega^2\right]\left[1+\Omega^2\right]}, \tag{6} \]

where

\[ n=\frac{C_{gk}+C_2}{C_k}, \qquad x=\frac{C_1}{C_a}. \]

Equating the derivative \(\dfrac{\partial A^2}{\partial \Omega^2}\) to zero, we obtain \(\Omega_{\max}^2=\dfrac{1}{q(1+n)}\) and

\[ A_{\max}=\frac{S R_k(1-x)}{1+q(1+n)}. \]

In this case the phase angle \(\psi_{\max}\) will be equal to

\[ \psi_{\max}=\frac{\pi}{2}-\operatorname{arctg}\sqrt{q(1+n)} -\operatorname{arctg}\frac{1}{\sqrt{q(1+n)}}=0, \]

since the last two angles complement each other to \(-\dfrac{\pi}{2}\).

Thus, the minimum value of the dynamic input capacitance is equal to

\[ C_{\mathrm{in.\ min}}= \frac{C_{gk}}{1+S R_k\cdot\dfrac{(1-x)}{1+q(1+n)}}. \]

For \(x=0.2,\quad S R_k=1.5,\quad q(1+n)=1\), we obtain, for example,

\[ C_{\mathrm{in.\ min}}=\frac{C_{gk}}{1.6}. \]

If, in this case, \(C_{gk}\) constitutes 0.4 of the total capacitance

\[ C_0=C_1+C_{gk}+C_0' \]

in the anode circuit, then the latter changes by only 15%.

Analysis of amplifier operation by the frequency method

In view of the complexity of taking into account the effect of changes in the input capacitance of the following stage, we shall confine ourselves to an analysis under the assumption that this capacitance is constant. In this case formula (3) remains valid for the complex gain factor. In accordance with (3), the expression for the normalized transfer coefficient will be

\[ \dot{M}=\frac{\dot{K}}{K_0} = \frac{1+j(k+q)\Omega+j^2 kq\Omega^2} {1+j\left[q+(1-x)m+1+(1-x)(\gamma-1)\right]\Omega+\cdots} \]

\[ \cdots \frac{\cdots}{+j^2\left[k+q+(1-x)xm+k(1-x)(\gamma-1)\right]\Omega^2+\cdots} \]

\[ \cdots \frac{\cdots}{+j^3 k\left[q+x(1-x)m\right]\Omega^3} = \frac{1+j a_1\Omega+j^2 a_2\Omega^2} {1+j b_1\Omega+j^2 b_2\Omega^2+j^3 b_3\Omega^3}. \tag{7} \]

To determine the optimum correction parameters corresponding to a “flat” frequency response, we obtain two equations

\[ \kappa^2+q^2=\left[q+(1-x)m+1+(1-x)(\gamma-1)\right]^2 -2\left[\kappa+q+(1-x)xm+\kappa(1-x)(\gamma-1)\right], \tag{8} \]

\[ \kappa^2 q^2=\left[\kappa+q+(1-x)xm+\kappa(1-x)(\gamma-1)\right]^2 -2\kappa\left[q+(1-x)m+1+(1-x)(\gamma-1)\right] \cdot \left[q+x(1-x)m\right]. \tag{9} \]

The first of them is represented by a parabola, whose vertex corresponds to
\(\kappa=-[\gamma(1-x)+x]\). The system of equations (8), (9) can be solved graphically, assigning \(\kappa\) and calculating \(q\) from equations (8) and (9). In Fig. 3 equations (8) and (9) are represented graphically for the region

Fig. 3.

of positive values of the parameters \(\kappa\) and \(q\). The course of the curves in Fig. 3 shows that the solution can also be found rather quickly by the method of successive approximations. For this purpose, assigning \(\kappa\) of order 1, we calculate \(q\) from equation (9), and then substitute the \(q\) found into equation (8) and determine \(\kappa\). Owing to the gentle course of curve 2 (equation (9)) and the steep slope of curve 1 (equation (8)), the very first approximation is already rather close to the required solution of the system (8), (9), and a second approximation proves entirely sufficient. For \(x=0\), \(\gamma=2.5\), \(m=0.08\), the optimum values of \(\kappa\) and \(q\) were obtained as \(\kappa=1.83\), \(q=1.84\). The corresponding normalized frequency response, calculated from the formula

\[ M=\sqrt{\frac{1+A_1\Omega^2+A_2\Omega^4}{1+A_1\Omega^2+A_2\Omega^4+B_3\Omega^6}}, \]

where \(A_1=a_1^2-2a_2,\ A_2=a_2^2,\ B_3=b_3^2\), is shown in Fig. 4 by curve 2.

For \(x'=0.5,\ \gamma=2.5,\ m=0.03\) we have \(\kappa=1.14,\ q=1.2\). The frequency response for this case is shown by curve 3 in Fig. 4. In the ideal case, when \(x=1\), i.e., the entire capacitance of the anode circuit is concentrated between the anode and cathode of the tube of the given stage, the numerator and denominator of expression (7) are reduced by \(1+jq\Omega\), and the latter becomes equal to

\[ \dot{M}=\frac{1+j^2\kappa\Omega}{1+j\Omega+j^2\kappa\Omega^2}, \tag{10} \]

i.e., it coincides with the analogous expression for a circuit with parallel inductive correction (curve 4, Fig. 4). This was to be expected, since owing to the absence of the capacitance \(C_2\), the feedback due to the current charging this capacitance is absent. The feedback at high frequencies produced by the current charging \(C_2\) can be eliminated by increasing the time constant \(C_kR_k\) so that \(q \gg 1\), for example by choosing as \(C_k\) a capacitor of capacitance \(5000\text{–}10000\ \text{pF}\). In this case, in the denominator one may neglect the terms standing next to \(q\) (leaving only the quantity \(\kappa\) in \(b_2\)), and expression (7) is again reduced by \(1+jq\Omega\), becoming identical with (10).

Fig. 4.

Thus, in the circuit of Fig. 1, as compared with the conventional circuit with simple correction, two large-capacitance capacitors are eliminated, while the gain and passband remain the same.

A serious drawback of the amplifier under consideration is its increased instability. It is associated with the fact that part of the parasitic voltage \(\dot{U}_n\) (Fig. 2) is here applied from the terminals of the power supply through \(R_\phi\) and \(C_\phi\) to the resistance \(R_k\) in the grid circuit of the first stage, whereas with the usual connection of the anode filter the first stage is not encompassed by parasitic feedback. The indicated drawback can be eliminated by means of the compensation described below.

Increasing the stability of an amplifier with a common filter

Let us find the voltage \(U_2'\) that appears at the anode of the first tube due to coupling through the common anode power-supply source. Omitting in the equivalent circuit of Fig. 2 the elements that are significant only for the high-frequency region, and replacing the voltage source \(\dot{U}_n\) by a current generator

\[ \frac{\dot{U}_n}{R_\phi}, \]

we obtain (for \(\dot{U}_1=0\)) the following equations of nodal potentials:

\[ \dot U_k\left(S+S_\mathrm{e}+\frac{1}{R_k}+\frac{1}{R_{i\mathrm{e}}}+j\omega C_\phi\right) -\dot U_\mathrm{e}\left(\frac{1}{R_{i\mathrm{e}}}+j\omega C_\phi\right)=0, \]

\[ -\dot U_k\left(S_\mathrm{e}+\frac{1}{R_{i\mathrm{e}}}+j\omega C_\phi\right) +\dot U_\mathrm{e}\left(\frac{1}{R_a}+\frac{1}{R_\phi}+\frac{1}{R_{i\mathrm{e}}} +j\omega C_\phi\right)-\dot U_2\frac{1}{R_a} =\frac{\dot U_n}{R_\phi}, \]

\[ -S\dot U_k-\dot U_\mathrm{e}\frac{1}{R_a}+\dot U_2\frac{1}{R_a}=0. \]

Hence

\[ \dot U_2'=\dot U_n\cdot \frac{ S+S_\mathrm{e}+\frac{1}{R_k}+\frac{1}{R_{i\mathrm{e}}} +\frac{SR_a}{R_{i\mathrm{e}}} +j\omega C_\phi\left(1+SR_a\right) }{ S+S_\mathrm{e}+\frac{1}{R_k}+\frac{1}{R_{i\mathrm{e}}} +\frac{R_\phi}{R_kR_{i\mathrm{e}}} +j\omega C_\phi\left(1+\frac{R_\phi}{R_k}\right) }. \]

For \(\dfrac{R_\phi}{R_k}=SR_a\) we have \(\dot U_2'=\dot U_n\); the voltage of the parasitic feedback is transmitted to the input of the second stage in the same way as in the absence of the anode filter, i.e., it turns out to be tens of times greater than in a rheostat amplifier with the same parameters.

The voltage transfer coefficient from the grid to the anode in the circuit of Fig. 2 for the low-frequency region is equal to

\[ K_{12}= -\frac{ \frac{S}{R_k}\left(\frac{1}{R_a}+\frac{1}{R_\phi}+\frac{1}{R_{i\mathrm{e}}}\right) +\frac{S}{R_\phi R_{i\mathrm{e}}} +\frac{S}{R_kR_a} +j\omega C_\phi S\left(\frac{1}{R_k}+\frac{1}{R_\phi}\right) }{ \frac{1}{R_aR_\phi} \left[ S+S_\mathrm{e}+\frac{1}{R_k}+\frac{1}{R_{i\mathrm{e}}} +\frac{R_\phi}{R_kR_{i\mathrm{e}}} +j\omega C_\phi\left(1+\frac{R_\phi}{R_k}\right) \right] }. \]

Recalculating \(U_2'\) from the anode to the grid of the first stage, we obtain

\[ \dot U_{2n}=\frac{\dot U_2'}{K_{12}}=-\dot U_n\cdot \]

\[ \cdot \frac{ \frac{1}{R_aR_\phi} \left[ S+S_\mathrm{e}+\frac{1}{R_k}+\frac{1}{R_{i\mathrm{e}}} +\frac{SR_a}{R_{i\mathrm{e}}} +j\omega C_\phi\left(1+SR_a\right) \right] }{ \frac{S}{R_k}\left(\frac{1}{R_a}+\frac{1}{R_\phi}+\frac{1}{R_{i\mathrm{e}}}\right) +\frac{S}{R_\phi R_{i\mathrm{e}}} +\frac{S_\mathrm{e}}{R_kR_a} +j\omega C_\phi S\left(\frac{1}{R_k}+\frac{1}{R_\phi}\right) } = \]

\[ =-\dot U_n\cdot\frac{a+j\omega b}{c+j\omega d}. \tag{11} \]

To compensate the feedback voltage, we shall use the network \(R_1 C_{1n} C_{2n} R_2\) (Fig. 1). Here \(R_2\ll R_9\ll R_{g1}\); \(R_3\) serves to prevent the amplifier from being driven when the signal source is disconnected. The capacitor \(C_1\), together with \(R_2\), forms one arm of the compensated divider, the other arm of which consists of \(R_{g1}\) and the input capacitance. In this way the danger of large distortions at high frequencies due to \(R_2\) is eliminated.

The voltage taken from the compensating circuit is equal to

\[ \dot U_{n1}=\dot U_n\cdot \frac{\dfrac{1}{R_2}+j\omega C_{2n}} {\left(1+\dfrac{C_{2n}}{C_{1n}}\right)\dfrac{1}{R_2} +j\omega C_2\left(1+\dfrac{R_1}{R_2}\right)} = \]

\[ = \dot U_n\,\frac{A+j\omega B}{C+j\omega D}. \tag{12} \]

Compensation of feedback in the first stage takes place if
\(\dot U_{n1}-U_{n2}=0\) at all frequencies. For this it is necessary that

\[ \frac{a}{c}=\frac{A}{C}, \qquad \frac{b}{d}=\frac{B}{D} \quad \text{and} \quad \frac{a}{b}=\frac{A}{B}. \tag{13} \]

Substituting into (13) the values of the corresponding coefficients from (11) and (12), we find the relations for calculating the parameters of the compensating circuit.

\[ \frac{R_1}{R_2} = \frac{S R_a\cdot\dfrac{R_{\phi}}{R_k}-1}{1+S R_a} \simeq \frac{R_{\phi}}{R_k}\cdot\frac{S R_a}{1+S R_a} =\nu, \tag{14} \]

\[ \frac{C_{2n}}{C_{1n}} = \frac{ -\dfrac{R_{\phi}}{R_k}\left[\left(S+S_e\right)R_{ie}+S R_a\right] +S R_a\left(\dfrac{R_{ie}}{R_k}+1\right) }{ \left[\left(S+S_e\right)R_{ie}+S R_a\right] +\left(\dfrac{R_{ie}}{R_k}+1\right) } - \]

\[ -1 \simeq \frac{ \dfrac{R_{\phi}}{R_k}\left[\left(S+S_e\right)R_{ie}+S R_a\right] +\dfrac{S R_a R_{ie}}{R_k} }{ \left[\left(S+S_e\right)R_{ie}+S R_a\right] +\dfrac{R_{ie}}{R_k} } =\chi, \tag{15} \]

\[ C_{2n}R_2 = \frac{ C_{\phi}R_{ie}(1+S R_a) }{ \left[\left(S+S_e\right)R_{ie}+S R_a\right] +\left(\dfrac{R_{ie}}{R_k}+1\right) } \simeq \]

\[ \simeq \frac{ C_{\phi}R_{ie}(1+S R_a) }{ \left[\left(S+S_e\right)R_{ie}+S R_a\right] +\dfrac{R_{ie}}{R_k} } =\lambda. \tag{16} \]

With the proposed compensating circuit it is also possible to eliminate the parasitic feedback in the first two stages. Indeed, recalculating the feedback voltage present at the anode of the second tube to its grid, we obtain (assuming the first two stages to be identical):

\[ \dot U_2''=-\dot U_n\cdot\frac{a+j\omega b}{c+j\omega d}. \]

If the first stage is corrected at low frequencies, the distortions in it may be neglected and \(\dot U_2''\) may be recalculated to the grid of the first tube by the formula

\[ \dot U_{n3} = - \frac{\dot U_2''}{K_0} = \frac{\dot U_n}{K_0}\cdot \frac{a + j\omega b}{c + j\omega d}. \]

The compensation condition will then have the form

\[ \dot U_{n1} + \dot U_{n3} - \dot U_{n2} = 0 \quad \text{or} \]

\[ \frac{A + j\omega B}{C + j\omega D} - \left(1 - \frac{1}{K_0}\right) \frac{a + j\omega b}{c + j\omega d} = 0. \]

Hence

\[ \frac{R_1}{R_2} = \frac{K_0}{K_0 - 1}\,\gamma, \tag{14′} \]

\[ \frac{C_2}{C_1} = \frac{K_0}{K_0 - 1}\,\varkappa. \tag{15′} \]

The expression for \(C_2R_2\) remains the same.

The questions of low-frequency correction of the amplifier in Fig. 1 were considered earlier [3]. It was shown that an amplifier with a common filter is equivalent to the usual correction circuit with an anode filter, having, in comparison with that used, a larger filter capacitance and a smaller resistance \(R_{\phi}\) ¹). Thus, in the amplifier of Fig. 1, not only are the separate capacitances \(C_k\) and \(C_e\) absent, but a reduction of the capacitor \(C_{\phi}\) is also permitted.

REFERENCES

1. Zeidler H. M. and Noe J. D., Pentriode Amplifiers. PIRE, 1948, No. 11.
2. X. Von-Xo. A compact wide-band amplifier. Diploma project, TPI, 1959.
3. Suslov I. A., Correction of distortions at the tops of pulses in amplifier stages with an unbypassed cathode resistance when feeding the screen grid from an anode filter. Izvestiya TPI, vol. 86, 1958.

¹) See formulas (11) and (12) in [3].

1. Detailed calculations of the dependence of \(C_{\mathrm{in}}\) on the frequency and circuit parameters are given in [2]. ↩