Some Considerations on the Choice of the Type of Receiving-Amplifying Tubes for a Multistage Resonant Amplifier

I. Sh. Solomonik

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

When choosing receiving-amplifying tubes for a broadband resonant amplifier, one must take into account the amplifier’s tendency toward self-excitation, the instability of the amplifier passband when tubes are replaced, and the need to amplify signals with a broad frequency spectrum. In order for the amplifier being designed to satisfy all these requirements, it is usually necessary, through a number of successive approximations, to find the most acceptable compromise parameters of the amplifier; this leads to nonoptimal use of the selected tube types.

Very often, for broadband resonant amplifiers, an effort is made to use tubes with a large transconductance, which in many cases leads to unjustified expenditure of power-supply energy, since for a given frequency of the signals being amplified and for the selected set of tube parameters it is not possible to realize a large tube transconductance. It can be shown that, for a definite frequency of the received signals, there exists an optimal set of tube parameters that ensures fulfillment of all the above-mentioned technical requirements imposed on the amplifier.

It is known that the gain coefficient of a stage amplifying the necessary frequency spectrum is determined from the expression

\[ K_{\Delta F}=\frac{S}{2\pi \Delta F \varphi(n)C}, \]

where \(S\) is the transconductance of the tube characteristic;
\(\Delta F\) is the passband of an \(n\)-stage resonant amplifier;
\(\varphi(n)\) is a coefficient accounting for the widening of the passband for one amplifier stage;
\(C\) is the total capacitance of the resonant circuit.

However, when the amplifier operates in the high-frequency region, it is risky to accept this gain coefficient without checking the stage for its tendency toward self-excitation. Therefore the gain coefficient is checked by the formula of V. I. Siforov [1]

\[ K_{\Delta F}<K_{\mathrm{st}}=0.42\sqrt{\frac{S}{\omega C_{ga}}}, \]

where \(K_{\mathrm{st}}\) is the maximum stable gain coefficient;
\(\omega=2\pi f\) is the angular frequency of the signals being amplified;
\(C_{ga}\) is the feedthrough capacitance of the tube.

We shall regard as the optimum operating mode of a wide-band resonant amplifier the mode in which the maximum stable gain coefficient of each stage \(K_{\mathrm{st}}\) is equal to the gain coefficient of a stage passing the entire required frequency spectrum \(K_{\Delta F}\):

\[ 0.42\sqrt{\frac{S}{\omega C_{ga}}} = \frac{S}{2\pi \Delta F \varphi(n)C}. \tag{1} \]

Taking into account the permissible relative change in the capacitance of the resonant circuit of one stage when tubes are replaced,

\[ \frac{\Delta C}{C}=\xi d=\frac{\xi \Delta F \varphi(n)}{f} \tag{2} \]

and replacing in expression (1) the product \(\Delta F\varphi(n)C\) by the quantity \(\dfrac{\Delta C}{\xi}f\) from expression (2), we obtain

\[ \frac{1.1}{\xi^2}f=\frac{SC_{ga}}{\Delta C^2}, \tag{3} \]

where \(\xi\) is a coefficient characterizing the stability of the passband when tubes are replaced.

For multistage amplifiers, usually \(\xi=0.25\div0.33\) [2]; in this case the change in passband due to tube replacement does not exceed 10%.

Fig. 1. Graph for choosing the quantity \(\xi=\varphi\left(\dfrac{\Delta F_p}{\Delta F_n}, n\right)\).

Below are given reference data (see the table) for the most common types of receiving-amplifying tubes, from which it is possible

Table

determine, using the proposed method, the optimal amplification frequencies for the specified requirements on the stability of the amplifier passband. In the last column of the table, for each tube type, the values of the optimal frequencies calculated for the case \(\xi=0.3\) are given.

If it is necessary to choose the type of tube for a multistage resonant amplifier under less “stringent” requirements on the stability of the passband, one may use the graph of A. A. Kolosov (Fig. 1), which establishes the dependence

\[ \xi=\varphi\left(\frac{\Delta F_p}{\Delta F_n},\, n\right), \]

where \(\Delta F_p\) is the assumed passband of the detuned amplifier (after replacement of the tubes);

\(\Delta F_n\) is the passband of the tuned amplifier (before replacement of the tubes);

\(n\) is the number of amplifier stages.

From the selected value of \(\xi\), and the tube parameters \(S\), \(C_{ga}\), and \(\Delta C\), we determine the optimal frequencies for the various types of receiving-amplifying tubes. For the amplifier being designed, we choose the tube for which the set of parameters

\[ \frac{SC_{ga}}{\Delta C^2} \]

corresponds most closely to the frequency of the signals to be amplified. In this case, the minimum capacitance of the resonant-amplifier circuit is chosen from the relation

\[ C=\frac{\Delta C}{\xi d}. \]

Conclusions

1. The optimal choice of the type of amplifying tube corresponds to the case in which the frequency of the signals to be amplified and the requirements on passband stability are related to the tube parameters by condition (3).

2. In the absence of tubes that exactly satisfy condition (3), it is necessary to choose a tube for which the set of parameters

\[ \frac{SC_{ga}}{\Delta C^2} \]

most closely satisfies condition (3), while still remaining less than

\[ 1.1\,\frac{f}{\xi^2}. \]

Literature

1. Siforov V. I., Radio Receiving Devices. Voenizdat, 1954.
2. Kolosov A. A., Resonant Systems and Resonant Amplifiers. Svyazizdat, 1949.