HIGH-POWER FINAL STAGE OF A HIGH-FREQUENCY GENERATOR BASED ON MODERN TUBES

N. A. LASHUK, V. I. TOLMACHEV

(Presented by the seminar of the High-Energy Laboratory, Nuclear Physics Research Institute)

To carry out a number of studies on the “Sirius” synchrotron, the need arose to develop a high-frequency (RF) generator with a power of 150–200 kW. In addition, in some cases it is necessary to increase the pulse power to 350 kW. In this connection, we were faced with the task of designing a generator of the required power and investigating the possibility of using it in a forced mode. The development of such a generator is possible only with the use of new, powerful, highly efficient radio tubes. In modern UHF generators, tetrodes with output power up to hundreds of kilowatts in continuous operation have become widespread [3]. Of the range of powerful modern tetrodes, the GU-53A tetrode with an output power of 80 kW most fully meets our requirements. Consequently, we can obtain the required power of 150 kW from two tubes. When operating tubes in a forced mode, a necessary condition is to ensure their nominal service life as guaranteed by the manufacturer. Of no small importance is the choice of the final-stage circuit, which largely determines the design, reliability, and cost of the generator as a whole. The main parameter determining the stability of operation of the stage is the value of the tube feedthrough capacitance. Table 1 gives the values of the interelectrode capacitances of GU-53A tubes for two connection circuits.

Table 1

As can be seen from the table, the feedthrough capacitance has the smallest value in the common-grid circuit. In addition, the advantage of the inverted circuit lies in a simpler method of neutralization (sometimes there is no need for it at all), which makes it possible to use powerful tubes effectively. On this basis, we chose a push-pull inverted circuit. Despite the fact that in the inverted circuit the principal advantage of tetrodes is lost—the high amplification factor

in power; this loss is compensated for by the high stability of operation of the stage.

In the case when it is necessary to obtain maximum power from the generator with good efficiency, the critical mode is used; in this case the utilization factor of the anode voltage approaches unity, and the minimum residual voltage at the anode amounts to \((5 \div 15\%)\) of the value of \(E_a\). To obtain the critical mode, the value of the anode load must be chosen from the following considerations [2]:

\[ R_{a\text{cr}}=\frac{U_{a\text{cr}}}{I_a}<\frac{E_a-U_{\sim}}{i_{a0}\cdot h_i}, \tag{1} \]

where \(E_a\) is the value of the supply voltage,
\(h_i\) is the utilization factor of the anode current.

If the magnitude of the anode-current pulse is not limited by emission, then the output power does not decrease when the load resistance is reduced, and under certain conditions reaches a maximum. In generator tubes having a cathode made of thoriated carburized tungsten, the emission current is not limited by the saturation effect. Therefore, in calculations it may be assumed that the emission current is limited only by the permissible dissipated powers on the electrodes. Assuming that the residual voltage at the anode increases in proportion to the growth of the emission current, the maximum power delivered by the generator in the critical mode will be equal to [2]

\[ P_{\sim \max}=\frac{1}{2}\cdot\frac{E_a^2}{R_i^*}\cdot \frac{\dfrac{R_a}{R_i^*}} {\left[\dfrac{R_a}{R_i^*}+\dfrac{1}{\varphi(\Theta)}\right]}, \tag{2} \]

and the consumed power is

\[ P_0=E_a\cdot i_M\cdot\psi(\Theta)= \frac{E_a^2\psi(\Theta)}{R_i^*\varphi(\Theta)} \left[ \frac{1} {\dfrac{R_a}{R_i^*}+\dfrac{1}{\varphi(\Theta)}} \right]. \tag{3} \]

The efficiency of the anode circuit is determined by the expression

\[ \eta=\frac{\varphi(\Theta)}{\psi(\Theta)}\cdot \frac{\dfrac{R_a}{R_i^*}} {\left[\dfrac{R_a}{R_i^*}+\dfrac{1}{\varphi(\Theta)}\right]}. \tag{4} \]

where \(R_a\) is the load resistance;

\[ \psi(\Theta)=\frac{I_{a0}}{I_{am}};\qquad \varphi(\Theta)=\frac{I_{a1}}{I_{am}} \]

is the coefficient of expansion of the anode-current pulses;

\(I_{am}\), \(I_{a1}\), and \(I_{a0}\) are the anode-current pulses, the first harmonic of the current, and the dc component;

\(\Theta\) is the anode-current cutoff angle.

The equivalent circuit of a generator operating in the mode of maxi-

low power, is shown in Fig. 1. The generator emf is equal to the constant anode supply voltage \(E_a\), and the internal resistance is \(\dfrac{R_i^*}{\varphi(\Theta)}\). From analysis of the equivalent circuit it is seen that the maximum output power \(P_{\sim \mathrm{opt}}\) is attained when the load \(R_a\) is equal to the internal resistance of the source. In this case

\[ P_{\sim \max}=\frac{1}{8}E_a^2\,\frac{\varphi(\Theta)}{R_i^*}. \tag{5} \]

In this mode the efficiency of the generator is very low. To achieve a higher efficiency it is necessary to operate with an increased load resistance, i.e.,

Fig. 1. Equivalent circuit of the generator.

\[ R_a>\frac{R_i^*}{\varphi(\Theta)}. \tag{6} \]

The generator efficiency reaches its greatest value at very large values of \(R_a\) and small cutoff angles. Usually, in the critical mode one takes \(R_a \simeq 20\,R_i^*\) equiv. and \(\Theta=90^\circ\).

\[ \tag{7} \]

For a stage using GU-53A tubes, \(R_i^*=16\ \Omega\), and for \(E_a=12\ \mathrm{kV}\),

\[ P_{\sim \max}=560\ \mathrm{kW}, \]

\[ P_{0\max}=1400\ \mathrm{kW}, \]

\[ P_{a\max}=P_{0\max}-P_{\sim \max}=840\ \mathrm{kW}. \]

In our mode \(F_i=4\ \mathrm{Hz}\), \(\tau_u=40\ \mu\mathrm{s}\), and the minimum duty factor

\[ q=\frac{T}{\tau_u}=6.25. \]

In this case an anode dissipation power \(P_a\) in the pulse of up to \(300\ \mathrm{kW}\) is permissible.

Proceeding from the above, and using (7), we calculated the stage using GU-53A tubes. The calculated data for one tube are given in Table 2.

Table 2

The power gain coefficient in this case is

\[ A=\frac{P_{\sim}}{P_{\mathrm{in}}}\simeq 15. \]

The schematic diagram of the stage is shown in Fig. 2. The anode circuit is made of tubes 220 mm in diameter, in the form of a short-circuited line whose length is adjusted by a bridge. Coupling to the load is inductive and is accomplished by means of variable vacuum capacitors of type KP1-4-5/100.

Fig. 2. Schematic diagram of the stage.

Power is delivered to the load through a coaxial feeder with a wave impedance of 51 ohms, made of tubes 140 and 60 mm in diameter. To make it possible to measure the incident and reflected waves, reflectometers are installed in the feeder. Matching of the generator’s balanced output to the unbalanced feeder is accomplished by means of a half-wave U-bend. The cathode of each tube is insulated at high frequency by quarter-wave coaxial lines. Owing to the low input resistance of the tubes \((R_{\mathrm{in}}\simeq 20\ \text{ohms})\), the excitation to each tube is fed through three parallel-connected RKK-5/18 cables. The control-grid and screen-grid circuits are thoroughly bypassed by capacitors.

The stage is designed for operation in both continuous and pulsed modes. In pulsed mode, modulation is performed by rectangular pulses applied to the anode and the second grid, while the pulse shape is regulated by modulation on the first grid. For tuning the stage, a load equivalent with a resistance of 51 ohms and an average power of

50 kW. The design provides complete shielding from RF radiation and good matching to the feeder.

Tuning of the stage was carried out in continuous mode at a low power level and did not present any special difficulties. The operation of the stage was very stable; no parasitic oscillations were observed. During tuning it was noted that the extrema of the grid and anode currents do not coincide, i.e., the stage requires neutralization of the feedthrough capacitance.

Tests at a high power level were carried out in pulsed mode, which is explained by the insufficient power of the high-voltage rectifier and of the load equivalent. Figures 3 and 4 give experimental data on the dependence of the generator power in the load on the anode voltage and the excitation voltage. As can be seen from the graphs, there is a large reserve in excitation power, since even at \(E_a = 10\) kV the stage enters an overdriven mode.

Fig. 3. Dependence of generator power
\(P_{\sim}=f(E_a)\) at \(E_v=\mathrm{const}\).

By increasing the voltage to 12 kV, it is possible to obtain a load power of up to 360 kW, which agrees well with the calculated data.

The power was measured calorimetrically. The accuracy of measurement by this method is determined mainly by the accuracy of measuring the water flow rate and is approximately \((10 \div 15)\%\). Simultaneously with the measurement of RF power in continuous mode, reflectometers were calibrated; with their aid the RF power was then measured in pulsed mode.

The expression for measuring power with reflectometers has the form [1]:

\[ P_{\sim}=\frac{U_{\phi}^{2}}{2Z_{\mathrm{n}}}(1-\Gamma^{2}) =\frac{K^{2}U_{\mathrm{p}}^{2}}{2Z_{\mathrm{n}}}(1-\Gamma^{2}), \tag{8} \]

Fig. 4. Dependence of generator power \(P_{\sim}=f(E_{v})\) at \(E_{a}=\mathrm{const}\).

Fig. 5. Dependence of power in the load on the voltage from the reflectometer.

where \(U_{\mathrm{f}}\) is the voltage amplitude in the feeder,
\(Z_{\mathrm{n}}\) is the load resistance.

\[ \Gamma=\frac{U_{\mathrm{o}}}{U_{\mathrm{p}}} \]

is the reflection coefficient,

\(U_{\mathrm{p}}, U_{\mathrm{o}}\) are the amplitudes of the incident and reflected waves from the reflectometer,

\[ K=\frac{U_{\mathrm{f}}}{U_{\mathrm{p}}} \]

is the coefficient that accounts for the relation between the voltage in the feeder and the voltage from the reflectometer.

This coefficient was calculated theoretically and then verified experimentally. In our case \(Z_{\mathrm{n}}=W_{\mathrm{f}}=51\ \Omega\), \(K=116\), and \(\Gamma=0.15\). In this case

\[ P_{\sim}=132\,U_{\mathrm{p}}^{2}. \tag{9} \]

Figure 5 shows the dependence of the power in the load on the voltage from the reflectometer.

The operation of the stage was investigated in several modes: with self-bias, with external bias, and in the mode of amplifying modulated oscillations. The results obtained are in good agreement with the calculated data.

REFERENCES

1. H. Meinke and F. Gundlach. Radio Engineering Handbook. Moscow, Gosenergoizdat, 1962.

2. D. P. Linde. Radio Transmitting Devices. Moscow, “Energiya,” 1969.

3. B. S. Agafonov. Calculation of Operating Modes of Shortwave and Longwave Generator Tubes. Moscow–Leningrad, “Energiya,” 1966.