SELF-CONTROLLED IONIC TRANSDUCER

I. G. KULEEV

(Presented by the scientific seminar of the Electromechanical Faculty)

The grids of ionic transducers are supplied from a special current source. The use of a special current source for this purpose is associated with certain inconveniences in operation and with additional costs. As a rule, the current source feeding the grid has a constant frequency, which in individual cases may not satisfy the consumer. An ionic transducer is proposed that does not require a current source for feeding the grids and permits frequency regulation over wide limits. Fig. 1 shows the circuit of such a transducer.

Below are given the results of an investigation of the self-excitation of the transducer, and analytical expressions are presented which describe the phenomena occurring during self-excitation.

Self-excitation of oscillations

It is known that the circuit shown in Fig. 1 has oscillatory properties. Investigations carried out by the author have shown that under certain conditions this circuit can be self-controlled, i.e., can produce sinusoidal voltages of variable frequency without receiving excitation from outside.

These conditions are:

1. The grid potential at the moment of ignition of the thyratron must be positive and equal to 1–2 V. As follows from Fig. 2, in this case ignition of the thyratron occurs at a small anode voltage, without causing a surge of anode current.

2. The rate of rise of the voltage on the grid and its derivative must be greater than zero.

Fulfillment of this condition ensures the excitation of undamped oscillations [1].

1. The grid potential must be shifted in the direction of leading the anode potential by a time greater than the deionization time, i.e., by an angle \(\Theta\).

To explain the first condition of self-excitation, let us use Fig. 2.

In Fig. 2 is shown the ignition characteristic of the TG-235 thyratron for positive grid potentials.

In Fig. 2, \(U_a\) is the anode voltage. We see that with negative potentials on the grid, ignition can occur only at large anode voltages. At small anode voltages, a large positive grid potential is also required for ignition. However, at \(U_a = 30 \div 40\) V, ignition of the thyratron occurs at a grid potential lying within the limits from \(+1\) to \(+2\) V. Consequently, if at the moment when a positive potential is applied to the anode, a positive, increasing potential is applied to the grid, and if it leads the anode ...

voltage by the angle \(\Theta\), then the self-excitation conditions will be fulfilled, and harmonic oscillations will appear in the circuit.

The physical picture of the operation of a self-controlled ionic transducer may be represented as follows.

Let us suppose that, other conditions being equal, the grid potential of the first device is positive and higher than the grid potential of the second device. The probability of ignition of the first device under these conditions will be greater than that of the second. From the moment current is passed by the first device, capacitor \(c'\) will begin to discharge through the resistance \(R\) and the first device. As a result, the grid of the second device will instantaneously receive a large negative potential, preventing ignition of the arc of the second device. The change in the grid potential of the second device will occur in accordance with the time constant of its circuit. When the grid potential of the second anode reaches a positive value, ignition of the second device will occur. The current of capacitor \(c_1\) at the moment of discharge, being superposed on the current of the first thyratron, will extinguish its arc. The large negative potential on the grid of the first thyratron, obtained as a result of the discharge of capacitor \(c''\) through the resistance \(R\) and thyratron 2, will not allow it to pass current until the grid potential of the first device reaches a positive value. Thereafter the phenomena repeat.

Fig. 1.

Fig. 2.

From consideration of the operating process of the transducer, we note that the anode and grid potentials consistently acquire positive values. Such coordination in the behavior of the anode and grid potentials is the first condition for self-excitation of the transducer.

To prove the second condition for self-excitation, let us write the following obvious equalities for the circuit (Fig. 1) for zero initial conditions.

In the equalities it is assumed that \(c' = c'' = c\),

\[ \frac{i_{c1}}{p c_1} = \frac{i_c}{p c} + i_c R, \]

whence

\[ i_{c1} = \frac{i_c c_1}{c} + i_c p c_1 R. \]

By Kirchhoff’s first law

\[ i_1 = i_c + i_{c1}. \tag{1} \]

Substituting the values of \(i_{c1}\), we obtain

\[ i_1 = i_c + \frac{i_c c_1}{c} + i_c p c_1 R. \]

Grid bias voltage

\[ U_g = i_c r_g, \]

whence

\[ i_c = \frac{U_g}{r_g}. \]

Substituting the value of \(i_c\) into equation (1), we shall have

\[ i_1 = -\frac{U_g}{r_g} + \frac{U_g c_1}{c r_g} + U_g \frac{p c_1 R}{r_g}. \]

After multiplying and dividing \(i_1\) by \(U_g\), we shall have

\[ -\frac{i_1 U_g}{U_g} + \frac{U_g}{r_g} + U_g \frac{c_1}{r_g c} + p \frac{U_g R c_1}{r_g} = 0. \]

Let

\[ \frac{i_1}{U_g} = s \]

be the firing slope of the thyratron; then

\[ p \frac{R c_1}{r_g} U_g + U_g\left(\frac{1}{r_g} + \frac{c_1}{r_g c} - s\right)=0 \]

or

\[ p U_g = -\frac{U_g}{R c_1}\left(1 + \frac{c_1}{c} - s r_g\right). \tag{2} \]

It follows from equality (2) that the function \(U_g\) and its derivative will have the same signs in the case when

\[ s r_g > 1 + \frac{c_1}{c}. \tag{3} \]

It is known that a first-degree equation describes undamped oscillations in the case when the function and its derivative are greater than 0. In our case the phenomena described by equation (2) will be undamped if inequality (3) is satisfied. From all that has been said it follows that the synchronously varying potentials of the anode and the grid will be undamped. However, these oscillations will not be increasing, since the firing potential of thyratrons reaches a certain critical value at \(U_g = 2\ \text{V}\), after which an increase in the grid potential has no effect on the converter voltage, which, as is known, is the greater, the smaller the firing potential of the thyratron. The firing characteristic of the TT-235 thyratron is shown in Fig. 2, on which the critical point is denoted by the letter \(k\). From inequality (3) it follows that the slope of the firing characteristic \(s\), which depends on the voltage on the grid \(U_g\), has an essential significance for self-excitation of the circuit. The dependence of the thyratron firing slope on \(U_g\) is presented in Fig. 2. From the curve (Fig. 2) it follows that the smaller \(U_g\), the greater \(s\). At very large \(s\), a large anode voltage is required for firing the thyratron (Fig. 2), which the circuit cannot provide, since with an increase in the firing voltage the anode voltage decreases. On the other hand, a large voltage on the grid \(U_g\) leads to a decrease in \(s\), and consequently to a decrease in the probability of self-excitation of the thyratron, since at small \(s\) the system passes into damped oscillations.

The foregoing reasoning and formulas completely prove the possibility of fulfilling the second condition of self-excitation.

The third condition for self-excitation of the thyratron is the shift of the grid voltage toward leading the anode voltage by the amount \(\Theta\).

The phase shift between the grid and anode voltages is provided by the capacitor \(c\) in the grid circuit (Fig. 1). The vector diagram of the voltages for the part of the circuit containing capacitance is shown in Fig. 3; from it it follows that the thyratron grid voltage \(U_g\) leads the anode voltage \(U_{c1}\) by the angle \(\psi\).

Fig. 3.

In Fig. 3, \(\Theta\) is the lead angle necessary for normal commutation.

For \(\psi > \Theta\), the transducer is not excited. Very large values of \(\psi\) lead to violation of the self-excitation condition, according to which

\[ 1 + \frac{c_1}{s} < s r_g. \]

CONCLUSIONS

The proposed method of converting direct current into alternating current has the following advantages in comparison with existing ones.

1. It is cheaper than existing methods.
2. It is suitable for obtaining frequencies from several tens of hertz to several tens of kilohertz.
3. It does not require a special installation for supplying the grids.
4. It is convenient in operation.

REFERENCES

1. Krylov N. N. Pulse Engineering. State Publishing House for Literature on Communications and Radio, Moscow, 1950.
2. Kuleev I. G. Conversion of direct current into single-phase alternating current of variable frequency. Izvestiya TPI, vol. 76, 1954.