ON THE CALCULATION OF AN EQUALIZING REACTOR FOR PARALLEL OPERATION OF IGNITRONS

V. M. Razin

Sometimes the overload capacity of an ignitron proves to be insufficient in magnitude. In such cases it is necessary to connect two ignitrons in parallel. If they are connected without any additional devices, then, owing to some difference in their characteristics, the distribution of the total current will be such that one ignitron will carry a greater load, or will take it entirely upon itself. To equalize the current in the anode circuits of both ignitrons, a so-called equalizing reactor is inserted in these circuits according to the diagram of Fig. 1 [1].

When such a reactor is used, an accidental increase of the current in one ignitron is accompanied by a corresponding increase of the voltage on the other ignitron and, consequently, by equalization of the currents in both ignitrons. In this case the equalizing reactor has practically no influence on the total current, if active losses are not taken into account, since the magnetomotive forces of the windings in the separate anode circuits are directed oppositely and the coefficient of coupling between these windings is close to unity.

However, as indicated in the literature [2] and confirmed in practice, there are as yet no circuits for ignitron firing that completely exclude the possibility of firing failures. This circumstance imposes certain restrictions on the choice of parameters of the equalizing reactor.

Let us consider the nature of these restrictions for one particular case of parallel operation of ignitrons in the discharge circuit of the diagram of Fig. 2.

In this circuit a capacitance \(C\), charged from some source to a voltage \(U\), is discharged into an inductance \(L\) through two parallel-connected ignitrons with the use of an equalizing reactor. The presence of failures in the firing of the ignitrons creates the possibility of overloading the ignitrons both in current and in voltage, which may adversely affect the service life of the ignitrons. By proper selection of the parameters in the circuit of Fig. 2, the magnitude of these overloads can be limited within definite bounds.

In parallel operation, the total maximum surge current passing through the ignitrons is:

\[ I_m=\frac{U}{\sqrt{\frac{L}{C}}}. \tag{1} \]

Here \(I_m\) is the amplitude of the total current, and \(U\) is the voltage on the capacitance \(C\) (before discharge).

Through each ignitron there flows a current:

\[ I_n=\frac{I_m}{2}. \tag{2} \]

In this case, we do not take into account at all the influence of the equalizing reactor. If, however, when firing pulses are applied simultaneously to the igniters of both ignitrons, only one of them is fired, then one may

Fig. 1

Fig. 2

assume that in this case the capacitance discharges into the circuit shown in Fig. 3.

Fig. 3

The accepted assumption will be valid in the case when the voltage drop across the ignited ignitron is much less than the voltage across the capacitance \(C\).

Under these conditions the ignitron that has fired alone passes the entire current in the discharge circuit. The amplitude of the current through this ignitron will be equal to:

\[ I_n < I'_n = \frac{U}{\sqrt{\dfrac{L+L_{op}}{C}}} < I_m . \tag{3} \]

In this case we take into account the influence of the inductance \(L_{op}\) of one winding of the equalizing reactor on the magnitude of the current amplitude in the discharge circuit.

As is seen from expression (3), the current amplitude in the circuit will be smaller than the magnitude of the total current amplitude during parallel operation of the ignitrons, but greater than the current amplitude through one ignitron under the same parallel operation. The magnitude of the ignitron current overload can be characterized by the current load factor \(K_T\), whose value is determined from the following expression:

\[ K_T=\frac{I'_n}{I_n}. \tag{4} \]

Solving (1), (2), (3), and (4) simultaneously, we obtain the following dependence of the ratio of the inductances of the reactor and the circuit on the magnitude of the current load factor:

\[ \frac{L_{op}}{L}=\frac{4}{K_T^2}-1. \tag{5} \]

The dependence of the inductance ratio on the current load factor for several values of this factor is presented in Table 1.

Table 1

On the basis of the data in Table 1, by specifying a certain value of the current load factor, one can determine the magnitude of the inductance of one winding of the equalizing reactor for this case. It also follows from these data that the ignitron will operate, in the event of missed firings, without overload if the inductance of one reactor winding is greater than the inductance of the discharge circuit by not less than a factor of three.

In parallel operation of ignitrons it is also necessary to take into account the circumstance that the ignitron that has not fired will in this case be under increased voltage. Under these conditions the equalizing reactor may be regarded as a voltage-boosting autotransformer with a transformation ratio of 1:2 (Fig. 3).

The voltage drop \(U_{op}\) across one winding of the equalizing reactor at the beginning of the discharge is determined from the expression:

\[ \frac{U_{op}}{U}=\frac{L_{op}}{L+L_{op}}=\frac{1}{1+\dfrac{L}{L_{op}}}. \tag{6} \]

The ignitron that has not fired will at this moment be under the voltage:

\[ U' = 2U_{op}. \tag{7} \]

By analogy with the definition of the ignitron current load factor, the ratio of the voltage amplitude on the ignitron that has not fired to the voltage amplitude on it during normal operation may conventionally be called the voltage overload factor \(K_n\). The value of the latter coefficient is evidently determined from the equality:

\[ K_n = \frac{U'}{U}. \tag{8} \]

Solving (5), (6), (7), and (8) together, it is not difficult to find the relation between the two coefficients:

\[ K_n = 2 - \frac{K_T^2}{2}. \tag{9} \]

The dependence of the voltage overload factor on the current load factor, calculated by formula (9), is presented in Table 2.

Table 2

Solving the equations given above, it can readily be established that \(K_n = 1\) when \(K_T = 1.43\) and \(L_{op}/L = 1\), i.e., the conditions can be found under which the voltage on the anode of the ignitron that has not fired will not exceed the permissible value.

Guided by the considerations set forth above, in each particular case one should determine the values of the coefficients \(K_T\) and \(K_n\), and, in accordance with this, select in the proper manner the ratio of the parameters in the circuit of Fig. 2. If necessary, considerations of this kind may also be used in the operation of ignitrons in circuits of another type, as well as in the parallel operation of thyratrons under the corresponding conditions.

Thus, with a proper choice of parameters in a circuit with parallel connection of ignitrons, it is possible to ensure such operating conditions that, even in the presence of ignition failures, the ignitrons will not experience overloads in current and voltage. This can thereby extend the service life of the ignitrons.

REFERENCES

1. B. M. Shlyaposhnikov. Ignitron Rectifiers. Transzheldorizdat, 1947.
2. A. A. Gorelik. Industrial Electronics. GEI, 1951.