The Theory of Linear-Sinoidal Oscillations

Abstract

Constant frequency arc discharges; theory assuming direct current supply and arc potential drop to remain constant.---A vacuum arc is shunted with inductance, capacitance and resistance in series which constitutes a discharge circuit. The arc is supplied with direct current through a large inductance. The arc vapor is ionized and de-ionized at a constant frequency. The variations of potential and current in the discharge circuit are termed linear-sinoidal oscillations. Mathematical expressions are derived for the following quantities in terms of the priming angle and damping angle, viz., the logarithmic decrement, ratio of natural frequency to discharge frequency, impedance factor and ratio of the effective discharge circuit current to the direct current. These quantities are expressed in terms of transcendental functions of the angles, hence relations between them are determined by means of a chart and a table. Expressions for potentials at the instants of priming (critical ionization) and unpriming are given. The relation between the values of the direct current and effective currents through the arc and in the discharge circuit is established. The actual fluctuation of the direct current supply is approximately determined. The counter E.M.F. of an oscillator having a coupled secondary oscillatory circuit varies in a manner similar to the counter E.M.F. of a motor.De-ionization of arc vapor; experimental determination of the rate.---An arc is extinguished by means of initiating a series of linear-sinoidal oscillations of decreasing frequency. The values of the priming angle, ratio of frequencies, discharge frequency, unprimed interval, re-ignition potential and other quantities are approximately determined for the initial oscillations. An expression for the numerical value of the rate of de-ionization is given.Stability of an arc oscillator.---The values of series resistance to produce stability depends upon discharge circuit resistance, rate of de-ionization and rate of change of the rate of de-ionization. Auxiliary means to produce a constant discharge frequency are required to stabilize an efficient arc oscillator for radio signalling.