Relations Existing between Voltage Impulses of Exponential Form and the Response of an Oscillating Circuit

Abstract

The superposition integral is used to express the voltage produced in the inductance of a tuned circuit in response to a voltage impulse of exponential form. The expression is given in terms of the voltage and time constant of the impulse and the frequency and decrement of the oscillating circuit. This method is more direct and more easily manageable than the conventional method which expresses the relations in terms of the current produced in the secondary or oscillating circuit in terms of the voltage applied to this circuit by the primary or exciting source. The conventional equation, Ldi/dt+Ri+q/C=E may be quite troublesome with certain forms of voltage E. Comparisons are made between oscillograms of an experimental circuit and curves calculated from theory. A simple graphical method is given for determining the constants of an exponential impulse from the response curve and known constants of the oscillating circuit. General conclusions are drawn which are of interest relative to radio interference.