A mathematical analysis of a series circuit containing periodically varying resistance

Abstract

IN RECENT years a great deal of attention has been given to the general theory and performance of circuits the parameters of which are functions of the time. The mathematical analysis of circuits of this type leads to the solution of linear differential equations with variable coefficients. Examples of linear time-varying circuits of practical importance occur in the theory of electrical communications. Frequency modulation circuits, for example, involve variations of capacitance or, to a lesser extent, inductance. The carbon microphone circuit consists of essentially of a variable resistance the value of which is varied by some source of energy outside the circuit. The condenser microphone circuit contains a variable capacitance. Super-regeneration involves circuits that contain a periodically-varying resistance parameter.