Steady-State Transmission through a Network Containing a Single Time-Varying Element

Abstract

This paper presents a method of steady-state analysis of a linear network, of arbitrary degree of complexity, containing a single periodically-varying element. The proposed method makes full use of circuit theoretical ideas, such as impedance matching and tearing apart, and of iteration techniques which are particularly suitable for automatic computation. The proposed method has the additional feature of leading to the amplitude and phase of all sidebands and of giving a bound on the error if the iterations are stopped at any particular point. More precisely, it is shown that, provided the impedance seen by the time-varying element becomes capacitive at very high frequencies, the complete solution can be found within an arbitrary amount of accuracy.