Application of the Operator method for Calculating the Charging Regimes of a Forming Line with Distributed Parameters

Abstract

This paper presents an analysis of systems described by linear differential equations using the operator method, with electrical circuits as an illustrative example. The key advantage of the operator method lies in its ability to transform a system described by differential equations into a system of algebraic equations. A classification and comparison of various methods for analyzing electrical circuits is provided. The transfer function is defined as the solution to the operator equation of a linear system, and it is demonstrated that this function serves as a generating function enabling both frequency-domain and time-domain analysis. An analytical relationship is established between the transfer function and the frequency/time characteristics of a linear circuit. Using a line with distributed parameters as an example, the paper derives the solution of partial differential equations and illustrates the benefits of the operator method. Lines with distributed parameters are widely used in radio engineering, telecommunications, and in charged particle accelerator physics as pulse signal generators. The frequency and time characteristics of such a line are calculated for arbitrary load and open-circuit conditions using various methods.