Existence and Uniqueness of a Periodic Solution of 3-Conductor Transmission Line System with Nonlinear Resistive Loads

Abstract

This paper is part two of the study of the electromagnetic compatibility characteristics of lossless transmission lines terminated by resistive polynomial type of nonlinear loads initially proposed by C. Paul. Based on the obtained system of two functional equations and two neutral equations for four unknown functions in part 1 of our analysis, we proved that the mixed problem is equivalent to an initial value problem for a functional system on the boundary. The system of functional equations is solved by fixed point method. Commonly, these problems are solved by numerical methods or by Laplace transformation method that is valid only for linear problems. Our results are verified versus real-world example. The method here proposed could be applied for nonlinear boundary conditions too.