Lossless Transmission Lines Terminated by Linear and Nonlinear RLC-Loads

Abstract

Here we consider lossless transmission lines terminated by a circuit consisting of linear and nonlinear RGCL-loads. First we overcome a difficulty caused by nonlinear boundary conditions utilizing Kirchhoff’s laws. The problem arising is to choose as many equations as are the unknown functions. Then we formulate the mixed problem for the hyperbolic system, reduce the mixed problem to an initial value problem on the boundary and obtain a neutral system with respect to new variables. Further on we prove an existence-uniqueness theorem for periodic solution in lossless case.