Associated resistive and discrete circuits in the qualitative analysis of networks of distributed and lumped circuits

The well-posedness of both the analytical and the numerical models describing networks of distributed and lumped circuits is studied, by means of a general procedure that is based on the extension to such networks of the concept of associated resistive circuit and discrete resistive circuit. In this way the analysis of the overall network reduces to the study of a pure resistive circuit, and conditions ensuring the existence, uniqueness and regularity of the analytical and numerical solutions are easily formulated. The associated and discrete circuits may be obtained by exploiting the features of a particularly convenient time-domain equivalent representation of transmission lines, that allows to uncouple the two line ends. Some case-studies are carried out, and suggestions are given in order to recast ill-posed problems in higher-order well-posed models