Modal waves in multiconductor transmission lines by using fundamental matrix response

Abstract

The differential equations that model voltage and current for a multiconductor transmission line are written in matrix form. Supposing a time exponential solution through of the modal analysis the modal waves are obtained and solution of a ordinary matrix differential equation, thus determining the amplitude for voltage and current. The modal waves are given in terms of the fundamental matrix solution associated to the ordinary matrix differential equation. The decomposition of the modal waves in forward and backward propagators are used for determine the reflection and transmission matrices for junction in transmission lines. Circulant symmetric transmission lines are discussed, case in that the values for the self-impedance are the same as well as the mutual-impedance values and the same considerations to the admittance matrix. In particular, for these transmission lines are characterized the propagation constants and is observed that the number of multiconductors has effects only on a specific propagation constant. Numerical example of one multiconductor transmission line is presented allowing to observe important aspects of the methodology developed.