Propagation on Overhead Transmission Lines I-Theory of Modal Analysis

This paper will investigate the technique of modal analysis applied to propagation of signals on overhead transmission lines. The propagation problem is first analyzed in phase quantities at a constant frequency and then with modal transformations in the original differential equations. From the model analysis, properties of modal transformations are deduced. This analysis shows that when earth correction terms are used in the description of the transmission line, the propagation constant matrix can be used to determine the modal transformations; it is also demonstrated that to evaluate the phase quantity results numerically it is necessary to perform a modal (eigenvalue) transformation. The general equations, evaluated for perfect earth, show that the surge impedance matrix can be used to determine the modal transformations, as has been done by previous authors.