Wave Propagation in Polyphase Transmission Lines a General Solution to Include Cases Where Ordinary Modal Theory Fails

The solution of transmission line equations is usually written as a superposition of so called natural modes of exponential type. These are obtained through the use of a suitable transformation that decouples the original sets or N simultaneous 2nd order wave equations for voltages and currents into N independent equations. For such a transformation to exist the fundamental product matrix ZY must be diagonalizable. In a previous paper it has been shown that physically realizable transmission lines are possible for which ZY is not diagonalizable and to which ordinary modal theory does not apply. In the present paper a new generalized modal theory is developed for the purpose of including non-diagonalizing cases.