Coupled mode theory in a lossy, nonlinear transmission line system

Abstract

A method of analysis that uses the coupled mode formulation has been developed to study the coupling phenomenon in a system of two lossy, identical transmission lines. These lines are uniformly coupled and also have uniformly distributed, nonlinear shunt capacitance and series inductance. The transmission lines are excited at one end with two voltage sources of the same frequency but of different amplitude and phase, and are terminated with proper load impedances at the other end. The coupled mode theory has been developed with the aid of quasiharmonic analysis of the codirectional, nonlinear coupled lines. The analytical expressions for the power carried by each mode in the transmission lines can be obtained for a special case of the low loss system in which the phase difference of two coupled modes is assumed to vary slowly with the position along the line. The derived analytical expressions are also used to study the effect of changing input conditions and circuit parameters on the location where relative minima and maxima occur.