27 . 0 Electromagnetic Wave Theory and Applications

A general method of analyzing the time-domain bi-directional coupling of a pair of nonuniformly coupled dispersionless transmission lines has been devised. The transmission line equations are decoupled using the method of characteristics and the equations are solved iteratively. In the cases with linear loads, the unit-step response can be obtained in closed-form to the first order approximation, and arbitrary excitations can be handled by convolution. General approximate solutions to the transient response on two identical, nonuniformly coupled transmission lines terminated with linear or nonlinear loads have been obtained through an iterative scheme. The iterative method is very useful when the coupling coefficients are slowly varying with position since the zeroth order or first order approximation would be sufficiently accurate yet much easier to calculate. Furthermore, with the help of newly devised special transformations, we have shown that both the codirectional coupling and contradirectional coupling of the problem with unit-step excitation and linear loads have closed form expressions up to the first order approximation. Arbitrary excitation can then be taken into account by convolution. This method is hence most efficient. As for nonlinear terminations, numerical integrations are performed along the characteristics. Examples have been given for both cases to illustrate the use of this method. Extension to problems in which the phase velocities of coupled lines are not equal, or where more than two coupled lines are involved, is also under consideration.