Discrete time-domain analysis of nonuniform lossless coupled transmission lines

In this paper, a discrete time-domain method to analyze multiple coupled nonuniform lossless transmission lines has been presented. The solution is based on the steplines approximation of the nonuniform transmission lines and quasi-TEM assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is decomposed into a large number of coupled steplines with different characteristics. Then, using modal decomposition method, the system of coupled partial differential equations for each step is decomposed to a set of uncoupled ordinary wave equation. Using time-domain approach and invoking the boundary condition at the discontinuities of the adjacent steps, each step is modeled as continuous time linear filter characterized by a time-domain transfer matrix. Finally, this continuous time linear filter (for band limited input signal), is modeled as a discrete time-domain linear filter with constant matrix coefficients using sampling theorem. The method proposed here can be implemented using general purpose software packages like MATLAB.