In this paper we present a time-domain method for analyzing multiple coupled nonuniform lossless transmission lines under pure TEM assumption. The method of the solution is based on the steplines approximation of the nonuniform transmission lines. Using steplines approximation the system of coupled nonuniform microstrip lines is subdivided large number of coupled steplines with different characteristics. Then using modal decomposition method the system of coupled partial differential equations for each step are decomposed to a number of uncoupled ordinary wave equations which are then solved using time-domain solution of the wave equation.
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