A coupled mode analysis of a parallel plate wave guide with non-uniform impedance boundaries is presented. Closed form solutions for the first order estimates of the modal amplitude coefficients are obtained assuming small variations. An analytical comparison with an exact mode-matching solution in the case of a stepwise change of the lower wall impedance is given and verified numerically. As an extension of the method, a wave guide with perfectly conducting but rough walls is analyzed. The possibility of selective mode coupling is pointed out.
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