Inhomogeneous layered planar structures: an analysis of reflection coefficient

In this paper we find the solution of telegrapher's equations for a non-homogeneous medium applying the theory of hypergeometric functions. Also we show that such a medium is described by means of a stratified structure, so we can use the developed theory for microwave components. We find the behavior of the reflection coefficient and compare it with other known results present in literature. Moreover, we show how an exponentially tapered non uniform transmission line (ETNUTL) can be treated as a high-pass filter. It is found that the exponential profile improves the performance of the filter and the normalized transmission coefficient is given for different values of tapering factor. Finally, we find a lumped equivalent circuit for the filter, whose elements are dependent on the tapering factor. The high-pass characteristics of an ETNUTL are verified with techniques in the frequency domain.