Exponentially tapered non-uniform transmission lines

We solve the transmission line equations for a non-uniform transmission line (NUTL). The analytical method used is different to the Kuroda´s one. First we find the solution in terms of voltage and current waves, then the expression of input impedance that allow us to find the R=const and X=const loci. In particular the solution is found for an exponential NUTL. We find the correspondent representation of the Smith chart. The NUTL has more advantages with respect to the uniform one. In fact we can use the generalised Smith chart to solve easily the problem of a NUTL loaded by a complex impedance. Moreover, we can use the NUTL to match lines with different sections and to model multilayered semiconductor structures. Finally, we show the normalised power behaviour for an exponentially tapered NUTL when the tapering factor is varying