Analytic solution of the Feldtkeller equation

In every reflectance-based application like broadband matching, circuit modeling, etc., a nonlinear equation following from energy conservation, the Feldtkeller equation, must be solved, in order to obtain real networks. In the literature, however, there is no analytic solution available but only numerical solutions. Consequently, the resulting error depends on the accuracy of the numerical tools. In this paper, an analytic solution is proposed, which is based on the modified ABCD-parameters of a lossless reciprocal two-port network. An algorithm is presented and examples are included to illustrate the implementation of the analytical method.