Synthesis Of Complex Lossless 2-Ports

A new synthesis algorithm is presented for the realization of a doubly terminated complex lossless two-port from a given canonic set of scattering polynomials. The synthesis algorithm is based entirely on polynomial evaluations and thus polynomial arithmetic and routines for zero finding are not needed. The accuracy problem due to coefficient sensitivity is avoided. In particular, explicit knowledge of the intermediate polynomials is not required. The simplicity and functionality of the algorithm are based on a new representation of elementary sections given by a set of canonic parameters, namely the transmission zero of the section, the reflectance evaluated at the transmission zero and, for reciprocal sections, the return group delay evaluated at the transmission zero. A great deal of freedom is available, since transmission zeros with any multiplicity and located anywhere in the complex plane are realized independently. Also, complex networks composed exclusively of either inductors or capacitors as the dynamic elements are possible. An example is given to illustrate the robustness of the algorithm.