Complex Normalization of Scattering Matrices and the Problem of Compatible Impedances

A new complex normalization procedure for scattering matrices is reviewed and an existence theorem is presented for determining whether a given matrix is the scattering matrix of a passive system with a known complex normalization. The new technique is applied to the problem of impedance transformation using lossless networks (compatible impedances), and the technique is shown to lead to the problem´s complete solution. Examples which -illustrate the procedure are given.