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.