On complex normalized scattering matrices [n-port networks]

A review is presented of recent results on the relations between an n-port N terminated in n passive non-Foster load impedances and the augmented network N_a that is obtained when N is augmented by the reactance two-ports of the Darlington realizations of the load impedances. The author emphasizes the perfect equivalence of the complex normalized scattering matrix of N and the unit-normalized scattering matrix of N_a . It is shown that the newly derived factorization scheme leads to the minimal solution under the additional condition that the complex normalized scattering matrix of a reciprocal multiport should be symmetric. If reciprocity is not an issue, another definition of complex normalized scattering parameters (based on nonreciprocal Darlington models of the loads) is available