On the factorization of scattering transfer matrices of multidimensional lossless two-ports

The problem of cascade decomposition of arbitrary bivariate lossless two-ports is addressed via factorization of the associated scattering transfer matrix. Necessary and sufficient conditions for the existence of solution to the factorization problem so formulated, are obtained. It is shown that the criterion for factorability can be expressed in terms of solvability of a set of linear simultaneous equations, which is overdetermined in general. Since no restrictions are imposed on the type of transmission zeros of the given scattering transfer matrix, earlier results in the literature can, in principle, be viewed as special cases of the results obtained here.