On synthesizable multidimensional lossless two-ports

A study is presented of the problems of factorization of the scattering matrix and the scattering hybrid matrix associated with lumped multidimensional lossless two-port networks into two matrices of similar types. Necessary and sufficient conditions for such factorability are derived. Special attention is paid to the factorization of scattering matrices when the two-port is symmetric and antimetric. Interrelationships between the conditions for factorability of the lossless scattering matrix, scattering transfer matrix, and scattering hybrid matrix are discussed using nontrivial examples. The results presented identify a larger class of synthesizable, but otherwise arbitrary, lossless, multidimensional two-ports than was previously available.>