On the factorization of transfer matrices of lossless two-ports

The problem of factorizing the transfer matrix is treated in a rigorous way for all lumped finite lossless two-ports, including those containing gyrators and imaginary resistances. It is shown how, for a given order in which the factorization should be realized, all solutions can be obtained in a simple way once an acceptable solution of a certain set of fundamental equations, consisting of a certain number of linear homogeneous equations in + 2 unknowns, has been found. A simple procedure for establishing these fundamental equations is given.