Study of the compatibility of 1-D and 2-D bounded real functions

Recently Zhu and Chen presented a unified theory concerning the compatibility of two impedances. The authors present an alternate simplified formulation to the compatibility problem using Belevitch´s canonical scattering parameter representation for two-ports. The problem is addressed in terms of compatibility of two bounded real-functions, ρ₁(s) and ρ₂(s). It is established that the crux of the problem is identifying an auxiliary polynomial λ such that a certain polynomial involving λ is strictly Hurwitz or scattering Hurwitz after cancellation of the factors involving the transmission zeros. Although results are presented in the analog network, with suitable modification, the results could be formulated in a discrete time network. When transmission zeros associated with ρ ₂(s) are all at s = ∞/0 it is necessary to test for Hurwitz property of a polynomial and there is no need to find the auxiliary polynomial λ