Double broadband matching and the problem of reciprocal reactance 2n-port cascade decomposition

Let N, N1, N2 and N3 be prescribed reciprocal reactance 2n-ports. Then, under certain mild restrictions, this paper supplies answers to the following two related problems:. P1. Find the necessary and sufficient conditions for the physical extractability of N1 from the front-end of N. P2. Given that N2 and N3 are individually physically extractable from the back and front-ends of N. respectively, find a set of sharp sufficient conditions for their simulations physical extractability from N. The criteria are formulated in terms of the associated scattering matrices and are reasonably simple to apply. Moreover, they also have a clear-cut network significance involving transmission zeros. to illustrate their use, a recent result for the design of non-degenerate double broadband-matching equalizers6 is generalized to a 2n-port setting in Theorem 2, corollary 2. Lastly, to round out the development, impedance versions of both Theorem 1 and Theorem 2, corollary 2, are presented in Section 2. This restatement is accomplished with the aid of a new Darlington 2n-port embedding for passive reciprocal n-ports that is phrased entirely in the language of impedance matrices.