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

Let N, N 1 , N 2 and N 3 be prescribed reciprocal reactance 2n‐ports. Then, under certain mild restrictions, this paper supplies answers to the following two related problems:. P 1 . Find the necessary and sufficient conditions for the physical extractability of N 1 from the front‐end of N. P 2 . Given that N 2 and N 3 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 equalizers 6 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.