New theorems in the synthesis of passive multiplexers
Coupling networks that divide the frequency spectrum into separate frequency bands and also provide desired filtering are known as multiplexers. In this paper we present four new theorems concerning the synthesis-theoretic structure of lumped passive multiplexers constructed as lossless reciprocal n-ports. In particular we prove in Theorem 1 that any set of n – 1 admissible power gains, complementary or otherwise, can be realized by a series interconnection of n–1 appropriately chosen non-Foster positive-real functions. In Theorems 2–4 we establish various necessary and sufficient conditions for the realization of bounded-real gains s21(p),…, sn1(p) given both in magnitude and phase. These conditions reveal that the general problem is one of Nevalinna-Pick interpolation. Lastly, five worked examples are used to illustrate all facets of the theory.