On the Realization of an nth-Order G Matrix

Abstract

Synthesis of a single-element-kind network from a given short-circuit parameter matrix of order n, leading to a topological configuration involving <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n + 1</tex> nodes, is now known, having been given by the author and several others working on this problem almost simultaneously. This form of realization is, however, not completely general, and therefore it is possible for a given matrix to be physically realizable even though the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(n + 1)</tex> -node realization procedure fails. The present paper discusses this more general problem and leads to some useful results which do not, however, represent a complete solution.