REALIZATION OF OPEN-CIRCUIT RESISTANCE MATRICES

Abstract

The general realization of tranetormerl„ees *apart networks is an important but still an unsolved problem in the field at network Theory. However, some significant results have boon obtained regarding spmf special Classes of this general problem. Intact, the realization of a short..circuit Conductance matrix by a resistive n-port network has been studied in great details. But surprising as it may seem, the realization of open-circuit resistance matrices has received comparatively much loss attention. This dissertation is completely detoted to a stu der of the, necessary and sufficient conditions for a given matrix to be realisable as an Open+-circuit resistance matrix of a class of a-port networks. Some Interesting and significant new results have been pointed and they are properly illustrated with the help of suitable examples* A theorem in the field of matrix algebra, not usually quoted In the literature of Network Theory and dealing with the decomposition of a real symmetric matrix Into a product of triangular matrices has been used as a basic tool In the Apposed realization tecb«* nique. Further, two important new theorems pertinent to triangular matrices decomposing a uniformly tapered ii *atria have been stated and proved. These theore*s have been used as necessary and sufficient conditions for the realization of a given matrix as the open•• circuit resistance matrix of an a port network hay-ing ports arranged in the form of a linear tree. The resulting n•port network would be such that the portetree configuration will have sudoessIve Eijparts numbered in an ascending order. It is sincerely hoped that the results of the theorems eaugorated in this dissertation will be of some help in the problem of deriving a realize. tion procedure for open-circuit resistance matrices of more general type of part.tree structure