Topological Synthesis of Non-Reciprocal Resistance Networks

The paper deals with the topological synthesis of non-reciprocal resistance networks specified by the so-called driving-conductance matrix. Synthesis of non-reciprocal networks has already been treated by H. J. Carlin and Y. Oono, and their networks are specified by scattering matrices and consequently n-port impedance matrices. One of the merits of this paper, which differs from their paper, is in the determination of the connection and ideal transformers. Factors which determine the network are the connection and element resistances, and they therefore make possible the determination of the node-branch incidence matrix and resistances so that the driving-conductance matrix may equal the given matrix. When we denote the branch e.m.f. matrix by V and the branch-current matrix by I, I = GV, where G is called the driving-conductance matrix, which is assumed to be given, and, in general, G¿ ¿ G. If a maximal set of solutions for Gx = 0 and x¿G = 0 is denoted by X as the matrix expression, X is called the zero factor of G. Provided that the zero factor X satisfies the character of a node-branch incidence matrix, the connection can be fixed directly. If not, the connection is determined by the part of X which satisfies the character of a node-branch incidence matrix, and the ideal transformers needed are determined by the other part. After the connection and the ideal transformers are determined, the branch resistances are determined by comparing the given matrix with the matrix calculated from the newly determined connection and the unknown branch resistances.