Topological Synthesis of Transfer-Admittance Matrices

Combinatorial topology is useful for handling not only problems in analysis, but also problems in synthesis. In this paper, the author shows topological foundations and one of the typical methods for network synthesis. This paper deals with topological synthesis of an electrical network specified by a given transfer-admittance matrix. Factors that determine the network are the connection and branch impedances which then make it possible to determine the node-branch incidence matrix and branch impedances so that the transfer-admittance matrices of the network may equal the given. matrix. This node-branch incidence matrix is determined by a zero factor of the given transfer-admittance matrix. Therefore, whether ideal transformers are necessary or not depends on whether this zero factor satisfies the character of a node-branch incidence matrix. After the connection and ideal transformers are determined, we can determine branch impedances by comparing the given matrix with the matrix calculated from the newly determined connection and the unknown branch impedances.