Canonic RLC n-port networks

Abstract

In this paper we consider square matrices whose elements are ratios of polynomials in the complex variable s. Tests are derived on any given complete set of matrix elements which determine if the matrix is realizable as the immittance matrix of a multiport network containing only resistors, capacitors and inductors, and possessing a connected port structure. Equivalent classes of networks as well as realizations containing a minimum number of network elements are obtained. A procedure is followed similar to the one used previously by the authors ( 1) to examine RC n-port synthesis. The following steps are taken: A Standard Form is created for immittance matrices of RLC systems; A given matrix is embedded in a “parent” matrix by use of augmented variables, and tests are found to determine whether critical network forms exist such that one of them be realizable for there to be any realization at all.