The K-Matrix and Its Application to N-Port Network Synthesis

Abstract

ABSTRACTIt is well known that paramountancy is a necessary as well as sufficient condition for the synthesis of a 3 × 3 matrix of real numbers as a 3-port resistive network without transformers. For matrices of order 4 and above, paramountancy is necessary, but not sufficient. However, if an n × n matrix of real numbers is dominant, it can be synthesized as the short circuit admittance matrix of an n-port network without transformers, but not as an open circuit impedance matrix.Conditions under which a given dominant matrix of real numbers can be synthesized both as the O.C. impedance matrix and the S.C. admittance matrix of a resistive n-port network, are presented in this paper. Such matrices are termed K-matrices. The method can be easily extended to all one-element and two-element kind networks by considering the residue matrices at the respective poles.A special type of filter designed on this basis is also shown.