Synthesis of Finite Passive n-Ports with Prescribed Two-Variable Reactance Matrices

Abstract

This paper solves the problem of synthesizing twovariable reactance functions and matrices, symmetric or nonsymmetric. This problem has not been solved so far even for twovariable reactance functions except for the case where the functions are prescribed as bilinear functions of one of the two variables. As the basis for solving the problem, several theorems are derived from the definitions of the two-variable reactance function and matrix. It is shown that an arbitrarily prescribed two-variable reactance matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W(\lamda,\mu )</tex> of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> is realizable as the immittance matrix of a passive "two-variable n-port", which is bilateral or nonbilateral accordingly as W is symmetric or nonsymmetric. Synthesis of a two-variable reactance function is included as a special case where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 1</tex> . Related problems are discussed in addition.