A general matrix factorization method for network synthesis

Abstract

THIS PAPER considers a new matrix factorization method for the synthesis of RLC two terminal-pair-networks. Equivalent matrices suitable for the synthesis of RLC ladder and parallel ladder networks are developed by linear transformations of matrix multiplication. The application of the method is demonstrated through the synthesis of a general minimum-phase transmission function as ladder networks <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> ‾ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> and a general nonminimum-phase transmission function as parallel ladder networks. The advantage of the present method is that superfluous elements in the realized ladder networks are reduced considerably. Furthermore, an unbalanced form can be obtained for realizing a nonminimum-phase transmission function which has generally been realized in the lattice form.1, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5&amp;</sup> #x0203E; <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sup>