Synthesis of Crossover Network Using O′Shea′s Transformation via URC

Abstract

This paper describes method of synthesis two-way cross-over network, namely low-pass filter and high-pass filter. Firstly, we introduce synthesis method of obtain all-pass filter. We introduce O′Shea′s transformation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\bm{P}}( {\bm{s}} ) = {\bm{cosh}}\sqrt {{\bm{SRC}}}$</tex> and Wyndrum′s transformation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">${\bm{W}}( {\bm{s}} ){\bm{\ }} = {\bm{\ tanh}}\sqrt {{\bm{SRC}}}$</tex> via uniformly distributed RC (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\overline {{\bm{URC}}}$</tex>) network. After obtaining a desired all-pass filter, as an elementary process. We construct low-pass filter and high-pass filter by means of all-pass filter basis. Simulation results MATLAB are carried out and stability are also investigated.