Determining transmission zeros of general Chebsyshev filters using genetic algorithm

A method to determine the least filter order and the optimum locations of transmission zeros (TZs) of general Chebsyshev filters is presented using genetic algorithm (GA). This method is based on constructing an objective error function according to given filter magnitude specifications, and then the filter order and transmission zeros (TZs) can be obtained by minimizing the proposed error function using genetic algorithm (GA). Once TZs and filter order are determined, coupling matrix of a given prototype can be obtained using established techniques. The filter with these TZs synthesized by this method has the characteristics of the highest stopband rejection and the least filter order under the premise of meeting given filter magnitude specifications. The proposed method has solved the first problem of coupling matrix synthesis of general Chebsyshev filters. Application examples illustrate the validity of this method.