Single-Parameter Optimization Method for Extracting Coupling Matrix from Lossy Filters

This paper presents a novel single-parameter optimization method for extracting coupling matrix from either measured or electromagnetic simulated S-parameters of a narrow band coaxial-resonator filter with losses. Having had the polynomials of the S-parameters of a filter by the Cauchy method with removing phase shift, the rational polynomials can be obtained. Once the rational polynomials having been determined, a single-parameter optimization method is proposed to obtain ε and the coupling matrix with an assigned topology, which can be extracted using well established techniques. The measured S-parameters compared with the S-parameters obtained from the coupling matrix, and the attenuation factor K is easily determined. The loss effects will be removed after obtaining the value of the attenuation factor K. The approach is useful and can be used in computer-aided tuning of microwave filters. Example is presented to illustrate the validity of the proposed method.