A Generalized Coupling Matrix Extraction Technique for Bandpass Filters With Uneven-Qs

In this paper, a vector fitting (VF) based analytical extraction method, which is capable of accurately extracting the coupling matrix and the uneven unloaded Qs of each electric resonators of a filter, is presented. Having had the complex poles and residues determined using VF, the coupling matrix can be obtained by a sequence of complex orthogonal transformations. As a side product, the unloaded Qs for each resonator will be directly obtained from the complex diagonal elements of the coupling matrix. To demonstrate the effectiveness of the proposed method, an ideal demonstrative example along with two practical challenging filter tuning examples, namely, an eight-pole dual-mode dielectric filter and an eight-pole dual-mode predistortion filter, are demonstrated. An excellent match between the responses of the measured data and those from the extracted coupling matrix with actual unloaded Q factors can be seen.