This paper presents a two-stage optimization method for accurately extracting the coupling matrix (CM) and the unloaded quality factor (unloaded Q) of each resonator from the measured (or simulated) S-parameters of lossy cross-coupled resonator bandpass filters. The method can be used in computer-aided tuning (CAT) of microwave filters to accelerate filter design and physical realization. In our method, the Cauchy method is employed for determining characteristic polynomials of the S-parameters in the normalized low-pass frequency domain, and the CM and unloaded Q are extracted by two-stage optimization method using genetic algorithm. With respect to the previous methods available in the literatures, the proposed method allows the CM extraction of the filter with source-load coupling. Moreover, the accuracy and robustness of the method can be improved due to the usage of the second stage optimization. The proposed method is applied to the diagnosis of a general coupled resonator filter with/without source-load coupling.
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