A Vector-Fitting Formulation for Parameter Extraction of Lossy Microwave Filters

In this letter, a formulation based on the vector fitting is applied to extract the equivalent circuit model from the frequency response of lossy cross-coupled microwave filters. By approximating the lossy response with short-circuit admittance parameters in partial fractional expansion form, the proposed method can evaluate the unloaded quality factor of resonators and extract the transversal coupling matrix simultaneously. The methodology of the vector fitting can identify the poles and residues of the short-circuit admittance parameters even when the poles are on the complex plane. And the extracted transversal coupling matrix can further transform into the prescribed form corresponding to the physical layout. The proposed method can be used in the tuning process of filter designs where the extraction of a coupling matrix is essential. To verify the method, a cross-coupled quadruplet filter is used as an example