Modeling of Coupled Resonator Networks via Constrained Vector Fitting Incorporating Shared and Local Poles

This article presents a constrained vector fitting (CVF) framework for accurate computer-aided tuning (CAT) of coupled-resonator microwave filters. By leveraging a novel hybrid pole structure that combines shared and local poles, the proposed method robustly models admittance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y$</tex-math> </inline-formula>-) parameter data, even when affected by unknown reference plane shifts. A model postprocessing strategy is then employed to iteratively solve for the loading phase using an analytical method and perform de-embedding. Additionally, the CVF method explicitly enforces physical realizability constraints—such as residue condition and the number of transmission zeros (TZs)—during the least-squares solution process using an Augmented Lagrangian framework. This ensures that the extracted coupling matrix (CM) directly corresponds to a physically realizable circuit. Validation on a seventh-order cavity filter with complicated loading demonstrates CVF’s high accuracy in fitting measured data, effective phase correction, and reliable CM extraction, establishing it as a robust solution for practical filter synthesis and tuning.