Robust Parameter Extraction Technique Based on Complex-Frequency-Domain EM Behavior for Neuro-TF Modeling of Microwave Filters

The neuro-transfer function (Neuro-TF) modeling approach has been widely used to accelerate the electromagnetic (EM) modeling and optimization process. In the standard Neuro-TF approach, the extracted transfer function (TF) parameters (e.g., poles/residues or zeros/poles) are complex values in the real frequency domain (i.e., the $j\omega $ -axis). Since the complex TF parameters are in the Laplace domain, the standard Neuro-TF approach inherently has a nonuniqueness parameter extraction issue with respect to geometrical parameters change. This article addresses this issue and proposes a robust parameter extraction technique based on complex-frequency-domain (CFD) EM behavior for Neuro-TF modeling of microwave filters. We approximately consider the real domain of CFD as a loss in this article. Therefore, we want to extract TF parameters not only from the frequency domain but also from the loss domain. In the proposed technique, we introduce the model-order reduction (MOR) technique to expedite the parameter extraction process, enabling fast frequency and loss sweeps simultaneously. The introduction of the MOR technique avoids the discrete solving of the EM response of each loss in the CFD, thus expediting the proposed parameter extraction process. The extracted parameters using the proposed technique have better correspondence with the information of CFD, improving the smoothness of extracted TF parameters. Therefore, the proposed technique enhances the robustness of TF parameter extraction and subsequently improves the accuracy of the Neuro-TF modeling over a relatively wide geometrical range. This article utilizes five microwave filter examples to demonstrate the advantages of the proposed method.