Fast and accurate extraction of microwave filter coupling matrix via physics-informed deep learning.

Tuning microwave filters presents a significant challenge owing to their inherent complexity. An accurate determination of the coupling matrix from the target S-parameters plays a crucial role in both filter tuning and design optimization. This study introduces a physics-informed deep neural network (PIDNN) framework for extracting coupling matrices directly from the target S-parameters of microwave filters. The proposed approach integrates physical circuit knowledge into the learning model to enhance physical insight and precision. To validate its performance and robustness, the PIDNN is evaluated on fifth- and eighth-order filters and benchmarked against two alternative neural models: a convolutional neural network (CNN) representing a conventional deep learning approach, and a radial basis function neural network (RBFNN) as a representative shallow model. Comparative results demonstrate that the PIDNN achieves superior accuracy and computational efficiency in retrieving coupling matrices corresponding to the specified target S-parameter responses.