Parametric Modeling Incorporating Joint Polynomial-Transfer Function With Neural Networks for Microwave Filters

This article proposes a novel parametric modeling technique incorporating a joint polynomial-transfer function with neural networks (short for neuro-PTF) for electromagnetic (EM) behaviors of microwave filters. In the proposed technique, the polynomial function is introduced together with the pole-residue-based transfer function to represent the EM responses. The pole-residue-based transfer function is used to represent the whole EM response at the beginning and is subsequently divided into multiple subtransfer functions where each subtransfer function contains one pair of pole/residue. A novel smoothness-discriminating algorithm is proposed to judge the smoothness of each subtransfer function response and separate the pole/residue pairs whose subtransfer function response is determined to be smooth. The proposed method introduces low nonlinear polynomial functions to re-fit the smooth parts of subresponse and remains the nonsmooth parts of subresponse for the highly nonlinear transfer functions to represent. By this way, the proposed method avoids the discontinuity problems of nonunique parameter extraction caused by fitting smooth curves using the highly nonlinear transfer function. Neural networks are proposed to learn the relationship between the polynomial coefficients/poles/residues and the geometrical parameters. Utilizing both advantages of the polynomial functions and transfer functions, the proposed method can produce more accurate models than the existing neuro-TF methods, especially with large geometrical variations. The accuracy and robustness of the proposed technique are demonstrated using three EM application examples of microwave filters.