Advanced Neuro-TF Modeling Technique Incorporating Quadratic Approximated Vector Fitting of Parametric Pole/Residue Extraction

This article proposes an advanced neuro-transfer function (neuro-TF) modeling method incorporating quadratic approximated vector fitting of parametric poles/residues extraction for electromagnetic (EM) parametric modeling of microwave components. In this technique, geometrical parameters are integrated into the vector fitting extraction process of the poles/residues. Systematic formulations are derived to introduce quadratic approximations representing the relationship of poles/residues and geometrical parameters during vector fitting. Using the proposed formulation, quadratic coefficients are calculated instead of the separate calculation of poles/residues during the vector fitting process. Consequently, the poles/residues for different geometrical samples are formed as quadratic functions using the calculated quadratic coefficients with respect to geometrical parameter values. Since the poles/residues for different geometrical samples are represented using the same quadratic coefficients during the vector fitting process, relatively smooth poles/residues of the transfer function can be extracted from EM responses with respect to geometrical parameters. After the quadratic approximated vector fitting process, the neural networks are trained to fit the extracted poles/residues data of transfer functions with respect to geometrical parameters to provide initial weights in the neural networks for the overall neuro-TF training process. After initial neural network training, the neuro-TF model is trained to learn the relationship between the EM responses, e.g., the $S$ -parameters, with respect to geometrical parameters. The proposed technique is effective and robust, especially in solving discontinuity issues with large geometrical variations. The proposed technique is demonstrated by EM parametric modeling of three microwave examples.