No abstract

Neuro-transfer function (neuro-TF) approaches have become more and more popular in parametric modeling for electromagnetic (EM) behavior of microwave components. Existing pole-residuebased neuro-TF approach has better capability of dealing with high-order problem than the rationalbased neuro-TF approach, but has the discontinuity issue and the associated non-smoothness issue of the poles/residues when the geometrical variations become large while the rational-based neuro-TF approach does not have. This paper addresses this situation and presents a novel hybrid-based neuro-TF technique which systematically combines both pole-residue and rational formats of the transfer functions. Starting with the pole-residue-based transfer functions, we propose a novel technique to automatically identify the poles/residues that are smooth-continuous and the poles/residues that have the discontinuity and nonsmoothness issues. The proposed technique converts the poles/residues that have those issues into the coefficients of the rational-based transfer function to solve the discontinuity and non-smoothness issues in the existing pole-residue-based neuro-TF approach. The proposed technique remains the smooth-continuous poles/residues in the pole-residue format of the transfer function to maintain the capability of handling highorder problem. Compared with the existing neuro-TF modeling methods, the proposed technique can obtain better accuracy in challenging applications of large geometrical variations and high order. The proposed technique is illustrated by two examples of parametric modeling of microwave components. INDEX TERMS Parametric modeling, microwave components, neural networks, hybrid-based transfer function, parameter extraction.

The rational-based neuro-transfer function (neuro-TF) method is a popular method for parametric modeling of electromagnetic (EM) behavior of microwave components. However, when the order in the neuro-TF becomes high, the sensitivities of the model response with respect to the coefficients of the transfer function become high. Due to this high-sensitivity issue, small training errors in the coefficients of the transfer function will result in large errors in the model output, leading to the difficulty in training of the neuro-TF model. This paper proposes a new decomposition technique to address this high-sensitivity issue. In the proposed technique, we decompose the original neuro-TF model with high order of transfer function into multiple sub-neuro-TF models with much lower order of transfer function. We then reformulate the overall model as the combination of the sub-neuro-TF models. New formulations are derived to determine the number of sub-models and the order of transfer function for each sub-model. Using the proposed decomposition technique, we can decrease the sensitivities of the overall model response with respect to the coefficients of the transfer function in each sub-model. Therefore, the modeling approach using the proposed decomposition technique can increase the modeling accuracy. Two EM parametric modeling examples are used to demonstrate the proposed decomposition technique.