An Adaptive Sampling Process for Automated Multivariate Macromodeling Based on Hamiltonian-Based Passivity Metrics

This paper introduces a fully automated greedy algorithm for the construction of parameterized behavioral models of electromagnetic structures, targeting at the same time uniform model stability and passivity. The proposed algorithm is able to determine a small set of parameter configurations for which an external solver provides on the fly the sampled scattering parameters of the structure over a predetermined frequency band. These samples are subjected to a multivariate rational/polynomial fitting process, which iteratively leads to a parameterized descriptor realization of the model. The main novel contribution in this work is the adoption of a model-based approach for the adaptive augmentation of an initially small set of frequency responses, each corresponding to a randomly-selected parameter configuration. In particular, the locations of the in-band passivity violations of intermediate macromodels constructed at each iteration are used as a proxy for the model-data error in those regions where input data are not available. This physics-based consistency check, which is enabled by recent developments in multivariate passivity characterization based on Skew-Hamiltonian-Hamiltonian (SHH) spectra, is combined with standard space exploration metrics to obtain a small-size and automatically-determined distribution of points in the parameter space, leading to the construction of an accurate macromodel with a very limited number of external field solver runs. The embedded passivity check and enforcement process guarantees that either the final model is passive throughout the parameter space, or the residual violations, if present, are negligible for practical purposes. Several examples validate the proposed approach for up to three concurrent parameters.