Regularized and Compressed Large-Scale Rational Macromodeling: Theory and Application to Energy-Selective Shielding Enclosures

In this article, we introduce a robust procedure for the extraction of passive rational macromodels of low-loss electromagnetic structures with massive port counts. Such structures pose inherent challenges that make standard macromodeling tools and approaches inadequate, mainly due to complexity and sensitivity at low frequency. The proposed approach involves a preprocessing stage in which port response data from a full-wave electromagnetic solver are regularized and extrapolated to dc using an asymptotic modal representation. The resulting data samples are then processed by a dedicated compression algorithm that represents the full set of input–output responses in terms of a few basis functions, which are constructed by enforcing an exact low-frequency modal asymptotic behavior, possibly including higher order dc zeros. These zeros are preserved in any stage of rational fitting and passivity enforcement, resulting in dc and low-frequency compliant compressed passive macromodels. Numerical results with up to 400 ports demonstrate the superior performance and accuracy of the computed models with respect to state-of-the-art approaches. In particular, the resulting models preserve their accuracy irrespective of the loading conditions, including the limit cases of short and open terminations.