Uniformly Stable Parameterized Macromodeling Through Positive Definite Basis Functions

Reduced-order models are widely used to reduce the computational cost required by the numerical assessment of electrical performance during the design cycle of electronic circuits and systems. Although standard macromodeling algorithms can be considered to be well consolidated, the generation of macromodels that embed in a closed-form some dependence on the design variables still presents considerable margins for improvement. One of these aspects is the enforcement of uniform stability throughout the parameter space of interest. This article proposes a novel parameterized macromodeling strategy, which enforces by construction that all macromodel poles are stable for any combination of possibly several independent design variables. The key enabling factor is the adoption of positive definite multivariate basis functions for the representation of model variations induced by the parameters. This representation leads to robust model generation from tabulated frequency responses, at a computational cost that is dramatically reduced with respect to competing approaches. This result arises from a number of algebraic constraints for stability enforcement that depends on the model complexity (number of basis functions) and not on the model behavior as a function of the parameters. As a byproduct, the proposed strategy lends itself to a much improved scaling with the dimension of parameter space, allowing to circumvent the curse of dimensionality that may occur when the number of independent parameters grows beyond few units. To this end, we exploit representations based on positive definite radial basis functions. The benefits of the proposed approach are demonstrated through an extensive experimental campaign applied to both passive and active devices and components, comparing the performance of different model parameterizations in terms of accuracy, time requirements, and model compactness.