Bivariate Macromodeling with Passivity Constraints

This paper presents a novel theoretical formulation and an associated algorithm for the computation of passive parameterized macromodels from tabulated scattering data. The main contribution is the construction of passivity constraints for parameterized models as a finite set of linear matrix inequalities, thanks to a suitable expansion into Bernstein polynomials. These constraints are embedded in the model identification process, leading to a convex formulation of passivity enforcement, with guaranteed convergence and without requiring any expensive multivariate passivity check. Two numerical examples demonstrate the effectiveness of the proposed approach.