An Efficient Residue Perturbation Scheme for Passivity Enforcement of <i>S</i>-Parameter Rational Models

Rational black-box macromodels are widely used in behavioral studies of electrical interconnects and package structures. These models are required to be passive to guarantee stable time-domain simulations. This article describes a highly efficient variant of the passivity enforcement method known as residue perturbation, adapted for use with scattering parameter models. The efficiency improvement is achieved by sparsity-aware conversion of the associated constrained least squares problem into a compacted nonnegativeleast squares problem, which is solved for using an efficient solver. The method is shown to be suitable for large scale cases with many ports and frequency samples, giving fast computations with low memoryrequirements. Relevant examples from package and interconnect modeling are solved in a short calculation time on a normal PC.