Passive Modeling of One-Port Networks Through SOS Orthogonal Rational Functions

Signal and power integrity design in the time domain requires equivalent circuit models for interconnects and packages, whose descriptions may only be available as tabulated impedance or admittance parameters. Accurate models for these components should maintain their physical properties including causality, stability, and passivity. Our recent work introduced algorithms based on sum-of-squares (SOS) polynomials to address the problem of generating passive scalar models, such as driving point impedances or admittances, based on an existing causal, stable, but non-passive model. We used a scaled Chebyshev basis to avoid the poor conditioning of the monomial basis in SOS constraints. However, the division by the denominator still impacts the numerical accuracy. In this paper, we improve the conditioning of the problem by embedding the denominator polynomial in the basis, resulting in orthogonalized rational functions through Arnoldi iteration.