PASSOS: Passive Approximation Through Sum-of-Squares 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. Sum-of-squares (SOS) polynomials, which are guaranteed to be non-negative, can be used to address the problem of generating passive scalar models, such as driving point impedances or admittances, based on an existing causal, stable, but nonpassive model. However, the poor conditioning of a monomial basis in SOS constraints prevents large-order modeling. In this article, we expand the SOS framework to reciprocal multiport admittance or impedance network parameters by introducing a methodology based on SOS matrices. In addition, orthogonalized rational functions are incorporated to solve the conditioning problem by embedding the denominator polynomial in the basis.