A Comparative Study of Passivity Enforcement Schemes for Linear Lumped Macromodels

Abstract

This paper presents a comparative study of several passivity enforcement schemes for linear lumped macromodels. We consider three main classes of algorithms. First class is represented by those methods based on a direct enforcement of positive/bounded real Lemma constraints via convex optimization. Second class includes those algorithms that enforce the passivity constraints at discrete frequency samples. These schemes are here formulated as second-order cone programs in order to optimize performance. Finally, we consider algorithms based on Hamiltonian eigenvalue perturbation. These three classes are applied to a significant set of benchmark examples, essentially various kinds of high-speed interconnects and packages, with the aim of comparing their performance in terms of accuracy, efficiency, applicability, and robustness. These examples are specifically selected in order to be critical for one or more algorithms, in terms of excessive accuracy degradation, computational complexity, or even lack of convergence. One important result is that carefully designed weighting schemes may dramatically improve performance for all considered algorithm classes. Index Terms-Bounded real lemma, Hamiltonian matrices, inverse weighting, linear macromodeling, passivity, positive real lemma, second-order cone programming.

Modeling and design for beyond-the-die power integrity

“…It is because that the interconnection of stable systems is not necessarily stable; while the interconnection of passive systems is always passive. [13] offers a good review of all the passivity enforcement techniques for these models created from S-parameters, which can be characterized into three categories: The first category is based on the direct enforcement of certain passivity constraints by means of convex optimization. The second category enforces the passivity constraints at a few carefully selected discrete frequency samples by means of second-order cone programming.…”

Rational Modeling Algorithm for Passive Microwave Structures and Systems

“…Nevertheless, passivity of the macromodel is of crucial importance since a non-passive macromodel may lead to unstable transient simulations in an unpredictable manner [12,13]. This paper applies a new passivity enforcement technique that is able to enforce passivity to a non-passive rational macromodel by means of an overdetermined least-squares fitting algorithm [14].…”

Passivity Test of Immittance Descriptor Systems Based on Generalized Hamiltonian Methods

“…T HIS brief is motivated by the demand of passive modeling of on-chip components and electrical circuits in VLSI simulations [1], [2]. Passivity can be interpreted as the inability of a system to internally generate energy, which is of great importance for stable global simulations.…”

“…However, nonpassive models may be generated from some stability-preserving algorithms (e.g., [3]) or even some theoretically passivitypreserving techniques (e.g., [1]) on finite-precision machines. As a remedy, passivity enforcement techniques [2] can eliminate or mitigate passivity violations. These enforcements need to locate the possible nonpassive regions via a passivity test in advance.…”

“…For regular (or nonsingular) systems, numerous passivity assessments have been proposed. The reader is referred to [2] and [4], and the references therein.…”