Sensitivity-based weighting for passivity enforcement of linear macromodels in power integrity applications

Abstract

The electrical performance of Power Distribution Networks (PDNs) is usually assessed by computing frequency responses through quasi-static or full-wave electromagnetic solvers. Such responses, often available in the scattering form, are then fed to suitable macromodeling algorithms for the extraction of compact reduced-order behavioral models that can be seemlessly simulated in the time domain by standard circuit solvers. Such algorithms perform a rational fitting of the raw scattering responses, followed by a passivity check and enforcement step. The resulting macromodel is typically very accurate when compared to the raw scattering responses. It may however happen that the responses of the PDN macromodel exhibit significant deviation from the true system responses under realistic loading conditions, which include appropriate models for active device blocks, decoupling capacitors, voltage regulators, etc. We highlight the source of this accuracy loss, and we propose a sensitivitybased weighting strategy that is able to optimize and tune the macromodel accuracy based on its specific nominal termination network. The particular focus of this paper is the definition and the inclusion of optimal weigths in the passivity enforcement loop, which is recognized as the most challenging step. The result is a reliable macromodeling flow, which is able to produce passive, accurate and efficient reduced-order models of general PDN structures for power integrity analysis and verification.

Addressing Load Sensitivity of Rational Macromodels

“…This latter requirement is often overlooked in the vast literature available on the subject: typically one is satisfied when a scattering macromodel S(s) accurately reproduces the scattering responses Sk from a field solver by minimizing the fitting error in (9). However, usage of the model under different operating conditions may lead to an amplification of the inevitable approximation errors involved in the rational approximation process, up to a point where the port-behavior in such operating conditions becomes corrupted [14]- [16], [18]. This paper intends to overcome the above limitations.…”

“…The more general case in which the actual loading conditions can include one arbitrary (but known) termination network has been studied in [15], where the authors introduced the socalled Modal Vector Fitting (MVF) scheme and addressed an approach to control the accuracy of the macromodel under the prescribed load. Also, in [16], [17], a tailored error weighting approach was proposed to compensate the macromodel sensitivity, both during the generation and the passivity enforcement post-processing stages.…”

Passivity verification and enforcement—A review paper

“…Very recent developments() include more advanced techniques of passivity enforcement, ie, passive macromodeling method that results in close‐to‐band violations by extending frequency samples efficiently, sensitivity‐weighted passivity enforcement method especially for power distribution networks. In literature,() the author presents 2 enforcement methods based on localization.…”

Regularized and Compressed Large-Scale Rational Macromodeling: Theory and Application to Energy-Selective Shielding Enclosures

“…For instance, fitting scattering responses with port reference R 0 usually result in a model that is very accurate when loaded with resistances close to R 0 . However, when the terminations differ significantly, the model accuracy may deteriorate [14]. Consider as an example the limit cases of short-and open-circuit terminations, for which model behavior can be checked by computing its admittance or impedance responses.…”