An iterative reweighting process for macromodel extraction of power distribution networks

Grivet-Talocia, S.; Ubolli, A.; Bandinu, M.; Chinea, A.

doi:10.1109/epeps.2013.6703481

Cited by 4 publications

(10 citation statements)

References 17 publications

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“…It has been shown in [23] that the macromodel-based PDN impedance Z PDN (jω k ), obtained by replacing the original samplesŜ k in (2) with S(jω k ), may differ significantly from the referenceẐ PDN,k . This consideration led to the definition of a first-order sensitivity Ξ k , defined as…”

Section: Background and Problem Statementmentioning

confidence: 99%

“…This frequency-dependent sensitivity Ξ(s) models the amplification of the macromodel approximation errors due to the nonlinear transformation from S(s) to Z PDN (s) due to the loading network. It was shown in [23] that the generation of the macromodel using a modified (weighted) error metric…”

Section: Background and Problem Statementmentioning

confidence: 99%

“…In the following, we will assume that the weights are such that w k = Ξ k , i.e., they coincide with the first-order sensitivity. A weight refinement procedure that further optimizes the weights is documented in [23].…”

Section: Background and Problem Statementmentioning

confidence: 99%

“…Unfortunately, this is not sufficient for the macromodel to be reliably used in power integrity verification. In fact, it has been shown in [23] that, when connecting the proper terminations to the macromodel ports (VRM, decoupling capacitors, active device models) and computing the resulting PDN voltage drop excited by active device switching, the results may be inaccurate. The root cause for this problem turns out to be the sensitivity of the target impedance Z PDN to perturbations in the scattering responses.…”

Section: Introductionmentioning

confidence: 99%

“…The inevitable approximation error of the macromodel can be amplified by the feedback provided by the PDN termination network, although this error is well under control in the scattering domain, corresponding to 50 Ω terminations. The developments in [23] provide a good solution to avoid this issue in the rational fitting stage of the macromodel generation. The sensitivity is computed numerically from the original scattering data based on the nominal termination network, and used as a frequency-dependent weight in the definition of the target norm that the rational fitting engine aims at minimizing during model identification.…”

Section: Introductionmentioning

confidence: 99%

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

Ubolli¹,

Grivet-Talocia²,

Bandinu³

et al. 2014

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2014

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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.

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Section: Background and Problem Statementmentioning

confidence: 99%

Section: Background and Problem Statementmentioning

confidence: 99%

Section: Background and Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Ubolli¹,

Grivet-Talocia²,

Bandinu³

et al. 2014

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2014

Self Cite

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On Tuning Passive Black-Box Macromodels of LTI Systems via Adaptive Weighting

Grivet-Talocia

Ubolli

Chinea³

et al. 2016

Scientific Computing in Electrical Engineering

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This paper discusses various approaches for tuning the accuracy of rational macromodels obtained via black-box identification or approximation of sampled frequency responses of some unknown Linear and Time-Invariant system. Main emphasis is on embedding into the model extraction process some information on the nominal terminations that will be connected to the model during normal operation, so that the corresponding accuracy is optimized. This goal is achieved through an optimization based on a suitably defined cost function, which embeds frequencydependent weights that are adaptively refined during the model construction. A similar procedure is applied in a postprocessing step for enforcing model passivity. The advantages of proposed algorithm are illustrated on a few application examples related to power distribution networks in electronic systems.

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