Bounded Input Dissipativity of Linearized Circuit Models

We introduce the concept of Bounded Input Dissipativity (BID) for the characterization from an energy perspective of linearized models of nonlinear circuit blocks. Such linearized models are commonly employed in the design of large systems to approximate circuit blocks that operate in the neighborho...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Regular papers, 2020-06, Vol.67 (6), p.2064-2077
Main Authors: Bradde, Tommaso, Grivet-Talocia, Stefano, Calafiore, Giuseppe C., Proskurnikov, Anton V., Mahmood, Zohaib, Daniel, Luca
Format: Article
Language:English
Subjects:
Amplitudes
analog circuits
behavioral models
Bias
Circuit design
Circuit simulation
Computational modeling
Computer simulation
Dissipative systems
equivalent circuits
Integrated circuit modeling
Linear matrix inequalities
Linearization
local activity
macromodels
Mathematical analysis
Mathematical model
Nonlinear circuits
power dissipation
Runtime
small-signal models
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Summary:We introduce the concept of Bounded Input Dissipativity (BID) for the characterization from an energy perspective of linearized models of nonlinear circuit blocks. Such linearized models are commonly employed in the design of large systems to approximate circuit blocks that operate in the neighborhood of some well-defined and asymptotically stable bias point and lead to a dramatic reduction in circuit simulation runtime. Even if the original circuit block always behaves as a dissipative system, its linearized model may behave as dissipative or non-dissipative depending on the amplitude of its small-signal port voltages and currents, compared to the corresponding constant bias or supply signal components. This paper presents a theoretical framework for the analysis of such a conditional dissipativity and introduces BID criteria based on the feasibility of Bilinear or Linear Matrix Inequalities. These criteria allow to estimate the maximum small-signal input amplitude that guarantees the dissipativity of the linearized model. Various examples demonstrate the validity of the proposed theory, including a test case showing how spurious and physically inconsistent instabilities may arise if the proposed BID conditions are not verified.
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2020.2972961