Selective determination of floquet quantities for the efficient assessment of limit cycle stability and oscillator noise

Fabio L. Traversa; Fabrizio Bonani

doi:10.1109/TCAD.2012.2214480

Selective determination of floquet quantities for the efficient assessment of limit cycle stability and oscillator noise

Fabio L. Traversa, Fabrizio Bonani

Department of Electronic Engineering

Research output: Contribution to journal › Article › Research › peer-review

13 Citations (Scopus)

Abstract

We present a mixed time-frequency domain algorithm for the approximate computation of the Floquet quantities (exponents and both direct and adjoint eigenvectors) resulting from the linearization of index-1 differential-algebraic equations around a periodic limit cycle. The approach allows to select the number of Floquet exponents to be calculated approximating the matrix of the obtained eigenvalue problem. The error in the evaluation (for both exponents and eigenvectors) is proved to tend to zero along with the ratio between the norms of the neglected and retained rows of the relevant matrix. © 2013 IEEE.

Original language	English
Article number	6416094
Pages (from-to)	313-317
Journal	IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume	32
Issue number	2
DOIs	https://doi.org/10.1109/TCAD.2012.2214480
Publication status	Published - 4 Feb 2013

Keywords

Circuit simulation
Floquet theory
frequency domain analysis

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10.1109/TCAD.2012.2214480

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abstract = "We present a mixed time-frequency domain algorithm for the approximate computation of the Floquet quantities (exponents and both direct and adjoint eigenvectors) resulting from the linearization of index-1 differential-algebraic equations around a periodic limit cycle. The approach allows to select the number of Floquet exponents to be calculated approximating the matrix of the obtained eigenvalue problem. The error in the evaluation (for both exponents and eigenvectors) is proved to tend to zero along with the ratio between the norms of the neglected and retained rows of the relevant matrix. {\textcopyright} 2013 IEEE.",

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Selective determination of floquet quantities for the efficient assessment of limit cycle stability and oscillator noise. / Traversa, Fabio L.; Bonani, Fabrizio.

In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 32, No. 2, 6416094, 04.02.2013, p. 313-317.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Selective determination of floquet quantities for the efficient assessment of limit cycle stability and oscillator noise

AU - Traversa, Fabio L.

AU - Bonani, Fabrizio

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N2 - We present a mixed time-frequency domain algorithm for the approximate computation of the Floquet quantities (exponents and both direct and adjoint eigenvectors) resulting from the linearization of index-1 differential-algebraic equations around a periodic limit cycle. The approach allows to select the number of Floquet exponents to be calculated approximating the matrix of the obtained eigenvalue problem. The error in the evaluation (for both exponents and eigenvectors) is proved to tend to zero along with the ratio between the norms of the neglected and retained rows of the relevant matrix. © 2013 IEEE.

AB - We present a mixed time-frequency domain algorithm for the approximate computation of the Floquet quantities (exponents and both direct and adjoint eigenvectors) resulting from the linearization of index-1 differential-algebraic equations around a periodic limit cycle. The approach allows to select the number of Floquet exponents to be calculated approximating the matrix of the obtained eigenvalue problem. The error in the evaluation (for both exponents and eigenvectors) is proved to tend to zero along with the ratio between the norms of the neglected and retained rows of the relevant matrix. © 2013 IEEE.

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KW - Floquet theory

KW - frequency domain analysis

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DO - 10.1109/TCAD.2012.2214480

M3 - Article

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JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

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M1 - 6416094

ER -

Selective determination of floquet quantities for the efficient assessment of limit cycle stability and oscillator noise

Abstract

Keywords

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