Robust periodic steady state analysis of autonomous oscillators based on generalized eigenvalues

R. Mirzavand, E.J.W. Maten, ter, T.G.J. Beelen, W.H.A. Schilders, A. Abdipour

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Abstract

In this paper, we present a new gauge technique for the Newton Raphson method to solve the periodic steady state (PSS) analysis of free-running oscillators in the time domain. To find the frequency a new equation is added to the system of equations. Our equation combines a generalized eigenvector with the time derivative of the solution. It is dynamically updated within each Newton–Raphson iteration. The method is applied to an analytic benchmark problem and to an LC oscillator. It provides better convergence properties than when using the popular phase-shift condition. It also does not need additional information about the solution. The method can also easily be implemented within the Harmonic Balance framework.
Original languageEnglish
Title of host publicationProceedings of the 8th Conference on Scientific Computing in Electrical Engineering (SCEE 2010), 19-24 September 2012, Toulouse, France
EditorsB. Michielsen, J.R. Poirier
Place of PublicationBerlin
PublisherSpringer
Pages293-302
ISBN (Print)978-3-642-22452-2
DOIs
Publication statusPublished - 2012
Eventconference; SCEE 2010; 2010-09-19; 2010-09-24 -
Duration: 19 Sep 201024 Sep 2010

Publication series

NameMathematics in Industry
Volume16
ISSN (Print)1612-3956

Conference

Conferenceconference; SCEE 2010; 2010-09-19; 2010-09-24
Period19/09/1024/09/10
OtherSCEE 2010

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    Mirzavand, R., Maten, ter, E. J. W., Beelen, T. G. J., Schilders, W. H. A., & Abdipour, A. (2012). Robust periodic steady state analysis of autonomous oscillators based on generalized eigenvalues. In B. Michielsen, & J. R. Poirier (Eds.), Proceedings of the 8th Conference on Scientific Computing in Electrical Engineering (SCEE 2010), 19-24 September 2012, Toulouse, France (pp. 293-302). (Mathematics in Industry; Vol. 16). Springer. https://doi.org/10.1007/978-3-642-22453-9_31