DocumentCode :
664632
Title :
A new numerical approach for the efficient computation of Floquet multipliers within the harmonic balance technique
Author :
Traversa, Fabio Lorenzo ; Bonani, Fabrizio ; Cappelluti, F.
Author_Institution :
Dept. d´Eng. Electron., Univ. Autonoma de Barcelona, Bellaterra, Spain
fYear :
2013
fDate :
2-7 June 2013
Firstpage :
1
Lastpage :
3
Abstract :
We present a novel numerical approach to the computation of the relevant Floquet eigenvalues and eigenvectors associated to large-signal periodic limit cycles within the framework of the harmonic balance technique. The currently available harmonic balance computation techniques for the Floquet quantities involve a large generalized eigenvalue problem, that provides a large set of eigenvalues containing the required Floquet exponents and a replica of them with imaginary part augmented by multiple integers of the fundamental angular frequency (we call this the Floquet eigenvalue split set). In our proposal, numerical efficiency is attained transforming the large generalized eigenvalue problem into a sequence of second order nonlinear systems whose size is of the same order as the standard harmonic balance problem. Such transformation avoids the determination of the Floquet eigenvalue split set and allows for the calculation of a predefined subset of the relevant Floquet quantities. For the discussed example, an advantage of 3 orders of magnitude in computation time is obtained. An important added value is that through this technique the automatic tracing of bifurcation curves is easily implemented through continuation methods.
Keywords :
bifurcation; eigenvalues and eigenfunctions; nonlinear systems; power supply quality; Floquet eigenvalues; Floquet eigenvectors; Floquet multipliers; bifurcation curves; generalized eigenvalue problem; harmonic balance computation; harmonic balance problem; multiple integers; second order nonlinear systems; Bifurcation; Eigenvalues and eigenfunctions; Harmonic analysis; Jacobian matrices; Limit-cycles; Mathematical model; Nonlinear systems; Circuit simulation; Design automation; Floquet theory; Harmonic balance;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Microwave Symposium Digest (IMS), 2013 IEEE MTT-S International
Conference_Location :
Seattle, WA
ISSN :
0149-645X
Print_ISBN :
978-1-4673-6177-4
Type :
conf
DOI :
10.1109/MWSYM.2013.6697643
Filename :
6697643
Link To Document :
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