Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform

Autores
Robbio, Federico I.; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chen, Guanrong
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the results obtained from a completely different approach that measures the frequency content of a signal by using digital signal processing techniques such as the Fast Fourier Transform (FFT). The accuracy of the approximation is evaluated by computing the Floquet multipliers of the variational system based on the fact that for periodic solutions one multiplier must be +1. The separation from this theoretical value is proportional to the error of the approximation. A limitation of the frequency domain method is encountered when being used for continuing the secondary branch of limit cycle bifurcations, such as pitchfork and period-doubling bifurcations. Two examples are shown to illustrate the main results: Colpitts' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles.
Fil: Robbio, Federico I.. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Paolini, Eduardo Emilio. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Chen, Guanrong. University of Hong Kong; China
Materia
HARMONIC DISTORTION
ELECTRONIC OSCILLATOR
HARMONIC BALANCE
CHUA'S CIRCUIT
COLPITTS' OSCILLATOR
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/105539
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/105539
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transformRobbio, Federico I.Paolini, Eduardo EmilioMoiola, Jorge LuisChen, GuanrongHARMONIC DISTORTIONELECTRONIC OSCILLATORHARMONIC BALANCECHUA'S CIRCUITCOLPITTS' OSCILLATORhttps://purl.org/becyt/ford/2.2https://purl.org/becyt/ford/2A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the results obtained from a completely different approach that measures the frequency content of a signal by using digital signal processing techniques such as the Fast Fourier Transform (FFT). The accuracy of the approximation is evaluated by computing the Floquet multipliers of the variational system based on the fact that for periodic solutions one multiplier must be +1. The separation from this theoretical value is proportional to the error of the approximation. A limitation of the frequency domain method is encountered when being used for continuing the secondary branch of limit cycle bifurcations, such as pitchfork and period-doubling bifurcations. Two examples are shown to illustrate the main results: Colpitts' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles.Fil: Robbio, Federico I.. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Paolini, Eduardo Emilio. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; ArgentinaFil: Chen, Guanrong. University of Hong Kong; ChinaWorld Scientific2007-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105539Robbio, Federico I.; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chen, Guanrong; Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform; World Scientific; International Journal Of Bifurcation And Chaos; 17; 05; 12-2007; 1623-16350218-12741793-6551CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0218127407017951info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127407017951info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:49:07Zoai:ri.conicet.gov.ar:11336/105539instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:49:07.545CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
title Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
spellingShingle Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
Robbio, Federico I.
HARMONIC DISTORTION
ELECTRONIC OSCILLATOR
HARMONIC BALANCE
CHUA'S CIRCUIT
COLPITTS' OSCILLATOR
title_short Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
title_full Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
title_fullStr Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
title_full_unstemmed Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
title_sort Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform
dc.creator.none.fl_str_mv Robbio, Federico I.
Paolini, Eduardo Emilio
Moiola, Jorge Luis
Chen, Guanrong
author Robbio, Federico I.
author_facet Robbio, Federico I.
Paolini, Eduardo Emilio
Moiola, Jorge Luis
Chen, Guanrong
author_role author
author2 Paolini, Eduardo Emilio
Moiola, Jorge Luis
Chen, Guanrong
author2_role author
author
author
dc.subject.none.fl_str_mv HARMONIC DISTORTION
ELECTRONIC OSCILLATOR
HARMONIC BALANCE
CHUA'S CIRCUIT
COLPITTS' OSCILLATOR
topic HARMONIC DISTORTION
ELECTRONIC OSCILLATOR
HARMONIC BALANCE
CHUA'S CIRCUIT
COLPITTS' OSCILLATOR
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.2
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the results obtained from a completely different approach that measures the frequency content of a signal by using digital signal processing techniques such as the Fast Fourier Transform (FFT). The accuracy of the approximation is evaluated by computing the Floquet multipliers of the variational system based on the fact that for periodic solutions one multiplier must be +1. The separation from this theoretical value is proportional to the error of the approximation. A limitation of the frequency domain method is encountered when being used for continuing the secondary branch of limit cycle bifurcations, such as pitchfork and period-doubling bifurcations. Two examples are shown to illustrate the main results: Colpitts' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles.
Fil: Robbio, Federico I.. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Paolini, Eduardo Emilio. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Moiola, Jorge Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería Eléctrica y de Computadoras; Argentina
Fil: Chen, Guanrong. University of Hong Kong; China
description A frequency domain method is used to estimate the harmonic contents of a smooth oscillation arising from the Hopf bifurcation mechanism. The harmonic contents up to the eighth-order are well estimated, which agree with the results obtained from a completely different approach that measures the frequency content of a signal by using digital signal processing techniques such as the Fast Fourier Transform (FFT). The accuracy of the approximation is evaluated by computing the Floquet multipliers of the variational system based on the fact that for periodic solutions one multiplier must be +1. The separation from this theoretical value is proportional to the error of the approximation. A limitation of the frequency domain method is encountered when being used for continuing the secondary branch of limit cycle bifurcations, such as pitchfork and period-doubling bifurcations. Two examples are shown to illustrate the main results: Colpitts' oscillator with a pitchfork bifurcation of cycles, and Chua's circuit with a period-doubling bifurcation of cycles.
publishDate 2007
dc.date.none.fl_str_mv 2007-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/105539
Robbio, Federico I.; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chen, Guanrong; Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform; World Scientific; International Journal Of Bifurcation And Chaos; 17; 05; 12-2007; 1623-1635
0218-1274
1793-6551
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105539
identifier_str_mv Robbio, Federico I.; Paolini, Eduardo Emilio; Moiola, Jorge Luis; Chen, Guanrong; Harmonic distortion analysis based on Hopf bifurcation theorem and fast fourier transform; World Scientific; International Journal Of Bifurcation And Chaos; 17; 05; 12-2007; 1623-1635
0218-1274
1793-6551
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0218127407017951
info:eu-repo/semantics/altIdentifier/doi/10.1142/S0218127407017951
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv World Scientific
publisher.none.fl_str_mv World Scientific
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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