Chaos and bifurcation in a third-order phase locked loop

The chaos induced in a new type of phase locked loop (PLL) having a second-order loop filter is investigated. The system under consideration is modeled as a third-order autonomous system with sinusoidal phase detector characteristics. The modern of nonlinear theory such as bifurcation and chaos is a...

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Bibliographic Details
Published inChaos, solitons and fractals Vol. 19; no. 3; pp. 667 - 672
Main Authors Harb, Bassam A., Harb, Ahmad.M.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2004
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Summary:The chaos induced in a new type of phase locked loop (PLL) having a second-order loop filter is investigated. The system under consideration is modeled as a third-order autonomous system with sinusoidal phase detector characteristics. The modern of nonlinear theory such as bifurcation and chaos is applied to a third-order of PLL. A method is developed to quantitatively study the type of bifurcations that occur in this type of PLL’s. The study showed that PLL experiencing a Hopf bifurcation point as well as chaotic behaviour. The method of multiple scales is used to find the normal form near the Hopf bifurcation point. The point is found to be supercritical one.
ISSN:0960-0779
1873-2887
DOI:10.1016/S0960-0779(03)00197-8