IEICE TRANSACTIONS on Fundamentals
Melnikov Analysis for a Second Order Phase–Locked Loop in the Presence of a Weak CW Interference
Summary :
This letter presents the results of an analysis concerning the global, dynamical structure of a second order phase–locked loop (PLL) in the presence of the continuous wave (CW) interference. The invariant manifolds of the PLL equation are focused and analyzed as to how they are extended from the hyperbolic periodic orbits. Using the Melnikov integral which evaluates the distance between the stable manifolds and the unstable manifolds, the transversal intersection of these manifolds is proven to occur under some conditions on the power of the interference and the angular frequency difference between the signal and the interference. Numerical computations were performed to confirm the transversal intersection of the system–generated invariant manifolds for a practical set of parameters.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.11 pp.1887-1891
- Publication Date
- 1994/11/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section LETTER (Special Section of Letters Selected from the 1994 IEICE Spring Conference)
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Hisa–Aki TANAKA, Shin'ichi OISHI, Kazuo HORIUCHI, "Melnikov Analysis for a Second Order Phase–Locked Loop in the Presence of a Weak CW Interference" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 11, pp. 1887-1891, November 1994, doi: .
Abstract: This letter presents the results of an analysis concerning the global, dynamical structure of a second order phase–locked loop (PLL) in the presence of the continuous wave (CW) interference. The invariant manifolds of the PLL equation are focused and analyzed as to how they are extended from the hyperbolic periodic orbits. Using the Melnikov integral which evaluates the distance between the stable manifolds and the unstable manifolds, the transversal intersection of these manifolds is proven to occur under some conditions on the power of the interference and the angular frequency difference between the signal and the interference. Numerical computations were performed to confirm the transversal intersection of the system–generated invariant manifolds for a practical set of parameters.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_11_1887/_p
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@ARTICLE{e77-a_11_1887,
author={Hisa–Aki TANAKA, Shin'ichi OISHI, Kazuo HORIUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Melnikov Analysis for a Second Order Phase–Locked Loop in the Presence of a Weak CW Interference},
year={1994},
volume={E77-A},
number={11},
pages={1887-1891},
abstract={This letter presents the results of an analysis concerning the global, dynamical structure of a second order phase–locked loop (PLL) in the presence of the continuous wave (CW) interference. The invariant manifolds of the PLL equation are focused and analyzed as to how they are extended from the hyperbolic periodic orbits. Using the Melnikov integral which evaluates the distance between the stable manifolds and the unstable manifolds, the transversal intersection of these manifolds is proven to occur under some conditions on the power of the interference and the angular frequency difference between the signal and the interference. Numerical computations were performed to confirm the transversal intersection of the system–generated invariant manifolds for a practical set of parameters.},
keywords={},
doi={},
ISSN={},
month={November},}
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TY - JOUR
TI - Melnikov Analysis for a Second Order Phase–Locked Loop in the Presence of a Weak CW Interference
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1887
EP - 1891
AU - Hisa–Aki TANAKA
AU - Shin'ichi OISHI
AU - Kazuo HORIUCHI
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 1994
AB - This letter presents the results of an analysis concerning the global, dynamical structure of a second order phase–locked loop (PLL) in the presence of the continuous wave (CW) interference. The invariant manifolds of the PLL equation are focused and analyzed as to how they are extended from the hyperbolic periodic orbits. Using the Melnikov integral which evaluates the distance between the stable manifolds and the unstable manifolds, the transversal intersection of these manifolds is proven to occur under some conditions on the power of the interference and the angular frequency difference between the signal and the interference. Numerical computations were performed to confirm the transversal intersection of the system–generated invariant manifolds for a practical set of parameters.
ER -
English
