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.
| Original language | English |
|---|---|
| Pages (from-to) | 1887-1891 |
| Number of pages | 5 |
| Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |
| Volume | E77-A |
| Issue number | 11 |
| Publication status | Published - 1994 Nov |
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ASJC Scopus subject areas
- Hardware and Architecture
- Information Systems
- Electrical and Electronic Engineering
Cite this
Melnikov analysis for a second order phase-locked loop in the presence of a weak CW interference. / Tanaka, Hisa Aki; Oishi, Shinichi; Horiuchi, Kazuo.
In: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, Vol. E77-A, No. 11, 11.1994, p. 1887-1891.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Melnikov analysis for a second order phase-locked loop in the presence of a weak CW interference
AU - Tanaka, Hisa Aki
AU - Oishi, Shinichi
AU - Horiuchi, Kazuo
PY - 1994/11
Y1 - 1994/11
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=0028546702&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0028546702&partnerID=8YFLogxK
M3 - Article
VL - E77-A
SP - 1887
EP - 1891
JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
SN - 0916-8508
IS - 11
ER -