### 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

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*,

*E77-A*(11), 1887-1891.

**Melnikov analysis for a second order phase-locked loop in the presence of a weak CW interference.** / Tanaka, Hisa Aki; Oishi, Shinichi; Horiuchi, Kazuo.

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E77-A, no. 11, pp. 1887-1891.

}

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 -