### Abstract

A study of the dynamical properties, such as lock-in or lock-out condition, for mutually coupled phase-locked loops (PLLs) incorporating lag filters and triangular phase detectors, is presented. The system is analyzed in the context of nonlinear dynamical system theory. The symmetry of the mutually coupled PLL's system reduces the original fourth-order ordinary differential equation (ODE) that governs the phase dynamics of the voltage-controlled oscillators (VCO) outputs to the third-order ODE, for which the geometric structure of the invariant manifolds provides an understanding as to how and when lock-in can be obtained or out-of-lock behavior persists. In addition, two-parameter diagrams of the one-homoclinic orbit are obtained by solving a set of non-linear (finite dimensional) equations.

Original language | English |
---|---|

Title of host publication | IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings |

Place of Publication | Piscataway, NJ, United States |

Publisher | IEEE |

Pages | 317-321 |

Number of pages | 5 |

Publication status | Published - 1994 |

Event | Proceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems - Taipei, Taiwan Duration: 1994 Dec 5 → 1994 Dec 8 |

### Other

Other | Proceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems |
---|---|

City | Taipei, Taiwan |

Period | 94/12/5 → 94/12/8 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings*(pp. 317-321). Piscataway, NJ, United States: IEEE.

**Synchronization limit and chaos onset in mutually coupled phase-locked loops.** / Tanaka, Hisa Aki; Oishi, Shinichi; Horiuchi, Kazuo.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings.*IEEE, Piscataway, NJ, United States, pp. 317-321, Proceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems, Taipei, Taiwan, 94/12/5.

}

TY - GEN

T1 - Synchronization limit and chaos onset in mutually coupled phase-locked loops

AU - Tanaka, Hisa Aki

AU - Oishi, Shinichi

AU - Horiuchi, Kazuo

PY - 1994

Y1 - 1994

N2 - A study of the dynamical properties, such as lock-in or lock-out condition, for mutually coupled phase-locked loops (PLLs) incorporating lag filters and triangular phase detectors, is presented. The system is analyzed in the context of nonlinear dynamical system theory. The symmetry of the mutually coupled PLL's system reduces the original fourth-order ordinary differential equation (ODE) that governs the phase dynamics of the voltage-controlled oscillators (VCO) outputs to the third-order ODE, for which the geometric structure of the invariant manifolds provides an understanding as to how and when lock-in can be obtained or out-of-lock behavior persists. In addition, two-parameter diagrams of the one-homoclinic orbit are obtained by solving a set of non-linear (finite dimensional) equations.

AB - A study of the dynamical properties, such as lock-in or lock-out condition, for mutually coupled phase-locked loops (PLLs) incorporating lag filters and triangular phase detectors, is presented. The system is analyzed in the context of nonlinear dynamical system theory. The symmetry of the mutually coupled PLL's system reduces the original fourth-order ordinary differential equation (ODE) that governs the phase dynamics of the voltage-controlled oscillators (VCO) outputs to the third-order ODE, for which the geometric structure of the invariant manifolds provides an understanding as to how and when lock-in can be obtained or out-of-lock behavior persists. In addition, two-parameter diagrams of the one-homoclinic orbit are obtained by solving a set of non-linear (finite dimensional) equations.

UR - http://www.scopus.com/inward/record.url?scp=0028754825&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028754825&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0028754825

SP - 317

EP - 321

BT - IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings

PB - IEEE

CY - Piscataway, NJ, United States

ER -