### 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 |
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Pages | 317-321 |

Number of pages | 5 |

Publication status | Published - 1994 Dec 1 |

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 |
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City | Taipei, Taiwan |

Period | 94/12/5 → 94/12/8 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*Synchronization limit and chaos onset in mutually coupled phase-locked loops*. 317-321. Paper presented at Proceedings of the 1994 IEEE Asia-Pacific Conference on Circuits and Systems, Taipei, Taiwan, .