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 |
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ASJC Scopus subject areas
- Electrical and Electronic Engineering
Cite this
Synchronization limit and chaos onset in mutually coupled phase-locked loops. / Tanaka, Hisa Aki; Oishi, Shinichi; Horiuchi, Kazuo.
IEEE Asia-Pacific Conference on Circuits and Systems - Proceedings. Piscataway, NJ, United States : IEEE, 1994. p. 317-321.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
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 -