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

Hisa Aki Tanaka; Shin'ichi Oishi; Kazuo Horiuchi

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

Hisa Aki Tanaka, Shin'ichi Oishi, Kazuo Horiuchi

School of Fundamental Science and Engineering

Research output: Contribution to conference › Paper

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
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
City	Taipei, Taiwan
Period	94/12/5 → 94/12/8

ASJC Scopus subject areas

Electrical and Electronic Engineering

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Tanaka, H. A., Oishi, S., & Horiuchi, K. (1994). 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, .

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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.",

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AU - Tanaka, Hisa Aki

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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.

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