Chaos from third-order phase-locked loops with a slowly varying parameter

Author

Chu, Yu-Huang ; Chou, Jui-Hsiung ; Chang, Shyang

Author_Institution

Dept. of Electr. Eng., Nat. Tsing Hua Univ., Hsin Chu, Taiwan

Volume

37

Issue

9

fYear

1990

fDate

9/1/1990 12:00:00 AM

Firstpage

1104

Lastpage

1115

Abstract

The dynamic behavior of a third -order PLL (phase-locked loop) is studied by using a second-order loop filter for tracking frequency variable signals. The authors prove the existence of horseshoe chaos in the three-dimensional nonautonomous systems by the perturbation methods based on the ideas of Melnikov. This approach makes it possible to treat three-dimensional, periodically forced, slowly varying oscillators. The Lyapunov exponents and Lyapunov dimension are also calculated to confirm the theory. Theoretical results indicate that the parameter ranges where the chaos could occur are realistic in the typical designs. Computer simulations are performed to obtain the actual chaotic attractors

Keywords

chaos; oscillators; perturbation theory; phase-locked loops; Lyapunov dimension; Lyapunov exponents; PLL; chaotic attractors; dynamic behavior; frequency variable signals; horseshoe chaos; perturbation methods; second-order loop filter; slowly varying oscillators; slowly varying parameter; third-order phase-locked loops; three-dimensional nonautonomous systems; Chaos; Computer simulation; Demodulation; Filters; Frequency shift keying; Orbits; Oscillators; Perturbation methods; Phase locked loops; Steady-state;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.57599

Filename

57599