Chaos, intermittency and control of bifurcation in a ZC₂-DPLL

Abstract

Nonlinear dynamics of a dual sampler-based zero crossing digital phase lock loop (ZC₂-DPLL) has been investigated. Analysis supported by detailed numerical studies shows that the system enters a chaotic state through a cascade of period doubling bifurcation. The dynamics of the system have been quantified with the dynamical measures of Lyapunov exponent and correlation dimension. Further, it has been found that for certain system parameters intermittency occurs in the system. The occurrence of intermittency has been proved using the Pomeau–Manneville principle. The phenomenon of bifurcation control in a ZC₂-DPLL using time delay feedback has been explored. It has been found that for some suitably chosen control parameters bifurcation phenomena can be controlled such that the stable locked zone of a bifurcation controlled ZC₂-DPLL can be extended, which enhances the application potentiality of a ZC₂-DPLL.

Keywords:

• digital phase locked loop
• stability analysis
• bifurcation control
• intermittency
• chaos