Nonlinear dynamics of a class of symmetric lock range DPLLs with an additional derivative control

Abstract

Nonlinear dynamics of a class of symmetric lock range digital phase-locked loops (SLR-DPLLs) has been investigated using nonlinear dynamical theoretical and computational tools. It has been observed that the system shows a period doubling route to chaos. For certain system parameters the loop exhibits intermittent behavior. The analytical bifurcation analysis shows that inspite of the broader frequency acquisition range than a conventional one the stability of the loop degrades appreciably when the input signal frequency is less than the nominal frequency of the digitally controlled oscillator. The system dynamics have been characterized by measuring the Lyapunov exponent and the correlation dimension. Further it has been shown that the stability range of a SLR-DPLL can be extended using a modified loop filter incorporating time delay feedback technique. The modified SLR-DPLL (MSLR-DPLL) with this additional derivative control along with the loop digital filter (LDF) shows faster convergence than the unmodified one for proper choice of system design parameters. Consequently, the MSLR-DPLL becomes more suitable for practical applications.