Nonlinear dynamics of first-order DPLL with FM input and phase detector DC offset

Phase-locked loops are important systems that are used extensively in engineering applications. Previously, the nonlinear dynamics of a first order digital phase-locked loop (DPLL) with frequency modulated input and small values of modulating frequency were considered (O´Donnell, B. and Feely, O., European Conf Circuit Theory and Design, 2003; Vasylenko, A. and Feely, O. Int. J. Bifurcation and Chaos, vol.12, no.7, p.1633-42, 2002). The effect of a phase detector DC offset on the behavior of the loop and in particular its lock range is now explored. A modulated input to the system causes a perturbation of the fixed-point in the lock region and results in a uniform scatter or a ´belt´ of points for this region. The bifurcation properties of these ´belts´ are numerically distinct from the fixed-point approach.