Limit cycles in Digital Bang-Bang PLLs

This paper examines the nonlinear dynamics of a model of a second order Digital Bang-Bang Phase-Locked Loop (DBB-PLL). A continuous model of the DBB-PLL is developed. This paper focuses on the occurrence and behaviour of limit cycles. In particular, limit cycle trajectory equations are determined. The parameter space boundary for this class of limit cycles is then found. A further theorem extends this analysis to the case of the discrete system, where a continuum of cycles is found to occur. A direct relationship between the input phase deviation amplitude and the occurrence of limit cycles is observed.