Dynamical patterns of bang-bang phase-locked loops

This paper examines the nonlinear dynamics of a model of a second order bang-bang phase-locked loops (BB-PLL). The system behaviour is categorised into four distinct dynamical patterns, the transient behaviour (global attraction) and three steady-state possibilities (locking, slew-rate limiting and limit cycles). In order to give further insight into the occurrence of these dynamical patterns, a continuous model of the system is introduced.