Transient analysis of bang-bang phase locked loops

This work gives insight into the behaviour of second-order bang-bang phase locked loops in the far from lock region. This region, while largely unexplored, is of particular interest as PLL behaviour in this region determines locking time and capture range. By analysing PLL cycle slipping behaviour in this region, the transient response for the system is derived. Expressions for first-order system stability and locking time are also presented.