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

Closed-Form Analytical Equations to Transient Analysis of Bang-Bang Phase-Locked Loops

Due to the nonlinear nature of the Bang-Bang phase-locked loops (BBPLLs), its transient analysis is very difficult. In this paper, new equations are proposed for expression of transient behavior of the second order BBPLLs to phase step input. This approach gives new insights into the transient behavior of BBPLLs. Approximating transient response to reasonable specific waveform the loop transient time characteristics such as locking time, peak time, rise time and over shoot are derived with acceptable accuracy. The validity of the resulted equations is verified through simulations using MATLAB SIMULINK. Simulation results show the high accuracy of the proposed method to model BBPLLs behavior