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

In this paper an exact transient analysis of Bang-Bang PLLs (BBPLLs), as a nonlinear system, is presented. New equations are proposed for expression of transient behavior of the BBPLL with first order filter in response 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.