An approach to transient analysis of bang-bang phase locked loops for phase step inputs

This paper presents a new method to obtain the transient time features of second order bang-bang phase locked loops (BBPLLs) in response to phase step input such as rise time, peak time, over shoot and settling time. This method introduces the closed-form equations with acceptable accuracy by Approximating transient response to reasonable specific waveform. This approach gives new insights into the transient behavior of the BBPLLs. The validity of resulted equations is verified through simulations using MATLAB SIMULINK. Simulation results show the high accuracy of the proposed method to model BBPLLs behavior.