Acquisition performance of a digital phase locked loop with a four-quadrant arctan phase detector

The acquisition performance of a digital phase locked loop (DPLL) with a four-quadrant arctan based phase detector (PD) is discussed. In the noiseless case, unlike the traditional sine function based phase locked loops, the acquisition process of the four-quadrant arctan based phase locked loops is less tedious. We look into the pull-in process together with a time-series analysis of the DPLL for the noiseless case. The phase-plane portrait of the loop is also discussed, for both the noiseless and the noisy conditions.