Performance analysis of a digital phase-locked loop with a hyperbolic nonlinearity

The treatment of phase locked loops (PLL) has been heavily looked into over the past several decades on its performances and analysis, and is a very old topic. However the usage of it has never been reduced with the rapid evolvement of various open loop and closed loop systems. In this paper we analyse the performance of an arctan based digital phase locked loop (DPLL) with a hyperbolic nonlinearity for single-tone carrier tracking. We purposely introduce the nonlinearity for improved performance of the closed loop system. We look at the acquisition performance of the DPLL by considering the phase plane portrait and the lock-in range of the loop. The steady state (SS) performance of the loop is analysed by considering the open loop SS statistical distribution of the phase noise.