Acquisition Time of Second-Order Aided PLL

The analysis of a second-order tracking loop operating in the frequency-search mode is carried out by the quasi-stationary approach. An arbitrary phase detector characteristic is assumed and perfect or imperfect integrating filters are considered. The theory leads to a closed-form expression of the acquisition time versus the relevant system parameters, the initial detuning, and the search rate. The limitations of this analysis concern the absence of noise and the hypothesis of large initial detuning.