On the pull-in time of second-order phase-locked loops with noisy input signals

The pull-in time of second-order phase-locked loops with different nonlinear phase-detector characteristics is investigated theoretically and experimentally. In the absence of noise some approximate results are derived by means of a quasi-stationary approach and the limits of the approximation are discussed. A hardware measurement set-up is used to determine the pull-in time with noisy input signals. Statistical characteristics - as mean value, standard deviation, and a worst-case estimate - are thereby derived. The influence of the system parameters, especially the realization of the phase-detector, are shown.