A Model Distribution for the Phase Error in Second-Order Phase-Locked Loops

This paper describes a model distribution for the phase error in the second-order phase-locked loop (PLL) of greatest practical interest. Experimental results relative to the distribution of the phase error and its properties are given. The experimental measurements are used to complement the analytical model in a signal-to-noise region where the linear PLL theory does not apply. Compared to the actual measurements of the second-order loop performance, it is shown that the model distribution provides excellent agreement over the useful range of most phase-locked receivers.