First Slip Times Versus Static Phase Error Offset for the First- and Passive Second-Order Phase-Locked Loop

Static phase error offsets occur in first-order and passive second-order phase-locked loops, whenever the rest frequency of the local oscillator and the carrier are different prior to acquisition. The effect of the offset is to degrade performance and in particular to decrease the mean time to first slip. This paper studies first slip times via computer simulation. The mean time to first slip is displayed graphically as a function of signal-to-noise ratio (SNR) for various static phase error offsets and values of the damping parameter.