Second-Order Phase-Lock-Loop Acquisition Time in the Presence of Narrow-Band Gaussian Noise

Phase-lock acquisition time of a perfect (proportional plus integral control) second-order phase-lock loop (PLL) in the presence of narrow-band Gaussian noise is studied by means of computer simulation. 100 nonoverlapping sequences of pseudorandom noise are generated. In the presence of each noise sequence, phase-lock acquisition is simulated at each of five pairs of initial phase error φ0and initial frequency error φ0. For each with each noise sequence, phase-lock acquisition is simulated at nine different ratios of signal-to-noise energy at the PLL input. If the PLL phase detectors were linear rather than sinusoidal, the range of PLL output signal-to-noise ratios simulated would extend from 4 to 50 dB. The 4500 acquisitions of phase lock simulated are represented by 45 distribution functions that explicitly indicate the effect of PLL output signal-to-noise ratio on PLL phase-lock acquisition time.