Title :
Analysis of lock-loss events in discrete-time phase locked loop (PLL)
Author :
Brecher, L. ; Sommer, N. ; Weinstein, E.
Author_Institution :
Broadband Commun. Israel, Texas Instrum., Herzlia, Israel
Abstract :
Lock-loss phenomena were studied extensively for continuous-time phase locked loop (PLL), and closed form analytical expressions for the mean time to lose lock (MTLL) has been derived under the assumptions that the input is a phase modulated sine wave, and that the additive noise associated with the input can be added to the detector output. The analysis of the discrete-time phase detector is more complicated as the associated discrete-time stochastic equation depends on the signal constellation as well as on the detector non-linearity. In this study we present an approach for analyzing lock-loss events and for calculating the MTLL in first-order discrete-time PLL, and prove that the time to lose lock is approximately exponentially distributed. The results can be applied to any linear modulation scheme and, in particular, to any QAM modulation scheme, and can be used for qualitative understanding of the problem as well as for performance assessment and parameter optimization. In that context it is shown that the Leclert-Vandamme phase detector is more robust to the lock-loss problem at the cost of slightly larger residual phase error, compared with the more conventional Simon and Smith phase detector.
Keywords :
circuit noise; circuit simulation; continuous time systems; exponential distribution; phase detectors; phase locked loops; phase modulation; stochastic processes; Leclert-Vandamme phase detector; MTLL; PLL; QAM modulation; Simon and Smith phase detector; additive noise; closed form analytical expressions; continuous-time phase locked loop; detector nonlinearity; detector output; discrete-time phase detector; discrete-time phase locked loop; discrete-time stochastic equation; exponentially distributed time to lose lock; first-order discrete-time PLL; input phase modulated sine wave; lock-loss event analysis; lock-loss phenomena; mean time to lose lock; parameter optimization; performance assessment; residual phase error; signal constellation; Additive noise; Constellation diagram; Detectors; Nonlinear equations; Phase detection; Phase locked loops; Phase modulation; Quadrature amplitude modulation; Signal analysis; Stochastic resonance;
Conference_Titel :
Electronics, Circuits and Systems, 2004. ICECS 2004. Proceedings of the 2004 11th IEEE International Conference on
Print_ISBN :
0-7803-8715-5
DOI :
10.1109/ICECS.2004.1399691