STATISTICAL ANALYSIS OF DIGITAL PLL USING MARKOV CHAINS

A. A. Samokhvalov, Moscow Bauman State Technical University (the Kaluga Branch), Kaluga, Russia

SYNCHROINFO JOURNAL. Volume 5, Number 5 (2019). P. 2-5.

Abstract

The obtaining of most important statistical characteristics (such as distribution density of probabilities of phase-error, out-of-lock probability, variance of phase-error, out-of-lock mean time, mean time of transient process) of digital phase-lock loops problem using Markov chains is considered., Digital PLL proposed by Holmes [1], has been examined in this paper. The results of analytical solutions and computational modeling are being compared.

Keywords: synchronization, Markov chains, digital phase-locked loops.

References

[1] Holmes J.K. Performance of a first-order transition sampling digital phase-locked loop using random-walk models. IEEE Trans. 1972. Vol. COM-20, 2, pp. 119-131.
[2] Best, Roland. E Phase-locked loops: design, simulation, and applications. Roland E.Best. 3rd ed. 1997.
[3] Shakhtarin B.I. Stochastic processes in the radio engineering P.1: linear systems, 2nd ed. Moscow, Radio i svyaz’, 2002, 568 p.
[4] Shakhtarin B.I. Statistical dynamics of synchronization systems. Moscow, Radio i svyaz’, 1998, 488 p. [5] Shakhtarin B.I. Analysis of synchronization systems involving noise. Moscow, IPRZHP, 1996, 252 p.