Phase-Locked Loop Stability Based on Stochastic Bounds
Abstract
In this paper we study the stability of a phase-locked loop (PLL) in the
presence of noise. We represent the noise as Brownian motion and model the circuit
as a nonlinear stochastic differential equation, with the noise lumped at the phase
detector input. We show that for the PLL, the theory of asymptotics of singular
diffusions can be applied and we use this theory to develop a new figure of merit
which we call a stability margin. The stability margin provides easily computable
bounds on the acceptable noise levels for which stability is guaranteed. Through
simulation, we show that such a sufficient bound provides a realistic prediction for
PLL stability
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Cite this version of the work
Robert J. A. Baker, Bosco Leung, Christopher Nielsen
(2015).
Phase-Locked Loop Stability Based on Stochastic Bounds. UWSpace.
http://hdl.handle.net/10012/17492
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