Coloured noise analysis of a phase-locked loop system: beyond Itô and Stratonovich stochastic calculi (Q286496)

The phase-locked loop (PLL) system is an appealing electronic circuit that synchronises the oscillator output signal with the reference signal. It is revealed that the PLL system fails to achieve the locking condition in the presence of small noise influences. The authors accomplish the PLL noise analysis in coloured noise framework that is more general as well as confirms the real noise statistics in contrast to the white noise. The extended phase space and stochastic differential rules for the random state vector satisfying vector stochastic differential equation are exploited to accomplish the PLL coloured noise analysis.