Noise analysis of phase-locked loops

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Noise analysis of phase-locked loops (2002)

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by Amit Mehrotra

Venue:	IEEE Trans. Circuits Syst. I, Fundam. Theory Appl
Citations:	36 - 1 self

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@ARTICLE{Mehrotra02noiseanalysis,
    author = {Amit Mehrotra},
    title = {Noise analysis of phase-locked loops},
    journal = {IEEE Trans. Circuits Syst. I, Fundam. Theory Appl},
    year = {2002},
    pages = {1309--1316}
}

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Abstract

Abstract—This work addresses the problem of noise analysis of phase-locked loops (PLLs). The problem is formulated as a stochastic differential equation and is solved in the presence of circuit white noise sources yielding the spectrum of the PLL output. Specifically, the effect of loop filter characteristics, phase-frequency detector, and phase noise of the open-loop voltage-controlled oscillator (VCO) on the PLL output spectrum is quantified. These results are derived using a full nonlinear analysis of the VCO in the feedback loop and cannot be predicted using traditional linear analyses or the phase noise analysis of open-loop oscillators. The computed spectrum matches well with measured results; specifically, the shape of the output spectrum matches very well with measured PLL output spectra reported in the literature for different kinds of loop filters and phase detectors. The PLL output spectrum computation only requires the phase noise of the VCO, loop filter and phase detector noise, phase detector gain, and loop filter transfer function and does not require the transient simulation of the entire PLL which can be very expensive. The noise analysis technique is illustrated with some examples. Index Terms—Noise analysis, phase-locked loops, stochastic differential equations. I.

Keyphrases

phase-locked loop noise analysis phase noise stochastic differential equation pll output spectrum loop filter phase detector gain traditional linear analysis open-loop voltage-controlled oscillator open-loop oscillator loop filter characteristic circuit white noise source loop filter transfer function computed spectrum match phase detector different kind phase noise analysis transient simulation noise analysis technique feedback loop full nonlinear analysis phase detector noise phase-frequency detector pll output index term noise analysis entire pll output spectrum match pll output spectrum computation

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