The Companion of the Enrico's Chart for Phase Noise and Two-Sample Variances

Abstract

Phase noise and frequency stability both describe the fluctuation of stable periodic signals, from somewhat different standpoints. Unique compared to other domains of metrology, the fluctuations of interest span over at least 13 orders of magnitude, from $10^{4}$ in a mechanical watch to $10^{-17}$ in atomic clocks; and over 12-15 orders of magnitude in the frequency span, or the time span where the fluctuations occur. Say, from $\mu$Hz to GHz Fourier frequency for phase noise, and from sub $\mu$s to years integration time for variances. Being this domain ubiquitous in science and technology, a common language and tools suitable to the variety mentioned are a challenge. This article is at once (1) a tutorial, (2) a review covering the most important facts about phase noise, frequency noise and two-sample (Allan and Allan-like) variances, and (3) a user guide to "The Enrico's Chart of Phase Noise and Two-Sample Variances." In turn, the Chart is a reference card collecting the most useful concepts, formulas and plots in a single A4/A-size sheet, intended to be a staple on the desk of whoever works with these topics. It available from Zenodo DOI: 10.5281/zenodo.4399218 under Creative Commons 4.0 CC-BY-NC-ND license.Comment: 24 pages, 15 figures, 3 tables, 136 reference