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

Phase noise and frequency stability both describe the fluctuation of stable periodic signals, from somewhat different standpoints. Frequency is unique compared to other domains of metrology, in that the fluctuations of interest span over at least 14 orders of magnitude, from $10^{-4}$ in a mechanical watch to $10^{-18}$ 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-microsecond to years integration time for variances. Because this domain is 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 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. The Chart is available under Creative Commons 4.0 CC-BY-NC-ND license from Zenodo, DOI 10.5281/zenodo.4399218. A wealth of auxiliary material is available for free on the Enrico's home page http://rubiola.org.Comment: 29 pages, 18 figures, 3 tables, 173 reference