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

Phase noise and frequency (in)stability both describe the fluctuation of stable periodic signals from somewhat different standpoints. Frequency is unique compared to other domains of metrology, in which its fluctuations of interest span at least 14 orders of magnitude, from 10(-4) in a mechanical watch to 10(-18) in atomic clocks. The frequency span of interest is some 12-15 orders of magnitude from mu Hz to GHz Fourier frequency for phase noise, while the time span over which the fluctuations occur ranges from sub-mu s 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 Enrico's home page: http://rubiola.org.

Automated summary

Phase noise and frequency (in)stability describe the fluctuation of stable periodic signals from different perspectives. Frequency spans a wide range of magnitudes, from 10(-4) in a mechanical watch to 10(-18) in atomic clocks. The frequency span of interest for phase noise is from mu Hz to GHz Fourier frequency, while the fluctuation time spans from sub-mu s to years integration time for variances. The development of a common language and tools suitable for this domain is challenging due to its ubiquity in science and technology.