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

Abstract

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 that 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 the Enrico's home page http://rubiola.org. This version includes the corrections for an unfortunate error in the normalization of the Hadamard version, and some corrections for trivial (albeit sometimes subtle) mistakes.

32 pages, 20 figures, 3 tables, 173 references, list of symbols

References in corpus (7)

• Photonic microwave signals with zeptosecond level absolute timing noise
• Applications of the optical fiber to the generation and to the measurement of low-phase-noise microwave signals
• Light-shift mitigation in a microcell-based atomic clock with Symmetric Auto-Balanced Ramsey spectroscopy
• A generalization of the Leeson effect
• Tutorial on the double balanced mixer
• Response and Uncertainty of the Parabolic Variance PVAR to Non-Integer Exponents of the Power Law
• The Statistics of the Cross-Spectrum and the Spectrum Average: Generalization to Multiple Instruments

Cited by in corpus (8)

• Intracavity filtering in SESAM mode-locked fiber lasers: soliton effects and noise performance
• Fully digital platform for local ultra-stable optical frequency distribution
• Phase noise analysis of mutually synchronized spin Hall nano-oscillators
• Classical and Quantum Frequency Combs for Satellite-based Clock Synchronization
• Dual-Frequency Comb in Fiber Fabry-Perot Resonator
• Phase noise measurement of semiconductor optical amplifiers
• A plug-and-play solution for characterizing two-way optical frequency transfer over free-space
• On-Chip Frequency Noise Cancellation in Nanomechanical Resonators using Cavity Optomechanics