Metrology and 1/f noise: linear regressions and confidence intervals in flicker noise context

1/f noise is very common but is difficult to handle in a metrological way. After having recalled the main characteristics of stongly correlated noise, this paper will determine relationships giving confidence intervals over the arithmetic mean and the linear drift parameters. A complete example of processing of an actual measurement sequence affected by 1/f noise will be given

A Cryogenic Sapphire Resonator Oscillator with 1e-16 mid-term fractional frequency stability

We report in this letter the outstanding frequency stability performances of an autonomous cryogenique sapphire oscillator presenting a flicker frequency noise floor below 2e-16 near 1,000 s of integration time and a long term Allan Deviation (ADEV) limited by a random walk process of 1e-18/sqr(tau). The frequency stability qualification at this level called for the implementation of sophisticated instrumentation associated with ultra-stable frequency references and ad hoq averaging and correlation methods.Comment: 4 pages, 2 figure

Stabilite temporelle des oscillateurs: nouvelles variances, leurs proprietes, leurs applications

SIGLEINIST T 77061 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

The Companion of the 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. 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

A Bayesian Method for Oscillator Stability Analysis

The power spectral density of frequency fluctuations of an oscillator is generally modeled as a sum of power laws with integer exponents (from-2 to +2). However, a power law with a fractional exponent may exist. We propose a method for measuring the level of such a noise process and determining the probability density of the exponent. This yields a criterion for compatibility with an integer exponent. This method is based upon a Bayesian approach called the reference analysis of Bernardo-Berger. The application to a sequence of frequency measurement from a quartz oscillator illustrates this paper. Index Terms oscillator characterization, time stability, noise analysis, Bayesian analysis I