Statistics of atomic frequency standards
Abstract
A theoretical development is presented which results in a relationship between the expectation value of the standard deviation of the frequency fluctuations for any finite number of data samples and the infinite time average value of the standard deviation, which provides an invariant measure of an important quality factor of a frequency standard. A practical and straightforward method of determining the power spectral density of the frequency fluctuations from the variance of the frequency fluctuations, the sampling time, the number of samples taken, and the dependence on system bandwidth is also developed. Additional insight is also given into some of the problems that arise from the presence of "flicker noise" (spectrum proportional to |ω|-1) modulation of the frequency of an oscillator. The theory is applied in classifying the types of noise on the signals of frequency standards made available at NBS, Boulder Laboratories, such as: masers (both H and N15H3), the cesium beam frequency standard employed as the U. S. Frequency Standard, and rubidium gas cells. "Flicker noise" frequency modulation was not observed on the signals of masers for sampling times ranging from 0.1 second to 4 hours. In a comparison between the NBS hydrogen maser and the NBS III cesium beam, uncorrelated random noise was observed on the frequency fluctuations for sampling times extending to 4 hours; the fractional standard deviations of the frequency fluctuations were as low as 5 parts in 1014.
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The Allan variance is usually used to calculate the uncertainty of the optical clock frequency.
“The Allan variance is usually used to calculate the uncertainty of the optical clock frequency [41,42].”
From Performance Evaluation and Requirement Analysis for Chronometric Leveling with High-Accuracy Optical Clocks (2022) · cites this paper as [42]
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- Authors
- Allan, D. W.
- Affiliations
- National Institute of Standards and Technology (US)
- Corresponding author
- Allan, D.W.
- Venue
- Proceedings of the IEEE
- Published
- 1966
- Volume
- 54
- Issue
- 2
- Pages
- 221-230
- ISSN
- 0018-9219 (ISSN-L)
- OpenAlex
- W2159012223
- Cited by
- 2,692
- References
- 0
- Citations by year
- 2026: 72 · 2025: 113 · 2024: 103 · 2023: 122 · 2022: 105 · 2021: 110 · 2020: 101 · 2019: 106 · 2018: 104 · 2017: 99 · 2016: 118 · 2015: 114 · 2014: 111 · 2013: 106 · 2012: 115
- FWCI
- 6.45
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Proceedings of the IEEE (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Frequency and Time Standards
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Electrical Measurement Techniques
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Scientific Measurement and Uncertainty Evaluation
- Keywords
- atomic clocks, frequency variation, power spectral density, 1/f noise, frequency modulation, hydrogen maser, cesium frequency standard, oscillator noise
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