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Frequency Stability

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An Introduction to Modern Timekee** and Time Transfer

Part of the book series: Springer Series in Measurement Science and Technology ((SSMST))

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Abstract

The stability of clock largely depends on its underlying oscillator. A clock’s time can be mathematically described as the phase of an oscillator of known period, and its behavior can be modelled as a polynomial. We distinguish accuracy from precision, and describe noise types relevant to precise timekee**. These noise types can be identified and quantified by many stability measures. In the frequency domain, the stability is related to the Power Spectral Density, which is the amount of sinusoidal variation in the time, phase, or frequency of a clock. In the time domain, we describe the Allan deviation, Modified Allan deviation, Hadamard deviation, Parabolic deviation, Time deviation, Maximum Time Interval Error, Total deviation, Theo1, TheoBr, and their overlap** variants. The complementary relationship between and among these statistics is described. Finally, we describe the three-cornered hat and Groslambert methods for estimating the three or more individual component time-domain variances in an “absolute” sense, from the statistics of the differences between their redundant pairs.

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Author information

Authors and Affiliations

  1. Department of Physics, The University of Burdwan, Burdwan, West Bengal, India

    Parameswar Banerjee

  2. CSIR National Physical Laboratory, New Delhi, India

    Parameswar Banerjee

  3. Masterclock, Inc., Silver Spring, MD, USA

    Demetrios Matsakis

  4. U.S. Naval Observatory, Washington, DC, USA

    Demetrios Matsakis

Authors
  1. Parameswar Banerjee
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  2. Demetrios Matsakis
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Banerjee, P., Matsakis, D. (2023). Frequency Stability. In: An Introduction to Modern Timekee** and Time Transfer. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-031-30780-5_4

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