Oscillators and the Characterization of Frequency Stability: an Introduction

  • Vincent Giordano
  • Enrico Rubiola
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 550)


This paper provides an introduction to basic concepts commonly used in time and frequency metrology, and is addressed to other scientific communities. Thus no attempt is made to provide an exhaustive review. Instead, attention is focused on the most important tools used by physicists and engineers involved in time and frequency metrology. We first explain the principles of the oscillator through an example. Then we introduce the concepts of frequency reference, oscillating loop, frequency stability and accuracy. Finally, we define the power spectrum density of frequency fluctuations and the Allan variance as means to characterize the stability of frequency standards.


Surface Acoustic Wave Power Spectrum Density Frequency Stability Frequency Standard Dielectric Resonator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 2.
    J. A. Barnes, Models for the interpretation of frequency stability measurements, NBS Technical Note no. 683, August 1976.Google Scholar
  2. 3.
    J. Rutman, “Characterization of phase and frequency instabilities in precision frequency sources: fifteen years of progress”, Proc. of the IEEE, Vol. 66, no. 9 pp. 1048–1075, September 1978.Google Scholar
  3. 4.
    E. S. Ferre-Pikal, J. R. Vig, J. C. Camparo, L. S. Cutler, L. Maleki, W. J. Riley, S. R. Stein, C. Thomas, F. L. Walls, J. D. White, “Draft revision of IEEE STD 1139-1988 standard definitions of physical quantities for fundamental frequency and time metrology—random instabilities”, Proc. 51st Frequency Control Symposium pp. 338–357, Orlando (FL, USA), 28–30 May 1997.Google Scholar
  4. 8.
    E. A. Gerber, A. Ballato, Precision Frequency Control, Academiic Press, 1985. ISBN 0-12-280601-8 (vol. 1), and 0-12-280602-6 (vol. 2).Google Scholar
  5. 9.
    J. Vanier, C. Audoin, The Quantum Physics of Atomic Frequency Standards, Adam Hilger 1989. ISBN 0-85274-434-2.Google Scholar
  6. 10.
    Chronos Group, Frequency Measurement and Control, Chapman and Hall 1994. ISBN 0-412-48270-3.Google Scholar
  7. 11.
    C. Audoin, N. Dimarcq, V. Giordano, J. Viennet, “Physical origin of the frequency shifts in cesium beam frequency standards—related environmental sensitivity”, IEEE Trans. on UFFC vol. 39 no. pp. 412–421, May 1993.Google Scholar
  8. 12.
    A. El Habti, F. Bastien, E. Bigler, T. Thorvaldsson, “High-frequency surface acoustic wave devices at very low temperature: Application to loss mechanisms evaluation”, J. Acoust. Soc. Am. vol. 100 no. 1 pp. 272–277, July 1996.CrossRefADSGoogle Scholar
  9. 13.
    D. Kajfez, Guillon, Dielectric Resonators, Artech House 1986.Google Scholar
  10. 14.
    A. N. Luiten, A. G. Mann, D.G. Blair, “Ultrahigh Q-factor cryogenic sapphire resonator.”, Electronics Letters vol. 29 no. 10 pp. 879–881, May 1993.CrossRefADSGoogle Scholar
  11. 15.
    J. A. Barnes, Tables of bias functions B 1 and B 2 for variances based on finite samples of processes with power law spectral densities, NBS Tech. Note no. 375, Washington D.C., January 1969.Google Scholar
  12. 16.
    P. Lesage, C. Audoin,“Effect of dead-time on the estimation of the two-sample variance”, IEEE Trans. on Instrumentation and Measurement vol. IM-28 no. 1 pp. 6–10, March 1979.CrossRefGoogle Scholar
  13. 17.
    P. Flandrin, “Wavelet analysis and synthesis of fractional brownian motion”, IEEE Trans. on Information Theory vol. 38 no. 2 pp. 910–917, March 1992.CrossRefMathSciNetGoogle Scholar
  14. 18.
    P. Lesage, C. Audoin,“Charecterization of frequency stability: uncertainty due to the finite number of measurements”, IEEE Trans. on Instrumentation and Measurement vol. IM-22 no. 4 pp. 157–161, June 1973.CrossRefGoogle Scholar
  15. 19.
    A. G. Mann, G. Santarelli, S. Chang, A. N. Luiten, P. Laurent, C. Salomon, D. G. Blair, A. Clairon, “A high stability atomic fountain clock using a cryogenic sapphire interrogation oscillator”, Proc. 52nd Frequency Control Symposium pp. 13–17, Pasadena (CA, USA), 27–29 May 1998.Google Scholar
  16. 20.
    G. J. Dick, R. T. Wang, R. L. Tjoelker,“Cryo-cooled sapphire oscillator with ultra-high sability”, Proc. 52nd Frequency Control Symposium pp. 528–533, Pasadena (CA, USA), 27–29 May 1998.Google Scholar
  17. 21.
    V. Candelier, J. Chauvin, C. Gellé, G. Marotel, M. Brunet, R. Petit, “Ultrastable oscillators”, Proc. 12th European Frequency and Time Forum pp. 345–351, Warsaw (Poland), 10–12 March 1998.Google Scholar
  18. 22.
    V. Giordano, “Noise sources in frequency standards”, Ann. Télécommun. vol. 51 no. 7–8 pp. 335–343, July 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Vincent Giordano
    • 1
  • Enrico Rubiola
    • 1
    • 2
  1. 1.LPMOCNRS UPR3203 associée à l’Université de Franche-ComtéBesançonFrance
  2. 2.Dipartimento di Elettronica, and INFM UDR PolitecnicoPolitecnico di TorinoTorinoItaly

Personalised recommendations