Detection of Chaos in the Noise of Electronic Oscillators by Time Series Analysis Methods

  • C. Eckert
  • M. Planat
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 550)


Frequency fluctuations of an electronic oscillator are studied by time series analysis methods in order to detect an eventual underlying attractor. Measurements are performed by a period counting technique with a reference signal of 10 MHz and various frequencies of the local oscillator. Three different behaviours of the Allan variance are observed, depending on the mean frequency of the beat signal. The results of time series analyses clearly show that two of these behaviours are associated with the presence of a chaotic process, whereas the third is more intricate. When applied to data computed from continued fraction expansions of real numbers, these methods lead to the same conclusions. For two kinds of truncation, the data present a chaotic behaviour, which is not obvious for the third kind. A correspondence between the behaviour of the frequency fluctuations and the way of truncating the continued fraction expansions can thus be proposed.


Correlation Dimension Beat Frequency Local Slope Continue Fraction Expansion Allan Variance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • C. Eckert
    • 1
  • M. Planat
    • 2
  1. 1.Laboratoire de Physique et Applications des SemiconducteursCNRSStrasbourg Cedex 2France
  2. 2.Laboratoire de Physique et Métrologie des OscillateursCNRSBesançon CedexFrance

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