Allan Plot of an Oscillator with Deterministic Perturbations

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The Allan deviation is a statistical measure of the relative frequency instability of an oscillator on a sampling period . This Demonstration simulates an oscillator having white frequency noise plus deterministic perturbations. The upper graph shows the time series of relative frequency fluctuations and the lower graph shows the corresponding Allan plot . You can modify the noise amplitude, add a drift or an oscillation, and observe the resulting change in Allan deviation. Each of the three perturbations contributes to the Allan deviation as follows: the white frequency noise gives rise to , the linear drift adds a contribution (green curve), and the oscillation results in (red curve).

Contributed by: Gianni Di Domenico (March 2011)
(Université de Neuchâtel)
Open content licensed under CC BY-NC-SA



Snapshot 1: oscillator with white frequency noise

Snapshot 2: oscillator with white frequency noise plus a deterministic oscillation

Snapshot 3: oscillator with white frequency noise plus a linear drift

The Allan deviation is the square root of the Allan variance defined by:


where is the relative frequency fluctuations average over the integration time .


[1] C. Audoin and B. Guinot, The Measurement of Time, Cambridge: Cambridge University Press, 2001.

[2] J. Vanier and C. Audoin, The Quantum Physics of Atomic Frequency Standards, Philadelphia: Hilger, 1989.

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