# Allan Plot of an Oscillator with Deterministic Perturbations

Allan Plot of an Oscillator with Deterministic Perturbations

The Allan deviation (τ) 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 (τ). 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 (τ)∝, the linear drift adds a contribution (τ)=dτ (green curve), and the oscillation results in (τ)=b(πτ/T) (red curve).

σ

y

τ

y(t)=(ν(t)-)/

ν

0

ν

0

σ

y

σ

y

-1/2

τ

y(t)=dt

σ

y

-1/2

2

y(t)=bcos(2πt/T)

σ

y

2

sin(πτ/T)