Allan Plot of an Oscillator with Deterministic Perturbations

white frequency noise amplitude

0.05

oscillation amplitude

0.012

oscillation period (s)

100

drift (1/s)

5.×

-6

10

The Allan deviation

σ

y

(τ)

is a statistical measure of the relative frequency instability of an oscillator on a sampling period

τ

. This Demonstration simulates an oscillator having white frequency noise plus deterministic perturbations. The upper graph shows the time series of relative frequency fluctuations

y(t)=(ν(t)-

ν

0

)/

ν

0

and the lower graph shows the corresponding Allan plot

σ

y

(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

σ

y

(τ)∝

-1/2

τ

, the linear drift

y(t)=dt

adds a contribution

σ

y

(τ)=

-1/2

2

dτ

(green curve), and the oscillation

y(t)=bcos(2πt/T)

results in

σ

y

(τ)=b

2

sin(πτ/T)

(πτ/T)

(red curve).