Allan variance plot

1. What is Allan variance and how is it used?
2. How do you read Allan variance?
3. Why do we use Allan variance?
4. How do you calculate Allan deviation?
5. What is Tau in Allan variance?

What is Allan variance and how is it used?

Allan variance is a statistical analysis tool for identifying various noise types that exist in a signal. Developed in the mid-1960s, the Allan variance was used to measure the frequency stability of precision oscillators. Later, this technique was applied to other areas as well.

How do you read Allan variance?

An Allan deviation of 1.3×10−9 at observation time 1 s (i.e. τ = 1 s) should be interpreted as there being an instability in frequency between two observations a second apart with a relative root mean square (RMS) value of 1.3×10−9. For a 10-MHz clock, this would be equivalent to 13 mHz RMS movement.

Why do we use Allan variance?

Allan deviation is widely used for plots (conventionally in log–log format) and presentation of numbers. It is preferred, as it gives the relative amplitude stability, allowing ease of comparison with other sources of errors.

How do you calculate Allan deviation?

Standard deviation is the square root of variance. So to get Allan deviation from Allan variance, we just take the square root of every variance measure we calculated above.

What is Tau in Allan variance?

Allan variance is used to measure the frequency stability of oscillation for a sequence of data in the time domain. It can also be used to determine the intrinsic noise in a system as a function of the averaging time. The averaging time series τ can be specified as τ = m/fs.