Allan deviation explained

Allan Deviation is a unitless measure of stability, typically used to quantify the stability of clocks and other oscillators.

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

How do you interpret Allan deviation?

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 deviation?

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 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.