Allan variance
![A clock is most easily tested by comparing it with a far more accurate reference clock. During an interval of time τ, as measured by the reference clock, the clock under test advances by τy, where y is the average (relative) clock frequency over that interval. If we measure two consecutive intervals as shown, we can get a value of (y-y')2—a smaller value indicates a more stable and precise clock. If we repeat this procedure many times, the average value of (y-y')2 is equal to twice the Allan variance (or Allan deviation squared) for observation time τ.](/Images/godic/202412/18/AllanDeviation.svg4449.png")
![Example plot of the Allan deviation of a clock. At very short observation time τ, the Allan deviation is high due to noise. At longer τ, it decreases because the noise averages out. At still longer τ, the Allan deviation starts increasing again, suggesting that the clock frequency is gradually drifting due to temperature changes, aging of components, or other such factors. The error bars increase with τ simply because it is time-consuming to get a lot of data points for large τ.](/Images/godic/202412/18/AllanDeviationExample4449.gif")
The Allan variance (AVAR), also known as two-sample variance, is a measure of frequency stability in clocks, oscillators and amplifiers. It is named after David W. Allan. It is expressed mathematically as
The Allan deviation (ADEV) is the square root of Allan variance. It is also known as sigma-tau, and is expressed mathematically as