Allan Variance - Interpretation of Value

Interpretation of Value

Allan variance is defined as one half of the time average of the squares of the differences between successive readings of the frequency deviation sampled over the sampling period. The Allan variance depends on the time period used between samples: therefore it is a function of the sample period, commonly denoted as τ, likewise the distribution being measured, and is displayed as a graph rather than a single number. A low Allan variance is a characteristic of a clock with good stability over the measured period.

Allan deviation is widely used for plots (conveniently 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.

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. If the phase stability of an oscillator is needed then the time deviation variants should be consulted and used.

One may convert the Allan variance and other time-domain variances into frequency-domain measures of time (phase) and frequency stability. The following link shows these relationships and how to perform these conversions: http://www.allanstime.com/Publications/DWA/Conversion_from_Allan_variance_to_Spectral_Densities.pdf