Considerations on the measurement of the stability of oscillators with frequency counters

The most common time-domain measure of frequency stability, the Allan variance, is typically estimated using a frequency counter. Close examination of the operation of modern high-resolution frequency counters shows that they do not make measurements in the way commonly assumed. The consequence is that the results typically reported by many laboratories using these counters are not, in fact, the Allan variance, but a distorted representation. We elucidate the action of these counters by consideration of their operation in the Fourier domain, and demonstrate that the difference between the actual Allan variance and that delivered by these counters can be very significant for some types of oscillators. We also discuss ways to avoid, or account for, a distorted estimation of Allan variance.