Variance " with Increased Oscillator Characterization Ability

Time and Frequency Division National Bureau of Standards Boulder, Colorado 80303 ;ummary Heretofore, the Allan Variance," u *(r), has become the de facto standard for measudng oscillator instabilitv in the time-domain. Often oscillator frequency instabilities are resonabl modelable with a power law spectrum: S (f) e" where y is the normalized frequency,yf is th; Fourier frequency, and a is a constant over some range of Fourier frequencies. It has $een shown that for power law spectrum a *(r) T and that IJ = -a-l for -3<a< + 1, wherr T is tie nomimal sample time over which each value of y is measured. The modified "Allan Variance" developed in this paper yields p z -a-l for all a in the range -3<a, which removes the previous ambiguity: p = -2 for +l<a. In other words, with the modified "Allan Valiance" one can easily distinguish between white phase noise (a = +2) and flicker phase noise (a = +1) -commonly occurring for the short term instabilities of quartz crystal oscillators and active hydrogen masers. the same, i.e., r-2. It is not at all uncosmton for white PM and flicker PM to occur in precision oscillators for r of the order of one second and shorter. The modified Allan variance, as developed in this paper, depends as t-2 for a = +l and as ~-3 for a = +2. This yields a clear distinction in somewhat