NIST Technical Note 1337: Characterization of Clocks and Oscillators

Proc. 35th Ann. Freq. Control Symposium, USAERADC0I1, Ft. ~Ionmouth, UJ 07703, May 1981A MODIFIED "ALLAN VARIANCE" WITH INCREASEDOSCILLATOR CHARACTERIZATION ABILITYDavid W.Allan and James A. BarnesTime and Frequency DivisionNational Bureau of StandardsBoulder, Colorado 80303Summarythe same, Le., - t-2. It is not at all uncommonHer~tofore, the "Allan Variance," cr 2(t), hasbecome the de facto standard for measuring oscillatorinstabil ity in the time-domain. Often osci 11 ators for t of the order of one second andfor white PM and flick.er PM to occur in precisionoscill ator frequency instabil iti es are resonabJ,ymodel able with a power law spectrum: Sshorter. The modified Allan variance, as developedin this paper, depends as t- 2 for or ::: +1 and as(f) ~ ,...,where y is the normal i zed frequency. y f is theFourier frequency, and or is a constant over somet-range of Fourier frequencies. It has been shown3 for or ::: +2. This yields a clear distinction inthat for power law spectrum cr 2(t) ~ t~, and that the time domain between these heretofore somewhat~ ::: -or-1 for -3