NIST Technical Note 1337: Characterization of Clocks and Oscillators

the averaging time To. If we average groups of the measurements of yet), thenthe dead times between the original measurements are distributed periodicallythroughout the new average measurements (see figure 4). DefineM+i-11M I Yn' (5)n=iwhere Yi are the raw or original measurements based on dead time TO-TO.Also define the two-sample variance with distributed dead time as(6)with T = M7 0and T MT o .We can now define B 3as the ratio of the N-sample variance with distributeddead time to the N-sample variance with dead time accumulated at the end as infigure 1:a 2 (N,M,T,T)B 3 (N,M,r,J-L) (7)a 2 (N, T, T)Although B 3(N,M,r,J-L) is defined for general N, the tables in the Appendixconfine treatment to the case where N = 2. There is little value in extendingthe tables to include general N. Though the variances on the right in eq (7)depend explicitly on N, T and T, the ratio B 3(N,M,r,J-L) depends on the ratior = T/7, and on J-L as developed later in this paper.In words, B 3(2,M,r,J-L) is the ratio of the expected two-sample variance withperiodically distributed dead time, as shown in figure 4, to the expected twosamplevariance with all the dead time grouped together as shown in figure 1.Both the numerator and the denominator have the same total averaging time anddead time, but they are apportioned differently. The product B 2 (r,J-L) •B 3(2,M,r,J-L) is the distributed dead-time variance over the Allan variance fora particular T, 7, M and J-L.6TN-30l