NIST Technical Note 1337: Characterization of Clocks and Oscillators

Some useful asymptotic forms of B 3 can be found. In the case of large M andM> r, we may write that~ 1 :$3/l4 in(2)2 in(r) + 3'/l O.:$ 2,(8)One simple and important conclusion from these two equations is that for thecases of flicker FM noise and random-walk FM noise, the r~ dependence forlarge r is the same whether or not there is periodically distributed deadtime. The values of the variances differ only by a constant, and in thelatter case the constant is 1. This conclusion is also true for white FMnoise, and in this case the constant is also 1.In the cases r » 1 and -2 :$ /l :$ -1, we may write for the asymptotic behaviorof B 3-/l-1 , (9)as was determined empirically. In this region of power-law spectrum the B 3function has an Madependence for an fa spectrum.6. The Bias FunctionsThe bias functions can be written fairly simply by first defining thefunction,F(A) (10)The bias functions becomeB 1(N,r,,u) ==N-11 + In=11 +N-nN(N-1)~ F(r)F(nr)( 11)7TN-302