NIST Technical Note 1337: Characterization of Clocks and Oscillators

Table 2. Ratio of mod a~('r) to a~( T) versus n for common power-law noise types Sy(t) = haf. n is thenumber of time or phase samples averaged to obtain mod a~( T = n T 0 where To) is the minimum sample time.W his 21r times the measurement bandwidth f h•= mod a~(f)R(n) vs. n r = nT oa~(r)n a = -2 a = -1 cr = 0 cr = +1 Q = +2~ TO = ) wt, TO = 10 ~ TO = 100 I."hr o = 10 41 1.000 1.000 1.000 1 . 000 1.000 1.000 1.000 1.0002 0.859 0.738 0.616 0.568 0.543 0.525 0.504 0.5003 0.840 0.701 0.551 0.481 0.418 0.384 0.355 0.3304 0.831 0.681 0.530 0.405 0.)59 0.317 0.284 0.250- i 5 0.830 0.684 0.517 0.386 0.324 0.279 0.241 0.2006 0.828 0.681 0.514 0.349 0.301 0.251 0.214 0.16707 0.827 0.679 0.507 0.343 0.283 0.235 0.195 0.143I8 0.827 0.678 0.506 0.319 0.271 0.219 0.180 0.12510 0.826 0.677 0.504 0.299 0.253 0.203 0.160 0.10014 0.826 0.675 0.502 0.274 0.230 0.179 0.137 0.071420 0.825 0.675 0.501 0.253 0.210 0.163 0.119 0.050030 0.825 0.675 0.500 0.233 0.194 0.148 0.106 0.033350 O. '825 0.675 0.500 0.210 0.176 0.134 0.0938 0.0200100 0.825 0.675 0.500 0.186 0.159 0.121 0.0837 0.0100Limit 0.825 0.675 0.500 ( ).37 ) linor-- 1.04 +3 In~T -+