On the measurement of frequency and of its sample variance with high-resolution counters
Journal Article
·
· Review of Scientific Instruments
- Universite Henri Poincare (LPMIA and ESSTIN), 2 r. Jean Lamour, Vandoeuvre Les Nancy, F-54519 (France)
A frequency counter measures the input frequency {nu} averaged over a suitable time {tau}, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from {sigma}{sub {nu}}{sup 2}{proportional_to}1/{tau}{sup 2} to {sigma}{sub {nu}}{sup 2}{proportional_to}1/{tau}{sup 3}. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance {sigma}{sub y}{sup 2}({tau})=E{l_brace}(1/2)(y{sub k+1}-y{sub k}){sup 2}{r_brace} of the fractional frequency fluctuation y, the result is the modified Allan variance mod {sigma}{sub y}{sup 2}({tau}). But if a sufficient number of contiguous measures are averaged in order to get a longer {tau} and the data are fed into the same formula, the results is the (nonmodified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood. The typical domain of interest is the the short-term stability measurement of oscillators.
- OSTI ID:
- 20722217
- Journal Information:
- Review of Scientific Instruments, Journal Name: Review of Scientific Instruments Journal Issue: 5 Vol. 76; ISSN 0034-6748; ISSN RSINAK
- Country of Publication:
- United States
- Language:
- English
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