3-26
Q is proportional to the decay-time, and is inversely proportional to the linewidth of resonance (see next page).
•
•   The higher the Q, the higher the frequency stability and accuracy capability of a resonator (i.e., high Q is a necessary but not a sufficient condition).  If, e.g., Q = 106, then 10-10 accuracy requires ability to determine center of resonance curve to 0.01% of the linewidth, and stability (for some averaging time) of 10-12 requires ability to stay near peak of resonance curve to 10-6 of linewidth.
•
•   Phase noise close to the carrier has an especially strong
dependence on Q (L(f) µ 1/Q4).
What is Q and Why is it Important?
   See the next page for other definitions of Q, and see chapter 5 for additional information about the Q of quartz resonators. When the signal is decaying, as shown on the next page, the energies in the definition above are averaged over the cycle.  Close to the carrier, a factor of two difference in Q results in a factor of 16 difference in phase noise.


IEEE Std 100-1996, The IEEE Standard Dictionary of Electrical and Electronics Terms, http://shop.ieee.org/store/

H. Hellwig, "Frequency Standards and Clocks: A Tutorial Introduction," NBS Technical Note 616, 1977, Time and Frequency Division, NIST, Boulder, CO 80303.

V. B. Braginsky, V. P. Mitrofanov & V. I. Panov, Systems with Small Dissipation, The University of Chicago Press, 1985.

E. I. Green, "The Story of Q," American Scientist, pp. 584-595, 1955.