5-18
Empirically determined Q vs. frequency curves indicate that the maximum achievable
Q times the frequency is a constant, e.g., 16 million for AT-cut resonators, when f is in MHz.
100
60
40
20
10
8
6
4
2
1
0.8
0.6
0.4
0.2
0.1
0.1
0.2
0.4
0.6
1.0
2
4
6
8
10
20
40
60
100
Text Box: Value of Q, in millions
Value of Q, in millions
Frequency in MHz
Most probable internal
friction curve for quartz;
excluding mounting losses
Diameter of shaped quartz
plates, in vacuum
90 mm
30 mm
15 mm
Flat quartz plates, in air
Internal Friction (i.e., the Q) of Quartz
   See chapter 3 for further information about Q.  Also see “Ions in Quartz - Simplified Model” earlier in chapter 5 for information about acoustic losses due to aluminum-alkali centers.


A. W. Warner, "Design and Performance of Ultraprecise 2.5-mc Quartz Crystal Units," Bell System Technical Journal, pp. 1193-1217, Sept. 1960; also in "An Ultraprecise Standard of Frequency," W. L. Smith, final report for U. S. Army contract DA 36-039 sc-73078, p. 13, 1 Dec. 1960, AD-253034.

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