4-43
r
m
R
R
R
R
r
m
Y
Z
AT-cut
BT-cut
49o
35Όo
-1’
0’
1’
2’
3’
4’
5’
6’
7’
8’
-1’
0’
1’
2’
3’
4’
5’
6’
7’
8’
Dq
Y-bar quartz
Z
25
20
15
10
5
0
-5
-10
-15
-20
-25
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Text Box: Df f
Df
f
Text Box: (ppm)
(ppm)
Temperature (oC)
q = 35o 20’ + Dq, j = 0
for 5th overtone AT-cut
q  = 35o 12.5’+ Dq, j = 0 for
fundamental mode plano-plano AT-cut
Frequency-Temperature vs. Angle-of-Cut, AT-cut
   The inset in the above illustration shows how an AT-cut plate and a BT-cut plate are related to the directions in a quartz bar.  The illustration shows how the AT-cut’s f vs. T characteristics change as the  angle of cut (see “Zero Temperature Coefficient Quartz Cuts” in chapter 3) is varied in one minute of arc increments.
   The  = 0 curve shows the f vs. T characteristic at the “reference angle,” which is  = 35o12.5’ for a fundamental mode AT-cut resonator.  At the reference angle, the turnover points coincide with the inflection point.  The reference angle varies with design, i.e., with overtone, plate contour, etc.


“Quartz Resonator Handbook - Manufacturing Guide for AT-Type Units,” edited by R. E. Bennett, prepared for the US Dep’t of the Army, pp. 77-103, 1960, AD-274031.