Vibration Modes
The quartz plate, like all plates, has many modes of vibration.
There are three basic modes of vibration as illustrated in the following figure.
(a) Flexure mode (bending or bowing); Cuts: 5° X, NT;
Frequency ~ 100 kHz.
(b) Extensional Mode (displacement along the length of the plate); Cuts: MT, GT;
Frequency: 40 – 200 kHz.
(c) Shear Mode (sliding two parallel planes in opposite directions).
This mode is subdivided into:
Face Shear; Cuts:
CT, DT; Frequency: 100 – 600 kHz.
Thickness Shear;
Cuts: AT, BT, SC; Frequency: 1 – 30 MHz (fundamental mode); 30 – 90 MHz (3rd
harmonic overtone mode); 60 – 150 MHz (5th harmonic overtone mode);
etc.
Properly oriented electrodes excite the desired mode of vibration.
Although a large number of different cuts have been developed, some are
used only at low frequency, others are used in applications other than frequency
control, and still others have been made obsolete by later developments.
Except for the low-frequency tuning fork resonators used in quartz
watches and clocks, almost all quartz resonators in today’s applications use a
thickness-shear mode. At frequency
above approximately 1 MHz, AT-cut and SC-cut are primarily used.
For frequencies below about 1 MHz, thickness-mode resonators generally
become impractical because of size, since the blank diameter must be much
greater than the thickness.
AT- and SC- cut Resonator Frequency
The fundamental frequency of a thickness-shear resonator is inversely
proportional to its thickness. The
thinner the crystal blank, the higher the frequency. There are additional resonance at the 3rd, 5th, etc. harmonic overtones,
whose frequencies are approximate, but not exact, odd multiples of the
fundamental resonance frequency. Resonators are ordinarily designed to optimize the
characteristics of one or another of these resonances, such as the fundamental
or the third overtone, but the other overtones necessarily still exist. AT-cuts are commonly manufactured in the frequency range from 1 MHz to
250 MHz and above, and in this range are usually the optimum choices for most
applications. However, the AT-cut
is sensitive to stresses in the body of the resonator, whether caused by
temperature gradients due to rapid external temperature changes, or by external
forces. For applications where
extreme stability is required, this stress sensitivity is a drawback, and newer
crystal cuts such as the SC (Stress Compensated)-cut have been developed that minimize these effects.
An SC-cut crystal is one of a family of double rotated crystals (quartz
crystals cut on an angle relative to two of the three crystallographic axes).
Others in the family include the IT-cut and FC-cut.
The SC-cut represents the optimum double rotated design as its particular
angle ~ 35°15
ø ~ 21°54
provides maximum stress compensation. The SC-cut is also a thickness mode resonator, and as such is basically
available in much the same frequency range as the AT-cut, but its commercial
availability is much more limited due to difficult manufacturing process.
