Frequency Control with Quartz Crystals
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Engineering Bulletin E-6: Frequency Control with Quartz Crystals |
The frequency of a crystal is influenced to an appreciable extent by the temperature at which it is operated. The magnitude of this effect is determined by the manner in which the crystal is cut from the natural quartz, the shape and size of the crystal, the precision of grinding, and the characteristics of the quartz itself. It is expressed as the number of cycles change per million cycles of crystal frequency per degree Centigrade variation in temperature and is termed the temperature coefficient of frequency or the frequency-temperature coefficient. A positive (+) temperature coefficient indicates that the crystal frequency increases with increasing temperature, whereas a negative () coefficient indicates that the frequency will decrease with increasing temperature.
The frequency-temperature coefficient of a quartz crystal varies, with individual cuts, from minus 25 to plus 100 cycles per megacycle per degree Centigrade. With X-, C-, or E-cut crystals, the frequency at any temperature can be determined from a knowledge of the frequency temperature coefficient and the crystal frequency at any other temperature. Such calculations are not accurately possible with low frequency-temperature coefficient crystals (often referred to as "zero" temperature coefficient crystals) because the curve of frequency versus temperature is not generally a straight line; in fact, the coefficient may be positive over one part of the total temperature range and negative over other portions. It is commercial practice, with these crystals, to state the average frequency-temperature coefficient over a given range of temperature (generally 20°C. to 55°C.).
The operating temperature of a crystal is dependent on the ambient temperature, the amount of heat developed by the crystal in oscillating and the rate of heat dissipation by the crystal holder. It can be seen, therefore, that for highest frequency stability, unless automatic temperature control is employed, a crystal holder having high heat dissipating abilities should be used. In addition, the intensity of vibration should be maintained at the lowest possible value to keep the developed heat at a minimum. Where a very high degree of frequency stability is required, the crystal temperature should be controlled by a constant-temperature oven.
Any quartz crystal has two, and sometimes three, widely separated possible frequencies of oscillation. This is due to the fact that a vibrating body of this general type can be caused to vibrate in at least two different manners (modes). Furthermore, an improperly finished plate-type crystal may have one or two additional frequencies close to the thickness frequency. This is possible when the faces are insufficiently plane and parallel such that the crystal may oscillate at slightly different frequencies over small portions of the surface.
By properly choosing the mode of vibration, it is possible to manufacture quartz crystals of practical dimensions over a very wide frequency range. In the present state of development, they are produced in the full range from 16kc. to 30,000kc.
X-cut plates, also known as the Curie Cut, were the first type of quartz oscillating crystals to be developed. These crystals oscillate through the thickness at a frequency largely determined by that dimension. They have a negative frequency-temperature coefficient which ranges from 20 to 25 cycles per megacycle per degree Centigrade. The manufacture of X-cut plates is practical for frequencies from 250kc. to about 10,000kc.
For the lower radio frequencies from 16kc. to 250kc., the physical dimensions of X-cut plates, and other plate-type crystals, become too great to be practical. To reduce the crystal size to satisfactory dimensions, the crystals are cut as "bars" in which one dimension is considerably greater than the remaining two. Such crystals oscillate along the greatest dimension and their oscillating frequency is largely controlled by that dimension. When properly designed, X-cut bars have a negative frequency-temperature coefficient ranging from about 4 to 15 cycles per megacycle per degree Centigrade.
Y-cut plates, which oscillate in shear, can be made in the frequency range from 200kc. to about 8000kc. A simple illustration of shear vibration can be performed by sliding the palm of one hand back and forth over the other. This, however, is not a perfectly true picture since the center plane in such a crystal is theoretically motionless while the two outer faces have maximum motion in opposite directions (see figure 6). The frequency-temperature coefficient of Y-cut plates is positive and can be from 60 to 100 cycles per megacycle per degree Centigrade. This high frequency change with temperature, coupled with the fact that the crystals will suddenly change frequency at various points over a wide temperature range, has caused the use of Y-cut crystals to be discontinued in favor of other types.
Both X- and Y-cut crystals in the frequency range from 85kc. to 10,000kc. have been almost entirely superseded by low frequency-temperature coefficient crystals. These crystals, which oscillate in shear, have a very small frequency change with temperature thereby affording excellent frequency stability under varying temperature conditions.
Three types of low temperature coefficient crystals are employed to cover the entire frequency range, each type being particularly suited to its own range. From 85kc. to 400kc. special bar-type crystals, (Footnote 3) developed by Bliley Engineers, are employed. A-cut plates are used from 400kc. to 4000kc. and B-cut plates from 4000kc. to 11,000kc. A- and B-cut plates have similar electrical characteristics but the B-cut plates are better for the higher frequencies since they have, for a given frequency, a considerably greater thickness than the A-cut plates.
Footnotes:
3. Patent No. 2,213,031
Above 11,000kc., fundamental low-drift plates become quite thin and fragile. The upper frequency range of such crystals is, however, extended to 18,000kc. by using A-cut plates and finishing them such that they can be excited at the third harmonic of their fundamental frequency. Such crystals are most practical but do not oscillate quite as freely as the fundamental plates (refer to section entitled CRYSTAL ACTIVITY). In figure 6 is illustrated the motion of a shear oscillating crystal at the fundamental and at the third harmonic.
The Bliley C (Footnote 4) and E-cut (Footnote 5) crystals were developed to increase the upper frequency limit of quartz oscillating crystals. These are harmonic-type crystals cut and finished such that they are excellent oscillators at the calibrated harmonic frequency. C-cut crystals, which have a frequency temperature coefficient of plus 20 cycles per megacycle per degree Centigrade, are employed to cover the frequency range from 11,000kc. to 23,000kc.
Footnotes:
4. Patent Pending
5. Patent No. 2,157,808
E-cut crystals, which have a frequency-temperature of coefficient of plus 43 cycles per megacycle per degree Centigrade, are thicker, for a given frequency, than any other crystal and are used to cover the frequency range from 23,000kc. to 30,000kc.
An interesting fact concerning harmonically vibrating crystals is that a strict harmonic relation does not exist between the fundamental and the working frequency. That is, the working frequency is not necessarily exactly three times the fundamental in a third-harmonic crystal. The variation from a true harmonic relationship is caused by the difference in the manner of vibration and is not constant for all crystals; the frequency deviation between the third harmonic and three times the fundamental can be as high as 50kc.
