It is shown that the qualities sought in a frequency standard are present to a high degree in properly mounted plates or rods of quartz, or steel rods excited by quartz plates, making use of the piezo-electric reactions of the quartz upon a resonant high-frequency circuit. The transverse effect (vibrations perpendicular to the impressed electric field) is chiefly utilized in the construction of piezo-electric resonators. Any given resonator may be excited to resonant vibration at its fundamental frequency or at any one of several overtone frequencies. The logarithmic decrement is very small, of the order of 0.001 or less. Hence a tube generator circuit of variable frequency may be tuned to a natural frequency of the resonator with very great precision.
The reactions of the resonator upon the circuit may be expressed in terms of characteristic changes in capacity and resistance. Curves illustrating this are shown, and it is seen that at resonance the resonator functions as a pure resistance.
In the construction of resonators, a quartz plate cut in the form of a comparatively narrow rod is placed loosely between two brass side-plates on an insulating base. Effects of changing temperature and of spacing of side-plates are discussed. For frequencies below 50 kilocycles per second steel rods are employed, excited to longitudinal vibration by having small quartz plates cemented to them at the center. By this construction frequencies as low as 3000 cycles have been reached. The upper limit in frequency, using very shoft quartz rods, is about three million cycles. Over this range the frequency of a vacuum tube generator may be synchronized with the resonator with a precision of one hundredth percent or better. Some of the various electric circuits that can be employed are briefly described.
The application of the resonator as a frequency stabilizer, and also as a device for generating electric oscillations, is explained. For these purposes either the transverse effect or the longitudinal effect (vibrations parallel to the electric field) may be used.
W. G. CADY, "PIEZO-ELECTRIC STANDARDS OF HIGH FREQUENCY," J. Opt. Soc. Am. 10, 475-489 (1925)