550 



BELL SYSTEM TECHNICAL JOURNAL 



Several other factors have had an important bearing on the final stabiUty 

 of quartz resonators. One of the most important of these is the care that 

 must be exercised during fabrication in order to avoid setting up stresses in 

 the material that subsequently can be relieved only slowly. By slow grind- 

 ing with adequately fine abrasive such effects can be kept very small. 

 Etching with hydrofluoric acid has resulted in much further improvement 

 through the removal of stressed surface material and all potentially loose 

 material which, formerly, often caused anomalous aging effects. Artificial 

 aging by heating, and thorough cleaning before and after plating, have also 

 contributed greatly to the final stability of the crystal unit. The resonator 

 finally is mounted in high vacuum in a glass envelope in order to eliminate 

 losses due to sound radiation and friction, and to protect it from surface 

 contamination and chemical action. 



oiO 

 Z_J 



: 



-20 



30 



20 30 40 50 60 70 80 90 



TEMPERATURE IN DEGREES CENTIGRADE 



Fig. 22 — Frequency-temperature characteristics for three types of quartz resonators. 



Even the most perfect quartz resonator, in an ideal mounting, is unable 

 to keep time unless it is maintained in oscillation; and, like a pendulum, its 

 rate will depend in large part on the manner in which it is driven. The same 

 general principles apply to both cases, except that usually a pendulum is 

 driven by impulses which should be applied when the velocity is maximum, 

 while a quartz resonator is usually driven by a sinusoidal force arising 

 through the piezoelectric coupling, and so phased that the maximum force 

 occurs when the velocity is maximum. This, in fact, is a required condition 

 for maximum rate stability. The graphical analysis of Fig. 5 applies equally 

 for the case of sine wave drive, since the sine wave can be considered as the 

 summation of an impulse at its peak and of sets of pairs of impulses sym- 

 metrically disposed with respect to it. Obviously, the phase errors for each 

 such pair of impulses cancel, bringing us back to Airy's condition, but with 

 the broader view that, for the feedback or driving wave to have minimum 

 effect on the rate of an oscillator, the force wave must be in phase with the 

 velocity of the resonator. 



