MANUFACTURING DEVIATIONS IN CRYSTAL UNITS 265 



respectively, and the resonant frequency by +.05% and —.02%, respec- 

 tively. For an X-cut plate rotated +5°, a deviation of ± 1° will change the 

 inductance —0.9%, and +0.6%, respectively, and the resonant frequency 

 by ±0.7%. 



Deviations in angle of rotation will, in general, aflfect temperature coeffi- 

 cient. The effect is illustrated by Fig. 1.19 of Chapter I,^ which, for X-cut 

 plates, shows the relation between temperature coefficient and angle of 

 rotation. Ths curve shows that the temperature coefficient is practically 

 zero for an angle of rotation of +5°. For that reason this particular cut is 

 used whenever a low-temperature coefficient is desired. The curve also 

 shows that at this point the slope of temperature coefficient as a function of 

 angle of rotation is zero. Hence, for the +5° X-cut plate, which is most 

 important from the standpoint of temperature coefficient, there will be 

 little change due to a deviation in the angle of rotation. 



In GT-cut plates the effect of deviation in the angle of orientation must 

 be considered in combination with deviations in linear dimensions. Mason 

 shows^ that for an angle of rotation of +51 degrees 7.5 minutes and a 

 width-to-length ratio of .859, a temperature coefficient close to zero may be 

 obtained from —25° C to +75° C. He also has shown that this tempera- 

 ture coefficient varies with both the angle of rotation and the width-to- 

 length ratio. Because of this, it has been found possible to compensate for 

 small deviations in the angle of rotation by adjusting the Unear dimensions. 

 The net effect of a deviation in angle of rotation, after it has been so com- 

 pensated, is to raise (or lower) the temperature region of zero temperature 

 coefficient by 11° C for each 10-minute increase (or decrease) in angle of 

 rotation. In GT-cut plates, the width dimension directly controls the 

 primary resonance. For this reason, it is preferable to adjust temperature 

 coefficient by varying the length dimension rather than the width. The 

 crystal plates are cut larger than desired. The frequency of resonance and 

 the temperature coefficient are then adjusted simultaneously by grinding 

 either the width or length dimension as required. Experimental work 

 carried on by L. F. Willey of the Laboratories shows that an increase of 1.0 

 per cent in the width-to-length ratio results in an increase in temperature 

 coefficient of approximately +1.35 parts per million per degree C. In his 

 experimental work Willey used the ratio of the secondary to the primary 

 frequency as a convenient measure of the width-to-length ratio. The in- 

 ductance constant for GT plates, which is about 17 henries per milhmeter 

 of thickness, will increase by less than 1% for deviations in any of the 

 angles of rotation of as much as 30 minutes. However, the inductance may 

 depart appreciably from nominal due to the adjustment of width and 

 length dimensions. 



* "New Quartz-Crystal Plate, GT, Produces Constant Frequency Over Wide Tem- 

 perature Range", W. P. Mason, Proc. I. R. E., May, 1940, page 220. 



