MANUFACTURING DEVIATIONS IN CRYSTAL UNITS 



267 



lished by Mason.^ This information shows that for small ratios of axes 

 the resonant frequency will be directly proportional to the width dimension. 

 However, as the ratio is increased to 0.5, a change of l%in the width dimen- 

 sion will change the frequency by only 0.5%. 



The effect of the width dimension on the inductance of the plates fre- 

 quently is important. Fig. 14.6 illustrates the relation between inductance 

 and the ratio of axes. From these curves the effects of deviations in width 

 can be deduced. For the two longitudinal plates, the inductance is almost 

 inversely proportional to width. For the flexure plate, the decrease of 



2820 

 2S00 

 2780 

 2760 



5 2740 



o 2720 

 it 



>- 2700 



z 



^ 2680 



z 



8 2660 



>- 



^ 2640 



o- 2620 



"^ 2600 



2580 



2560 



2540 



2520 



.1 .2 .3 .4 .5 .6 7 8 



RATIO OF WIDTH TO LENGTH 



Fig. 14.5. — Frequency constant of the longitudinal mode of X-cut quartz plates as a 

 function of their ratio of width to length. 



inductance with increase in width is much more rapid. With a ratio of 

 a.xes of 0.6 the inductance decreases about as a square power, while with a 

 ratio of 0.1 the decrease is about as the third power. 



The width dimension of the +5° plate has an appreciable effect on the 

 temperature coefficient of the plate. Mason has shown* that while the 

 temperature coefficient is zero for a long narrow bar, it increases quite 

 rapidly as the width dimension increases, due to coupling between the 

 face shear and the longitudinal modes. In the case of an —18.5° plate, 

 coupling with other modes is relatively weak. Hence its temperature co- 



^ "Motion of a Bar Vibrating in Flexure Including the Effects of Rotary and Lateral 

 Inertia", W. P. Mason, Jour. Acous. Soc. America, April, 1935, pages 246-249. 



