412 



BELL SYSTEM TECHNICAL JOURNAL 



ture coefficient and in fact for certain ratios of the three axes the coeffi- 

 cient approaches zero. 



z yj 



- > 40 



u. z 

 W o 



30 



uj - 



cr S 



D 



b ^ 



< UJ 



cr a 



CL 1/1 



lij □: 



H < 



20 



123456789 la 



DEPTH OF OPTICAL AXES IN MILLIMETERS 



Fig. 5 — Temperature coefficient of a perpendicularly cut crystal. 



When the crystals are used in filters, two quantities are usually- 

 specified, the resonant frequency of the crystal and the capacitance of 

 the series condenser. The shunt capacitance of the crystal is usually 

 incorporated with an electrical capacitance which is specified by other 

 considerations. The resonant frequency is determined principally by 

 the mechanical axis length. The capacitance of the series condenser 

 is determined by the ratio of the area to the thickness or by Ulmlle. 

 The third condition is given by the fact that the length of the optical 

 axis should be kept as small as possible in order that any subsidiary 

 resonances shall be as far from the principle resonance as possible. 

 The curves of Figs. 3 and 4 and the fact that the resonant frequency of 

 a given shaped crystal varies inversely as the length, can be used to 

 determine the dimensions of the crystal. It is obvious that the 

 crystal should not be used in the region 0.2 < Ujlm < 0.3 on account of 

 the two prominent resonant frequencies. 



Use of Crystals and Condensers as Filter Elements 

 Considering crystals as representable by the simple electrical 

 circuit shown on Fig. 2A , these circuits can be utilized as elements in 

 electrical networks. They may, of course, be used in a network em- 

 ploying any kinds of electrical elements. Since, however, their Q is 

 high, it would be advantageous not to employ any electrical elements 

 which do not also have a high Q, in order that the dissipation intro- 

 duced by these elements may not be a matter of consideration. The 



