ELECTRICAL WAVE FILTERS 



411 



The solid curve of Fig. 4 shows a measurement of the ratio, r, of the 

 capacitances in the simple representation of the crystal shown by Fig. 

 2A. This ratio is measured by determining the resonant and anti- 



170 



O 160 



3 4 5 6 7 



DEPTH OF OPTICAL AXES IN MILLIMETERS 



Fig. 4 — Ratio of capacitances of a perpendicularly cut crystal. 



resonant frequencies of the crystal, r is related to these by the 

 formula 



fAVfR' = 1 + 1/r, 



(4) 



where /a is the anti-resonant frequency and/ij the resonant frequency. 

 Figure 5 shows a measurement of the temperature coefficient of the 

 resonant frequency for the same set of crystals. It will be noted that 

 as the optical axis increases in depth, the temperature coefficient 

 increases and that crystals with smaller dimensions along the optical 

 axis in general have much smaller coefficients. Increasing the thick- 

 ness along the electrical axis has the efifect of decreasing the tempera- 



