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BELL SYSTEM TECHNICAL JOURNAL 



and contract in opposite phase. Hence there is Httle change in frequency 

 constant or temperature coefl&cient, but there will be a large change in in- 

 ductance. Th change in inductance can be estimated roughly by compar- 

 ing the twinned plate with an untwinned plate in which activity has been 

 reduced by removing electrical charge from part of the surface. The area 

 of the surface from which this charge is removed would be twice the twinned 

 area and located at about the same position in the plate. 



It is believed that a small amount of electrical twinning is more serious 

 than a similar amount of optical twinning, because the twinned areas are 

 of opposite angular sense. Each of the two areas has a different modulus 

 of compliance and the effective modulus of the plate has a value intermediate 

 between the two different values of modulus. Therefore, the frequency 

 constant of the plate will be intermediate between that of the desired cut 

 and its electrical twin. For a small amount of twinning, the direction and 

 rate of change of frequency can be estimated from the comparison shown on 

 Table I between the standard filter cuts and their electrical twins. 



Table I 



This verifies the experimentally observed fact that for —18.5° X-cut 

 plates, twinning increases the frequency, while for +5° X-cut and GT plates, 

 twinning decreases the frequency. Even for small amounts of twinning 

 the inductance will increase rapidly for plates of any orientation. When 

 the amount of twinning becomes large, the equivalent inductance approaches 

 infinity. That is, the crystal will not be set in motion by an applied voltage. 



The quantitative effect of twinning (probably electrical) has been meas- 

 ured on one set of plates by R. M. Jensen. Figure 14.8 includes a 

 photograph of the plates used, illustrating the extent of the twinning in 

 each. All of the plates are —18.5° X-cut plates, having the dimensions 

 30.88 X 10.56 X .86 mm. The tabulation below the photograph compares 

 the inductance and resonant frequency measured for each of the plates 

 with the one, designated AN-3, which shows the least effect of twinning. 

 While there is a good correlation between the amount of twinning in the 

 plates and their change in electrical performances, it is not practical to 

 estimate accurately the effect of a given amount of twinning. For this 

 reason, crystal plates having any twinning should not be used for crystal 

 units for filters. 



