QUARTZ CRYSTAL PLATES 



531 



in frequency of these circuits with temperature if there were no 

 coupling between them. The change of the frequencies of the coupled 

 system with temperature is shown by the curves co' and co". It will 

 be seen that both these frequencies pass through regions of zero 

 temperature coefficient. 



Such frequency-temperature curves can be derived graphically by a 

 construction similar to that shown in Fig. 13. This figure illustrates 

 what happens when the tuning of both circuits No. 1 and No. 2 is 

 varied, and consists of a series of the usual coupling curves (the 



Fig. 13 — Effect on the angular frequencies of a system of two coupled circuits as the 

 individual circuits are tuned simultaneously in opposite directions. 



coupled frequencies plotted as a function of wo), each set of curves 

 of the series being drawn for a dilTerent value of coi. When the 

 temperature is increased from Ti to T2, the uncoupled frequency of 

 circuit No. 2 is reduced by an amount Aaj2 and the uncoupled frequency 

 of circuit No. 1 is increased by an amount Acoi. The result is the 

 frequencies co' and co" move from curve to curve in the direction shown 

 by the lines AB and CD. 



Now if the variation of the temperature coefficient of a crystal 

 plate when used in an oscillator circuit be examined at a given tempera- 

 35 



