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BELL SYSTEM TECHNICAL JOURNAL 



of the crystal. This may be explained by referring to Fig. 12.27 which 

 shows curves of the reactance Xc of the crystal plotted as a function of fre- 

 quency. The frequency at which oscillations occur depends principally 

 upon the value of circuit capacitance Ci . Equation (12.43) shows that 

 the frequency must adjust itself to a value at which Ct resonates with 

 the reactance of the crystal. This value of reactance is represented on the 

 curve as Xco and the corresponding frequency of oscillations as Jo • The 



Fig. 12.27 — Two crystals having the same figure of merit but with different reactance 



characteristics A'^ and A'^ will operate with different amplitudes according to the 



relative values of <pco and tp'o respectively 



circuit capacitance (or Xco) has been so chosen in the illustration that /<, 

 lies equidistant between the resonant frequency /i and the anti-resonant 

 frequency /2. Then at this value of /« , </?c is a maximum, as shown by the 

 (pc curve, and for a given value of (pg this will result in the greatest activity. 

 Now let the capacitance Co of the crystal be increased. The frequencies /i 

 and /2 will then become closer and at the same time the height of the ipc 

 curve is reduced. Assume also that the Q is increased in order to maintain 

 the same value of M and hence the same maximum value for <^c • The 

 reactance-frequency curve for the modified crystal and the corresponding 



