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BELL SYSTEM TECHNICAL JOURNAL 



seen that the smaller the value of Ci (lower the plate reactance) the less 

 effect will the tube constants /x , Rp and C3 have upon the frequency. The 

 circuit is therefore more stable. For this reason it has become customary 

 to measure the frequency of crystals with the capacitance C2 reduced to a 

 value below that which gives maximum amplitude of oscillations. 



12.23 Amplitude of Oscillations for G-C Connection of Crystal 



A measure of the amplitude of oscillations is obtained from (12.28) 

 which expresses the necessary conditions for oscillations to be maintained. 

 In order for oscillations to start the expression must be negative, and, as 

 the amplitude builds up, Rp increases which reduces the negative terms 



C2— ► C2— ^ 



A B 



Fig. 12.14 — The variation of grid to cathode capacitance (A) and oscillator frequency 

 (B) with change in plate circuit capacitance. Crystal connected grid to cathode 



until the equality is satisfied. The difference between the positive and 

 negative terms is therefore a measure of the amplitude of oscillations. 

 Equation (12.28) may be written 



b + ^] 



^ -1 $n + — I = ^ 



where yl is a measure of the amplitude, 



Rr 



(12.32) 



\p — mCsWo 



\ r ~" '»-'0 L'2 I 



\CO0 L2 / 



1 + R\(-^ - W0C2) 



(12.33) 



and 

 ^, = R 



2 /Co + C4Y 



Co C4 



Co + C4 



+ C„ + C3 + 



liCz 



1 + 



Kp\ — CO0C2 I 



\coo Li / _ 



(12.34) 



