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BELL SYSTEM TECHNICAL JOURNAL 



which involves all the elements in the effective crystal circuit, and this term 

 is much more expressive of the quality of a crystal. The figure of merit is: 



M='^^=^ (15.3) 



Ai Co r 



where "r" is the ratio of the paralleling capacitance to the series branch 

 capacitance. Figure of merit is useful for expressing the quality of a crystal 



Lc 



Rc! 



(A) 



(B) 



(C) 



Fig. 15.1 — Electrical equivalent circuits of a piezoelectric crystal — (A) At any fre- 

 quency between the resonant frequency coi, and anti-resonant frequency ur, (B) and (C) 

 at any specific frequency between coi and W2- 



GENERATOR INSERTED 



HERE IN P I METER 



(IMPEDANCE=Zi_) 



Fig. 15.2 — Generalized oscillator circuit of the Pierce or Miller type. 



in its holder or mount; however by definition it is independent of the value of 

 Rl , and does not permit a ready evaluation of the performance of the crystal 

 in an oscillator of the type that may be represented by Fig. 15.2. Any 

 oscillator that operates the crystal in the positive region of the reactance vs. 

 frequency characteristic exhibits capacitive reactance and negative 

 resistance paralleled across the terminals to which the crystal is connected. 

 The operation of the crystal when connected to an oscillator will be influenced 

 by the magnitude of these two terms, and the combination must operate at 



