PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



179 



Since the frequency is a function of the internal plate resistance of the 

 tube {Rp) and this is in turn a function of the other circuit variables, the 

 frequency equation (12.30) is not sufficient to calculate the frequency. 

 However, qualitative effects of the various circuit components upon fre- 

 quency are obtained by assuming Rp an independent variable. It is readily 

 seen that an increase in Rp increases the frequency. The effect of the air 

 gap between crystal and electrodes, which is represented by the capacitance 

 Ci , and the effect of the capacitance across the crystal Cg are illustrated in 

 Fig. (12.13).* To determine the frequency change caused by tuning of 



O 80 



CRYSTAL 

 i^Q = r34 KC 

 I8.3X I8.3X3.3& MM 



fQ= 865 KC 

 AIR GAP=32 



0.2 0.3 0.4 



AIR GAP IN MM 



^ 



10 



20 



IN ^^^^f 



Fig. 12.13 — Experimental curves, showing the effect of crystal air gap and grid 

 capacitance on the frequency of oscillations 



the plate circuit (variations of C2) requires the calculation of the change of 

 the variable part of C< . This quantity is 



mCs 



(12.31) 





1 +R\(^ - CO0C2) 

 \coo Li / 



The plot of Cv is shown in Fig. (12.14A). The frequency decrease is pro- 

 portional to the increase in C„. This is indicated in Fig. (12.14B). Oscil- 

 lations stop before the point uaCi = — T is reached. The frequency thus 



CO0-L2 



varies in the same manner as shown in Fig. (12.6) but the curve is reversed 

 because of the fact that the independent variable is taken as C2 instead of 

 the frequency function of C2 . 



The frequency change resulting from variations in the grid-plate capaci- 

 tance C3 depends also upon the value of C^ as seen from (12.31). It is also 



* See also: "The Piezoelectric Resonator and the Effect of Electrode Spacing upon Fre- 

 quency," Walter G. Cady, Physics, Vol. 7, July 1936. 



