PIEZOELECTRIC CRYSTALS IX OSCILLATOR CIRCUITS 



173 



and experimental values shown on the curves is attributed to the difference 

 between chosen and actual value of Ri . The effect of the input loss of the 

 tube is not shown because the grid current was disregarded; however, this 

 loss may be reduced to an equivalent Ri . The resistance of the plate cir- 

 cuit i?2 affects the frequency in a similar manner. The effects of these 

 resistances on frequency are less for low values of plate circuit impedances. 

 The required value of Rp gives a measure of amplitude of oscillation 

 because it is necessary for oscillations to build up until the internal plate 

 resistance is equal to the calculated value. It is found that Rp increases 



Fig. 12.9 — Experimental curves, showing the relation between the frequency and the 

 resistance of the oscillatory circuit 



gradually to a maximum as tlie common frequency for the two types of 

 circuits is approached then abruptly drops. 



Vigoureux analyzes the crystal oscillator in a manner similar to 

 Terry and correlates his interpretations of the equations with considerable 

 experimental data, some of which are shown in Figs. 12.7, 12.8, 12.9 and 

 12.10. He points out that there is an optimum value of grid capacitance 

 with the cr>'stal connected between grid and plate and a certain amount 

 of grid-plate capacitance is required when the crystal is connected between 

 grid and cathode. 



Wheeler does not assume a linear static tube characteristic but 

 represents it by a three-term nonlinear expression. The results are more 

 complex and it is necessary in the end to disregard certain resistance terms. 



