PIEZOELFX'TRIC CRYSTALS IN OSCILLATOR CIRCUITS 



IcSS 



frequency. Heegner explains a number of crystal oscillator circuits by 

 the method briefly outlined above. 



L2 



I ^ 



I 



)MV9 I 

 I 

 I 



P -r^^ -r^9 



Fig. 12.18 — The oscillator circuit (A) is equivalent to the filter circuit (B) 



Fig. 12.19 — Oscillator circuit in which the crystal operates at its series 

 resonant frequency 



12.30 Vector Method or Oscillator Analysis 



A convenient method of examining the effect of certain circuit variables 

 on frequency and the necessary conditions for oscillation is by the vector 

 representation of the voltages and currents in the circuit. Much of Heis- 

 ing's^'* early work on the analysis of electric oscillators by vector methods is 

 directly applicable to crystal oscillators. Boella analyzed the crystal 

 oscillator circuit by this method and treated in detail the effect of the 

 decrement of the crystal on the oscillating frequency. Since some engineers 

 prefer this method of qualitative analysis to approximate equations it will 

 be briefly explained. 



The vector diagrams for the two conditions, crystal between grid and 

 plate and between grid and cathode, are shown in Figure 12.20A and B as 

 applied to the circuit diagrams, Figure 12.12A and B, respectively when in 

 the simplified form of Figure 12.11. The necessary conditions for oscilla- 



