PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 



187 



as the plate impedance is increased and as the losses in any of the circuit 

 elements increase. This is necessary for the proper angle oi\p -\- ^p' in the 

 vector diagram. With the G-P connections, the departure from /o and 

 change in/o as the decrement of the quartz varies are in the same direction, 

 while for the grid-cathode connection they vary in opposite directions, 

 and the net result will depend upon the value of the internal plate resistance 

 and plate circuit impedance. The curves of Figure 12.21 show that the 



Fig. 12.21 — The change in reactance characteristic of a crystal resulting from a change 



in decrement 



change in fa for a given change in decrement is less for smaller values of 



"77 (larger values of series capacitance C3). That is, the effect of the de- 

 C0C3 



crement of the crystal upon the oscillating frequency is small when the crys- 

 tal is operated near its frequency of resonance. 



12.40 Negative Resistance Method of Analysis 



The methods of analyzing oscillator circuits described in the previous 

 sections define the operation in terms of the individual circuit elements and 

 the crystal is treated as one of the circuit elements. Certain advantages 

 result, however, by grouping all the circuit elements, except the crystal. 



