PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 163 



ance, rather than the capacitance Cady spoke of. Miller^ also produced a 

 circuit with a two-electrode crystal connected between grid and cathode but 

 with a tuned circuit in the plate lead, which circuit required the crystal to 

 provide inductive reactance. 



It was not until after Van Dyke showed that the crystal could be repre- 

 sented by the circuit network of Fig. 12.3 that it was possible to explain 

 these various phenomena. With this view of the crystal, and using the 

 differential equation method of circuit analysis, Terry pointed out that, 

 as with electrical oscillators, the frequency is not completely governed by 

 the resonant element, in this case the crystal, but is influenced somewhat 

 by the circuit elements. The circuit as a whole is quite complex and the 

 equations are difficult to use. Wright and Vigoureux also made analyses 

 of the Pierce type oscillator. Because of the complexity of the equations, 

 the frequency, amplitude, or activity are not computed directly, but the 

 effects of the circuit variables are analyzed in a qualitative manner and 

 the results compared with experimental data. 



Oscillators employing crystals may be classified in a number of ways. 

 One classification is based upon whether or not the circuit without the 

 crystal is in itself an oscillator. If it is, the oscillator is called a "crystal 

 controlled" oscillator. If it is not, it is called a "crystal" oscillator. All 

 of Cady's oscillator circuits, except the one shown in Fig. 12.2, are of the 

 first named class. This type of circuit will oscillate at a frequency deter- 

 mined by the tuned circuit if the crystal becomes broken or disconnected, 

 or if high resistance develops in the crystal, or if the electric tuned circuit 

 should become tuned too far from the resonant frequency of the crystal. 

 This property at times is an advantage and at other times a disadvantage. 

 This type of circuit will oscillate under control of the crystal with much 

 less active crystals than most of the other types. 



Nicolson's, Pierce's, Cady's of Fig. 12.2 and Miller's oscillators belong to 

 the second named class. They will cease oscillating if the crystal breaks, 

 develops high resistance or is disconnected. Failure of the oscillator to 

 function at all then serves as a warning that something has happened to 

 the crystal. 



This second named class of crystal oscillators has been used much more 

 than the first named. The crystal is the principal frequency determining 

 element in the circuit. Often there are required only resistances, or re- 

 sistances and an inductance, as the other elements to embody along with 

 the vacuum tube and crystal. The simplicity, low costs, and usually no 

 tuning, have made this class attractive. Most analytical studies of oscilla- 

 tor circuits have been made upon this class. For that reason the discussion 

 in this chapter will be limited to this class. 



An analytic study of the crystal oscillator can readily start by looking 



