REFLEX OSCILLA TORS 



495 



oscillation jumps to a large amplitude on the normal curve and then varies 

 uniformly. The discontinuities occur sometimes at one end of the charac- 

 teristic and sometimes at the other, and infrequently at both. It was first 

 thought that this behavior was caused by an improper load/ but further 

 investigation proved that the dependence on the load was secondary and 

 the conclusion was drawn and later verified that the effect had its origin in 

 the electron stream. For this reason the discontinuous behavior was called 

 electronic hysteresis. 



In any self-excited oscillator having a simple reasonant circuit, the os- 

 cillating circuit may be represented schematically as shown in Fig. 20. 

 Here L and C represent the inductance and capacitance of the oscillator. 

 Gr is a shunt conductance, representing the losses of the circuit, and Gi is 

 the conductance of the load. Henceforth for the sake of convenience we 



•Gr 



Fig. 20. — Equivalent circuit of reflex oscillator consisting of the capacitance C, induct- 

 ance L, the resonator loss conductance Gr, the load conductance G^ and the electronic 

 admittance W ■ 



will lump these and call the total Gl ■ Ye represents the admittance of the 

 electron stream. Such a circuit has a characteristic transient of the form 



V = Voe" 



(8.i: 



where 



Ge+Gi 



2C 



and 



Vlc' 



Oscillations will build up spontaneously if 



Geo + Gi < . (8.2) 



For stable oscillation at amplitude V we require 



Ge[V] + Gi = (8.3) 



(8.2) and (8.3) state that the amplitude of oscillation will build up until 

 non-linearities in the electronic characteristics reduce the electronic con- 

 ductance to a value equal and opposite to the total load plus circuit con- 

 ductance. Thus, in general 



Ye = G,o/'i(F) + jBeoF^iV) (8.4) 



' See Section IX. 



