REFLEX OSCILLATORS 511 



cerning the conductance the actual case would involve a transition from 

 the situation of Fig. 30b to that of Fig. 31. If a discontinuity in amplitude 

 occurs in which the amplitude does not go to zero, it will be accompanied 

 by a discontinuity in frequency, since the discontinuity in amplitude in 

 general wall cause a discontinuity in the susceptance. If this discontinuity 

 in susceptance occurs between values of the amplitude such as Va and Vh 

 of Fig. 30, we observe that the direction of the frequency jump may be 

 opposite to the previous variation. We also observe that if the rate of 

 change of susceptance with amplitude is greater than the rate of change of 

 susceptance with Ad, then in regions such as that lying between zero ampli- 

 tude of Vb the rate of change of frequency with A0 may reverse its direction. 



One can see that because of the longer drift time contributing to the third 

 transit the conductance arising on the third transit may be of the same 

 order as that arising on the second transit. In oscillators in which several 

 repeller modes, i.e., various numbers of drift angles, may be displayed, one 

 finds that the hysteresis is most serious for the mcdes with the fewest cycles 

 of drift in the repeller space. One might expect this, since for these mcdes 

 the contribution from the cathode space is relatively more important. 



Some final general remarks will be made concerning hysteresis. One 

 thing is obvious from what has been said. With the admittance conditions 

 as depicted, if all the electronic operating conditions are fixed and the load 

 is varied hysteresis with load can exist. This was found to be true ex-peri- 

 mentally, and in the case of oscillators working into misterminated long lines 

 it can produce disastrous effects. Where hysteresis is severe enough, it 

 will be found that what we have chosen to call the sink margin will be much 

 less than the theoretically expected value. An illustration of this is given 

 in Fig. 109. 



The explanation which we have given for the hysteresis in the reflex 

 oscillator depends upon the existence of two sources of conductance. This 

 was apparently a correct assumption in the case studied, since the elimina- 

 tion of the second source also eliminated the hysteresis. It is possible, 

 however, to obtain hysteresis in a reflex oscillator with only a single source. 

 This can occur if the phase of the electronic admittance is not independent 

 of the amplitude. Normally, in adjusting the repeller voltage the value 

 is chosen for the condition of maximum output. This means that the drift 

 angle is set to a value to give maximum conductance for large amplitude. 

 If the drift angle is then a function of the amplitude, this will mean that for 

 small amplitude it will no longer be optimum. Thus, although the limiting 



function ^ tends to increase the electronic conductance as the ampli- 



tude declines, the phase factor will oppose this increase. If the phase factor 

 depended sufficiently strongly on the amplitude, the decrease in Gr caused by 



