192 Oscillation-Hysteresis in Simple Triode Generators. 



starting (Cj) and stopping (C 2 ) the oscillations, expressed 

 as a fraction of; the total capacity, was certainly less than 

 10 00Q . It thus seems certain that for this region of grid- 

 potential values we are dealing with cases in which the 

 values of e and 7 in the series for i|r(v) are both positive, 

 and that for this region no oscillation hysteresis exist*. 



The actual observations are shown in fig. 8, in which the 

 ordinates represent the difference (C 2 — Ci) in the critical 

 capacities for starting and stopping oscillations and the 

 abscissae grid potentials. 



The agreement of experiment with the theory given above 

 was finally tested in another way. From the solution of (12) 

 we have for any oscillation characteristic with which oscil- 

 lation hysteresis is marked 



and A W~(*+^-), 



where T^ and R 2 are respectively the critical resistances for 

 starting and stopping an oscillation. From these relations 

 we have 



5eA*L 



£V 2 — XLi— nn 5 



so that the difference between the critical resistances should 

 be inversely proportional to the capacity of the oscillatory 

 circuit. Experiment showed this to be the case. 



Summary. 



A general non-linear theory of a simple triode generator 

 is developed, from which the possible and stable amplitudes 

 of the generator may be determined when the form of the 

 oscillation characteristic is given. The conditions necessary 

 for the possibility of two stable amplitudes for the same set 

 of tube and circuit parameters are examined, and it is found 

 that for two stable amplitudes to be possible, one of which 

 is zero, the expression for the oscillation characteristic, 

 when developed as a Maclaurin series, must have a positive 

 fifth differential coefficient and a negative third differential 

 coefficient. Experiments confirming this theory for such 

 cases are described, in which it is shown that the relation 

 between the oscillation amplitude and one of the circuit 

 parameters (e. g., resistance or capacity of the oscillatory 



