lations 



Oscillation-Hysteresis in Simple Triode Generators. 183 



This is in agreement with the result of the paper (Radio 

 Review, Nov. 1920) mentioned above. 



In such a case the limiting conditions for starting oscil- 



ions (i.e., -j — f-a = 0) are exactly the same as the 



limiting conditions for stopping an oscillation. That is to 

 say, the stationary amplitude is a single valued function of 

 the circuit parameters, and thus, if R or G is varied, the 

 whole process is reversible. 



Our experiments have shown, however, that it is often 

 necessary to take at least two more terms in the series to 

 represent the type of oscillation characteristic met with in a 

 practical case, and we shall now consider the amplitude and 

 stability of the oscillations for such a type of characteristic. 



From equations (5) and (9) we have at once 



da (a R\ 2 3 7 , 5 e 



or C^a 2 +(« + ^)a+|7« 4 +|«a 6 =0, . (11) 



while for any amplitude a to be stable, we must have 



«+^) + |y« 2 +^>0. • • - (12) 



A solution of (11) can be immediately obtained, but for 

 the present discussion such a solution is unnecessary. For 

 example, the stationary amplitudes are given by the real 

 roots of 



( 



, CR\ . . 3 , ;. 5 



a+ -r-) 



L7<* 2 + 57a 4 + 8 ea 6 = 0. 



These may be written 



«i 2 = 0, 



a 2 2 =-A+ VA 2 -B, 



« 3 2 = _A- */A 2 -B, 



\. a 3 7 ' ,-w 8 7 , OR v 



where A= -± and B=^(a+- T , 



5e 5e \ h J 



and the square roots are taken as having a positive real 

 part. 



The conditions of stability are given respectively for 



5. OR 

 «i -eB = — — +a>0, 



O h 



a 2 ea 2 2 > 0, 



« 3 — ea 3 2 >0. 



