Triode Generator with Two Degrees of Freedom. 709 



In order to satisfy (5 a) identically we equate separately 

 to zero the four coefficients A, B, C, D. Thus four equations 

 are obtained for the four variables a, b, a> p and co lr They 

 are found to be 



w I 4 -w I 2 (w 1 2 + ft) 2 2 ) + (l-/i ; > 1 V = 0. . (6 a) 



w u"«nW+»2 2 ) + 0-^>iW=0, . (6b) 



2(&)! 2 -f o) 2 2 — 2ft)j 2 ) -j- + {(1 — P)(o)! 2 a 2 - a) 2 2 ^i) 



-f ©/(a, - « 2 ) } a + f 7 a(a 2 + 26 2 ) { w 2 2 (l - F) - ft> x 2 } = 0, 



. . . (la) 



2((o l 2 -ta) 2 2 —2a) 1] 2 ) C ^ 4-{(l-F)( ft ) 1 2 a2 -a)o 2 a 1 ) 



+ a) n 2 (« l -a 2 )}6 4-J 7 ^^ + 2(y 2 ){a, 2 2 (l-Pj- Wn 2 }=0. 



... (lb) 



Equations (6 a) and (6 b) give us the coupling frequencies 

 a)j and o) n , while (la) and (7 £) enable us to find the pos- 

 sible stationary amplitudes a and b and to determine their 

 stabilit}-. 



Since (6 a) and (6 b) are of the same form it is necessary 

 to define coj and &> n quite definitely. We shall take 



^^(•i* + »,») + £ V« + «2 2 j 2 -4(l-^>iV, 



where the roots are to be taken positive, so that 



ft)! 2 > ft) I]: 2 , ft)! 2 . ft) 2 2 , 



and &> n 2 < ft)j 2 . ft)} 2 , ft> 2 2 . 



The equations (7a) and (lb) can further be written 



^=E 1 a 2 (a 2 -a 2 -26 2 ), J 



(8) 



J^E^W-^ 2 -^ 2 ), 

 where, with the aid of (6 a), (6 b), and (8), we have 



"<V <o I - — m n - f 



II •*' ,..2 •,.. 2 2' 



(9) 



• ■• (10) 



2 , % 2 



&)f ftJj-— ft) 



