336 BELL SYSTEM TECHNICAL JOURNAL 



However, a relationship exists between ti and to , 



/ 

 /i = /o + 



V 



Where 



V 



t'o V 1 + « sin oj/i ; 



/ 



/i = /o + 



Vo vl + a sin co/i 



Now if a « 1 



and 



and finally 



but 



so that finally 



/i = /o + - I 1 



sin wti + 



— = 1 + - — cos co/i 

 ah Vo 2 



ti 



( 1 + -^ cos w/i ) 



Vo 



( 1 + y cos cc/i j 



ii = io I 1 + y cos cc/i 



This says that the velocity variation impressed on the beam at the en- 

 trance to the drift space or conversion region has resulted in a current varia- 

 tion at the output. For those of you who think in vacuum tube parameters 

 it is of interest to differentiate this expression with respect to the a-c voltage 

 and obtain the transconductance 



dii 



dVa-c 



rewriting 





dii 



dV~ac 



dio_ 

 2V 



