648 BELL SYSTEM TECHNICAL JOURNAL 



and we can write i 



i = -J 



^^ (-- + !/) '-•«^) 



jh Be dEz 



' 2Vo[K-{d,-dY] ^^^'^^^ 



Here i^ is a parameter specifying the value of /3VcoCi . As (14.85) need 

 hold over only a rather small range of /3, and C is not independent of /3, 

 we will regard K as a constant. 

 The parameter P, corresponding to (14.85) is 



Pe = 



[K - (de - dYY 



2\/e/M Vo 

 Now, from (14.80), for large values of 9 



h d{de/do) ^ Jo d^jde/do) 



(14.86) 



(14.87) 



As 



and 



dg/da = c/ua , 



A = 



Pe = 



_Jo£_ 



2eUo Vo 

 A 



2d[K - (de - ey] 



Let us now expand (14.88) assuming A' to be very small 



P. = 



1 + 



K 



If we let 



2eide - eyi ' {e^ - ey 



K = A/4 



+ 



(14.12) 

 (14.88) 



(14.89) 

 (14.90) 



we see that these hrst two terms agree witli the expansion of the broad- 

 beam expression, (14.77). The leading term was not adjusted; the space- 

 charge parameter K was, since there is no other way of evaluating the 

 parameter in this case. 



In Fig. 14.9, the value of dPg as obtained, actually, from (14.73) rather 

 than (14.76), is plotted as a solid line and the value corresponding to the 



