658 



BELL SYSTEM TECHNICAL JOURNAL 



In this case 



-"^g^.. 



(*^"/^' - ^) + 0^] 



H' 



As pis small, we write approximately 



(15.29) 



(15.30) 



We see that we obtain an imaginary value of p only for the — sign in (15.28) 

 that is, if 



/3e//3i = 1 - ^V/5. (15.31) 



Fig. 15.3 — The usual arrangement is to have the finned structure positive and opposed 

 to a conducting plane. 



In this case 



p = ±;M(1 - a)/(l + ay"m/^j"'H. 



(15.32) 



In this case we obtain gain for any value of a smaller than unity. We note 

 that a = 1 is the value a assumes far from the axis in a two-dimensional 

 system of the sort illustrated in Fig. 15.2, for either a cosh or a sinh distribu- 

 tion in the -{-y direction. 



The assumption of — T = —j0i{l + p) in (15.22) will give forward (-{-z) 

 traveling-waves only. In order to investigate backward traveling-waves, we 

 must assume 



-r = +jm-\-p) 



(15.33) 



where again p is considered a small number. If we use this in (15.19), we 

 obtain 



+ 1 + /^ 



[(j. 



+ 1 + H --I 



311 



1^ 



'2/31 



j^'-'V^i 



_2a/3m 1 

 1 + a')^i] 



(15.34) 



H' 



