HIGH-FREQUENCY AMPLIFIER 51 



assumptions I' can be determined as a function of (a/Xs) and U can be deter- 

 mined as a function of 1'. We have from Equation (A-37) 



' + ,„^^. = l+Jf (A-37a) 



{U + 6/2)- iU - h/2Y W^ 



When t/ = 0, U'" = W\, = W\, , so that 



1 + 1' = 8{\VWbT- (A-42) 



and equation (A-37a) becomes 



(FTV2)' + (ir^f = (8/s')(n-.»/ir)' (a-37« 



the solution of which, for the increasing wave, is 



u = i(V2)[(i/2)(ir/ir.„)-(A/i + s{Wm/w)' - i) - i]^ (a-43) 



and the gain will be given by 



Gain/6 = 27j[(l/2)iW/\VMr-(VfT^W7/W " l) " l]^ (A-44) 



db/wavelength/unit b 



"Decibels gain/wavelength/unit b" is plotted against (W/Wm)~ in Fig. 3. 

 As (TF/ir.v)- becomes very large, the gain per wavelength approaches 

 27.3 b db. 



