644 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



trons moving to the right. A wave excited at the right with power flow to 

 the left has a positive value of /3 and will interact with electrons traveling 

 to the right. Let us consider such an interaction. 



First, as to the 6's. We see that, for a wave which varies with distance as 



where jS is a positive number and has power flow to the left, the sign of V jl 

 must be the opposite of what it would be if the power flowed to the right. 

 This can be taken into account by reversing the sign of K in (2.19), and 

 making 



53 = +j^lfii(^eaK (4.1) 



where K is now taken as a positive number. We can then take 



Here 5i represents a wave whose amplitude increases to the left, that is, 

 a wave which grows in the direction of energy flow. We might think that 

 this would immediately imply a gain similar to that obtained for energy 

 flow in the direction of electron motion, but this would be jumping at 

 conclusions. 



Suppose we taken z = at the left-hand or output end of the circuit. 

 There the electron stream enters unmodulated. There also we will assume 

 the circuit to be terminated so as to prevent reflection of power. At the right- 

 hand or input end of the circuit power will be fed in, giving an impressed 

 field E{. 



Suppose 61 , 82 and 63 are the appropriate 6's for this case. We see that our 

 boundary conditions are 



e~'^'\Ei^'''^ 4- E^oe'"'^ + £30^"'*'^) = Ei 



Eio . £20 I £30 _ Q 



61 62 ^3 



^10 E20 EzQ ^ 



di 02 dj 



