366 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1950 



3.5 



3.0 



2.5 



2.0 



9- 



^1.5 

 U 



1.0 



0.5 



1.4 



1.2 



1.0 



0.8 



ID 

 < 



0.6 



0.4 



0.2 





 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 



y 



Fig. 6 — Cw{y, (pa) of the fast and the slowest electrons versus y for Case 

 (10). A{y) is also plotted in dotted lines for reference. 



justing the impedance of the output circuit. This may be necessary in 

 practice for the purpose of avoiding possible regenerative oscillation. In 

 doing so, the voltage at 2 = D is the sum of the voltage of the forward 

 wave and that of the particular solution of the backward wave. In every 

 case, the output power is always equal to the square of the net voltage 

 actually at the output end divided by the impedance of the output cir- 

 cuit. 



We find from (14), (15) and (16) that the fundamental component of 

 electron charge density may be written as 



f s. \ h ( . dai{y) . da2(y)\ 



= Real component of 



1/0 



dai{y) 

 dy , 



+ 



doM 

 dy 



(26) 



jo)—Toz—by+Ji 



) 



where —Io/uq is the dc electron charge density, po . 



If (26) is compared with (12d) or (12c), it might seem surprising that 

 the particular solution of the backward wave is just equal to the funda- 



