WAVE PICTURE OF MICROWAVE TUBES 



1353 



is imaginary. In this case we can write 



ivi = -jKo 



lU = +jKo 



where Kn is real. We have 



P = [-jni2*Ko + (-ifif2*/vo)*] 



Either wave alone carries no power; there is power flow only when the 

 two waves are present simultaneously. The two waves vary with distance 

 as 



— j(w/«o)z (a>g'/«o)2. 



-jiuluQh) —{uq'luQlz 



SO the iiii* is constant \Aith distance. If this were not so the power would 

 change with distance, but as the resonators have been assumed to be 

 lossless, neither taking power from the beam nor adding power to the 

 beam, this is impossible. Thus, in a lossless system an increasing wave is 

 always one of a pair, and the other member decreases with distance in 

 such a way as to keep the product of the amplitudes of the two waves 

 constant with distance. Neither the increasing wave alone nor the de- 

 creasmg wa\'e alone carries any power, but the two together can carry 

 power. 



We will note that in the easitron the direction of the group velocity, that 

 is, the direction of causality, is the direction of electron flow. Thus, the 

 waves are both set up at the input resonator; it is there that boundary 

 conditions on both current and voltage must be satisfied. 



COUPLING OF MODES OF PROPAGATION 



We know that waves which increase and decrease exponentially with 

 distance are characteristic of a ladder network in which the susceptances 

 of the shunt and series arms have the same signs. They occur in other 

 networks as well. Consider a smooth transmission line loaded periodically 

 with shunt capacitances, as shown in Fig. 6. Each capacitance reflects 



Fig. 6 — Capacitances connected across a smooth transmission line periodically 

 couple the forward and Ijackward waves and produce stop bands characterized by 

 growing and decaj'ing waves. 



