MAGNETRON AMPLIFIER 659 



As before we look for solutions for p where the terms multiplying p on the 

 left are small. The only vanishing consistent with positive values of jS« and 

 /3i is obtained for 



^'+l = +§^. (15.35) 



Under this condition (15.34) yields for p 



,.1 (l + «) (P,^^ ,.,-.. 



Thus we can obtain backward-increasing backward-traveling waves for all 

 values of a except a = — 1. For the situation shown in Fig. 15.3, with a 

 backward wave, a is always negative, approaching —1 at large distances 

 from the plane electrode, so that the gain is identical with that given by 

 (15.32). 



We note that (15.27), (15.32) and (15.36) show that p is proportional to 

 the product of current times impedance divided by voltage to the f power, 

 while, in the case of the usual traveling-wave tube, this small quantity 

 occurs to the \ power. The \ power of a small quantity is larger than the 

 \ power; and, hence for a given circuit impedance, current and voltage, the 

 gain of the magnetron amplifier will be somewhat less than the gain of a 

 conventional traveling-wave tube. 



