NOISE FIGURE 433 



our a-c convection current and velocity at the beginning of the hehx, and 

 /o and Mo the d-c beam current and velocity, and a- the area of the beam, 



t = —crqb 



V ^ Vb 



(10.23) 

 /o = alo 



Mo = Wo 



In addition, we will use transit angles di and 62 in place of /3i and iSo 



(10.24) 



02 = jd2 



We then obtain from (10.21) and (10.22) 



q = -j{h/u,){d, - 62)6- ''''^''\a (10.25) 



V = -e~^'''^''\'a (10.26) 



10.3 Overall Noise Figure 



We are now in a position to use (9.4) in obtaining the overall noise figure. 

 We have already assumed that the space-charge is small in the drift space 

 between the gun anode and the hehx (QC = 0). If we continue to assume 

 this in connection with (9.4), the only voltage is the helix voltage and for 

 the noise caused by the velocity fluctuation at the cathode, I'a , F = at 

 the beginning of the helix. Thus, the mean square initial noise voltage of 

 the increasing wave, Ff, , will be, from (10.21), (10.22), (9.4) and (10.9), 



Vl = (2(4 - 7r)kT,CBVo/Io)\ S^dsidi - d.X + (52 + h) |- 



I (1 - V6i)(i - h/h) r' 



(10.27) 



As before, we have, from the thermal noise input to the helix 



'Vlt = kTBK(\ (1 - 52/5,)(l - 53/5i) f' (10.5) 



and the noise figure becomes 



F = \ + V\s/V\t 



F = 1 + (i/2)(4 - 7r)(r,/r)(i/c)| 5253(^1 - e2)c + (60 + h) |- (10.28) 



Here use has been made of the fact that 



C = KJ/Wq 



