CHAPTER X 

 NOISE FIGURE 



Synopsis of Chapter 



BECAUSE THERE IS no treatment of the behavior at high frequencies 

 of an electron flow with a Maxwellian distribution of velocities, one 

 might think there could be no very satisfactory calculation of the noise figure 

 of traveling-wave tubes. Various approximate calculations can be made, 

 and two of these will be discussed here. Experience indicates that the second 

 and more elaborate of these is fairly well founded. In each case, an approxi- 

 mation is made in which the actual multi-velocity electron current is re- 

 placed by a current of electrons having a single velocity at a given point but 

 having a mean square fluctuation of velocity or current equal to a mean 

 square fluctuation characteristic of the multi-velocity flow. 



In one sort of calculation, it is assumed that the noise is due to a current 

 fluctuation equal to that of shot noise (equation (10.1)) in the current enter- 

 ing the circuit. For zero loss, an electron velocity equal to the phase velocity 

 of the circuit and no space charge, this leads to an expression for noise figure 

 (10.5), which contains a term proportional to beam voltage Vn times the 

 gain parameter C. One can, if he wishes, add a space-charge noise reduction 

 factor multiplying the term 80 I'oC. This approach indicates that the voltage 

 and the gain per wavelength should be reduced in order to improve the noise 

 figure. 



In another approach, equations applying to single-valued-velocity flow 

 between parallel planes are assumed to apply from the cathode to the cir- 

 cuit, and the fluctuations in the actual multi-velocity stream are repre- 

 sented by fluctuations in current and velocity at the cathode surface. It is 

 found that for space-charge-limited emission the current fluctuation has no 

 effect, and so all the noise can be expressed in terms of fluctuations in the 

 velocity of emission of electrons. 



For a special case, that of a gun with an anode at circuit potential I'o , 

 a cathode-anode transit angle ^i , and an anode-circuit transit angle ^-j , an 

 expression for noise figure (10.28) is obtained. This expression can be re- 

 written in terms of a parameter L which is a function of P 



/' = 1 + (i)(4-7r)(r,/r)(i/c)L 



P = (di - do)C 



426 



