FLUCTUATION NOISE IN VACUUM TUBES 637 



to the input circuit whose magnitude at the grid expressed in mean 

 square volts is given by 



V' - ^kT,{r„l^f[_Tfl{T,r,;) + \lr,-]F. (4) 



Since the noise of thermal agitation is always present:, this equation 

 gives the absolute minimum to which fluctuation noise in an amplifying 

 tube can be reduced after all other causes have been eliminated. It 

 shows that for the ideal low noise tube in which thermal noise in the 

 plate circuit is the limiting factor, the noise level may be reduced by a 

 decrease in the cathode temperature, a decrease in the effective 

 frequency band, or by an independent decrease in the plate resistance 

 or increase in the amplification factor. In order to operate at a 

 minimum noise level the tube should work into a load resistance which 

 is large in comparison with rpTo/Tp. Under this circuit condition the 

 noise level is inversely proportional to /j.'^/rp, a quantity often defined 

 as the '"figure of merit" of an amplifying tube. 



Shot Effect and Flicker Effect in the Presence of Space Charge 



The theory of the shot effect in the absence of space charge has 

 been studied quite completely both theoretically and experimentally 

 by many investigators.^ The results, however, are not applicable 

 to the study of noise in thermionic vacuum tubes used in high-gain 

 amplifiers, since a high degree of space charge is required in tubes 

 used for this purpose. Llewellyn has extended the theory of the shot 

 effect to cases where partial temperature saturation exists, and ob- 

 tained a general equation to cover all conditions.^ This equation 

 reduces to the following form when the load impedance is a pure 

 resistance: 



E. 



2ej{dildjy[_rpr,l{rp + r,)J f | G,(f) \ Mf. (5) 



Es^ is here the mean square shot voltage across the measuring device, 

 i the total space current, j the total current emitted by the cathode, 

 and e the electronic charge (1.59 X 10~^^ coulomb). 



A precise experimental verification of this equation is very difficult 

 because of the difficulty in determining di/dj accurately. Thatcher,*^ 

 however, has made shot measurements in the presence of space charge 

 (1 ^ di/dj ^ 0.66) which verify the theory within the experimental 

 error of the determination of dijdj. 



^W. Schottky, Ann. d. Physik, 57, 541 (1918); T. C. Fry, Jour. Franklin Inst., 

 199, 203 (1925); A. W. Hull and N. H. Williams, Phys. Rev., 25, 147 (1925). 

 « Everett W. Thatcher, Phys. Rev., 40, 114 (1932). 



