640 BELL SYSTEM TECHNICAL JOURNAL 



with oxide coated cathodes. Since the flicker effect is due to locaHzed 

 variations in the emission of the cathode, one would expect it to dis- 

 appear in the presence of a complete space charge condition. 



The experimental curve for the barium oxide coated filament, 

 Fig. 1, shows a flicker effect many times larger than the shot effect on 

 which it is superimposed. At low space currents the mean square 

 flicker effect voltage increases faster than the pure shot noise, a square 

 law rather than a linear relationship being followed. As space charge 

 sets in, the flicker effect voltage goes through a maximum and then 

 decreases with increased space current in the same manner as does 

 the shot effect voltage. In spite of the large flicker effect, as complete 

 temperature saturation is approached the total noise is even less than 

 that found with the thoriated tungsten filament which has no flicker 

 effect. This illustrates clearly the effectiveness of space charge in 

 smoothing the space current. 



When the control grid of a vacuum tube is floating at its equilibrium 

 potential, the noise level is much higher than when the grid is con- 

 nected through an input circuit to the cathode. This increase in 

 noise is primarily due to thermal noise in the extremely high input 

 resistance of the tube and to shot noise arising from small grid currents.^ 

 The magnitude of the thermal noise may be calculated, knowing 

 that the input impedance of the tube consists of its input resistance, 

 Yg, in parallel with its dynamic grid-to-ground capacitance. In such 

 a combination the real resistance component, R{j), is related to the 

 pure resistance, Vg, and the dynamic capacitance, c, according to the 

 equation 



RU) = rgl{\ + ^^''chgT). (7) 



According to equation (1) the mean square thermal noise input 

 voltage is then 



V? = UTrg fdflil -{- Air'chgT). (8) 



With the grid floating at its equilibrium position (usually slightly 

 negative with respect to the cathode) the grid current is composed of 

 two components equal in magnitude but opposite in sign. The one 

 component consists of electrons reaching the grid, while the other 

 consists of positive ions reaching and electrons leaving the grid. The 

 electrons are liberated from the grid by secondary emission, the photo- 

 electric effect, thermionic emission, and soft X-rays. It should be 

 pointed out that space charge does not reduce the noise produced by 

 8 L. R. Hafstad, Phys. Rev., 44, 201 (1933). 



