90 BELL SYSTEM TECHNICAL JOURNAL 



This equation shows the expected fact that for a given value of At it 

 is better to keep the direct photo-electric current small (high modula- 

 tion). It also brings out the curious result that when the direct 

 voltage drop in the coupling resistance is much more than 1/20 volt 

 the noise is largely shot noise and the signal-to-noise ratio is in- 

 dependent of the coupling resistance, while if this voltage is much less 

 than 1/20 volt the thermal noise predominates and the signal-to- 

 noise ratio is proportional to the coupling resistance. 



Shot Effect and Flicker Effect With Space Charge 



When, as in an amplifier tube, the current in the tube is limited 

 partly or wholly by space charge rather than by the cathode tempera- 

 ture, then the conditions are changed ^^' ^^' ^^ in two respects. First, 

 while the electrons still are emitted from the cathode at random times, 

 they must arrive at the plate in a more orderly manner. Simple 

 statistical laws no longer apply, the flow of current is smoother and the 

 fluctuations are greatly reduced. Second, the impedance of the tube 

 is no longer infinite, but has a finite value. The equation for the shot 

 effect (equation (7)) now must be modified,^- ^^' ^^ by substituting for 

 the current i the quantity j{dijdjY, where j is the total current emitted 

 by the filament and dildj is the rate of change of space current with 

 emission current for the particular conditions used in the observation 

 of the fluctuating voltage. Furthermore, in place of the coupling 

 impedance Z the effective impedance Z^ of this in parallel with the 

 tube resistance fp must be used. The equation now reads 



F= 26i(^^.)' r Z.^GHJ. (10) 



In the absence of space charge j and i are identical, dildj is unity, and 

 Ze becomes Z, so that the equation then represents the pure shot 

 effect. With increasing space charge the value of difdj approaches 

 zero and Ze becomes smaller so that the shot eff"ect becomes very 

 small. Similarly the flicker effect, being connected with the process 

 of emission and not with the subsequent history of the electrons, also 

 is made ineffective by the space charge. In fact, in well designed 

 tubes the fluctuation noise of both shot effect and flicker eff^ect in the 

 space current appears to be reduced to such an extent as to be 

 negligible. 



Ions in the Space Charge 



The effect of ions in the grid current already has been discussed. 

 Ions also may cause fluctuations in the plate current of the tube. 



