166 BELL SYSTEM TECHNICAL JOURNAL 



Conversely, we are led to wonder whether a current less bunched than 

 that produced by random emission might not have less noise. The most 

 smoothly distributed current we can imagine is that of /o electrons per 

 second emitted at evenly spaced intervals. Obviously, such a current will 

 have a spectrum consisting of frequencies w/o , integral multiples of /o . 

 Thus for/ < /o , there will be no "noise" and similarly for /o < / < 2/o , 

 2/0 </< 3/0, etc. 



For a current of 10 ma,fo = 6.3 X 10^^; thus, even for small currents an 

 evenly spaced emission would have no a-c components in the radio-fre- 

 quency range; this is a comforting thought in considermg space-charge 

 reduction of noise, which is discussed in section 5. However, purely to 

 satisfy our curiosity we may pursue the matter a little further. If we 

 assume that each electron constitutes an instantaneous pulse of current, a 

 simple harmonic analysis shows that the a-c current component of fre- 

 quency nfo will have a mean square value 



fn = 2e/o/o. (29) 



Thus, in each interval /o wide centered about a frequency nfo there will be a 

 mean squared a-c current equal to that which would be associated with the 

 same band for random emission with the same current. By making the 

 emission regular we have not reduced the mean square "noise" current in a 

 broad frequency range; we have merely changed its frequency distribution 

 from a uniform distribution to a distribution of sharp, high peaks. 



IV. Partition Noise 



Consider a tetrode, shown in Fig. 4, with a cathode current Ic , a screen 

 current /, , and a plate current Ip . 



The grid current is taken as zero. Suppose that the screen is very fine, 

 so that every electron leaving the cathode has the same chance of striking 

 the screen, regardless of its point of departure. We may now regard the 

 function of the screen as that of a peculiarly simple electron multiplier, 

 for which n can be zero (electron striking screen) or 1 (electron passing 

 screen). 



The probability of an electron passing the screen is Ip/h • Accordingly, 

 from (19) and (23), 



n = Ip/Ic (30) 



n^ = Ip/Ic (31) 



Suppose we write the noise in the cathode current as 



72 = r^lelcB (32) 



Here P, a factor less than unity, is introduced to account for the "space 

 charge noise reduction" in space charge 1 united flow. 



