164 BELL SYSTEM TECHNICAL JOURNAL 



This is the expression for shot noise in a randomly emitted current, as in 

 temperature limited emission or in photo electric emission. 



III. Noise Other Than Shot Noise: Electron Multipliers 



Let us consider a class of systems in which the average output current is 

 proportional to the average input current, in which an electron of charge, e 

 entering produces an output charge, ne instantaneously, and in which the 

 probability that any electron will produce n electrons is pn . 



If the input current is /o , the average output current is 



/ = nlo (18) 



n = J2nPn. (19) 



n 



It is easy to persuade ourselves that any frequency component of current, 

 noise or signal, will produce an output current il times as great; this happens 

 to be true, and we will use the fact. 



Let us consider our device when it has randomly emitted electrons as an 

 input. At the output we will see appear groups of 1, 2, 3 etc. electrons, 

 each group caused by the entrance of a single electron. If Iq is the total 

 input current, the output current consisting of groups of n electrons is 



In = niopn. (20) 



Each group carries a charge ne. We may now use (17) to write the noise 

 in the part of the current carried by groups of n electrons, replacing the 

 electronic charge, e, by the group charge, ne 



¥, = 2{ne){nIopn)B. (21) 



As there is no correlation between entering electrons, the total mean square 

 output noise current will be the sum of the noise components carried by 

 groups consisting of different numbers n of electrons. Summing (19) with 

 respect to n we obtain 



if = leloBn^ (22) 



n' = J^n'p,,. (23) 



Now, the input has been taken as having shot noise. A part of the noise 

 output is to be attributed to this input shot noise amplified by the device; 

 that is, it will be fi^ times the input shot noise. 



^ = n^lehB. (24) 



The part of the noise output current due to the fact that an electron does 



