NOISE IN RESISTANCES 



163 



continue to reach 1, but some of the low- velocity electrons leaving 1 would 

 be turned back from 2. 



It is well known^ that if a Maxwellian velocity distribution is assumed 

 for the electrons leaving 1, the electrons which can overcome the retarding 

 field and reach 2 are found to constitute a current 



he 



eVikT 



(14) 



Here /o is the total current carried by electrons leaving 1 and V is the voltage 

 of 2 with respect to 1 , which has been assumed to be negative. 



Fig. 3 — An electronic resistance formed by two opposed cathodes at the same tem- 

 perature acts as a generator of thermal noise. 



By differentiating (14) we can obtain the diode conductance G at F = 0, 

 and we find 



kT 



u 



(15) 



From (3) when the diode is short circuited and the voltage is zero we have 

 a mean square noise current 



i2 = 4kTGB = il (ikTB) = 4eIoB. 

 kl 



(16) 



This noise is the sum of the noise due to two independent noise sources 

 (the noise in the two currents /o). That due to either current 7o is* 



P = 2eIoB. 



(17) 



* In this section, we are concerned with short transit angles only and no distinction 

 need be made between the current induced in the circuit, /, and the electron convection 

 current. 



