SHOT NOISE IN DIODES 593 



Part I — ^General Low Frequency Analysis 



In the development of the general equations for the direct current 

 in vacuum tubes with space charge, account has been taken of the 

 fact that the electrons are emitted from the cathode with Maxwellian 

 velocity distribution. This fact has been verified experimentally by 

 Germer,^ and the resulting equations for the relation between current 

 and voltage have been derived and investigated by Fry,^ Langmuir/ 

 and others. In the extension of this analysis to tube noise, it is only 

 necessary to assume that the number of electrons emitted with any 

 velocity does not remain constant, but fluctuates with time according 

 to the well-known laws of probability. In the analysis on this basis, 

 the frequencies involved will be considered to be sufficiently low so 

 that any transit time effect is negligible. 



Below is given a list of the definitions of various symbols to be used in 

 the tube noise study of a parallel plane diode. The practical system of 

 units is employed throughout. 



n(Uc)dUc = instantaneous rate of emission per unit area of the cathode 



of electrons with initial velocities between Uc and 



Uc + duc in the rjc-direction, regardless of the velocity 



components in the other directions, 

 = no(uc)dUc + 8{Uc)dUc, 

 no(Uc)dUc = average rate of emission of electrons with A:-directed 



velocities between Uc and Uc + dUc, 

 b{iic)duc = instantaneous deviation from average rate of emission, 

 / = instantaneous anode current per unit area, 

 V — instantaneous potential with respect to cathode of a plane 



at a distance x from the cathode, 

 V — instantaneous potential with respect to cathode of the 



potential minimum, 

 u — instantaneous velocity at ric-plane of electrons which had 



an initial x-directed velocity of Uc at the cathode, 

 x' = instantaneous position of potential minimum, 

 e = charge on electron = — 1.59 X 10~"^^ coulombs, 

 m = mass of electron — 9.01 X 10~^^ grams, 

 h = ratio of dyne cms. to joules = 10~^, 

 e = permittivity of a vacuum in practical units = 8.85 X 10~^* 



farads/cm., 

 k = Boltzmann's gas constant = 1.372 X 10~^* watts/degree 



Kelvin, 

 A^ — average total number of electrons emitted per second per 



unit area from the cathode, 

 T — absolute temperature of the cathode. 



