SHOT NOISE IN DIODES 607 



eh drjo 



Thus, as the potential minimum voltage is reduced to zero, the tube 

 noise as given by (45) reduces to the well known shot effect equation. 



For some space charge at the cathode, the value of X in (45) has 

 definite limiting values for both very low and for very large plate 

 voltages. For a very small value of tjo, that is for negative plate 

 voltage, the value of B defined in (47) is very large because df(r)o)/dr{o 

 becomes infinite as tjo is decreased to zero. Thus as r^o ^ 



\^^^^B''J^ye-y'dy=y (49) 



Hence, for any value of space charge, the effective plate resistance 

 temperature for negative plate voltages is one-half of the cathode 

 temperature, under the restriction that no potential minimum exists 

 between the cathode and anode. 



Since the diode is usually operated with a positive plate voltage, the 

 value of the effective plate resistance temperature for a large value of 

 rjo is of more interest. For rjo' not equal to zero, and a large value of 

 plate voltage, it can be readily shown that the values of /(rjo) and of D 

 are much larger than any other quantities involved in the equation for 

 X. After a bit of mathematical operation, it may be shown that the 

 limiting values for/(r/o) and D are 



^ =W' [h^'" +■ ^^^"1"'^' + . • • - {4yW +•••)] 



From these relations, the limiting value of X for a large plate voltage 

 is given by 



\ = 3 f y\ ^y -Jl ^-'''dy = 3^1-^) = 0.644. (50) 



Thus, for any value of space charge, as long as a potential minimum 

 exists, a sufficiently large value of plate voltage may always be found 

 for which the effective plate resistance temperature is 0.644 times the 

 cathode temperature. 



