606 BELL SYSTEM TECHNICAL JOURNAL 



noise of the plate resistance at an effective temperature which is a 

 function of that of the cathode. 



In general, the effective value of the diode plate resistance tempera- 

 ture for any operating condition is very difficult to obtain because of 

 the complexity of the final noise equations (45) and (46). However, 

 the limiting value of the ratio of the effective plate resistance tempera- 

 ture to that of the cathode, denoted by "X" in (45), may be evaluated 

 very readily for certain limiting conditions. 



One encounters the first of these conditions when the plate potential 

 and cathode emission are such that the potential minimum has moved 

 just up to the cathode, and is in fact on the point of disappearing. 

 This condition is secured by decreasing the space charge to values less 

 than are required for the formation of a potential minimum away from 

 the cathode. In the equations, it is represented by letting the quantity 

 770' approach zero, where 770' is the natural logarithm of the ratio of the 

 saturation current to the anode current. For this set of operating 

 conditions, all the electrons emitted from the cathode will go to the 

 anode, and hence the condition is appropriate to the study of pure shot 

 noise. 



A second condition is obtained when the plate potential is equal in 

 value to the potential of the minimum. Physically, this condition 

 means that the minimum has moved just up to the anode, and requires 

 a negative value for the plate potential. Mathematically, it is repre- 

 sented by a zero value for the quantity 170, where 770 is equal to the 

 difference between 770' and (e/kT)Vp. For negative plate voltages 

 greater in magnitude than that of the potential minimum, all electrons 

 having an initial kinetic energy greater than eVp will reach the anode 

 regardless of the presence of the space charge existing between the two 

 electrodes. For these conditions, the diode becomes a temperature 

 limited current device. 



A third limiting condition occurs when the plate potential is large in 

 magnitude compared with that of the potential minimum referred to 

 the cathode. In this condition a potential minimum still exists. It is 

 represented in the mathematics by letting the quantity 770 become 

 large. This condition represents the normal operating condition for 

 the diode. 



As the space charge is decreased, making 770' very small, from (47), 

 the diode plate impedance becomes very large through the action of 

 dF(r]o')ldr]o' which becomes infinite as 770' approaches zero. As all 

 other quantities involved remain finite, the mean square noise current 

 for a very small space charge is 



