Effect of Space Charge and Transit Time on the Shot Noise 



in Diodes 



By A. J. RACK 



The theoretical analysis of the effect of space charge upon the 

 "shot noise" in a planar diode shows that for practically all 

 operating conditions, the tube noise is equivalent to the thermal 

 resistance noise of the plate resistance at 0.644 times the cathode 

 temperature. Noise in diodes of other than planar shapes is 

 discussed and it is concluded that the same relation holds. It is 

 shown that transit time produces the same high frequency modi- 

 fication for both the thermal and shot tube noise, and that the tube 

 noise is decreased by transit time. 



IN the study of noise in vacuum tubes, the elTect of the space charge 

 upon the shot noise has been a subject of considerable interest and 

 practical importance. Several papers have been written in which it is 

 shown that the shot noise is decreased by the space charge, and that the 

 tube noise in a diode with space charge is equivalent to the thermal 

 resistance noise of the plate impedance at a temperature slightly 

 greater than half of that of the cathode.^' -• ^' ^ The most compre- 

 hensive analysis was made by Schottky and Spenke. These authors, 

 employing a different method from the one here presented, have 

 obtained the same general conclusions given in this paper, although 

 they prefer to express the result in the form of a modified shot-noise 

 equation, whereas for reasons developed below, the writer prefers the 

 thermal form. The theoretical analysis and discussion presented here 

 was undertaken to show in more detail the extent of the range of the 

 operating condition for which the thermal resistance equivalent of tube 

 noise is valid and to study the effect of transit time upon both the shot 

 and thermal tube noise. 



For convenience, the paper is divided into three parts. In the first 

 section is given an exact mathematical treatment of the tube noise at 

 low frequencies in a parallel plane diode for any degree of space charge. 

 A discussion of the final tube noise equation obtained through this 

 analysis, and the extension of these results for the planar diode to any 

 other shape diode is given in Part II, where the presentation is such 

 that the section may be read independently of the theoretical analysis 

 in Part I. Through several approximations. Part III treats the effect 

 of transit time upon tube noise in the planar diode. 



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