Effect of Space Charge and Transit Time on the Shot Noise in Diodes

N the study of noise in vacuum tubes, the effect 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. 1 - 2i 3- 4 The most comprehensive analysis was made by Schottky and Spenke. These authors, employing a different method from the one here presented, have obtained the s a m e general conclusions given in this paper, a l t h o u g h I 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 I I , where the presentation is such that the section may be read independently of the theoretical analysis in Part I.