The space-charge smoothing factor

The author has recently expressed the properties of a planar diode in terms of a set of differential coefficients, many of which can be experimentally determined. In the present paper these differential coefficients are used to derive a relation between the anode-current fluctuations and the fluctuation in the total emission. The fluctuation in the total emission is then calculated, and found in general to be much greater than the full shot noise. By inserting this result in the equation for the anode-current fluctuations it is found that the space-charge smoothing factor can be expressed in a very simple form. Its value can be determined experimentally from measurements of the characteristic at two slightly different cathode temperatures and the distance from cathode to anode. No measurement of temperature or total emission is necessary. It is well known that the fluctuations of valves and resistors can be expressed in identical forms, each involving a temperature. The results obtained in the paper show, however, that the fluctuations of a resistor are quite different from those of a valve, since they are not calculable from the shape of the characteristic without a knowledge of the temperature.