The capacitance between diode electrodes in the presence of space charges

The capacitance between the electrodes of a planar condenser with no space charge can be calculated by finding the rate of change of charge on either electrode with the potential between them. In the presence of space charges, however, the result is different if the charge on the cathode is considered rather than the charge on the anode. The method is therefore not valid in this application. Accordingly, taking Child´s approximation of zero emission velocities, the matter is reconsidered to take into account the charges which leave or accumulate between the electrodes when the anode potential is changed. It is then found that the capacitance of the active area of a space-charge-limited diode is zero, while that of a saturated diode varies from twice the cold capacitance to the cold capacitance as the anode voltage is changed from the saturation voltage to very high values at which space charge is negligible. Another feature of the results obtained is the sudden transition from high to low capacitance as the anode potential varies. These results have a bearing on the efficiency and design of klystrons, affect the theoretical position in regard to the fluctuations of diodes, and reveal errors in the equations hitherto commonly used in the study of electron-inertia effects.