A Contribution to Tube and Amplifier Theory

A formula adapting Maxwell's solution for a plane grating to the plane triode differs from those obtained by previous workers. The triode is simulated by a diode whose electrode separation exceeds the cathode-grid clearance by an amount which is calculated from electrostatic considerations. Corresponding results are derived for the cylindrical triode by means of conformal representation, and are shown to agree better with experiment than the formulas of King and of van der Bijl. The nonuniformity of the electric field due to the presence of the grid, "grating effect," is not marked at the cathode surface, as generally supposed, the field at the cathode being sensibly uniform along the length of the cathode even for grids for which the distance between wires is equal to the cathode-grid clearance. This result is obtained directly from Maxwell's treatise. As the electrons approach the grid the nonuniformity then becomes important and the space-current stream is subject to electron optical considerations. These cause the known departures of g
m
from theory in openmesh tubes. The effects of space charge on the measured amplification factor are briefly discussed. It is shown that μ is two stages removed from the Maxwell shielding constant μ
0
. The importance of the cathode-plate capacitance is mentioned and an expression given for its approximate value under operating conditions.