Mathematical Theory of the Four-Electrode Tube

This paper gives the mathematics of the four-electrode tube, including in the most general case expressions for the plate and two grid currents in terms of applied voltages in the two grid circuits and the impedances of all three circuits. The results are exact, variation in the amplification factors being included. Because of the complexity of the general equations, these expressions for the currents have been developed: I, in terms of one grid-filament voltage and external impedances in plate and other grid circuit, assuming no voltage in latter; II, in terms of grid-filament voltages of both grid circuits and external impedance in plate circuit; III, in terms of applied voltages in both grid circuits and external impedances in plate and two grid circuits. The results of I show the effect of an external impedance in the non-control grid of a "screen-grid" or "space-charge-grid" tube; II covers the approximate theory of a "double-function" tube; III gives a more exact and comprehensive theory of the tube in any use.