Analysis of a transmission-line type of thermionic-amplifier valve

An analysis is made, using circuit theory, of a transmission line consisting of two helices in proximity to an earthed straight conductor. Inductive and capacitive coupling between the two coils is taken into account, and it is shown that two waves in each direction, travelling with different phase velocities, can coexist. A possible type of thermionic-amplifier valve is envisaged which consists of a long straight cylindrical cathode surrounded concentrically by a helical grid and an outer helical anode. Valve action is allowed for by modification to the shunt-admittance parameters associated with the two coils. It appears that waves in the slower mode, in which the anode and grid voltages are out of phase, are amplified according to an exponential law; waves in the faster mode, where the grid and anode voltages are in phase, are attenuated by a similar amount. It is found that in a particular mode the grid and anode voltages are amplified, or attenuated, equally. To make it possible to match the ends of the lines completely, the two helices must be wound in opposite directions and the coefficients of inductive and capacitive coupling must be equal. Design formulae are evolved and a numerical example is cited. Attractive features which would be possessed by such a valve include high gain at low impedance, large bandwidth and the availability of a push-pull output derivable from a single-ended input. The bilateral property would make the tube useful as a repeater amplifier in a two-way communication link. However, considerable constructional difficulties are anticipated.