On the amplification factor of the triode

Abstract

The paper discusses why a triode has the property that any assigned anode current is a function of the anode potential plus a constant times the grid potential. Unlike the classic methods of approach, the paper sets out to find the values which these two voltages must have if and when an assigned anode current is flowing. It starts by reminding the reader that, if a given current is crossing the barrier of a diode, the electrons in that stream propel themselves by means of their own mutual repulsions and are not assisted by the attraction of the positive charge on the anode. The means by which the anode potential operates is through the positive charge which it causes to exist on the cathode, thereby regulating the proportion of the total cathode emission which crosses the barrier. Once this current is assigned, the electrons in it continue to gather kinetic energy until they are brought suddenly to rest by colliding with an anode interposed in their path. The potential of this anode is determined from the kinetic energy they have attained.If a negatively charged grid is interposed in the path of a given stream of current leaving a barrier, it is shown that this negative charge produces scarcely any electric force in the region between the barrier and the plane of the grid. Accordingly, this negatively charged grid will have scarcely any effect on the motion of the electrons approaching it: its presence will not, per se, tend appreciably to change the current which is crossing that barrier. However, once the electrons have passed through the meshes of the negative grid they will experience a strong repulsive force from it and will thereby be accelerated in their path. At any point in that path they will have attained additional kinetic energy from the work put into them by the negative charge on the grid: accordingly, the velocity with which they strike the anode is known and thus the potential which that anode must have is known. By means of the particle dynamics of their flight it is found that, for any assigned current, there is a linear relation between the anode voltage and the negative charge on the grid, placed there by means of a battery connected between the grid and the cathode.Although the charge on the grid produces a negligible electric force at points in the neighbourhood of the barrier, the force at the surface of the grid wires is large because the grid wires are very thin. Thus the work done from the barrier to the surface of a grid wire is finite, occurring mostly in the near vicinity of the grid wire: it is calculable, by familiar methods, per unit of charge on the grid. The net work from the barrier to a grid wire is the difference between the work against the grid charge and the work against the force caused by the electrons composing the anode current. This difference is the potential of the grid, i.e. the voltage of the grid battery required to maintain an assigned charge on the grid when there is an assigned anode current. This relation between grid charge and grid voltage can then be combined with the previously found linear relation between grid charge and anode voltage, for an assigned current, and from this emerges an expression for the amplification factor of the triode when it is passing an assigned anode current. It turns out to be independent of anode current and to have the value deduced long ago for a triode in which the anode current was vanishingly small, and previously thought to be valid only in this limiting condition. A proof that the amplification factor is independent of current—a fact well known by experiment—is believed to be novel.