Amplification Factor of Triodes with ElliptiG: Grids Having Support Rods

A capacitance equivalence method to determine the amplification factor of 'triodes with irregular geometry was proposed by O'Neill. This ,method I does not intrinsically take into its purview the presence of support rods of appreciable radius. In a previous communication, the author derived the :equicapacitance structure for elliptic grids using a method based on O'Neill's principle. In this paper the analysis given' there at is supplemented V\hth a cr'iteria for obtaining an equivalent radius for the support rods, which J;ould produce nearly the same screening fraction, if the position of these ro~s is reckoned at the circumference of the equivalent circular grid. The amplification factor formula is consequential. INTRODUCTION T H, E field analysis of vacuum tube triodes ~ving elliptic grids and circuI~r cathode have been reported1,3. Two of the methods currently available are O'Neill's approximation with the limiting geometry as the parallel planes1 and a approximation due to the author having a cylindrical limiting configuration3, the libit being decided by the applicability of the formula with maximum accuracy. But Both these formulae do not take into consideration intrinsically the presence of support rods. Thus, their application is limited to structures wherein the effect of suppor1 rods can be neglected or structures wherein the support rods are not in the active r gion, e.g. sub-miniature tubes with a cantilever construction and tripod mounting, But in many of the conventional tubes the support rod effect figures prominentl~ and the determination of the amplification factor of triodes necessitates the field aralysis of triodes having support rod radius comparable to the dimensions of the grid. Several manufacturing concerns make use of sectionalization approximations but ~khese are necessarily laborious and are ideally suited for a final design. But, the p eliminary trial and error design requires more direct methods which are in the nature of formulae whose dimensions are not specified numerically. One such method which can oe utilized conveniently for preliminary designs is O'Neill's equivalence capacitance I method. This paper gives a criteria for calculating the screening fraction due to the support rods, when these are physically related to the equi-capacitance cylindrical grlid. PREVIOUS WORK 1 O'Neill, has shown,2, to a first approximation, that the space-charge saturated currents in relation to the tube structure will be the same in any two tube for s wherein the electrostatic capacitance between the cathode and the plate per unit length is 171