Abstract :
This paper calculates the field, inside a rectangular wave guide, produced by a given set of currents at the origin. In particular, if the guide is excited by a single current filament on its mid-line then the field is found per unit current in this filament and also the radiation resistance of the filament. The solution is generalized to apply to a guide with a closed end. In Appendix 8.2 is calculated the field per unit current when the wave guide is very narrow, being then commonly called an attenuator. The solution for the guide is more complete than those which are common knowledge, in so far as the field is related to the current producing it, and this extension may be novel. In order to assess the sensitiveness of the classic solution to the exact form of the guide, the solution is found for a guide which has a vanishingly small taper. Then it is found that perfect cut-off cannot occur even when the width of the guide at the exciting filament is less than ??: the explanation is that in such a guide of infinite length there is often a point at which the width exceeds ??. It seems probable from this that complete cut-off will not occur if the generator is situated in a length of guide whose width is less than ??, provided this length is joined to a guide whose width exceeds ??. However, it appears that the expression for the radiation resistance of a current sheet, with sinusoidal loading, is general and applies to a guide having any taper, and in particular when the taper is zero and the sides have become parallel. It is concluded from this that the expressions for radiation resistance are very tolerant to small imperfections in the shape of the guide, and, in general, that the well-known and classic solution is very reliable for practical application, provided only that the cut-off property is not interpreted with complete rigour. For the sake of completeness the formal solution is recorded for a current filament at any point in a tapered guide which has a co- nvex back of any radius; and also the solution for a current enclosed in a box having two sides which are arcs of concentric circles of any radius and two sides which are any radii of these circles. These two solutions are thought to be novel.
