Coupling Holes Between Resonant Cavities or Wave-Guides Evaluated in Terms of Volume Ratios

A hole in a common wall is used to provide coupling between two resonant cavities (k=coefficient of coupling) or between two waveguides (x or b=normalized reactance or susceptance) or between cavity and waveguide (p=loading power factor of cavity). Referring to either side of a thin common wall, the field intensity in the center of a small hole is 1/2 what it would have been at that location on the wall. Between two equal regions, the coupling (k, x or b) by magnetic or electric field is expressed as 1/4 the ratio of the effective volume of the hole over the effective volume of each region, by duality (Booker´s principle), the effective volume (related to the polarizability) of an aperture in a thin wall is identified with that of an analogous thin body in a uniform field. For a resonant cavity loaded by coupling to a waveguide, the loading power factor is p=kx; this theorem is proved by reference to an equivalent network. Various cases of coupling by two-dimensional and three-dimensional fields are formulated in terms of area or volume ratios, especially between pillbox resonators (rectangular, circular, or coaxial-circular) and between rectangular waveguides with common side walls or top and bottom walls. The effective area or volume of a small hole in a thin conducting wall is given for various symmetrical shapes, in a magnetic or electric field.