The coupling problem between two half spaces that are connected by a section of a circular waveguide with a small aperture on both ends is solved by using an equivalent network representation. The conditions for aperture-cavity resonances and the maximum field in the waveguide are determined. It is shown that, for certain combinations of aperture sizes, the maximum field is quite sensitive to the effective dielectric constant of the last half space. This phenomenon may be used to measure plasma density. The effects of off-centered apertures are studied by the introduction of a reduction coefficient.