Axially symmetric source field penetration through a circular aperture in a thin impedance plate

The field penetration through a circular aperture in an infinite plane with a nonzero surface impedance excited by an axially symmetric source is analytically investigated. The problem is formulated in terms of an original dual integral-equation approach and solved through the Method of Moments in the Hankel spectral domain. The proposed formulation is applied to the calculation of the axial magnetic field when the source is a current loop of finite radius coaxial with the aperture and it is shown that it is possible to separate the contributions of the aperture and of the non-zero impedance plate to the transmitted field. In the case of low frequencies and small apertures, closed-form expressions are also derived. Moreover, the approach is also applied to the case of a perfectly conducting plane giving rise to results which coincide with those recently presented in the literature. Finally, the accuracy of the proposed approach is validated through full-wave calculations.