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Expressions are derived for the smallest achievable radiation quality factor () of an electrically small antenna in front of a conducting plane. Applying the low-frequency approximation to the source region involving an electric or a magnetic point dipole plus their images behind the plane, an expression is formed for the field in the radiation zone. The contribution of nonpropagating energy in the near field is obtained explicitly using a spherical harmonics decomposition. The radiation is found to depend on the radius (relative to wavelength) of the smallest sphere that encloses the antenna and its image, the ratio of the vertical and horizontal dipole moments, as well as the positions of the dipoles relative to each other and to the plane. A number of simple wire structures are analysed with NEC (based on the Method of Moments), and the approximate obtained from their fractional bandwidth are compared to the corresponding theoretical minima.

The invention of an image system for a boundary value problem adds to a significant understanding of the structure of the problem, both at the mathematical and at the physical level. In this paper, the interior and exterior Neumann functions for the Laplacian in the cases of spherical and ellipsoidal domains are represented in terms of images. Besides isolated images, the presence of the normal derivative in the Neumann condition demands an additional continuous distribution of images, which in the spherical cases, can be restricted to a one-dimensional manifold, whereas for the ellipsoid, both a one-dimensional and a two-dimensional distribution of images is needed.

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