Expressions are derived for the smallest achievable radiation quality factor (Q) 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 non-propagating energy in the near field is obtained explicitly using a spherical harmonics decomposition. The radiation Q 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 Q obtained from their fractional bandwidth are compared to the corresponding theoretical minima.
Sten, J., Hujanen, A., & Koivisto, P. (2001). Quality factor of an electrically small antenna radiating close to a conducting plane. IEEE Transactions on Antennas and Propagation, 49(5), 829-837. https://doi.org/10.1109/8.929637