Estimation of far-field distances for antennas close to ground and implications for simple gain measurement methods

The widely quoted far-field distance of 2D²/λ for simple gain measurements is shown to be inappropriate for antennas that are operated in the vicinity of a ground plane, as well as for simple dipole antennas in free space. A more general expression for these systems has been derived from consideration of a pair of point sources, from which the 2D²/λ result can also be derived as a limiting case. It is also shown that the commonly used phase error criterion of π/8 radians is too large to ensure acceptable accuracy in simple gain measurements for dipole antennas, both in free space and above a ground plane.