Further investigations of fundamental directivity limitations of small antennas with and without ground planes

In this paper, we have presented a heuristic formula for the maximum achievable directivity of single-port antennas of any size. The formula is well rooted in electromagnetic theory in the low and high frequency ends. It has been tested by comparison with reported theoretical directivities of some practically realized antennas in the intermediate frequency range where the diameter of the smallest enclosing sphere is between 0.1lambda and 4lambda, and it seems to work as a practical limitation.