A homogeneous ring array of axial dipoles will radiate a vertically polarized field that concentrates to an increasing degree around the horizontal plane with increasing increment of the current phase per revolution. There is reason to believe that by using a corresponding antenna system with tangential or radial dipoles, a field may be obtained that has a similar useful structure as the above-mentioned ring array, but which in contrast to the latter is essentially horizontally polarized. In this paper a systematic investigation has been made of the field from such an antenna system with tangential or radial dipoles. Recently it was stated in the literature that it is impossible to treat the general case where the increase of the current phase per revolution is arbitrarily large by using ordinary functions. The results obtained in this paper disprove this statement. A similar investigation has been made of the field from the antenna system with tangential dipoles described above in the case where the current distribution on this system is a standing wave instead of a progressing wave. When the increment of the current phase per revolution converges towards infinity, the gain of the antenna systems treated here converges towards infinity, too, i.e. supergain occurs. Based on the theory of supergain an approximate expression has been derived for the minimum value of the radius of the antenna system, which it is possible to use in practice.