Boundary-value problems associated with source-excited planar-equiangular-spiral antennas

Several boundary-value problems associated with the planar-spiral geometry are considered. A source-excited-sheath problem is formulated exactly, and a formal solution in terms of Hankel´s inverse transform is presented. The approximate form of the current density on the sheath structure is obtained. A push-pull-excited 2-arm thin-wire antenna is discussed next. It is found that the approximate current-density solution is closely related to that of the corresponding sheath version. The approximate form of the current density is found to exhibit a slow-wave character along the radial dimension. Some far-field patterns are computed by the vector-potential method. The results of the current densities and the radiation patterns are found to be in favourable agreement with the experimental results. A short discussion on the solution of a multiarm antenna is also given. The approximate current density and the far-field patterns are also computed for a 4-arm antenna. Some general conclusions are presented.