This report begins with a review of reduced size ultra-wideband (UWB) antennas and the peculiar problems that arise when building a UWB antenna. It then gives a description of a new type of UWB antenna that resolves these problems. This antenna, dubbed the hemispheric conical antenna, is similar to a conventional conical antenna in that it uses the same inverted conical conductor over a ground plane, but it also uses a hemispheric dielectric fill in between the conductive cone and the ground plane. The dielectric material creates a fundamentally new antenna which is reduced in size and much more rugged than a standard UWB conical antenna. The creation of finite-difference time domain (FDTD) software tools in spherical coordinates, as described in SAND2004-6577, enabled this technological advance.