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A detailed characterization of the input impedance of ultrawide-band (UWB) dielectric horn antennas is presented using the finite-difference time-domain (FDTD) technique. The FDTD model is first validated by computing the characteristic impedance of two conical plate transmission lines (including planar bow-tie antennas) and comparing the results to analytical solutions. The FDTD model is next used to calculate the surge impedance of dielectric horn antennas using the conical plates as launchers. Design curves of the surge impedance for different choices of geometries and dielectric loadings are provided. The modeled antennas are particularly attractive for applications such as UWB ground penetrating radars (GPR) applications.