Bow-tie antennas on a dielectric half-space: Theory and experiment

A new formulation is discussed for the rigorous calculation of the radiation pattern of a bow-tie antenna of finite length and infinitesimal thickness, placed on a lossless dielectric substrate. The analysis is based on a representation of the current density on the metal surface of the antenna as a sum of an imposed (quasistatic) term and a set of current modes with unknown amplitudes. Free-space fields that are expressed in terms of continuous spectra of symmetrized plane waves are matched to the current modes using the method of moments. The resulting set of equations are solved for the unknown current amplitudes. The calculations show that for increasing bow length the antenna impedance spirals rapidly to a value predicted by transmission line theory. The theory also shows that the -plane pattern of a two wavelength, bow-tie antenna is dominated by low-loss current modes propagating at the dielectric wavenumber. As the bow tie narrows, the loss of the modes increases, and the dominant wavenumber tends to the quasistatic value. Pattern measurements made at 94 GHz are shown to agree well with theoretical predictions. Measurements for a long-wire antenna, a linear array of bow-tie elements, and a log-periodic antenna are also presented.