Resonance of input impedance of bow-tie antenna placed on ground surface

In the paper we have derived the following equation 4 f 0 L equi = c/ sqrt(e equi ) where f 0 is the resonant frequency of the antenna input impedance, c is the speed of light, L equi and e equi are respectively the equivalent length of antenna and the equivalent dielectric constant of the medium formed by half-space ground and half-space air. When measuring in air, the dielectric constant is known. One can obtain the antenna equivalent length from the measured f 0, by using the above equation. When L equi is obtained, one then can calculate e equi from a measured f 0 for the case when placing antenna on material interface. One can further estimate the ground dielectric constant by using the equation: e equi = (e iar + e ground )/2. Bow-tie antennas with different flange angles are constructed for experiments, in order to discuss the application of the above equation. The lengths of those antennas are all 30cm (length of the antenna conductor: 15cm). But the flange angles of the antenna conductors are respectively: 15, 40, 60, 75, 90 degrees. The antenna input reflections are measured over the frequency band up to 500 MHz, for cases when the antennas are placed in air and on sand, stone and water surfaces.