Input resistances of horizontal electric and vertical magnetic dipoles over a homogeneous ground

Abstract
Expressions for the total power flow from a vertical oscillating magnetic dipole and a horizontal electric dipole are employed to determine the input resistances of both types of antennas placed above a homogeneous and isotropic ground. Theoretical curves of the input resistance are drawn for the two cases as a function of the normalized height of the antenna above the ground for fixed values of the permittivity and the ratio of conduction and displacement currents. The input resistance is affected appreciably when the conductivity is altered only by a factor of ten. The curves show marked changes with change in permittivity when the displacement current is not negligible compared to the conduction current. The ratio of the height of the antenna above the ground to the radiated wavelength should be kept smaller than 0.3 to obtain any appreciable variation of the input resistance with changes in either the conductivity or the permittivity. Factors determining a judicious choice of the height and the wavelength are discussed. A comparison between a horizontal electric dipole and a vertical magnetic dipole is made, so far as their input resistances are concerned.