Time-Domain Study of Arbitrary Dipole in Planar Geometry with Discontinuity in Permittivity and Permeability

摘要

Transient fields arising from a general impulsive dipole above ground characterized by permittivity and permeability are studied. A detailed analysis for an electric dipole excitation is given and the analog problem of a magnetic source can be solved by applying the duality transform. The mathematical description of this problem is made using Hertz vector, which is solved in terms of definite integrals. From this solution, the actual fields are obtained through simple differentiations. In two important special cases, these integrals defining the Hertz vector can be given in closed forms. This happens if the observation point is located on the same normal as the source dipole or if these both are located at the interface. Hence, certain electromagnetic field components have also an exact solution in terms of elementary functions.