Analysis of Radiation Field Excited by a Vertical Electric Dipole in a Four-Layered Region

Abstract

Electric dipoles are the fundamental components of a planar multi-layered circuit. Present work focuses on the theoretical investigations of radiation field due to a vertical electric dipole in a four-layered region composed of a perfect conductor covered with two dielectrics and the air above. Locating a vertical electric dipole (VED) on or near the air-dielectric boundary, approximate formulas are obtained. The resultant analytical formulas have the merit of offering unique insights about the characteristics of the radiation field including direct waves, reflect waves, lateral waves, and trapped surface waves. The amplitude of the field along the boundary exhibits the dependence of ρ −1/2 , which is an intrinsic characteristic of trapped surface waves, where ρ is the propagation distance. In addition, the radiation field is further examined for propagation distance and propagation characteristics of the interference phenomenon. Furthermore, when the observation angle Θ ≥ 88 • , the lateral wave still exists; however, the trapped surface wave is a major component of the total field. The proposed formulas have potential to develop planar four-layered circuit structures.