Fields produced at any distance by a Hertzian dipole – generalizations – approximations

Abstract

ABSTRACTThe exact integral expressions for the azimuthal magnetic field, Hφ (r/h,θ), and the polar electric field, Eθ (r/h, θ), produced at any polar‐angle, θ, and at any distance, r, from the center of a Hertzian dipole of height h were recently derived‐reported in this journal (Knop, Microwave Opt Technol Lett 54 (2012), 1970–1975). Numerical computations‐plots of these fields as a function of the polar angle θ with the distance parameter of r/h were there given for the case of a dipole of h/λ = 0.10, where λ is the free space operating wavelength. These computations‐plots are here extended to the cases of h/λ = 0.05 and 0.01. Computations and plots of these fields as a function of r/h with θ as a parameter are also given. Critical comparisons to the h/λ = 0.10 case are then made and generalizations formed for the fields' behavior as h/λ decreases. Approximate closed‐form equations/formulas for the fields are also presented. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2726–2734, 2013