Fields produced at any distance by a hertzian dipole

Abstract

AbstractExact integral expressions for the electromagnetic fields produced at “any distance,” r, from the center of a Hertzian dipole of height h are derived in this study (it is believed for the first time) by correct‐analytical integration of its infinitesimal fields.Numerical integration of these expressions gives the amplitude and phase as a function of the polar angle, θ, with the normalized distance, r/h, as a parameter for 0.05 ≤ r/h ≤ 5, of both the azimuthal magnetic field, Hφ (r/h,θ), and the polar electric field, Eθ(r/h,θ), for a dipole of h/λ = 0.10, where λ is the free‐space operating wavelength. Plots of these results then reveal, in detail, the interesting rapid‐transitional behavior of these fields for points in the sphere bounded by the dipole (r/h < 0.50) to those outside of it (r/h > 0.50). The latter outer fields approach a sinθ behavior only as r/h approaches 5.0. Generalizations for any h/λ ≤ 0.10 are discussed. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:1970–1975, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26934