Abstract
Dipole antennas over the boundary between two different media have been widely used in the fields of geophysics exploration, oceanography, and submerged communication. In this paper, an analytical method is proposed to analyse the near-zone field at the extremely low frequency (ELF)/super low frequency (SLF) range due to a vertical magnetic dipole (VMD). For the lack of feasible analytical techniques to derive the components exactly, two reasonable assumptions are introduced depending on the quasi-static definition and the equivalent infinitesimal theory. Final expressions of the electromagnetic field components are in terms of exponential functions. By comparisons with direct numerical solutions and exact results in a special case, the correctness and effectiveness of the proposed quasi-static approximation are demonstrated. Simulations show that the smallest validity limit always occurs for component H2z, and the value of k2ρ should be no greater than 0.6 in order to keep a good consistency.
Highlights
International Journal of Antennas and Propagation theoretical work like [22] was well summarized, and all field components for these four different types of dipoles located on the boundary were presented over the quasistatic range
In 2010, Parise [27] established the exact closed-form expressions of the electromagnetic field components excited by a vertical magnetic dipole lying on the surface of a flat and homogeneous lossy half-space, but Hρ is still in terms of Bessel functions, and these formulas are valid only when both of the dipole source and the observation point are embedded on the boundary
Integral Expressions for the Field Excited by an extremely low frequency (ELF)/super low frequency (SLF) vertical magnetic dipole (VMD)
Summary
For the beginning of simplification, we should figure out the definition of “quasistatic” or “near-field” involved in this paper It is defined as the situation where the distance from the source to the observation point is far less than a wavelength (kρ ≪ 1) [15, 18]. If the frequency remains invariable, distances satisfying this condition contain the “near-field”; otherwise, if the distance is fixed, qualified frequencies form the “quasi-static” state It is readily understood from the definition, when the “quasi-static” assumption is considered, ω ⟶ 0 and k2ρ ≪ 1 hold. We have derived the analytical expressions when z d 0 To understand this method better, computations and discussions under several different conditions will be carried out
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