Loop Antennas With Uniform Current in Close Proximity to the Earth: Canonical Solution to the Surface-to-Surface Propagation Problem

Abstract

Abstract-In a recent study, the classical problem of a large circular loop antenna carrying uniform current and situated at the Earth's surface has been revisited, with the scope to derive a totally analytical explicit expression for the radial distribution of the generated magnetic field. Yet, the solution arising from the study exhibits two major drawbacks. First, it describes the vertical magnetic field component only. Second, it is a valid subject to the quasi-static field assumption, which limits its applicability to the low-frequency range. The purpose of the present work is to provide the exact canonical solution to the problem, describing all the generated electromagnetic field components and valid in both the quasi-static and non-quasi-static frequency regions. These two features constitute an improvement with respect to the preceding solution. The canonical solution, which is obtained by reducing the field integrals to combinations of known Sommerfeld integrals, is seen to be also advantageous over the previous numerical and analytical-numerical approaches, since its usage takes negligible computation time. Numerical simulations are performed to show the accuracy of the obtained field expressions and to investigate the behavior of the above surface ground-and lateral-wave contributions to the fields in a wide frequency range. It is shown that in the near-zone the two waves do not predominate over each other, while the effect of the lateral wave becomes negligible only when the source-receiver distance is far greater than the skin depth in the Earth.

Exact Expressions for the Near Field of a Thin Uniform Circular Loop Current with Application to Loops Lying on a Half Space

“…Equation ( 79) is identified as the equivalent power series for the closed form of B T 0z (0) given in [27], Equation (51), simplified for the case of ρ = 0,…”

“…Most approaches assume a uniform loop current but may either ignore displacement current, require a simplification of integral expressions or application of numerical methods. Recently however, exact expressions for a thin uniform loop current on a non-magnetic half space employing spherical functions have been published [27,28]. On the other hand, the exact solution of this configuration presented in this paper is based on elliptic integrals.…”

“…In addition, an exact series representation is derived for fields at the interface of two half spaces generated by a thin uniform loop current sitting on the half space interface. This specific loop configuration has been the subject of many investigations due to its importance for geoprospecting or surface wave propagation [22][23][24][25][26][27][28][29], metal detection [30,31] and non-destructive analysis of materials [32]. Most approaches assume a uniform loop current but may either ignore displacement current, require a simplification of integral expressions or application of numerical methods.…”

“…The expressions allow the rapid computation of the self-impedance of a loop on a half space, as well as the mutual impedance of closely spaced loops that may form part of a larger coaxial array. Computational results are compared to the expressions employing spherical functions [27,28].…”

Far-fields Radiated of a Small Circular Loop Antenna Utilized in Remote Probing of the Earth

“…Lately, Long et al [13] developed Chew technique and with the help of the complex image theory [14], he derived expression of the SI rapidly for the far-field depending on the stationary phase-point. Recently, many researchers such as Parise et al [15] studied the problem of a large circular loop antenna carrying uniform current and situated at the Earth's surface. They obtained a procedure that allows to derive the exact canonical solution to the problem.…”