Comments on “Exact Field Expressions for Circular Loop Antennas Using Spherical Functions Expansion”

Abstract

In a recent paper published in [1], Hamed has over-claimed his contribution (if any), and at the same time criticized the contribution by, and merit of, two of our papers published in [2], [3]. Herewith, we would like to address some critical issues inside the paper in [1]. ContributionsThe major idea and the starting formulation in [1] follow exactly the standard procedure in textbooks, e.g., the book by Balanis [4]. Later on, Hamed used the following scalar Green's function [5, p. 209, Eq. (10.49)] (1)in his formulations, the same as their equations in [1, Eqs. (8)-(10)]. In fact, the scalar Green's function [5] and the dyadic Green's function [6] represent precisely the same thing, but expressed in scalar form and bi-vector (or matrix) form, respectively. They are related by (3) where denotes the wave number, and identifies the identity matrix.The vector form of the radiated electromagnetic fields expressed in [2] is very general, compact, simple, and straightforward. As commented by Werner [7], [8], "the real beauty of the technique introduced in [2] lies primarily in the straightforwardness of its application." We have compared in detail (in fact, term by term) the derived electric and magnetic field component expressions in [1,] with those in [2, Eqs. (11) and (12)]. The two sets of solutions are completely identical, except for the different time dependence factors assumed (i.e., ones conjugate is the other) and the different spherical harmonic mode indexes exchanged (i.e., is changed into ). Please note that the solutions provided in [2, Eqs. (8) and (9)] are the most general form valid for any kind of current distributions, while those of [1, Eqs. (22)-(24)] or those of [2, Eqs. (11) and (12)] are already reduced forms simplified for the current distributions expressed in terms of the Fourier series in [2, Eq. (10) ]. The subsequent procedure and also approximations assumed in [1] did not also differ much from those in [2]; although the expressions look different, they are actually identical. With the above points in mind, it is difficult to see the new contribution in [1]. In addition, with these straightforward and general approaches, the work in [2] was extended much further, as seen from those publications [9]-[13]. Misstatements and MisconceptionsThere are a number of misstatements and misconceptions. We have no obligation to trace out all of them. As examples, we would like to list some of the important ones below.• In Section-I, Introduction, Hamed considers that the manipulations in [1] are more straightforward and easier than those in [2], which is not convincible. In fact, the manipulations in [2] require only vector calculus which was taught in university undergraduate year-2 maths. There is nothing more than this. Also, it is much more compact and simpler to use vector form instead of the scalar form to represent electric and magnetic field components. Finally, the relationship between the manipulations in [2] and [1] was governed by, and only by, (3). Therefore, there is no difference th...

Electromagnetic Fields Radiated by a Circular Loop With Arbitrary Current

“…Note that (4) and (5) are defined for an infinitesimal current element located at r ′ . In what follows, we compute G for an element located at (r ′ , θ ′ , φ ′ ), then derive the corresponding G for the current loop via (6).…”