We thank Dr. Skobelev for bringing [1]—and its English translation [2]—to our attention. We were not previously aware of these interesting and noteworthy papers, which seem to be the first to use what we, in [3] and [4], call the “effective current.” Despite this similarity, the overall purpose of our [3] and [4], as well as that of the related works [5] and [6], is quite different from that of [1] and [2]. References [3]–[6] use the effective current in order to overcome difficulties specifically associated with unsolvability (rather than with matrix ill-conditioning, or other shortcomings of computer hardware or software). The most notable such difficulty is the appearance of unphysical oscillations in both the real and the imaginary parts of the current obtained via the approximate kernel; the effective current is shown to present no such oscillations. We also show that the effective current is not exactly the same as the exact current, by which we mean the current of a tubular antenna obtained via the exact kernel. We study similarities and differences between the exact and effective currents analytically for the antenna of infinite length, and apply the understanding thus obtained to the realistic case of the finite antenna. For the infinite-length antenna, perhaps the two most striking differences are: (i) The effective current equals the current on the outer surface of the antenna [4] (on the other hand, it is well-known that the exact current equals the total () current). (ii) A difference of a factor of ½ near the driving point; this difference concerns the imaginary part of the current in the delta-function generator case [5], and the imaginary part of the derivative of the current, or the charge per unit length, in the case of the finite-gap generator [3]. Still for the infinite antenna, an important similarity [3], [5] is that the real parts of the exact and effective currents are (exactly) equal. Such results have no counterparts in [1] and [2].
Abstract:
In papers [1], [2], the authors extend the so-called effective current method to the Hallen's and Pocklington's equations with the finite-gap generator (FGG). The indicat...Show MoreMetadata
Abstract:
In papers [1], [2], the authors extend the so-called effective current method to the Hallen's and Pocklington's equations with the finite-gap generator (FGG). The indicated method considered earlier in [3] with a reference to [4] is associated with application of the method of auxiliary sources to the analysis of cylindrical dipole antennas [5]-[7]. The purpose of these comments is to draw the authors' and readers' attention to the existence ofpaper [8] where the Pocklington's equation with the FGG is solved for the axial current considered there to be auxiliary. The equation is solved by the Galerkin method using the piecewise sinusoidal basis and testing functions. The auxiliary axial current is used further for calculation of the surface current (which is referred to as the effective current in [1]-[4]), and the surface current itself is used for calculation of the input impedance. So, in some respects papers [1]-[7] just repeat the main idea and technique of paper [8], although of course papers [1]-[7] also contain a lot of their own new, interesting, and useful analytical and numerical results.
Published in: IEEE Transactions on Antennas and Propagation ( Volume: 62, Issue: 4, April 2014)