Asymptotic Study of the Radiation Operator for the Strip Current in Near Zone

Abstract

In this paper, we address the problem of how to efficiently sample the radiated field in the framework of near-field measurement techniques. In particular, the aim of the article is to find a sampling strategy for which the discretized model exhibits the same singular values of the continuous problem. The study is done with reference to a strip current whose radiated electric field is observed in the near zone over a bounded line parallel to the source. Differently from far zone configurations, the kernel of the related eigenvalue problem is not of convolution type, and not band-limited. Hence, the sampling-theory approach cannot be directly applied to establish how to efficiently collect the data. In order to surmount this drawback, we first use an asymptotic approach to explicit the kernel of the eigenvalue problem. After, by exploiting a warping technique, we recast the original eigenvalue problem in a new one. The latter, if the observation domain is not too large, involves a convolution operator with a band-limited kernel. Hence, in this case the sampling-theory approach can be applied, and the optimal locations of the sampling points can be found. Differently, if the observation domain is very extended, the kernel of the new eigenvalue problem is still not convolution. In this last case, in order to establish how to discretize the continuous model, we perform a numerical analysis.

NDF of the near-zone field on a line perpendicular to the source

“…The described configuration is shown in fig. 19 and it can be completely understood by linking the result provided here and those shown in [34].…”

NDF of the Near-Zone Field on a Line Perpendicular to the Source

“…Note that when x o = 0, the sinc kernel expressed by (38) approximates well the actual kernel of T T † w . The only difference between the two diagrams concerns the value of the two kernels along the lines given by the equation…”

“…In Figs. 10, 11 and 12 the kernel of T T † , T T † w , and the sinc kernel (38) are sketched in dB and normalized with respect to its own maximum.…”

NDF of the near-field of a strip source in orthogonal directions

“…It is worth noting that this study, and that developed in [34] represent the mathematical basis for addressing configurations where the observation domain is a generic curve. The latter are very interesting in applications since a generic curve of observation may represent the trajectory followed by an UAV-based system for in-situ evaluation of radiating systems [35]- [39].…”

“…The latter are very interesting in applications since a generic curve of observation may represent the trajectory followed by an UAV-based system for in-situ evaluation of radiating systems [35]- [39]. More in detail, the analysis made in [34] is suitable to study the case where the observation domain is a smooth curve slowly varying (in such case no stationary points appear in the kernel of the integral equation involved in the computation of the singular values). Instead, the analysis that we develop in this article allows to study configurations where the observation domain is a smooth curve rapidly varying (in such case a stationary point appears in the kernel of the integral equation for the computation of the singular values).…”