Edge Effects in Axial Arrays of Circular Rings

Abstract

A boundary value problem is solved for the current induced by any source, in particular for an incident plane wave, on any number of identical rings that are arranged to form an axisymmetric, linear array. The net aperture distribution along the finite array is approximated by a combination of three physically-identifiable components: a term from the related infinite array plus contributions from two independent edge-effect waves that originate from each of the two ends. However, if individually resonant loops are closer than a critical spacing, the entire structure exhibits a wild resonance and the simple approximation becomes invalid.

Eigenmodes and scattering by an axial array of tape rings

“…One motivation for the present paper is to corroborate and explain the numerical results in [1], where resonances are observed in axial arrays of closely-spaced loop antennas. The altogether different analysis of [1] is based on an integral equation for the current induced on circular rings, also of radius , and comprised of thin wires of radii . The thin-wire kernel is enlisted where the small skinniness parameter is .…”

“…Array fields and currents from plane wave, ring array, and isolated ring current sources have been studied. Typical results are included and discussed in Section VI, with particular emphasis on the existence or nonexistence of the surface-wave modes predicted by the method of Section V. Currents induced by a plane wave upon a thin tape grating agree with the currents on a ring array that are independently calculated [1].…”

“…1) are studied. These modes can also be excited by localized sources, and their existence explains the resonances that occur in axial arrays of closely-spaced loop antennas [1]. The tubes behave as ring elements in the limit as the tube length, or strip width labeled in Fig.…”

An Eigencurrent Approach for the Analysis of Finite Antenna Arrays

“…To compare the currents and obtained from the MoM and from the eigencurrent approach with coupled groups we introduce the relative difference defined by (15) where is the -norm. As shown in Fig.…”

“…In [4], [14], standing-wave behavior on finite arrays is studied by augmenting the infinite-array current by currents associated with waves propagating along the array surface and with waves reflected at the array ends. In general, the reflected waves are small, but they may become large for high-Q resonances [15]. As special cases of edge correction, we mention the approaches that consider an array as a periodic structure in a single direction [16] or as a periodic structure truncated to a half-infinite by infinite array [17], [18].…”