Equivalent Transmission Line Models for the Analysis of Edge Effects in Finite Connected and Tightly Coupled Arrays

Abstract

Abstract-In this paper we present an analysis of the edge effects in wideband connected arrays of slots and dipoles. Due to the strong mutual coupling between the elements, these arrays can support the propagation of guided waves along their surface. Such waves arise from the edges of the finite array and can be especially detrimental for the performance, since they can travel within the array without geometrical spreading. In this work we introduce Green's function based equivalent transmission line models to describe the propagation of the guided waves. The elements' active impedances are represented as periodic loads on these transmission lines. The equivalent models can be used as a simple and convenient tool to control and minimize the edge effects. Finite array simulations of relevant array structures are discussed. The evidence is that the active impedance and the inter-element capacitance can be tuned to attenuate and reflect the edge-born waves.

Equivalent Circuit Models of Finite Slot Antennas

“…The x-oriented slot is assumed to be electrically narrow and excited by a feeding gap, which is small in terms of the wavelength (δ-gap excitation). First, an infinite slot is considered as in [12], where it was shown that the voltage along the slot is represented accurately by:…”

“…However, introducing losses in the ground plane [12], [15] or a thin dielectric substrate, the pole singularity moves away from the branch point in the complex k x -plane, so that the polar contribution can be isolated. The location of the pole, k xp , can be found using a local-search algorithm (e.g.…”

“…The turn ratios of the two transformers are equal to n δ = F δ (−k xp ) and n g = F g (−k xp ). The characteristic impedance of the transmission line is [12]:…”

“…An additional advantage of the proposed method is that the characteristic impedance of the transmission line is derived by extracting the polar singularity contribution of the spectral domain Green's function as in [12], [13], thus can be generalized to arbitrary stratified media, as long as the polar and the branch singularity do not coincide.…”

Connected-Slot Array With Artificial Dielectrics: A 6 to 15 GHz Dual-Pol Wide-Scan Prototype

“…In connected arrays, it is especially important to assess the finite edge effects [25], [26]. To demonstrate the effect of the finiteness, we simulate infinite-by-finite arrays using the semi-analytical tool presented in [16].…”