Revisiting the Fraunhofer and Fresnel Boundaries for Phased Array Antennas

• DOI: 10.48550/arxiv.2411.02417
• Publication Date: 2024-10-21
• Authors: Mehdi Monemi; Mehdi Rasti; Matti Latva‐aho
• Keywords: Fresnel zone antenna; Fresnel number; Fresnel zone

This paper presents the characterization of near-field propagation regions for phased array antennas, with a particular focus on boundaries defined by Fraunhofer and Fresnel distances. These distances, which serve as critical understanding signal behavior, have been extensively studied characterized in literature single-element antennas. However, direct application these results to arrays, common practice field, is argued be invalid non-exact. work calls deeper accurately characterize such around More specifically, antenna, distance $d^{\mathrm{F}}=2D^2 \sin^2(\theta)/\lambda$ where $D$ represents largest dimension $\lambda$ wavelength $\theta$ denotes observation angle. We show that $d^{\mathrm{F}}$ experiences fourfold increase (i.e., $d^{\mathrm{F}}=8D^2 \sin^2(\theta)/\lambda$) provided $|\theta-\frac{\pi}{2}|>\theta^F$ (which holds most practical scenarios), $\theta^F$ small angle whose value depends number elements, case $|\theta-\frac{\pi}{2}|\leq\theta^F$, we $d^{\mathrm{F}}\in[2D^2/\lambda,8D^2\cos^2(\theta^F)/\lambda]$, precise obtained according some square polynomial function $\widetilde{F}(\theta)$. Besides, also prove antennas given $d^{\mathrm{N}}=1.75 \sqrt{{D^3}/{\lambda}}$ $\sqrt{8}$ times greater than corresponding conventional antenna same dimension.