A uniform asymptotic evaluation of the field radiated from collinear array antennas

Abstract

A uniform asymptotic representation of the electromagnetic field radiated from arbitrary collinear array antennas is presented. The asymptotic field is obtained applying the saddle-point technique to the radiation integrals after expressing the current excited along the array axis by means of a Fourier spectral representation. The resulting electromagnetic field is expressed in terms of propagating and evanescent truncated Floquet waves (FWs). The leading asymptotic term of the FWs exhibits an optical behavior and is responsible for the slow decay of the array near-field, which can be described as cylindrical in character. The transition toward the spherical wave propagation regime is due to the interference of the cylindrical field with the relevant scattered field from the array truncations, while the reactive energy storage is due to the evanescent FWs, as well as to the progressive inductive and progressive electrostatic FWs excited close the antenna axis. Using the asymptotic field representation, prediction formulas for the spatial locations where the array near-field exhibits peak deviation from the cylindrical decay, and where the transition from cylindrical to spherical wave propagation regime takes place, have been derived. The proposed analytical technique can be adopted to analyze the spatial field distributions and the radiation mechanisms of periodic and nonperiodic linear arrays.