An Asymptotic Approach for the Scan Impedance in Infinite Phased Arrays of Dipoles

Abstract

This work presents an analytic model to derive the scan impedance of planar infinite phased arrays of dipoles at a dielectric interface when only the (0, 0) Floquet mode propagates. The proposed model builds on the boundary conditions met by the fundamental Floquet mode at the interface to provide a novel derivation of the equivalent circuit for the scan impedance. The analysis is also extended to include the effect of a sufficiently thick grounded substrate that does not affect the elements’ current distribution and does not interact with the evanescent fields. Next, formulas for the ratio of intensity radiated toward each half-space for an interfacial array are provided. In a consecutive step, an asymptotic approximation is derived for the current distribution in arrays of arbitrary loaded dipoles, and the reactance of a dipole in the array environment is related to the inductance of a grid of wires. This model constitutes a useful tool to clearly identify the role of the different array variables (dipole dimensions, relative permittivity of the substrate, periodicity, end load, and scan angle in the principal planes) on the scan impedance by simple expressions and equivalent circuits. The model predictions are in good agreement with full-wave simulations and with previously published works.