The receive voltage transmission function of a phased array antenna element

Abstract

A general method has been developed for determining the voltage response of a phased array element to an incoming electric field. The incident field may arrive from any scan angle, and mutual coupling effects are accounted for in terms of the array element active reflection coefficient. The method defines a receive voltage transmission function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{T}(\theta, \phi, f)</tex> as a term whose product with the incident electric field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{i}</tex> ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\theta, \phi, f</tex> ) results in the array element voltage response. The derivation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{T}(\theta, \phi, f)</tex> is obtained by treating each phased array antenna element as a receiving aperture, having an active impedance related to the mutual coupling in the array. The element effective length is formulated using an array element receive equivalent circuit, and the transmission function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{T}(\theta, \phi, f)</tex> is obtained using this effective length formulation. The usefulness of the transmission function for studying the response of a phased array element to particular radar signal waveforms is suggested, and an experimental evaluation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{T}(\theta \phi, f)</tex> is described using mutual coupling measurements on a 37-element crossed dipole test array.