Edge-Born Waves in Connected Arrays: A Finite$\,\times\,$Infinite Analytical Representation

Connected arrays constitute one of the most promising options for wideband phased arrays. Like most phased arrays, they are designed using infinite array theory. However, when finiteness is included, edge effects perturb their behavior. These effects are more severe when the arrays are designed to operate over very broad frequency ranges, since the mutual coupling between the elements facilitates the propagation of edge-born waves that can become dominant over large portions of the arrays. Finite array simulations, which would predict these behaviors, are computationally unwieldy. In this paper we present a Green's function based procedure to assess edge effects in finite connected arrays. First the electric current distribution on the array is rigorously derived. Later on, the introduction of a few simplifying assumptions allows the derivation of an analytical approximation for the current distribution. This latter provides meaningful insights in the induced dominant edge-wave mechanism. The efficiency of connected arrays as a function of their dimension in terms of the wavelength and of the loading feed impedances is investigated.