Application of Wait's Formulation to Connected Array Antennas

Wait's formulation on plane-wave scattering from wire grids is adapted, for the first time, to the electromagnetic analysis of lumped-element periodically loaded vertical wire-grid connected array antennas. Starting from this formulation, a novel analytical expression for the scan impedance of the array is derived, assuming an infinitesimal lumped element. We also report that as the period decreases and the wavelength increases, there is a simple relation between the scan impedance of the connected array antenna and the transmission-line equivalent circuit impedance of the lumped-element periodically loaded vertical wire-grid frequency selective surface. Consequently, to reduce the variation of the resonance frequency of the scan impedance with the scan angle, we employ the concept of adding an appropriate lumped element inductance to stabilize the resonance frequency of the frequency selective surface.