A Gibbsian model for finite scanned arrays

A finite-by-infinite array of thin half-wave dipoles with H-plane scan is used to show the existence of a Gibbs´ phenomenon-type standing wave in scan impedance (normalized by the infinite array value) over the elements of the array. The period of this wave is 0.5λ at broadside for λ/2 array spacing and increases as the scan angle increases by a grating lobe-type expression. A simple empirical model based on Gibbs oscillations is fitted to the scan-impedance wave; the model predicts the 1/(1-sinθ₀) period variation, and should be useful for systems trades and for preliminary design purposes