Bandwidth limits for lossless planar arrays over ground plane

Maximum bandwidth limits are developed for lossless planar arrays over a ground plane through use of Fano´s broadband impedance matching method and Richards´ transformation. It is demonstrated that such an array cannot exceed 8.3:1 bandwidth without material loading (for VSWR´2). It is also demonstrated that an additional dielectric superstrate layer can provide up to 12.1:1 bandwidth, without magnetic or lossy substrates. A simple analytic expression for the maximum bandwidth is given as a function of impedance mismatch (VSWR) and substrate material parameters. The dependence of bandwidth on aperture complexity is quantified, showing that a simple first-order aperture has a bandwidth limit of 5:1, without material loading.