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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.
(ProQuest: ... denotes formulae omitted.)
Introduction: Planar arrays are of great interest owing to their conformality and low cross-polarisation. Munk [1] demonstrated that Wheeler's 'continuous current sheet' array [2] is theoretically frequency independent. However, for unidirectional radiation, as well as for conformal platform integration, planar arrays must be backed with a conducting ground plane. The reflections from the ground plane destroy frequency independence and prevent unlimited bandwidth. Nevertheless, planar arrays above a ground plane have been successfully developed with relatively wideband performance [1, 3, 4]. Although analytical models are available for some arrays, e.g. [1, 3], other designs cannot easily be represented analytically (e.g. the fragmented aperture concept [4]). However, a simple circuit equivalent network may be developed to represent features common to all planar arrays. By applying Fano's impedance matching approach to this network, we establish a maximum bandwidth limit that holds for any lossless planar array above a ground plane. The effects of material loading and array complexity on bandwidth are also quantified. These results may thus provide guidance in designing wideband planar arrays against the theoretical limits.
Equivalent network: To simplify the modelling of a generalised planar array, we make the following assumptions. All radiating currents lie in a plane parallel to a perfectly conducting ground, as shown in Fig. 1a. The array is sufficiently large to be approximated as infinitely periodic. Also, the array is assumed to have negligible cross-polarisation and no grating lobes over the frequency band of interest. In addition, the aperture and possible material treatments have negligible ohmic losses. Under these assumptions, the array can be represented...