Offset reflector shaping for non-circular apertures

There has been recent interest in near-conformal, microwave and millimeter-wave antennas for airborne and ground transportable platforms. For reflector antennas to be effective in such applications, they must be both low profile and high efficiency. Reflector antenna concepts which exhibit high efficiency immediately suggest reflector shaping. Near-conformality imposes physical constraints which force the radiating aperture to be highly elliptical or rectangular. Since an elliptical or rectangular radiating aperture is required, a suitable expression must be selected for the aperture shape. It is important to select a form which is general enough to be useful but which yields integrals which have tractable, closed-form solutions. A piecewise-linear approximation is shown to fit this requirement. An approach is developed that involves manipulating the applicable constraints into a triangular matrix form whose solution is known to exist, is known to be unique, and is relatively straightforward to solve numerically. Elliptical, compact structures capable of being fitted into a complementary pedestal-positioner to form a low-profile antenna assembly are considered as examples.<>