Maximum Achievable Gain of Annular-Shaped Beams

The maximum achievable gain and the corresponding source distribution for an annular or “donut”-shaped beam produced by a circular aperture are studied. Expressing the source in terms of orthogonal basis functions and then applying Lagrange’s multiplier method, the optimum source distribution is determined. The residue calculus is then invoked for the closed-form expressions. Numerical results are shown and discussed. In applications such as direction finding and satellite tracking systems on moving vehicles, a high-gain annular beam is suitable for maintaining uninterrupted connectivity.