Design of an antenna feed system to produce a uniform field

An analytical approach is presented to find an excitation distribution of a multiple feed horn array radiating to an offset parabolic reflector to produce a uniform field over a region on earth. The reflector antenna is installed in a communication satellite. The aperture field method is used to predict the secondary pattern generated by the reflector antenna. Two antenna synthesis problems are involved in this discussion, namely the aperture synthesis and the planar array synthesis. The aperture synthesis is formulated into an integral equation. The integral equation is solved for the array factor by applying the Zernike polynomials. Applying the Zernike polynomials, the radiation integral is converted to a Fourier-Bessel series, then the field of the secondary pattern may be expressed as a function of the observation angles. The numerical results show that the shape of the principle beam of the secondary pattern may be classified into three categories which are the convex shape, the concave shape and the shape with some ripples.