An analytical solution for the umbrella reflector surface shape, including the pillowing contribution, is presented. The solution is simple and sufficiently accurate for most antenna applications, and apart from being useful as a design tool, it can be easily incorporated into an existing computer code, allowing for more realistic evaluations of the umbrella reflector electrical characteristics. The analytical solution was tested by numerically solving the equations using a successive overrelaxation procedure. The gain degradation and the gore-related sidelobes clearly show the significance of pillowing on the antenna radiation characteristics.
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