The development of compact high gain antennas for CubeSats can enable several advanced space missions at lower costs, and is an active area of research within the antenna community. A special class of reflector antenna, known as the umbrella reflector has regained much interest due to its ability to meet the demands of advanced space missions that require high gain and/or high spatial resolution. The umbrella reflector surface consists of a finite number of parabolic ribs, which are connected through surfaces called gores, which deviate from the true parabolic shape. This causes the radiation performance of the umbrella reflector surface to be far less intuitive than the conventional paraboloid. In this work, we provide a comprehensive understanding of the radiation mechanism of the umbrella reflector. We describe the techniques that have been investigated to determine the optimum feed position, study the dependency of the gain on the diameter and number of ribs and analyze the appearance of far-field grating lobes. Several closed form expressions are derived to aid the design of umbrella reflectors and achieve the tradeoff between mechanical complexity and RF performance.
