Equations for the first-order design of phased array fed reflector antennas

We use ray-optics theory to derive a set of analytical design equations for performing the initial design of two types of phased array fed reflector antennas, the Cassegrain and offset-fed paraboloid. With each set of equations programmed in a spreadsheet, we can evaluate the relationships between key array parameters, including array spot size, total array size, array position and reflector parameters, such as diameter and focal length. Simple parameter trades provide the starting antenna dimensions for more rigorous analysis by software such as TICRA's GRASP. We use GRASP to validate predictions made with our first order theory.