On the maximum off-axis gain of symmetrical pencil-beam antennas

For a general class of symmetrical pencil-beam antennas, the gain at a given off-axis angle can be maximized by choosing the proper antenna size. The maximum gain at the given angle relative to the on-axis gain is independent of the given angle and dependent only on the main-beam pattern. It is computed here for four commonly used gain functions. Its value, in all cases, is close to 4 dB. This result is important in the definition of service areas for communication and broadcast satellites.