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The Eleven antenna is a log-periodic folded-dipole-pair array with two unique radiation characteristics: a constant beamwidth and a fixed phase center location over a decade bandwidth. This paper presents a new compact design of a 1.2-10 GHz Eleven antenna, as a feed for reflector antennas by re-arranging the geometry of the outermost elements of the antenna. Due to the compact size, it is possible to put the whole feed system inside a compact cryostat and cool it down to cryogenic temperatures, in order to reduce the system noise temperature in radio telescope applications. The new compact Eleven feed has only a 40% volume of the original standard Eleven feed with a very similar performance. This reduces the capacity requirement for the cryogenic cooling system significantly and therefore the power consumption for future radio telescopes, such as the square kilometer array (SKA). The concept behind this compact design is analyzed in the paper. Simulations and measurements presented here have verified the design.