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The system design of a cryogenic 2-13 GHz feed is considered with emphasis on its application in future wideband radio telescope systems. The feed is based on the so-called Eleven antenna and the design requires careful integration of various sub-designs in order to realize cryogenic operation. The various sub-designs include the electrical design of the Eleven antenna, design of the critical center puck, alternative solutions for integrating the Eleven antenna with low-noise amplifiers (LNAs), mechanical and cryogenic design and tests, and system noise temperature estimation and measurements. A great deal of simulated and measured results are presented throughout this paper, including the electrical, mechanical and cryogenic performance, and an assessment of the system noise temperature. The objective of this work is to present a good feed candidate that is well-suited for VLBI2010 and SKA radio telescopes. Further developments needed to completely fulfill the requirements for these future wideband radio telescopes are also discussed.