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The design of a reader antenna is described for usage in radio frequency identification (RFID) systems at 13.56 MHz, as defined in the ISO-14443a standard. It presents the theory, with emphasis on the effect of the read out distance on the design, but also describes measurements on concrete designs to validate the formulas and statements. We also comment on practical problems that were encountered during the design process. The major contribution of this work is the generalization of the design theory for large read out distances where the conventional assumption of constant loop current no longer holds.