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A compact printed dipole antenna is proposed for radio frequency identification (RFID) applications. It consists of a combination of two kinds of fractal shapes with the aim of reducing antenna size. To ensure conjugate matching with the essentially complex impedance of the electronic chip directly embedded into the radiator, a double T-match structure is used. The antenna has been designed and optimised to cover the bi-band for the passive RFID tag at 915 MHz and 2.4 GHz. Details of the proposed antenna design and measured results are presented and discussed.