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A double band RFID reader antenna has been proposed and it can be used for 2.5GHz and 5.5GHz frequencies. In RFID reader, the respective frequencies are used for Automatic Vehicle Identification and Inventorymanagement applications. The concept of the fractal can be applied in design and analysis. A comparison of the return loss (S11)parameter is made between measured and simulated data from both transient domain solver and frequency domain solver.