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A modified contour integral method coupled with segmentation method has been used, for the first time, to analyze both the Sierpinski fractal carpet (SFC) antennas of different orders and an SFC antenna with electromagnetic band gap (EBG) ground plane. The close agreement between the calculated and measured results for resonant frequencies and input return losses indicates that this technique can be used to accurately predict the impedance characteristic. A novel stacked microstrip Sierpinski carpet fractal antenna using the EBG ground plane is also presented. Comparing to an ordinary microstrip fractal antenna, which has a maximum bandwidth of approximately 2%, the proposed antenna has a higher input impedance bandwidth of nearly 9%. The radiation patterns of the proposed antenna are improved due to the removal of unwanted radiation caused by the surface wave. The experimental measurement results of the proposed antenna are presented in this paper.