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This letter presents a novel electromagnetic band-gap (EBG) structure in microstrip technology based on nonuniform one-dimensional (1-D) Koch fractal patterns whose dimensions and period are modulated by a tapering function that significantly improves the width of the band-gap. This wide band-gap is achieved by maintaining the radius-to-period (r/a) ratio of the Koch fractal patterns larger than 0.5 in the whole structure. In the passband region, an improved flat response is obtained by tapering the dimensions of the Koch fractal patterns etched in the ground plane, together with the width of the microstrip line, with a Kaiser distribution that also modulates the periodicity of the fractals. A major consequence of this modulation of the periodicity of the pattern is that this structure is much more compact than a uniform conventional one.