Design Formula for Sierpinski Gasket Pre-Fractal Planar-Monopole Antennas [Antenna Designer's Notebook]

An improved formula for determination of resonant frequencies in different Sierpinski modes is developed from other existing formulas, using physical and analytical reasoning. The superiority of the proposed formula over other existing formulas is verified by comparing the results with those from experiments and simulations. A design formula for the side length of the generating Sierpinski triangle is also proposed by algebraic rearrangement of the formula for the resonant frequency.