The Design Of Antennas Based On Fractal Theory And Research Of Its Em Radiation Patterns

In this paper the application of fractal geometry theory to the design of antennas is researched. The affect of various mathematical parameters of fractal geometry on the property of fractal antennas has been determined by theoretical analysis or numerical emulation, which lays the theory foundation for the design of complex fractal antennas and fractal array antennas.Firstly, an improved fractal interpolation method is proposed, which can generate proper fractal interpolation curves from a set of co-linear interpolation points with an estimate of the lower limit of the curves'Hausdorff dimension. When the interpolation points are not co-linear, the improved interpolation method gives equal formula for calculating the fractal interpolation curves'Hausdorff dimension with the former interpolation method.Secondly, numerical emulations have been made in order to determine the influence of vertical proportion parameter and altitudinal scale parameter on the shape of fractal interpolation curves. Then by EM emulation with fractal antennas generated from corresponding fractal curves, the effects of vertical proportion parameter and altitudinal scale parameter on the fractal antennas'EM radiation property are determined.Finally, the radiation property of Sierpinski carpet microstrip antenna is researched. In the beginning, the expansion of plane wave with spherical wave functions is considered. It can be theoretically proved that the two expansions based from the wave transform method and vector potential method are equal. Then under the spherical coordinate system the EM radiation field of Sierpinski carpet microstrip antenna can be viewed as the compound of the radiation fields from several rectangle microstrip antennas or several parallel apertures. The numerical emulation results are identical with the theoretical analysis..