On the Convergency Properties of Fast Spherical Multipole Analysis for Frequency-Independent Log.-Per. Planar Antennas

The optimization of frequency independent planar antennas for applications in fading scenarios such as multiple-input multiple-output (MIMO) wireless systems and diversity configurations requires sophisticated and robust numerical field computational techniques. In order to derive low-order models to account for a realistic modeling of antenna radiation behaviour, a spherical mode expansion (SME) is derived that is based on the surface current distribution on planar antenna elements in free-space. Hence, the main focus of this paper is related to the in-depth characterization of the SME convergency properties of the modal field approach in terms of the field approximation behaviour in the special case of planar log.-per. four-arm antennas featuring trapezoidal shapes. The investigations yield a novel convergency criterion for the truncation of the spherical mode analysis that is directly related to the geometrical antenna properties