Realistic source modeling and tolerance analysis of a Luneburg lens antenna

A single Luneburg lens or an array of lenses fed by one or more horn antennas has found use in many applications requiring high-gain low-profile antennas. The numerical methods for calculation of the properties of these antennas are based on the spherical wave expansion (SWE) method [1-3]. In [1, 2] the feed horn antenna was modelled using an endfire array of two or four infinitesimal dipoles and this may lead to discrepancies between the measured and predicted results. Recently, an accurate SWE representation of any real source was presented in [3]. The calculation of the SWE coefficients of the source presented in [3] requires calculation of an integral over the volume containing the feed antenna. In this paper, we show that the SWE coefficients of a feed horn antenna may be accurately obtained using simpler two-dimensional integrals and the equivalent electric and magnetic current calculated over the plane containing the horn aperture. Further, we studied the effects of errors in the dielectric permittivities on the lens performance. The published results on the tolerance analysis, presented in [2, 4], assumed uniform change of the dielectric permittivities, i.e. the dielectric permittivities of all layers were either increased or decreased by the same amount. However, in practice random variation of the dielectric permittivities may be expected. We present results for these more general cases and show that the gain loss due to the errors in dielectric permittivities may be reduced significantly by adjusting the feed location.