Analysis of Infinite Phased Arrays Using a FEM-TD Formulation with an Accurate Floquet ABC

摘要

A formulation is presented for a three-dimensional time-domain finite-element method that can be used to analyze infinite phased-array antennas using one unit cell. The method solves for a transformed field variable (instead of solving directly for the electric field) in order to easily enforce periodic boundary conditions in the time domain. The infinite phased-array antennas considered in this article all reside on top of a perforated ground plane where the antenna elements are fed through the apertures in the ground plane by coaxial waveguides with an outer radius equal to that of the apertures'. In order to accurately model these types of antenna arrays, we have implemented a coaxial port that is capable of launching and absorbing a TEM mode in the waveguide. Moreover, the results presented in this article were obtained using an accurate Floquet absorbing boundary condition (ABC) to truncate the computational domain on the top surface of the unit cell. The formulation is general and can handle any scanning angle aside from end-fire where the ABC implementation breaks down. The applicability of the method is demonstrated by results from a Vivaldi antenna.