A Mode Matching - Finite Element - Spectral Decomposition Approach for the Analysis of Finite Arrays of Horn Antennas

摘要

A new hybrid Mode Matching-Finite Element Method (MM-FEM) [1] and Spectral Decomposition (SD) approach [2][3] is presented for the analysis of large arrays of horn antennas. The proposed methodology (MM-FEM-SD) retains advantages from the three involved techniques. The SD approach is used to reduce the finite large problem to a summation of infinite periodic problems through a Fast Fourier Transform (FFT) technique or by means of a Fourier closed form solution [4]. Floquet's expansion enables us to reduce the analysis to a single radiating element, whereas SD accounts for the presence of the remaining antennas by a proper phase shift. A key step in the analysis consists in resorting to a stepped waveguide model of the longitudinal inner profile of the elementary horn antenna. A MM procedure is employed to ensure the continuity of transverse fields over each waveguide discontinuity and over the radiating aperture. Floquet's modes and TE/TM waveguide modes have been exploited to compute the Generalized Scattering Matrix (GSM) of the radiating element. A two dimensional FE approach with tangential vector interpolation basis functions is employed to solve the eigenvectors and eigenvalues problem of unconventional shaped radiating apertures or waveguide sections. The flexibility of the FE method allow us to model complex irregular structures providing a very high degree of generality. The efficiency of MM and SD techniques enables us to solve very large array problems typically untreatable with fully three-dimensional approaches. A brief formulation of the proposed method is presented in the next section. Finally, some preliminary numerical results are shown to demonstrate the effectiveness of this approach.