On the Use of Hybrid Full-Wave CG-FFT and Spectrally Preconditioned CG-FFT Methods for Analyzing Large Microstrip Antenna Arrays

Abstract

<p>In this thesis, we investigate full-wave hybrid Conjugate Gradient - Fast Fourier Transform (CG-FFT) methods for analyzing microstrip arrays. In particular, we investigate spectral preconditioning with the CG-FFT methods.</p> <p>First, a general scheme is introduced for implementing CG-FFT using the spatial discretization. In comparison with other schemes, the proposed one yields greater accuracy and has higher efficiency because no finite difference approximations are involved, all the aliasing and truncation errors are eliminated and the size of the zero padded region is kept to a minimum.</p> <p>A hybrid full-wave CG-FFT method is then developed for analyzing microstrip structures. It combines the proposed CG-FFT scheme and the full-wave complex discrete image technique. With this combination, the spatially discrete scheme is realized which can be used for microstrip structure analysis without losing any full-wave information, while at the same time, measuring only minor computational cost and errors. Therefore the merits of the proposed scheme are extended to microstrip problems straightaway.</p> <p>To further improve the rate of convergence for the CG-FFT method, a new highly efficient spectrally preconditioned CG-FFT method is introduced. This technique takes full ad vantage of the FFT by constructing the special forms of preconditioners and performing the preconditioning in the frequency domain. It uses no any additional memory and only O(NlogN) additional operations for constructing and storing the preconditioner. At the same time it has superior convergence properties compared with the conventional CG-FFT method and other existing preconditioned methods.</p> <p>The hybrid CG-FFT algorithm developed in this thesis is easily interfaced to UNIX simulation software, including a draw editor and an automatic mesh generator. Using this software, we carry out numerical analyses of different types of microstrip antenna arrays. The analyses are corroborated by experimental measurements. A number of array parameters and boundary effects are studied. These are of interest to antenna design engineers, which include: (1) effect of the finite size of arrays, (2) effect of array shape, (3) spurious radiation from the array feed structures, (4) current distributions on the elements, (5) input impedance and (6) array radiation patterns. Conclusion and discussion are addressed. The performance capabilities of the hybrid full-wave CC-FFT method are demonstrated by a modeling study of very large microstrip reflectarrays. Proposals are made for an improved design for the large array, based on the results of the simulations.</p>