Efficient numerical analysis and design of reflectarray antennas

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2015
Erçil, Erdinç
The accurate numerical analysis of electrically large reflectarray antennas has been a challenging task since their advent because it becomes impractical to employ the generalized numerical electromagnetic tools for their numerical analysis. Therefore the classical approach is to resort to approximate methods. However, approximate methods trade off accuracy against memory and speed. In this thesis study; an approximate analysis technique is established such that it is more accurate than the present approximate analysis techniques and more efficient than the full wave analysis schemes in terms of memory requirement and speed. The technique relies on using characteristic modes as macro basis functions and reusing the dominant characteristic mode of the resonant element for all elements in the reflectarray. This utilization leads to obtaining a reduced matrix system where the number of unknowns is drastically decreased. As far as the far field is concerned, accurate results even with a single characteristic mode are achieved. The accuracy is attained owing to preservation of mutual coupling information via the original MoM impedance matrix. The solution is further accelerated by tabulating the entries of the reduced matrix as a function of interacting patch sizes and their relative displacements. It is observed that for sufficiently separated patches, the reduced matrix entry is almost a separable function of the two dimensional displacement between patches and patch sizes associated with the matrix entry. Tabulation is efficiently performed by exploiting this fact. Achieved acceleration is sufficient to use this analysis method in the design of reflectarrays. For a 1000 element array, the tabulation process takes 28 min on a platform with 3.3 GHz CPU clock speed. With the lookup table at hand, the solution time, which is important for the design iterations, is 0.38 seconds. The speed provided by the method makes it possible to employ gradient based optimization algorithms such as Steepest Descent or Conjugate Gradient Method, both of which are successfully applied to two design problems in the scope of the study.

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Citation Formats
E. Erçil, “Efficient numerical analysis and design of reflectarray antennas,” Ph.D. - Doctoral Program, Middle East Technical University, 2015.