Browsing by Subject "Sommerfeld integrals"

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    Derivation of Closed-Form Green’s Functions for a General Microstrip Geometry
    (1992) Aksun, M.I.; Mittra, R.
    The derivation of the closed-form spatial domain Green’s functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a super-state, whose thicknesses can be arbitrary. The spatial domain Green’s functions for printed circuits are typically expressed as Sommerfeld integrals, that are inverse Hankel transform of the corresponding spectral domain Green’s functions, and are quite time-consuming to evaluate. Closed-form representations of these Green’s functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. In this paper, we show we can accomplish this by approximating the spectral domain Green’s functions in terms of complex exponentials by using the least square Prony’s method. © 1992 IEEE
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    A novel approach for the efficient computation of 1-D and 2-D summations
    (Institute of Electrical and Electronics Engineers Inc., 2016) Karabulut, E. P.; Ertürk, V. B.; Alatan, L.; Karan, S.; Alisan, B.; Aksun, M. I.
    A novel computational method is proposed to evaluate 1-D and 2-D summations and integrals which are relatively difficult to compute numerically. The method is based on applying a subspace algorithm to the samples of partial sums and approximating them in terms of complex exponentials. For a convergent summation, the residue of the exponential term with zero complex pole of this approximation corresponds to the result of the summation. Since the procedure requires the evaluation of relatively small number of terms, the computation time for the evaluation of the summation is reduced significantly. In addition, by using the proposed method, very accurate and convergent results are obtained for the summations which are not even absolutely convergent. The efficiency and accuracy of the method are verified by evaluating some challenging 1-D and 2-D summations and integrals. © 2016 IEEE.