On the Poisson sum formula for the analysis of wave radiation and scattering from large finite arrays

1999-05-01
Poisson sum formulas have been previously presented and utilized in the literature [1]-[8] for converting a finite element-by-element array field summation into an alternative representation that exhibits improved convergence properties with a view toward more efficiently analyzing wave radiation/scattering from electrically large finite periodic arrays. However, different authors [1]-[6] appear to use two different versions of the Poisson sum formula; one of these explicitly shows the end-point discontinuity effects due to array truncation, whereas the other contains such effects only implicitly. It is shown here, via the sifting property of the Dirac delta function, that first of all, these two versions of the Poisson sum formula are equivalent. Second, the version containing implicit end point contributions has often been applied in an incomplete fashion in the literature to solve finite-array problems; it is also demonstrated here that the latter can lead to some errors in finite-array field computations.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION

Suggestions

On the Poisson sum formula for analysis of EM radiation/scattering from large finite arrays
Aydın Çivi, Hatice Özlem; Chou, HT (1998-01-01)
A useful procedure, that has been described previously in the literature, employs the Poisson sum formula to represent the solution to the fields of a three-dimensional (3D) large periodically spaced finite planar array problem configuration as a convolution of the infinite planar periodic array solution and the Fourier transform of the equivalent aperture distribution over the finite array. It is shown here that the Poisson sum formula utilized by Felsen and Carin (see J. Opt. Soc. Am. A, vol.11, no.4, p.1...
Investigation of tightly coupled arrays for wideband applications
Arda, Kaan; Dural Ünver, Mevlüde Gülbin; Department of Electrical and Electronics Engineering (2020-10)
This thesis aims to provide in depth research on tightly coupled dipole arrays to be used in ultrawideband apertures applications. First, operation principles of tightly coupled dipole arrays are investigated. Starting from the Wheeler’s current sheet aperture concept, some calculations on bandwidth and impedance concepts are conducted. B.A. Munk’s addition to the concept, use of capacitive elements between adjacent dipoles, are introduced. Array unit cell is modeled using equivalent circuit approach,...
Rigorous optimizations of three dimensional antenna arrays using full wave simulations
Onol, Can; Gokce, Ozer; Boyacı, Huseyın; Ergül, Özgür Salih (null; 2015-07-09)
We present optimizations of three-dimensional antenna arrays using heuristic techniques coupled with the multilevel fast multipole algorithm (MLFMA). Without resorting to any periodicity and infinity assumptions, antenna arrays are modeled with surface integral equations and simulated via MLFMA, which also enables the analysis of arrays with non-identical elements. Genetic algorithms and particle swarm optimization methods are employed on the complex data produced by MLFMA in phasor domain to find optimal s...
On the reduction of Gaussian inverse Wishart mixtures
Granström, Karl; Orguner, Umut (2012-09-12)
This paper presents an algorithm for reduction of Gaussian inverse Wishart mixtures. Sums of an arbitrary number of mixture components are approximated with single components by analytically minimizing the Kullback-Leibler divergence. The Kullback-Leibler difference is used as a criterion for deciding whether or not two components should be merged, and a simple reduction algorithm is given. The reduction algorithm is tested in simulation examples in both one and two dimensions. The results presented in the ...
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012)
Bayin, Selcuk S. (2012-08-01)
Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
Citation Formats
H. Ö. Aydın Çivi and H. Chou, “On the Poisson sum formula for the analysis of wave radiation and scattering from large finite arrays,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 958–959, 1999, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39994.