On the use of rational-function fitting methods for the solution of 2D Laplace boundary-value problems

A computational scheme for solving 2D Laplace boundary-value problems using rational functions as the basis functions is described. The scheme belongs to the class of desingularized methods, for which the location of singularities and testing points is a major issue that is addressed by the proposed scheme, in the context of the 2D Laplace equation. Well-established rational-function fitting techniques are used to set the poles, while residues are determined by enforcing the boundary conditions in the least-squares sense at the nodes of rational Gauss-Chebyshev quadrature rules. Numerical results show that errors approaching the machine epsilon can be obtained for sharp and almost sharp corners, nearly-touching boundaries, and almost-singular boundary data. We show various examples of these cases in which the method yields compact solutions, requiring fewer basis functions than the Nystr\"{o}m method, for the same accuracy. A scheme for solving fairly large-scale problems is also presented

23:1 Bandwidth ratio quasi‐lumped component balun on a multilayer organic substrate

In this study, the authors present the design and development of a novel ultra-wideband coupled-line balun on a multilayer liquid crystal polymer substrate. The balun is designed using a quarter wavelength (λ/4) asymmetric broadside coupled line. The defected ground structure and a lumped phase compensation circuit are developed to achieve wide bandwidth performance for the balun. The balun has a measured bandwidth ratio of 23:1, from 80 to 1860 MHz. Within the operating bandwidth, the experimental results demonstrate that the balun achieves an input return loss of better than 10 dB, an insertion loss of better than 1 dB, an amplitude imbalance of better than ±0.4 dB and a phase imbalance of better than ±10°. The size of the balun is 40.64 mm × 40.64 mm or 0.22 λg × 0.22 λg, where λg is the guided wavelength at the centre frequency of 970 MHz

Analysis of Electromagnetic Scattering Using Arrays of Fictitious Sources

The use of models of fictitious elemental current sources, located inside the scatterer, to simulate the scattered field, has proved to be an efficient computational technique for analyzing scattering by metallic bodies. This paper presents a novel modification of the technique in which the omnidirectional elemental sources are arranged in groups of array-sources with directional radiation patterns, and the boundary testing points are arranged in groups of testing arrays with directional receiving patterns. This modification, which is motivated by physical understanding, is equivalent to mathematical basis transformations. It renders the system matrix more localized and thereby enables the analysis of larger bodies. The new approach is applied to the case of TM scattering by a perfectly conducting square cylinder with side-length of 20. Reduction of 50% in the number of the non-zero elements of the system matrix is achieved with virtually no degradation in the accuracy of the RCS calcu..