Olav Breinbjerg

Higher order hierarchical Legendre basis functions for electromagnetic modeling

This paper presents a new hierarchical basis of arbitrary order for integral equations solved with the method of moments (MoM). The basis is derived from orthogonal Legendre polynomials which are modified to impose continuity of vector quantities between neighboring elements while maintaining most of their desirable features. Expressions are presented for wire, surface, and volume elements but emphasis is given to the surface elements. In this case, the new hierarchical basis leads to a near-orthogonal expansion of the unknown surface current and implicitly an orthogonal expansion of the surface charge. In addition, all higher order terms in the expansion have two vanishing moments. In contrast to existing formulations, these properties allow the use of very high-order basis functions without introducing ill-conditioning of the resulting MoM matrix. Numerical results confirm that the condition number of the MoM matrix obtained with this new basis is much lower than existing higher order interpolatory and hierarchical basis functions. As a consequence of the excellent condition numbers, we demonstrate that even very high-order MoM systems, e.g., tenth order, can be solved efficiently with an iterative solver in relatively few iterations.

A Review of the Scattering-Parameter Extraction Method with Clarification of Ambiguity Issues in Relation to Metamaterial Homogenization

The scattering-parameter extraction method of metamaterial homogenization is reviewed to show that the only ambiguity is that related to the choice of the branch of the complex logarithmic function (or the complex inverse cosine function). It is shown that the method has no ambiguity for the sign of the wavenumber and intrinsic impedance. While the method indeed yields two signs for the intrinsic impedance and thus the wavenumber, the signs are dependent. Moreover, both sign combinations lead to the same permittivity and permeability, and are thus permissible. This observation is in distinct contrast to a number of statements in the literature where the correct sign of the intrinsic impedance and wavenumber resulting from the scattering-parameter method is chosen by imposing additional physical requirements, such as passivity. The scattering-parameter method is reviewed through an investigation of a uniform plane wave normally incident on a planar slab in free space. The severity of the branch ambiguity is illustrated through simulations of a known metamaterial realization. Several approaches for proper branch selection are reviewed, and the suitability to metamaterial samples is discussed.

Electrically Small Magnetic Dipole Antennas With Quality Factors Approaching the Chu Lower Bound

This paper describes the modeling and analysis to modeling EMC immunity test by means of computer simulation with Finite Difference Time Domain (FDTD) method. To ensure the integrity of the results the log-periodic antenna was simulated separately and then included in a more complex model. Despite the many limitations of both the numerical models and the measurements, the models provide a satisfactory representation of the electrical field radiated by the antenna.We investigate the quality factor Q for electrically small current distributions and practical antenna designs radiating the TE10 magnetic dipole field. The current distributions and the antenna designs employ electric currents on a spherical surface enclosing a magneto-dielectric material that serves to reduce the internal stored energy. Closed-form expressions for the internal and external stored energies as well as for the quality factor Q are derived. The influence of the sphere radius and the material permeability and permittivity on the quality factor Q is determined and verified numerically. It is found that for a given antenna size and permittivity there is an optimum permeability that ensures the lowest possible Q, and this optimum permeability is inversely proportional to the square of the antenna electrical radius. When the relative permittivity is equal to 1, the optimum permeability yields the quality factor Q that constitutes the lower bound for a magnetic dipole antenna with a magneto-dielectric core. Furthermore, the smaller the antenna the closer its quality factor Q can approach the Chu lower bound. Simulated results for the TE10-mode multiarm spherical helix antenna with a magnetic core reach a Q that is 1.24 times the Chu lower bound for an electrical radius of 0.192.

An exact line integral representation of the physical optics scattered field: the case of a perfectly conducting polyhedral structure illuminated by electric Hertzian dipoles

An exact line integral representation of the electric physical optics scattered field is presented. This representation applies to scattering configurations with perfectly electrically conducting polyhedral structures illuminated by a finite number of electric Hertzian dipoles. The positions of the source and observation points can be almost arbitrary. The line integral representation yields the exact same result as the conventional surface radiation integral; however, it is potentially less time consuming and particularly useful when the physical optics field can be augmented by a fringe wave contribution as calculated from physical theory of diffraction equivalent edge currents. The final expression for the line integral representation is lengthy but involves only simple functions and is thus suited for numerical calculation. To illustrate the exactness of the line integral representation, comparisons of numerical results obtained from the surface and the line integral representations are performed. >

Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary condition (SIBC)

A novel combination of the method of auxiliary sources (MAS) and the standard impedance boundary condition (SIBC) is employed in the analysis of transverse magnetic (TM) plane wave scattering from infinite, coated, perfectly conducting cylinders with square cross sections. The scatterer is initially modeled by a SIBC surface and the scattering mechanism is subsequently analyzed via MAS. Although SIBC as well as MAS possess theoretical limitations with regard to an edge, the numerical results show that the MAS/SIBC method provides results of high accuracy for a range of structures with edges. The SIBC modeling of coated conductors with edges has previously been investigated in the literature and thus, this work focuses on comparing MAS and the method of moments (MoM) for SIBC surfaces (MoM/SIBC). A detailed complexity analysis shows that the MAS/SIBC method is, under certain conditions, more efficient than the MoM/SIBC method, proving that the proposed novel combination is a powerful and advantageous computational tool.

Theory and Practice of the FFT/Matrix Inversion Technique for Probe-Corrected Spherical Near-Field Antenna Measurements With High-Order Probes

A complete antenna pattern characterization procedure for spherical near-field antenna measurements employing a high-order probe and a full probe correction is described. The procedure allows an (almost) arbitrary antenna to be used as a probe. Different measurement steps of the procedure and the associated data processing are described in detail, and comparison to the existing procedure employing a first-order probe is made. The procedure is validated through measurements.

Reduction of Truncation Errors in Planar Near-Field Aperture Antenna Measurements Using the Gerchberg-Papoulis Algorithm

A simple and effective procedure for the reduction of truncation errors in planar near-field measurements of aperture antennas is presented. The procedure relies on the consideration that, due to the scan plane truncation, the calculated plane wave spectrum of the field radiated by the antenna is reliable only within a certain portion of the visible region. Accordingly, the truncation error is reduced by extrapolating the remaining portion of the visible region by the Gerchberg-Papoulis iterative algorithm, exploiting a condition of spatial concentration of the fields on the antenna aperture plane. The proposed procedure is simple and computationally efficient; it does not require any modification of the measurement procedure and it allows for the usual probe correction. Far-field patterns reconstructed from both simulated and measured truncated near-field data demonstrate its effectiveness and stability against measurement inaccuracies.

Higher order hierarchical discretization scheme for surface integral equations for layered media

This paper presents an efficient technique for the analysis of electromagnetic scattering by arbitrarily shaped perfectly conducting objects in layered media. The technique is based on a higher order method of moments (MoM) solution of the electric field, magnetic field, or combined-field integral equation. This higher order MoM solution comprises higher order curved patches for the geometry modeling and higher order hierarchical basis functions for expansion of the electric surface current density. Due to the hierarchical property of the basis functions, the order of the expansion can be selected separately on each patch depending on the wavelength in the layer in which the patch is located and the size of the patch. In this way, a significant reduction of the number of unknowns is achieved and the same surface mesh can be reused in a wide frequency band. It is shown that even for fairly large problems, the higher order hierarchical MoM requires less memory than existing fast multipole method (FMM) or multilevel FMM implementations.

Direct Optimization of Printed Reflectarrays for Contoured Beam Satellite Antenna Applications

An accurate and efficient direct optimization technique for the design of contoured beam reflectarrays is presented. It is based on the spectral domain method of moments assuming local periodicity and minimax optimization. Contrary to the conventional phase-only optimization techniques, the geometrical parameters of the array elements are directly optimized to fulfill the contoured beam requirements, thus maintaining a direct relation between optimization goals and optimization variables, and hence resulting in more optimal designs. Both co- and cross-polar radiation patterns of the reflectarray can be optimized for multiple frequencies, polarizations, and feed illuminations. Several contoured beam reflectarrays, that radiate a high-gain beam on a European coverage, have been designed and compared to similar designs obtained using the phase-only optimization technique. The comparisons show that the designs obtained using the proposed direct optimization technique are superior in performance, both for multi-frequency and dual-polarization designs. A reflectarray breadboard has been manufactured and measured at the DTU-ESA Spherical Near-Field Antenna Test Facility to validate the proposed technique. An excellent agreement of the simulated and measured patterns is obtained.

Coupling Reduction Between Dipole Antenna Elements by Using a Planar Meta-Surface

The mutual coupling between dipole antenna array elements using a planar meta-surface as superstrate is experimentally investigated. The meta-surface is based on grids of short metal strips and continuous wires. A comparison between the mutual coupling when the dipoles are radiating in free space and in presence of the superstrate is presented. On average, between 3 to 14 dB reduction of the mutual coupling is achieved when the superstrate is used. The effect of the mutual coupling on the radiation performance of the array is studied by spherical near-field measurements of the radiation pattern when one driven dipole is fed and the others are matched with 50 Omega loads. The back-projected field on the aperture and on the E-plane is shown.