M.C. van Beurden

Analysis of wide-band infinite phased arrays of printed folded dipoles embedded in metallic boxes

A theoretical method is presented to analyze the scan performance of infinite phased arrays of printed folded dipoles embedded in metallic boxes. By using the equivalence principle, each unit-cell is divided into an inhomogeneous interior region and a homogeneous exterior region. The exact dyadic Greens function for both regions is derived. The current distribution on the antenna elements and the corresponding active impedance are found by solving the pertaining integral equations with the method of moments. Numerical results show that the E-plane scan performance is improved significantly by placing the folded dipoles inside metallic boxes. Without the use of additional matching circuits a bandwidth of more than 16% was obtained over a wide scan range. A disadvantage of the use of metallic boxes is the strong appearance of a blind scan angle at the higher frequencies. Measurements of the element pattern of an 1152-element prototype show a very close agreement with the presented theoretical computations.

Gaps in present discretization schemes for domain integral equations

We discuss the stability of existing numerical schemes for domain integral equations modeling inhomogeneous dielectric objects in a homogeneous background of infinite extend. In particular, we focus on finite-energy conditions and we show that several numerical schemes do not properly impose these conditions.

Probabilistic Study of the Coupling between Deterministic Electromagnetic Fields and a Stochastic Thin-Wire over a PEC Plane

A stochastic approach is presented to statistically characterize uncertainties in electromagnetic interactions. A stochastically undulating thin wire over a perfectly conducting ground plane is studied. The aim of this paper is to present methods to compute the statistical moments of the voltage induced by a deterministic incident field. Three methods have been developed to compute these moments: a quadrature method, a perturbation approach and a Monte-Carlo method.

Analysis of stochastic resonances in electromagnetic couplings to transmission lines

Resonances present in coupling phenomena between a randomly varying thin-wire transmission-line, and an electro-magnetic field are stochastically characterized. This is achieved by using the first 4 statistical moments in order to appreciate the intensity of the resonance phenomena. The stochastic method proposed is applied to a thin-wire transmission line connected to a variable impedance, and, undergoing random geometrically localized perturbations.

Local normal vector field formulation for periodic scattering problems formulated in the spectral domain

We present two adapted formulations, one tailored to isotropic media and one for general anisotropic media, of the normal vector field framework previously introduced to improve convergence near arbitrarily shaped material interfaces in spectral simulation methods for periodic scattering geometries. The adapted formulations enable the definition and generation of the normal vector fields to be confined to a region of prolongation that includes the material interfaces but is otherwise limited. This allows for a more flexible application of geometrical transformations like rotation and translation per scattering object in the unit cell. Moreover, these geometrical transformations enable a cut-and-connect strategy to compose general geometries from elementary building blocks. The entire framework gives rise to continuously parameterized geometries.

Modelling the interaction of stochastic systems with electromagnetic fields

The analysis presented in this paper, shows how the basic statistics in the interaction of stochastic systems with electromagnetic fields, i.e., the average and the variance of linear observables, can be computed from the probability distributions defining the stochastic geometry. The most difficult part in this computation is the construction of the covariance operator which requires the solution of a series of integral equations over the average geometry. The RHSs of these integral equations are determined by an expansion of the covariance operator of a regular field trace on the stochastic geometry. This determines the computational complexity of the probabilistic approach. In the presentation of this paper, some numerical experiments on concrete examples are shown, and the computational complexity of the probabilistic approach are investigated whether it also determines the minimal computational effort of the statistical approach

3D harmonic modeling of magnetostatic fields including rectangular structures with finite permeability

A 3D semi-analytical harmonic modeling technique is presented, that is able to model magnetic fields in the vicinity of a rectangular slab of permeable material accurately. A stable solution for the constitutive relation for magnetic fields in the spectral domain is described, which makes it possible to incorporate a spatially varying permeability of a certain region in the solutions of magnetic-field quantities. The presented technique is compared to results obtained with the finite element method (FEM).

Design of a Wide-Band Phased-Array Antenna for the Next Generation Radio Telescopes

The next generation of radio telescopes will have two orders of magnitude more sensitivity than presentday radio telescopes. At this moment, a lot of effort is put in defining this new radio telescope: SKAI, the Square Kilometre Array Interferometer. For that purpose, four demonstrator phased-array systems are being developed at NFRA. The One Square Metre Array (OSMA) is the second demonstrator system and is currently being tested. For OSMA, a wide-band printed antenna element with an integrated balun was developed and tested experimentally. Electromagnetic models and corresponding software were used to predict and optimise the scan performance of the wide-band element in an array environment. Theoretical and experimental results of several prototype arrays will be presented in this paper.

Computational aspects of a spatial-spectral domain integral equation for scattering by objects of large longitudinal extent

With a 3D spatial spectral integral-equation method for EM scattering from finite objects, a significant part of the computation time is spent on a middle region around the origin of the spectral domain. Especially when the scatterer extends to more than a wavelength in the stratification direction, a fine discretization on this region is required, consuming much computation time in the transformation to the spatial domain. Numerical evidence is shown that the information in the middle region of the spectral domain is largely linearly dependent. Therefore, a truncated singular-value decomposition is proposed to make the computation time largely independent of the discretization on this middle region. For a practical example the increased computational efficiency and the approximation error of the singular-value decomposition are shown.

A characterization method for electromagnetic fields in a stack of lossy dielectric slabs with random material properties

The layered-medium model is used in modeling scattering by various media such as biological tissue and distributed Bragg reflectors. The impurities and imperfections of the real media are described in the model by adding uncertainties to them. Common ways to estimate the effect of these uncertainties on the behavior of the media are often time consuming. Here we present a method by which we can approximate the random behavior of the medium by a fair approximation. The approximation is done by transforming the integral equation that describes the behavior of a one dimensional layered slab structure.