Panagiotis J. Papakanellos

On the Oscillations Appearing in Numerical Solutions of Solvable and Nonsolvable Integral Equations for Thin-Wire Antennas

Differences between certain solvable and nonsolvable ill-posed integral equations, with the same nonsingular kernel, are discussed. The main results come from constructing a solvable equation in the context of straight thin-wire antennas. The kernel of this equation is the usual approximate (also called reduced) kernel, while its exact solution is the familiar sinusoidal current. Numerical solutions to this solvable equation are compared to corresponding numerical solutions of the usual-Halle¿n and Pocklington-equations with the approximate kernel; it is known from previous publications that these last two equations are nonsolvable and that their numerical solutions present severe oscillations when the number of basis functions is sufficiently large. It is found that the difficulties encountered in the former (solvable) equation are much less important compared to those of the nonsolvable ones. The same conclusion is brought out from other integral equations, arising in different contexts (thin-wire circular-loop antenna, Method of Auxiliary Sources, and straight wire antenna of infinite length). We discuss the consistency of our results with Picards theorem. The results in this paper supplement previous publications regarding the difficulties of numerically solving thin-wire integral equations with the approximate kernel.

Analysis of an infinite current source above a semi-infinite lossy ground using fictitious current auxiliary sources in conjunction with complex image theory techniques

The canonical problem of an infinitely long electric current line radiating above a lossy infinite half space is examined. The solution is based on the method of auxiliary sources (MAS). In this method one can, in general, apply a numerical solution by introducing sets of fictitious current sources whose fields are elementary analytical solutions to the boundary value problem, in order to approximately describe the actual electromagnetic (EM) fields in each domain. In general, the convergence rate and the accuracy of the MAS solution depend on the spatial distributions of the fictitious current sources sets and their locations in regard to the singularities of the actual EM field simulated by each set. Here, both the accuracy and the convergence rate of the method are examined, investigating complex image approximations in order to optimally choose the auxiliary sources placements. It is proved that the convergence rate and the accuracy of the method are significantly improved by utilizing the complex images as locations of the auxiliary sources. The main contribution of the paper consists in the application of MAS to an open structure, which involves lossy dielectrics excited by a nonuniform EM field, as well as in the optimal choice of the locations of the fictitious current sources according to complex image techniques.

A stochastically optimized adaptive procedure for the location of MAS auxiliary monopoles: the case of electromagnetic scattering by dielectric cylinders

A genetically optimized technique that fully automates the potentially laborious allocation of the auxiliary monopoles for the method of auxiliary sources (MAS) is presented for the problem of electromagnetic (EM) scattering by isotropic dielectric cylinders with various cross sections. The proposed technique uses as input information not only the geometry of the scatterer but also the exciting field and the material properties of the cylinders are implicitly taking part in the optimization procedure. The resulting auxiliary surfaces, where the simulating monopoles are situated, are appropriately adapted to the original boundary surface and the MAS modeling is greatly facilitated. In addition, certain considerations are taken into account in order to avoid undesirable numerical dependencies between the fictitious monopoles. Finally, the accuracy of the numerical method combined with overdetermined systems of equations is examined for isotropic cylinders of various geometries and dielectric characteristics.

Eliminating Unphysical Oscillations Arising in Galerkin Solutions to Classical Integral Equations of Antenna Theory: an Asymptotic Study

Previous works have discussed in detail the difficulties occurring when one applies numerical methods to Hallens and Pocklingtons integral equations for the current distribution along a linear antenna. When the so-called approximate kernel is used, the main difficulty is the appearance of unphysical oscillations near the driving point and/or near the ends of the antenna. Another work has proposed an easy-to-apply, possible remedy to overcome these unnatural oscillations. The basic idea is to define a new current from the near magnetic field produced by the original oscillating current. In the present paper, for the case of an antenna center-driven by a delta-function generator, we place this remedy on a much firmer basis by means of an asymptotic study for the case of the linear antenna of infinite length. We provide specific connections of our study to actual finite-length antennas.

Method-of-Moments Analysis of Resonant Circular Arrays of Cylindrical Dipoles

We perform a method-of-moments (MoM) analysis of a circular array of cylindrical dipoles. The array is known from earlier theoretical and experimental studies to possess very narrow resonances. The earlier theoretical studies were carried out using the “two-term theory.” The present paper is a direct continuation of a recent work showing that the problem possesses unique and particular difficulties. The main difficulties are overcome herein using a set of improved kernels in the usual Hallén-type integral equations (these kernels had been developed in previous works, and were successfully incorporated into the aforementioned two-term theory analyses). We make a detailed comparison of our MoM results to two-term theory results and, also, to the earlier experimental results.

Multi-objective genetic optimization of Yagi-Uda arrays with additional parasitic elements

The,design of modified Yagi-Uda arrays with additional parasitic elements in the area of the radiating dipole, acting either as reflectors or directors, is presented. The genetic algorithms are employed, and various objective functions concerning gain, front-to-back ratio, and the latter combined with desired input impedance, are examined. Comparisons are made among the modified and conventional Yagi-Uda configurations for different weighting coefficients of the fitness functions. The modified Yagi-Uda array outperforms the conventional Yagi-Uda array, because it achieves higher performance standards over an extended bandwidth around 2.4 GHz.

SURFACE-WAVE AND SUPERDIRECTIVITY ASPECTS OF EFFECTIVE CURRENT FOR LINEAR ANTENNAS ∗

Previous papers have defined the concept of effective current for linear antennas as a method of postprocessing the unphysical solutions obtained by applying discretization (Galerkin) methods to the usual integral equations that employ the “approximate” or “reduced” kernel. Such an unphysical solution can be thought of as an auxiliary, rapidly oscillating current located on the axis of the linear antenna, while the effective current is the magnetic field due to the oscillating current at a distance equal to the antenna radius (multiplied by a factor equal to the antenna circumference). In the present paper, we focus on the rapid decrease of the aforementioned magnetic field and point out similarities to surface waves, to the well-known phenomenon of superdirectivity, and to the method of auxiliary sources (MAS). Our study sheds light on the unusual nature of electromagnetic waves generated by currents with very rapid spatial variations. Subject to the condition that the discretization is fine, we treat th...

Original and Modified Kernels in Method-of-Moments Analyses of Resonant Circular Arrays of Cylindrical Dipoles

Properly dimensioned circular arrays of cylindrical dipoles are known to possess very narrow resonances. It is also known that analyzing such arrays using moment methods presents unique and particular difficulties, as application of such methods to the usual Hallen-type integral equations can yield meaningless results from which no further conclusions should be drawn. In the present paper, we apply moment methods to properly modified integral equations and obtain much more reliable results. We also observe that certain difficulties still remain, and discuss them in detail.

Efficient Modeling of Radiation and Scattering for a Large Array of Loops

A computationally efficient technique, based on the method of moments (MoM) formulation, is invoked in the characterization of radiation and scattering properties of an array of coaxial, circular, non-identical loops. A set of Pocklington-type integral equations for the loop currents is formulated and subsequently discretized by a standard procedure. Thanks to a suitable choice of the basis functions, the resulting matrix corresponding to the pertinent linear system is forced to consist of circulant blocks. This type of system is solvable by an innovative recursive algorithm, featuring several important advantages, such as lower memory and execution time consumption, over standard, purely numerical inversion. The overall procedure is simpler in implementation than already existing methods, based on Fourier analysis. The procedure invokes almost exclusively elementary functions, and is applicable to large arrays with respect to diameter or number of loops. Data for such configurations are presented for the first time in literature.

A Probabilistic Approach for the Susceptibility Assessment of Twisted-Wire Pairs Excited by Random Plane-Wave Fields

This paper presents a probabilistic approach for the susceptibility assessment of a twisted-wire transmission line in the presence of a plane-wave electromagnetic field with certain parameters (amplitude, polarization angle, direction-of-incidence angles) treated as random variables. The transmission line is located in free space and terminated in arbitrary loads. Closed-form expressions are provided for the probability density function of the induced far-end voltage in certain cases of field descriptions and excitation scenarios. A more general Monte-Carlo technique is also employed, in order to cope with cases yielding laborious integrals.