Electrostatic image theory for two anisotropic half-spaces

An image solution for the canonical electrostatic problem of a point charge in an anisotropic half-space bounded by another anisotropic half-space is presented. The image source is obtained in operator form by using Fourier-transformed Maxwell equations and transmission line theory. After applying Heaviside operator calculus the image operator can be interpreted as a combination of a point charge and a sector of planar charge. The new theory is shown to coincide with the previously known image solutions of less general anisotropic media. In addition to being applicable to any physically feasible anisotropic medium of electrostatics, the method can be used for steady-current conductivity problems via a duality transformation.     

Time-domain analytic and numeric analysis of vertical dipoles infront of a dielectric planar interface

Potentials excited by impulsive vertical electric and magnetic dipoles in a geometry of two dielectric media with a planar interface are studied both analytically and numerically. Closed-form expressions for the Hertzian potential are derived in cases when the observation point is on the axis of the dipole or when both the dipole and the observation point are located at the interface. Numerical results are given for more general observation points     

Two-dimensional image method for time-harmonic line current in front of a material cylinder

Contents The well-known electrostatic two-dimensional image theory involving a line charge parallel to a dielectric cylinder is extended to the electromagnetic problem where the source is a time-harmonic current and the permittivity and permeability of the cylinder may be different from those of the exterior space. The reflection and transmission images of the current line giving the field reflected from the cylinder and the field transmitted into the cylinder are presented in the form of cylindrical surface currents obeying explicit series expressions. It is shown that by choosing the image cylinders properly and extracting a line image source from each, the convergence of the series can be dramatically improved. The reflection image is seen to reduce to a double-line image on the axis when the distance of the line current from the surface of the cylinder becomes infinitely large.

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Zweidimensionale Spiegelungsmethode für zeitharmonische Linienströme vor einem permittiven und permeablen Zylinder

Übersicht Die aus der Elektrostatik für die Behandlung eines dielektrischen Zylinders im Feld einer Linienladung bekannte zweidimensionale Spiegelungsmethode wird auf elektro magnetische Probleme mit zeitharmonischen Linienströmen und einem permittiven und permeablen Zylinder übertragen. Die Spieglbilder des Stroms für den in den Zylinder ein dringenden und den reflektierten Anteil des Felds werden als zylindrische Flächenströme in Form explizit angegebener Reihen dargestellt. Die Wahl der Spiegelzylinder und der Spiegelströme beeinflußt die Konvergenz der Reihendarstellung. Ist der Linienstrom un-endlich weit vom Zylinder entfernt, so reduziert sich das Spiegelbild für das reflektierte Feld auf zwei Ströme auf der Achse.

     

Analysis of a three-dimensional dielectric mixture with finitedifference method

The present paper reports the results of a numerical analysis of electric fields in random dielectric materials. The effective permittivity of a three-dimensional (3D) dielectric mixture is calculated by the finite difference method. The results show the distribution of the effective permittivity of a mixture with different random inclusion positionings. New empirical mixing models are created as least squares approximations to fit the collection of numerical results. The calculated permittivity distribution is also compared with theoretical mixture models, showing that in case of clustered inclusions, the Bruggeman model is quite reasonable. On the other hand, if the inclusions in the mixture are separate, the results are closer to the Maxwell-Garnett model     

Effective permittivity of mixtures: numerical validation by theFDTD method

The present paper reports the results of an extensive numerical analysis of electromagnetic fields in random dielectric materials. The effective permittivity of a two-dimensional (2-D) dielectric mixture is calculated by FDTD simulations of such a sample in a TEM waveguide. Various theoretical bounds are tested in light of the numerical simulations. The results show how the effective permittivity of a mixture with random inclusion positionings is distributed. All possible permittivity values lie between Wiener limits, and according to FDTD simulations the values are almost always between Hashin-Shtrikman limits. Calculated permittivity distribution is also compared with theoretical mixture models. No model seems to be able to predict the simulated behavior over the whole range of volume fraction     

Time-domain analysis of horizontal dipoles in front of planardielectric interface

Time-domain solutions for fields due to an impulsive horizontal magnetic and electric dipole above a planar dielectric interface are studied analytically. General time-domain expressions for the Hertzian potentials corresponding to the electromagnetic fields in the upper medium are analyzed in a novel way by exploiting exact image theory. Analytic closed-form solutions are derived for certain special locations of the source and observation points. Some of the results are new, while the rest agree with the solutions in the literature     

Signal correlations and diversity gain of two-beam microcellantenna

The motivation of the present study is to investigate the possibility of using two independently directed antenna beams in a mobile base station to provide diversity gain and reduce fading problems in a microcellular environment. The signal correlation of the individual antenna beams is studied, and it is shown that correlation depends on beamwidth, separation angle of the antenna beams, and the location of the base-station antenna array. Signal correlations have been computed using narrow- and wide-beam antennas in two separate base-station antenna locations. Diversity gains of both antenna types have been optimized by selecting the beam orientations which minimize the signal correlation. The numerical simulations show that a considerable diversity gain can be obtained using this approach     

DC potential anomalies caused by a conducting body in ananisotropic conducting half-space

Image theory for dc problems involving a current source in an anisotropic half-space bounded by either a perfectly magnetically conducting (PMC) or electrically conducting (PEC) plane is being used to get the solution for the potential in integral form. A dipole approximation for a small sphere is developed     

Transient image theory for 2-D and 3-D conducting wedge problems

In the present paper, two- and three-dimensional transient scattering from a perfectly conducting wedge is studied. The exciting sources analyzed are an infinite impulsive line current parallel to edge of the conductor and an arbitrarily oriented electric dipole. The analysis presented is based on the time-harmonic image solution found for the scattered field. The frequency-domain image current corresponding to the field contribution from the wedge is an exact function expressed in terms of simple trigonometric functions. It is dependent only on the coordinates and the amplitude of the source, but it is independent of the observation point. It is shown that the transient scattering can be interpreted as arising from an image source by generalizing the time domain Green's function to complex source points     

Scalar green function method for microstrip antenna analysis based on the exact image theory

Exact image theory, applicable to the analysis of plane-stratified structures, is reviewed in general form and expressions corresponding to the microstrip geometry are given. It is seen that essential in this method is the calculation of two scalar Green functions, responsible for the effect of the geometry for the field. Exact expressions for these Green functions are found for the microstrip in terms of integrals of special functions. The Green functions are needed in the formulation of electric field integral equations for the surface currents of the microstrip. The Green functions are shown to possess the same type of singularity as the free-space Green function and also a similar limit when the distance grows larger, with the exception of a waveguide-mode term, which can be easily evaluated separately. Simple approximate expressions for the Green functions are evaluated, suitable for practical analysis of microstrip structures.