Surface Impedance Model Research Articles

Plane wave scattering by a material coated parabolic cylinder

An eigenfunction solution to the problem of transverse magnetic (TM) or transverse electric (TE) scattering by a coated parabolic cylinder is presented. Paralleling the well-known solution for the coated circular cylinder, eigenfunction expansions involving parabolic cylinder functions are obtained for the fields in the exterior and coating regions. Next, boundary conditions are enforced to obtain a pair of coupled equations for the unknown coefficients in the eigenfunction expansions for the fields. Unlike the corresponding solution for the coated circular cylinder, the eigenfunctions in the exterior and coating regions are not orthogonal, and an exact term-by-term solutions of these equations is not possible. Instead, the equations are solved by the method of moments. For thin coatings both an uncoupled-mode approximation and a surface-impedance model are described. In particular, for the TM polarization it is shown that a thin coating can be modeled by a specific nonuniform surface impedance for which an exact term-by-term solution is possible. Numerical data are presented, showing the convergence of the solution and comparing the solutions for the uncoupled-mode and surface-impedance models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Launching vertically polarised ground waves from a vertical magnetic dipole over an anisotropic surface

While a vertical magnetic dipole will radiate horizontally polarised waves over a homogeneous isotropic earth, the effect of anisotropy will convert some of the radiated energy to vertical polarisation. An analysis of this situation is outlined employing an anisotropic surface impedance model.

Electromagnetic wave propagation in a two‐dimensional tunnel with a modified cross‐junction

AbstractThis paper investigates theoretically and experimentally the electromagnetic wave propagation in a two‐dimensional tunnel with a modified cross‐junction in connection with radio communications in tunnels, underground, urban areas with high‐rise buildings and others. Modal expansions and Fourier transform are used as an analytical method, and the surface impedance model is employed as a boundary condition on the tunnel walls. The results presented here can be applied to special tunnels such as the T‐type, modified T‐type, L‐type and step‐type. Experiments based on a microwave simulation are performed by using tunnels composed of concrete slabs. It is found that, concerning electric field intensity, experimental and theoretical results agree well.

A surface impedance boundary condition for 3-D non destructive testing modeling

In this paper, the authors present an application of the surface impedance boundary condition to eddy current non destructive testing (NDT) modeling. When the skin depth is small, the electromagnetic field problem is reduced to an exterior field problem taking into account the influence of a ferromagnetic material (permeability,conductivity) by means of the boundary condition on the interface air-metal. The surface impedance model is implemented in a three dimensional boundary integral equation package and is compared with an axisymmetrical calculation. The comparison shows a good agreement between the two calculations. The application of the method is for NDT on surface cracks scanned with a circular coil fed with high frequency alternating current. In this case, the skin depth is small and the problem is three dimensional so that 2-D programs can't be used. For this special problem, the surface impedance boundary condition is particularly well adapted and the proposed method shows encouraging results.

Surface impedance models for corners and slots

The penetration of flux into metallic parts is limited by the skin effect at power frequencies and so, when analyzing eddy-current fields, such metallic parts may be excluded from the region of solution at a great saving in computing effort, by replacing the metal by a surface impedance. However, at corners, in slots and under saturated conditions, the model breaks down, as penetration increases. In this paper, we provide means for continued use of the these mode is under these conditions. The significance of this to memory requirements is all the more important because eddy current solutions involve 2 variables per node, so that as parts are eliminated from solution regions, matrix storage requirements, go down even faster.

Electromagnetic fields of corrugated conical horns with elliptical cross section described by Lamé functions

The corrugated conical horn with elliptical cross section is investigated. Use is made of the analytical solutions of the Lamé differential equations. In the investigations we use the anisotropic surface impedance model. The problem of wave propagation in an anisotropic elliptical cone is formulated as an eigenvalue problem. This problem is solved, and plots are given of the separation constant as a function of the opening angle of the cone with the aspect ratio of the elliptical cross section as a parameter. The radiation of an anisotropic elliptical horn excited by a hybrid mode is determined using the spheroconal wave expansion method. Satisfactory agreement between computations and measurements is obtained. It is found that with this type of horn it is theoretically possible to perfectly generate circularly polarized radiation patterns of elliptical cross section.

Three dimensional eddy current calculation using a network method

First order finite element or finite difference approximations to the electric and magnetic scalar potential Poisson equations are represented by network models. The resulting linked-circuit problem is solved using nodal variables for the larger, magnetic part of the problem and mesh variables for the smaller, conducting region. This method of solution is shown to compare favourably, in terms of number of variables, with conventional finite element techniques. A surface impedance model is also presented for the solution of saturated eddy-current problems. This model uses actual iron B/H curves rather than the approximations usually employed. Both calculation methods are verified using experimental results.

Surface impedance concepts of electromagnetic wave propagation in layered isotropic and anisotropic media

Integral representations for the electromagnetic field generated by an electric or magnetic dipole line source located within the atmosphere of the two‐layer configuration atmosphere‐ionosphere rendered anisotropic by a uniform static (terrestrial) magnetic field are evaluated by the method of steepest descent to give analytical expressions for the far field along the interface of the two media. These expressions are used to calculate the surface impedance tensor for the lower boundary of the ionosphere. The surface impedance tensor permits one to replace the continuity conditions by approximate boundary conditions along the interface. Results obtained for an arbitrary direction of the static magnetic field (arbitrary geomagnetic latitude) are specialized to polar and equatorial zones. For these cases, dependence of attenuation and phase velocity of the first few modes of the earth‐ionosphere waveguide on ionospheric height and on electric properties of the ground (which enter a scalar surface impedance for the ground plane) is shown. TM modes are much more sensitive to electrical properties of the adjoining media than TE modes. Attenuation is lower for propagation from west to east than in the reverse direction. Icy ground causes severe attenuation of TM but not of TE modes. Various other applications of the surface impedance model are reviewed.

Approximate analysis of electromagnetic scattering from corrugated conducting surfaces by surface impedance modeling

Scattering from a corrugated conducting surface is analyzed by an approximate method based on Leontovich boundary condition. Comparison of results with those based on a rigorous technique justifies the use of such approximate methods for shallow gratings.

Effects of conductivity, groove shape, and physical phenomena on the design of diffraction gratings*

Numerical solution of integral equations is used to explore the effects of material parameters and groove geometry on diffraction-grating performance. The material parameters are studied by first developing and verifying a surface-impedance model. The parameter values characteristic of good metals in the infrared regions indicate that the conductivity effects are of little significance. Small changes of groove shape produce relatively large changes of the grating response, implying that construction tolerances are quite important. Specific data on Brewster-angle effects and resonant anomalies are presented and suggestions are made for both the use and control of these physical effects.