Equivalent Magnetic Surface Currents Research Articles

Surface integral formulation for calculating conductor and dielectric losses of various transmission structures

The power-loss method, along with a surface integral formulation, has been used to compute the attenuation constant in microstrip and coplanar structures. This method can be used for the analysis of both open and closed structures. Using the surface equivalence principle, the waveguide walls are replaced by equivalent electric surface currents and dielectric surfaces are replaced by equivalent electric and magnetic surface currents. Enforcing the appropriate boundary condition, and E-field integral equation (EFIE) is developed for these currents. Method of moments with pulse expansion and point matching testing procedure is used to transform the integral equation into a matrix one. The relationship between the propagation constant and frequency is found from the minimum eigenvalue of the moment matrix. The eigenvector pertaining to the minimum eigenvalue gives the unknown electric and magnetic surface currents. >

The penetration of EM waves through loaded apertures

In many cases, the effectiveness of an electromagnetic shield is determined by apertures that exist in the shield. To minimize the penetration of EM fields through a large aperture, the aperture is sometimes loaded with conductive material. The solution of the loaded aperture problem can be reduced to the calculation of equivalent magnetic surface currents, M/spl I.oarr//sub s/, that exist over the surface of the aperture. In the paper, the relevant integro-differential equations have been solved using the method of moments to determine M/spl I.oarr//sub s/ for a small, square aperture loaded with a number of impedance sheets of practical interest. These values of M/spl I.oarr//sub s/ have been used to calculate the magnetic and electric insertion losses of these impedance sheets. The numerical results are compared with shielding measurements that have been made on carbon composite materials and wire meshes and grids.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

DishPat and FeedPat: Test beds for students to investigate design alternatives for dish antennas

Two programs are introduced to provide flexible and portable C-language programs for investigating design and analysis alternatives for prime-focus paraboloidal reflectors. FeedPat enables the study of the aperture illumination provided by a particular feed. DishPat computes the resulting radiation pattern and provides graphical output. Using simple piecewise-constant numerical integration, DishPat employs square subareas which are easy to manage and may be readily extended to handle a variety of reflector outlines as well as feed offsets. Equivalent magnetic surface currents limit the validity of the radiation to the forward half-space, but the loss in coverage is offset by the simplicity of the code. Not only useful for learning, the programs may be readily modified into practical design tools.

Equivalent surface sources using the second order vector potential formulation

The method outlined is especially advantageous with eddy current problems, because it allows the interfaces of all conducting regions to be replaced with equivalent magnetic surface charge and surface current. These equivalent sources are an immediate result of the field computation, and require virtually no additional computation. In terms of these equivalent sources, external fields are found quite accurately from surface integrations. With boundary element method techniques, this ability is especially valuable in terms of its accuracy and speed in finding global quantities such as force. The equivalent sources are directly related to the second-order vector potential, which has separability advantages in a number of coordinate systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time-domain electromagnetic penetration through arbitrarily shaped narrow slots in conducting screens

A time-domain integral equation is derived for the unknown electric field, or equivalent magnetic surface current, in a narrow slot in a conducting surface, and an efficient and stable numerical method is developed for solving this equation. The contour of the slot in the vanishingly thin conducting surface may be of any shape. The solutions are compared via Fourier transformation with those of the corresponding time-harmonic integral equation, and they are further validated by demonstrating close correlation between values of the calculated field on the shadow side of the conductor and data from laboratory measurements. For numerous slot lengths and shapes, time- and frequency-domain data illustrating the behavior of the slot field and penetrated field are presented and compared with measured results. The stability of the time-domain solution technique is investigated and found to be very high. The response of a slot to an EMP-type (electromagnetic pulse type) pulse is presented as an example. >

Characteristics of circular patch on thick substrate and superstrate

Accurate formulation for the wall admittance of a circular patch on a thick substrate/superstrate is presented. The principle of equivalence is invoked at the physical aperture of the patch, which yields equivalent electric and magnetic surface currents for the outside fields. The unknown electric current, in terms of the aperture electric field, is obtained from the field continuity condition on the aperture surface. Numerical results reveal that for a small substrate thickness, the equivalent electric current may be ignored. It should, however, be included in the analysis for larger substrate thicknesses. Numerical results for the wall conductance, wall susceptance, and radiation efficiency of a patch with various substrates and superstrates are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic scattering from arbitrary shaped conducting bodies coated with lossy materials of arbitrary thickness

A simple and efficient numerical technique is presented to solve the electromagnetic scattering problem of coated conducting bodies of arbitrary shape. The surface equivalence principle is used to formulate the problem in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents which represent boundary fields. The conducting structures and the dielectric materials are modeled by planar triangular patches, and the method of moments is used to solve the integral equations. Numerical results for scattering cross sections are given for various structures and compared with other available data. These results are proved accurate by a number of representative examples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scattering from multiple conducting and dielectric bodies of arbitrary shape

A simple moment-method solution is presented for the problem of electromagnetic scattering from structures consisting of multiple perfectly conducting and dielectric bodies of arbitrary shape. The system is excited by a plane wave. The surface equivalence principle is used to replace the bodies by equivalent electric and magnetic surface currents, radiating into an unbounded medium. A set of coupled integral equations, involving the surface currents, is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the bodies are approximated by planar triangular patches, and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the scattering cross sections are presented. The computed results are in very good agreement with the exact solutions and with published data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic properties of an insulated dipole antenna immersed in an arbitrary medium

Radiation characteristics of an insulated dipole antenna immersed in an arbitrary medium are studied using a complete formulation of the problem. Electric and magnetic equivalent surface currents are used to formulate a system of integrodifferential equations. These equations are solved using the method of moments construction with the proper selection of basis functions. The data obtained are found to be in good agreement with the available data in the literature. The effect of the insulator's permittivity on the near field and far field of the dipole is discussed. The use of coating material to control the effective length of the dipole is presented. The effect of the insulator's thickness on the far field is also studied. The input impedance of the insulated antenna in an arbitrary medium is obtained.

Transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section: TE case

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Electromagnetic transmission through a small radome of arbitrary shape

A simple moment solution is presented for the problem of electromagnetic transmission through a small radome of arbitrary shape. The radome is excited by either a plane wave (receive mode) or an elementary dipole inside the radome (transmit mode). The equivalence principle is used to replace the radome by a set of equivalent electric and magnetic surface currents radiating into an unbounded medium. A set of coupled integral equations involving the surface currents is obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. The surfaces of the radome are approximated by planar triangular patches and linearly varying vector functions are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. In the receive mode, the total field inside the radome is computed along a number of straight lines and in the transmit mode the far transmitted field is computed. A spherical and a Von Karman radome are studied. The computed results are in excellent agreement with the exact or other available published data.

An electromagnetic model for multiconductor connectors

An electromagnetic model for the response of multiconductor connectors is presented. The model is based on the canonical problem of the electromagnetic response of a thin circumferential slot in the shield of a cylindrical multiconductor transmission line (MTL). The problem is formulated for a shielded MTL of arbitrary cross section with impressed sources driving the interior of the MTL. The problem of interior-to-exterior coupling is solved by treating the slot as a thick aperture in the shield. The equivalence principle is used to divide the original problem into three separate parts. Two coupled integral equations are obtained for the equivalent surface magnetic currents, which are solved by the method of moments, and equivalent networks are presented. The equivalent networks consist of three generalized admittances, one of which is interpreted in terms of a connector admittance. >

Analysis of finite dielectric sheets with arbitrarily shaped metallization on both sides using the conjugate gradient‐fast fourier transform method

AbstractRadiation and scattering from finite dielectric sheets with arbitrary metallization on both sides is analyzed using the conjugate gradient‐fast Fourier transform (CG‐FFT) method to solve a system of integral equations (SIE), where the unknown functions are electric and magnetic equivalent surface currents. The results obtained indicate that the method is efficient and accurate.

RCS of two-dimensional structures consisting of both dielectrics and conductors of arbitrary cross section

The problem of determining the electromagnetic field scattered by two-dimensional structures consisting of both dielectric and conducting cylinders of arbitrary cross section is considered. The conductors may be in the form of strips and the dielectrics may be in the form of shells. The conductors may be partially or fully covered by dielectric layers, while the dielectrics may be partially covered by conductors. Only homogeneous dielectrics are studied. Both the transverse electric (TE) and the transverse magnetic (TM) cases are considered. The problem is formulated in terms of a set of coupled integral equations involving equivalent electric and magnetic surface currents radiating in unbounded media. The method of moments is used to solve the integral equations. Simple expansion and testing procedures are used. Numerical results for scattering cross sections are given for various structures. >

Electromagnetic scattering from dielectric bodies

Far-field results obtained by two different methods are compared for the problem of electromagnetic scattering from dielectric objects. The two methods are the surface integral formulation, utilizing equivalent electric and magnetic surface currents, and the volume formulation, utilizing the equivalent electric polarization current. Triangular patches are used in the surface formulation and cubical cells are used in the volume formulation. The far-scattered fields obtained by the two methods are in good agreement, thereby validating both the approaches for the analysis of scattering problems. Numerical problems associated with the fields in the source region are also addressed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

TE scattering from a conducting cylinder of arbitrary cross-section covered by multiple layers of lossy dielectrics

A simple moment solution is summarised for the problem of electromagnetic scattering from a perfectly conducting cylinder of arbitrary cross-section which is covered by multiple dielectric layers of arbitrary cross section. The system is excited by a plane wave polarised transverse electric to the axis of the cylinder. The equivalence principle is used to replace the cylinders by equivalent electric and magnetic surface currents radiating into an unbounded medium. A set of coupled integral equations involving the surface currents is obtained by enforcing the boundary conditions on the tangential component of the total magnetic field. The method of moments is used to solve the integral equations. Pulse expansion and point matching are used. Some of the limitations of the method are briefly discussed. Results for the surface currents and the scattering cross-sections are presented. Computed results are in very good agreement with the exact or other available published data.

E-Field and H-Field Solutions of TE Scattering from Multiple Conducting and Dielectric Cylinders of Arbitrary Cross-Section

A simple moment solution is given for the problem of electromagnetic scattering from two dimensional structures consisting of multiple perfectly conducting and lossy dielectric cylinders of arbitrary cross-section. The system is excited by a plane wave polarized transverse electric to the axis of the cylinders. The equivalence principle is used to replace the cylinders by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Some of the limitations of the method are briefly discussed. Results for the surface currents and the scattering cross sections are presented. Results computed using the E- field and/or the H- field formulation are in very good agreemen...

TM Transmission Through Dielectric-Filled Slots in a Conducting Cylindrical Shell of Arbitrary Cross Section

A simple moment solution is summarized for the problem of electromagnetic transmission through dielectric-filled slots in a conducting cylindrical shell of arbitrary cross section. The system is excited by a plane-wave polarized transverse electric (TE) to the axis of the shell. The equivalence principle is used to replace the shell and the dielectric by equivalent electric and magnetic surface currents radiating into an unbounded medium. Two different sets of coupled integral equations involving the surface currents are obtained by enforcing the boundary conditions on the tangential components of the total electric and magnetic fields. The method of moments is used to solve the integral equations. Pulses are used for both expansion and testing functions. Special attention is paid to circular and rectangular shells. Results for shell surface current, the internal field, and the aperture field are presented. For the case of air dielectric filling, the results computed using the electric field and/or the magnetic field formulation are in very good agreement with published data. In general, it is observed that the effect of filling a slot with a dielectric is not predictable from a simple theory. >

Analysis of optical waveguide junctions by means of an integral equation method

AbstractUsing a slab waveguide model we analyze the problem of waveguide mode transmission and reflection that occurs at the junctions of dielectric optical waveguide due to lateral offset, angular tilt, and gap between the guides, and deformations of the end faces. the analysis first develops a set of integral equations for the unknown equivalent electric and magnetic surface currents over the end faces. the integral equations are discretized through partitioning of the boundaries of both ends into small elements, and their solutions are expanded in a Neumann series, which makes it possible to obtain the solutions iteratively. Using reciprocity and mode orthogonality properties appropriately, the mode coupling coefficients are obtained. After discussing the relation between partition number of the boundaries and convergence of solutions, and the satisfaction of energy relations, we give numerical examples for the reflection and transmission coefficients of guided modes, the radiation losses and the radiation power patterns, choosing end shapes and their locations as the parameters.

Interaction of electromagnetic waves at rough dielectric surfaces

A systematic perturbation theory is developed to study the interaction of electromagnetic waves at rough dielectric surfaces. The Ewald-Oseen extinction theorem is used as the basis of the perturbation theory. Explicit expressions for both first-order and second-order fields (in terms of the surface roughness parameter) at all points in space are presented. The incident field is treated very generally and thus it can be in any state of polarization. The surface is characterized by a structure function and hence the results are valid both for periodic and statistical surfaces. The first-order fields are used to calculate various types of scattering cross sections for arbitrary incident fields characterized by coherence matrices. The coherence matrix for scattered fields is given. The equivalent electric and magnetic surface currents on a flat surface which would lead to the same expressions for first-order fields as those obtained for the rough surface, are calculated using the extinction theorem. The extinction cross section is calculated using an appropriately formulated optical theorem. This leads in a straightforward manner to a change in the value of the reflectivity as compared to the value on a flat surface. The experiment of Teng and Stern is discussed briefly in the light of the expressions for extinction cross sections. Finally, first-order and second-order fields are used to discuss Smith-Purcell radiation, i.e., the radiation emitted by an electron moving parallel to a grating surface. This case corresponds to the conversion of evanescent waves into homogeneous waves due to surface roughness. The relation of some of our results to those of Crowell, Elson, Ritchie, Juranek, Lalor, Marvin et al., Maradudin, and Mills is also discussed.