Field Integral Equation Method Research Articles

Electric field integral equation approach for accurate modeling of transmission loss properties and leakage phenomena in NRD-guide of arbitrary cross section

An electric field integral equation method has been developed for accurately modeling both transmission losses and leakage behaviors along nonradiative dielectric (NRD) guides of arbitrary cross-sectional shape and arbitrary inhomogeneous dielectric permittivity. The method is verified by comparing its modeling results with measured ones as well as with results obtained from a mode-matching method for bench-mark structures. The leakage properties of elliptical NRD guides and also the complete losses in trapezoidal NRD guides are studied in detail for the first time to demonstrate the advantages of the new method. © 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2007.

Improved Stable Scheme for the Time Domain Integral Equation Method

A novel technique for improving the stability of time domain electric field integral equation (TD-EFIE) method is presented. The method involving the introduction of a new class of temporal basis functions employs a modified form of TD-EFIE to generate stable transient responses from arbitrarily shaped conducting objects, which possesses the advantage of simplicity in implementation. Numerical examples are given to demonstrate the accuracy and the efficiency of the proposed method

Electromagnetic Scattering by Mixed Conductor-Dielectric Bodies of Arbitrary Shape

A volume-surface electric field integral equation method of moments formulation that makes use of rooftop basis functions defined over prism elements is presented. The new prism elements and their associated basis functions are designed to work either independently or in conjunction with basis functions previously defined over tetrahedral elements. Good agreement is found when comparing results obtained using the present formulation with analytical and experimental results

Analysing radio-frequency coil arrays in high-field magnetic resonance imaging by the combined field integral equation method

We present the combined field integral equation (CFIE) method for analysing radio-frequency coil arrays in high-field magnetic resonance imaging (MRI). Three-dimensional models of coils and the human body were used to take into account the electromagnetic coupling. In the method of moments formulation, we applied triangular patches and the Rao–Wilton–Glisson basis functions to model arbitrarily shaped geometries. We first examined a rectangular loop coil to verify the CFIE method and also demonstrate its efficiency and accuracy. We then studied several eight-channel receive-only head coil arrays for 7.0 T SENSE functional MRI. Numerical results show that the signal dropout and the average SNR are two major concerns in SENSE coil array design. A good design should be a balance of these two factors.

Magnetic field computation with integral equation method and energy-controlled relaxation

The magnetic field integral equation method is applied to linear and nonlinear magnetostatic problems. Two drawbacks of this method, the slow convergence rate and the dense system matrix, are tackled. The convergence behavior is improved by a novel algorithm that determines adaptive relaxation factors at every iteration step by an energy minimum principle. The dense matrix is compressed with the fast multipole method

Frequency Selective Shielding Screen by the Use of Artificial Media

We calculated the shielding characteristic of a three-dimensional array of strip conductors by using the electric field integral equation method and its expansion to an array structure. From reflection coefficients, the effective permittivity of the array is calculated. The effective permittivity becomes negative in the frequency range above resonance, in which the electromagnetic waves travel through the material in an evanescent mode and the transmission coefficient becomes very small.

Incorporation of first-order polarization coupling in UHF propagation over gently undulating terrain using a perfect reflecting surface model

A magnetic field integral equation method for the solution of propagation problems over large smoothly undulating surfaces is discussed. Unlike conventional methods that assume invariance of surface height transverse to the direction of propagation, we incorporate the effects of moderate transverse gradients along a radial profile. In this formulation, vertical and horizontal polarizations are coupled, and a vector integral equation must be solved along a radial path, in a quasi-three-dimensional approach. This provides a first-order correction modeling the depolarizing effects of transverse gradients. Off radial diffraction and multipath effects are neglected in the scheme. Numerical comparison is made with existing two-dimensional integral equation solutions, the uniform theory of diffraction, and measured data.

Treatment of singularities and quasi-static terms in the EFIE analysis of planar structures

This paper reports on some mathematical and numerical details of the application of the electric field integral equation (EFIE) method to the analysis of planar structures printed on multilayered substrates. Closed-form expressions for singular and hypersingular terms of the transverse electric field Green's dyadic (TEFGD) are identified so that they can be explicitly extracted out before solving the EFIE. The problems due to the presence of the hypersingular contribution, usually argued to preclude the application of the EFIE to planar structures, are solved. In addition, a low-frequency expansion of the TEFGD corresponding to a single layer substrate is carried out to recognize nonsingular electrostatic-type contributions that can eventually become very important for computational purposes.

Vector potential integral formulation for eddy-current probe response to cracks

A boundary integral vector potential formulation has been developed to evaluate eddy-current interactions with three-dimensional finite cracks in conductors. The approach is compared with an electric field integral equation method also used for solving crack problems in eddy-current nondestructive evaluation. An important advantage of the vector potential integral formulation is that the kernel has a weak singularity, but a drawback is that two unknown functions must be found on the crack surface. One of these functions, the current dipole density, represents the effect of the crack in terms of an induced source, and the other function is a solution of the two-dimensional Laplace equation. By contrast, the source density alone is needed for a complete solution of the electric field integral equation. In order to determine the surface Laplacian for finite cracks of arbitrary shape, a general numerical solution utilizing the boundary element technique is introduced. Numerical predictions of the eddy-current probe response to a crack give good agreement with experimental measurements, supporting the validity of the formulation.

Reduction of Multiply-Nested Dielectric Bodies for Wave Scattering Analysis By Single Source Surface Integral Equations

A recursive single source surface integral equation formulation for the problem of electromagnetic wave scattering by multiply-nested bodies yields an equivalent outer surface model that is independent of the material and the illumination in the exterior region, and therefore invariant under rotation and translation. The proposed algorithm is applicable to both far-field and near-field problems, and also gives, through a fast backward recursion, the field values at interior points. Such a reduced model may be duplicated and reused in an assortment of complex scattering problems without repeating the reduction calculation. Thus, the high computational efficiencies realized by the recursive formulation, with respect to the previous, direct, single source surface integral equation formulations, are further enhanced for problems involving some degree of repetition, as in geometry and material optimization of scattering structures under various types of illumination. Numerical examples are included in order to demonstrate the features and the efficiency of the recursive multiply-nested algorithm in comparison to direct, simultaneous solution of all unknowns by the electric field integral equation method.

Dual Polarised Electromagnetically coupled Multilayer Stacked Microstrip Patch Antenna

This paper presents the design of a dual polarised electromagnetically coupled microstrip patch antenna at S-band. Multilayer stacking of patches is employed to yield large operational bandwidth, high radiation efficiency and very low level of cross-polarisation in the radiated fields. Electric Field Integral Equation method (EFIE) was used in combination with Method of Moments (MOM) after deriving appropriate Green's functions for multilayer structure to analyse and design this configuration. The current distribution on each layer of the patch was computed to optimally control the resonance frequencies of upper and lower resonators. A four layer configuration was fabricated to experimentally validate the CAD developed. An overall 18% bandwidth was realised and cross polar component was suppressed to -23 dB. Experimental results match well with the theoretically predicted results.

Electro-optic near-field mapping of planar resonators

A comprehensive experimental and theoretical study for the determination of the electric near-field above planar resonators is presented. The transverse component of the electric field is mapped by external electro-optic (EO) sampling technique with high spatial and temporal resolution. The evolution of the near-field radiation pattern of the investigated 7-GHz planar resonator to the onset of the far-field pattern is traced by measurements at various heights above the sample. Frequency-dependent measurements allow to characterize the field pattern changes when the frequency is swept through the main resonance. Additional undesired resonances are identified by the detected mode pattern. The experimental data are reproduced by simulations based upon an electric field integral equation (EFIE) method.

On the electromagnetic field in a cavity fed by a tangential electric field in an aperture in its wall

Heretofore, the electromagnetic field produced by a specified tangential electric field in an aperture in the wall of an arbitrarily shaped cavity has most often been expanded in terms of cavity modes. An alternative approach, that of the electric field integral equation is presented. In this approach, the cavity field is expressed as the field of a surface density of tangential electric current, or a surface density of tangential magnetic current, or a combination of surface densities of tangential electric and magnetic currents on the boundary of the cavity. Each surface density is characterized by a single tangential vector function which is determined by the integral equation requiring that the part of the electric field tangent to the boundary of the cavity must reduce to the specified tangential electric field in the aperture and zero elsewhere on the boundary of the cavity. The electric field integral equation method is specialized to more easily determine the field inside an arbitrary cylindrical cavity excited by a tangential electric field in an aperture in its lateral wall. The method is further specialized to a circular cavity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An Iterative Loop-EMF Method for Calculating Induced EM Fields in Finite Bodies

ABSTRACT A new numerical method, iterative loop-EMF method, for quantifying the induced EM field in a finite, heterogeneous, non-magnetic body irradiated by an incident EM field has been developed. In this method, the body is modeled by an impedance network and Faraday's law is used to relate the induced loop electric field (or current) to the induced magnetic field. In the mean time, a coupled tensor field integral equation is used to iterate the induced electric and magnetic fields. This method can improve numerical accuracy of the existing tensor electric field integral equation method. The theoretical analysis and numerical examples are both presented. Good agreement is obtained by the comparison with the previous published results.

Analysis of infinite arrays of substrate-supported metal strip antennas

An electric field integral equation method is applied to a metal strip antenna on an electrically thick dielectric substrate of finite size in a uniform infinite array environment. An efficient solution is found using the method of moments. Metal strip folded dipole antennas are analyzed both with and without a coplanar strip feed line, and the effects of the substrate and feed line are investigated. A technique for minimizing the effect of feed line scattering is presented, and arrays of these elements are shown to be capable of good scanning performance over a wide range of beam-steer angles. A phased array simulator experiment is described and the measured results show good agreement with those obtained by analysis. The class of antenna elements studied may be fabricated using monolithic microwave integrated circuit (MMIC) technology, and the analysis described illustrates the expected characteristics for millimeter-wavelength phased arrays of this type. >

Numerical simulation of unsteady transonic flows using a field integral equation method

A numerical simulation based on the field integral equation method is developed to compute the flowfield about an oscillatory aerofoil in pitching or in heaving motion using the full potential equation. The wake is modelled by vortices convected by the local velocity and shed into the wake aft of the trailing edge. Numerical solutions are presented at a low reduced frequency of 0.162 so that comparison of the present solutions can be made with experimental data. The NACA 0012 aerofoil is used in these calculations.

Calculation of transonic flows by a field integral equation method

A field integral equation method is developed to solve the two-dimensional compressible potential equation for transonic flow over airfoils with embedded shocks at subsonic freestream Mach numbers. The perturbation velocities are induced by linear internal source and vorticity distributions on the mean camber line of the airfoil and nonlinear field source distributions external to the airfoil surface. Derivatives are calculated in the computational plane, and those in the physical plane are determined by using the Jacobian of the transformation

Diffraction of an H-polarized electromagnetic wave by a circular cylinder with an infinite axial slot

A comparison of three methods of solution for the problem of scattering and diffraction of a transverse electric (TE) polarized plane wave by an infinite circular cylinder having an infinite axial slot is presented. In one method of solution, the aperture field integral equation (AFIE) method, the fields in and around the cylinder are found from the aperture <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -field and the Green's functions for the interior and exterior of a cylinder. In the other two methods, the fields are determined from the surface current, which is obtained by solution of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -field integral equation (HFIE) or the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -field integral equation (EFIE). The field in the aperture of the cylinder is found from the three methods, and the advantages and disadvantages of each method of solution are discussed. In addition, it is also shown that for shell thickness less than 1/20 of a wavelength, the aperture fields do not differ signifcantly from those of an infinitely thin shell cylinder.