Equivalent Magnetic Currents Research Articles

Analysis of similar behaviors of planar and linear arrays

AbstractIn this paper, the method of moments is employed to analyze both planar and linear finite phased arrays of radiating slots fed by rectangular waveguides. The equivalent magnetic currents and active patterns due to these elements of phased arrays are discussed in detail. The relationship between linear and planar arrays is analyzed, and some similar behaviors are realized. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 196–199, 2001.

Near-field diagnostics of small printed antennas using the equivalent magnetic current approach

A near-field to far-field transformation based on the antenna representation by equivalent magnetic current (EMC) sources has been proposed and validated experimentally on large high-directivity antenna arrays. In this paper, the use of EMC is extended to the diagnostics of low-directivity printed antennas. The limitation of the near-field to far-field transformation applied to EMC models of low-directivity antennas, caused by the finite dimensions of the antenna ground plane, is demonstrated. A method to partially overcome this limitation by including the contribution of diffracted rays is implemented, and its effectiveness is demonstrated with antenna prototypes. It is shown that the agreement between the far-field patterns measured in an anechoic chamber and the patterns computed from the EMC model obtained from the near-field measurements is significantly improved upon, within a sector of /spl plusmn/90/spl deg/ with respect to the antenna boresight in the E plane. The influence of the near-field sampling density and topology of the EMC model on the accuracy of the predicted far-field pattern is examined.

Analysis of finite‐slot phased arrays fed by rectangular waveguides using method of moments

AbstractA rigorous integral equation formulation is made in this paper for the analysis of phased arrays of radiating slots fed by rectangular waveguides. The number of elements is assumed to be finite, and the integral equation used is that of the method of moments. According to the equivalence principle and magnetic field boundary conditions, an integral equation for obtaining slot surface equivalence magnetic currents is formulated. Then, the integral equation is rewritten into a matrix equation after the implementation of the method‐of‐moments procedure. The reflection coefficients as a function of scan angle of, and the inductive magnetic currents over, the array elements are analyzed and discussed in detail. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 132–136, 2001.

A novel design of an air-core type permanent magnet linear brushless motor by space harmonics field analysis

This paper presents a novel design technique and characteristic analysis of an air core type Permanent Magnet (PM) linear motor based on Space Harmonics Field analysis methodology. In the Space Harmonics Field analysis, Poisson equation is solved by the spatial distribution of current and PM, which is replacedly Equivalent Magnetizing Current (EMC). The process of magnetic field analysis is applied to the motor design and steady state analysis considering the driving characteristic. The validity of the proposed technique is confirmed with 2-D Finite Element (FE) analysis and experimental results.

Radial field retrieval for current reconstruction from spherical acquisition

An iterative algorithm for the retrieval of the radial component of the electric field is presented in conjunction with an efficient reconstruction algorithm to calculate an equivalent magnetic current (EMC) distribution from the electric field components obtained in a spherical acquisition.

Theory and experiment of the cavity-backed slot-excited dielectric resonator antenna

A slot-excited hemispherical dielectric resonator antenna backed by a rectangular cavity is studied theoretically and experimentally. The magnetic-type dyadic Green's function for the rectangular cavity is derived using the mode-matching method. An integral equation for the equivalent magnetic current is obtained by enforcing the boundary condition across the slot. The moment method with the Galerkin's procedure is then used to find the magnetic current in the slot and, hence, the input impedance of the antenna. Measurements were carried out to verify the theory and good agreement is obtained. The effects of the slot inclination angle, of the slot offset, and of the cavity size on the input impedance are discussed.

The field equivalence principle: illustration of the establishment of the non-intuitive null fields

The field equivalence principle, one of the fundamental concepts in electromagnetics, has numerous applications. However, for a beginning student, it is not easy to understand this concept thoroughly and to appreciate it. The dilemma faced by beginning students is illustrated. We have sources in a finite Region I, and an arbitrary mathematical surface separating Regions I and II. The equivalent problems for the exterior and interior regions are specified with the use of electric and magnetic equivalent currents impressed on the boundary surface. The acceptance of the establishment by the equivalent sources of the non-intuitive null field for the exterior problem (by the equivalent sources and the original source for the interior problem) is commonly bothersome and not comfortably realized. In order to clarify this, we revisit Love's and Schelkunoff s forms of the equivalence principle. Subsequently, we discuss two simple, analytically tractable illustrative examples, consisting of plane-wave fields in two half-space regions, separated by an infinite planar surface. In particular, the emphasis is on the establishment of the non-intuitive null fields developed by these equivalent sources. Various forms of equivalence are illustrated by simple analytical field expressions.

Study of a dielectric‐loaded slot antenna fed by a finite‐width substrate microstrip line

A dielectric‐loaded slot antenna fed by a finite‐width substrate microstrip line is studied theoretically and experimentally by using the spatial dyadic Green's functions. Emphasis is placed on the analysis of the new feeding method, the finite‐width substrate microstrip line, which is a versatile microstrip structure and can be made as a stand‐alone device. The dielectric load is a hemisphere placed over the slot. The volume equivalence theorem is used to establish the theoretical model of the microstrip line. A simple excitation method for the microstrip line is introduced and modified to fit our problem. The spatial domain multilayered dielectric sphere dyadic Green's functions are used to obtain the scattered electromagnetic fields from the hemispherical dielectric load. The microstrip‐line current, the microstrip‐substrate electric field, and the equivalent magnetic current on the slot are obtained and used to calculate the impedance and the radiation pattern of the antenna. Computed impedances of the unloaded slot antenna and the loaded slot antenna show good agreements with either published data or measurement values. Analysis shows that the permittivities of the microstrip substrate have a significant effect on the impedance level of the antenna. It is found that electrically dense (high permittivities) substrates can give better impedance‐matching between the feeding microstrip line and the slot antenna. The reduction of the antenna impedance by using a thinner substrate has also been demonstrated in our investigation.

TE _{11} -mode excitation of a circular aperture antenna covered by a layered dielectric hemi-spherical radome

This paper presents a full-wave analysis of the antenna radiation due to an aperture in a ground plane generating a circular waveguide TE11 wave, which is covered by a dielectric hemi-spherical radome of multi-layered geometry. Huygen's equivalence principle and the image theory are utilized to simplify the problem. The dyadic Green's function technique is applied to analyze the electromagnetic fields due to the circular aperture antenna with TE 11 field distribution. Following the conventional procedure, the magnetic dyadic Green's functions for radially three-layered and four-layered geometry are for- mulated to account for the full-wave contribution due to such an equivalent magnetic surface current. The coefficients of these dyadics are derived by duality substitution and reduction from the authors' earlier published work. The Fraunhofer electric fields are obtained using the far-zone approximation. In order to show the applicability of the analysis in this work and demon- strate the effects of the dielectric radome on the radiation patterns, computations of the power patterns, beamwidths, and total transmission losses are made and the results obtained here are compared with the existing results in the literature.

The novel technique considering slot effect by equivalent magnetizing current

This paper presents a novel analytical technique of a permanent magnet linear synchronous motor (PMLSM) based on the Equivalent Magnetizing Current (EMC) method. In particular, the paper focuses on the slot effect resulting in a change of the steady-state performance of the PMLSM. Computed results by the proposed technique are compared with those obtained by both the finite element method (FEM) and experiment.

Sequential reconstruction of equivalent currents from cylindrical near field

A formulation for the sequential calculation of equivalent magnetic current (EMC) components from known near field data over a cylindrical surface is presented. The maximum likelihood method is used to obtain each component of the EMC. Numerical results of source reconstruction and near field to far field transformation are presented.

Single integral equation for electromagnetic scattering by three-dimensional homogeneous dielectric objects

A single integral equation formulation for electromagnetic scattering by three-dimensional (3-D) homogeneous dielectric objects is developed. In this formulation, a single effective electric current on the surface S of a dielectric object is used to generate the scattered fields in the interior region. The equivalent electric and magnetic currents for the exterior region are obtained by enforcing the continuity of the tangential fields across S. A single integral equation for the effective electric current is obtained by enforcing the vanishing of the total field due to the exterior equivalent currents inside S. The single integral equation is solved by the method of moments. Numerical results for a dielectric sphere obtained with this method are in good agreement with the exact results. Furthermore, the convergence speed of the iterative solution of the matrix equation in this formulation is significantly greater than that of the coupled integral equations formulation.

A boundary-element solution of the Leontovitch problem

A boundary-element method is introduced for solving electromagnetic scattering problems in the frequency domain relative to an impedance boundary condition (IBC) on an obstacle of arbitrary shape. The formulation is based on the field approach; namely, it is obtained by enforcing the total electromagnetic field, expressed by means of the incident field and the equivalent electric and magnetic currents and charges on the scatterer surface, to satisfy the boundary condition. As a result, this formulation is well-posed at any frequency for an absorbing scatterer. Both of the equivalent currents are discretized by a boundary-element method over a triangular mesh of the surface scatterer. The magnetic currents are then eliminated at the element level during the assembly process. The final linear system to be solved keeps all of the desirable properties provided by the application of this method to the usual perfectly conducting scatterer; that is, its unknowns are the fluxes of the electric currents across the edges of the mesh and its coefficient matrix is symmetric.

An improved near- to far-zone transformation for the finite-difference time-domain method

Near- to far-zone transformation for the finite-difference time-domain (FDTD) method can be performed by integration of the equivalent electric and magnetic currents originating from scattered electric and magnetic fields on a surface enclosing the object. Normally, when calculating the surface integrals, either the electric or magnetic fields are averaged since the electric and magnetic fields are spatially shifted in the FDTD grid. It is shown that this interpolation is unnecessary and also less accurate than if an integration is performed on two different surfaces. It is also shown that the accuracy of the far-zone transformation can be further improved if the phase is compensated with respect to a second-order dispersion corrected wavenumber. For validation, scattering results for an empty volume, a circular disk, and a sphere are compared with analytical solutions.

Microstripline- and stripline-fed aperture-coupled cylindrical rectangular microstrip antennas

Stripline-fed and microstripline-fed aperture-coupled cylindrical rectangular microstrip antennas are investigated. The equivalence principle is invoked to separate the feedline and the antenna patch with equivalent magnetic currents distribution on the aperture region. The Lorentz reciprocity theorem is applied to find the interactions between the aperture and the feedline. The unknown patch current and aperture field are determined by solving coupled integral equations, which involve spectral-domain Green's functions, using Galerkin procedure. Numerical results of input-impedance and far-field patterns are compared with those for antennas on a planar surface.

Efficient electromagnetic analysis of a doubly infinite array of rectangular apertures

An accurate and rapid method is presented for solving the magnetic field integral equation for the equivalent magnetic currents representing a doubly periodic array of rectangular apertures. Ewald's method is used to accelerate the summations associated with periodic Green's function, allowing the Green's function to be determined to nearly machine precision. Galerkin's method is used to discretize the integral equation with Chebyshev polynomials used as the basis and testing functions. Efficient treatment of the "self-term" singularity is emphasized.

Stripline-fed arbitrarily shaped printed-aperture antennas

A full-wave analysis method is presented for modeling the radiation properties of a stripline-fed planar printed-aperture antenna element. In this formulation, both the finite length of stripline and the finite aperture may be of any arbitrary shape since their equivalent electric and magnetic currents are modeled with triangular patch basis functions. Galerkin's method is applied to numerically solve the coupled mixed-potential integral equation (MPIE). Exact spatial-domain Green's functions are used to account for all radiation, surface-wave, and mutual-coupling effects. Interactions between the stripline feed and the radiating aperture are rigorously included. Numerical analysis is presented for the following nonrectangular shapes: an exponentially tapered slot, an annular slot, an annular slot with opposing stubs, and a monofilar Archimedean spiral slot element. Results are shown for input return loss, radiation patterns, and axial ratio for the circularly polarized elements.

A hybrid FEM/SBR method to compute scattering by large bodies with small protruding scatterers

A hybrid method that combines the finite-element method (FEM) and the shooting-and-bouncing-ray (SBR) method is presented to compute scattering by large bodies with small protruding scatterers. In the method, the field equivalence principle is employed to replace the protruding scatterers by a set of equivalent electric and magnetic currents. The total scattered field then becomes the superposition of the field scattered by the large body without protrusions, which is calculated with the use of the SBR method, and the field radiated by the equivalent currents in the presence of the large body, which is also calculated with the use of the SBR method with the aid of the reciprocity theorem. The required equivalent currents are computed with the use of the FEM, which permits the handling of complex material composition of the protrusions. Two-dimensional examples are presented to demonstrate the feasibility of the proposed method. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 14: 78–84, 1997.

Three-dimensional eddy current analysis by the boundary element method

A boundary element method has been developed for the analysis of 3D eddy current problems. This method is based on the boundary integral equation formulation with equivalent electric and magnetic currents and electric charge as unknowns. Linear shape functions, defined parametrically over a quadrilateral element, have been selected for the Galerkin's method.

Parallel CARLOS-3D — an electromagnetic boundary integral method for parallel platforms

CARLOS-3D is a three-dimensional general purpose computer code for calculating the scattering from complex three-dimensional bodies. The code uses the method of moments technique with Galerkin testing, to solve the StattonChu, integral equations for the specified geometry. All of the surfaces describing the scatterer are replaced by equivalent electric and magnetic currents which are then determined via the solution of a matrix equation. The parallel implementation of this code is discussed together with the parallel in-core solver developed at Sandia National Laboratories. Results for the parallel performance of the code are presented.