Modeling of magnetic-field coupling with cable bundle harnesses

A field-to-line coupling model is developed for cable bundle harnesses in terms of the scattering currents and total line voltages. The equivalent distributed sources representing the effects of electromagnetic coupling are expressed as a function of the incident magnetic-field components. Such a formulation is particularly suitable to be used for the analysis of multiconductor transmission lines excited by a transient field, when data for the incident electric field are either inaccurate or not available. This model allows the accurate calculation of the induced voltages and currents on complex cable bundles. The effects on the induced voltages and currents due to ground losses and to the presence of the dielectric sheath in shielded and unshielded cables is discussed, considering bundles excited by either slow or fast transient fields. Numerical applications demonstrate the validity of the proposed procedure.     

The shielding of a plane wave by a cylindrical array of infinitely long thin wires

A plane wave is considered to be incident upon a cylindrical array of infinitely long perfectly conducting thin wires. The wave is assumed to have no magnetic field component in the direction of the wire axes. Exact expressions are found for the currents excited on the wires-and for the total electric and magnetic fields. Numerical computations are made to determine the currents on the wires and the fields inside the array. It is discovered that an important parameter is the number of wires in the array divided by the number of wavelengths that can be wrapped around the cylinder. If this parameter is large enough, the current distribution on the wires resembles that of a solid conducting cylinder, and the array of wires tends to behave like an electromagnetic shield. For smaller values of the parameter, the current distribution can be quite different, and the field inside the array may even be enhanced.     

A comparison between two kinds of equivalent currents to analyze conducting bodies with apertures using moment methods: Application to horns with symmetry of revolution

A system of integral equations (SIE) based on the unique-hess theorem that uses only electric equivalent currents (EEC) is formulated to analyze conducting bodies with apertures. This SIE is compared with an SIE that uses both electric and magnetic equivalent currents (EMEC). In general, to solve both SIE's numerically difficult computations of Cauchy principal-value integrals with highly singular kernels are required. These integrals appear when computing electric (magnetic) fields created by magnetic (electric) currents. Their evaluation can be avoided using the EEC approach in many practical cases when the main interest is in the radiation patterns of aperture antennas. The two SIE's are compared by carrying out an analysis of rotationally symmetric horns using the moment method (MM) in its formulation for bodies of revolution. Numerical results of electric currents and radiation patterns are presented for small horns of various geometries. These results compare quite well with measurements for both SIE's. However, the central processing unit (CPU) time for the EEC formulation is an order of magnitude smaller than for the EMEC formulation.     

Full-wave analysis of coupled perfectly conducting wires in amultilayered medium

A full-wave analysis of coupled perfectly conducting cylindrical wires in a multilayered dielectric medium is presented. The analysis is based on a Fourier series expansion of the unknown surface currents on each wire and on an integral equation for the longitudinal field on the wires. The calculations are not restricted to the propagation constants of the different modes, but explicit results are presented for the impedances associated with each wire and each eigenmode as a function of frequency. Propagation constants, longitudinal currents on the wires, and impedances lead to a complete equivalent circuit for the structures being considered     

FDTD modeling of arrays and grids of lossy conductors based on impedance sheet conditions

Fast finite-difference time-domain (FDTD) modeling techniques for arrays of parallel wires and wire meshes are developed. The analytical basis of the models lies in the use of impedance sheet conditions (Kontorovich conditions) for dense wire arrays and grids, connecting the tangential electric fields and the averaged currents in the plane of a wire array or grid. The proposed methods allow us to avoid the direct discretization of the fields inside the wires, greatly simplifying the modeling task. The conductor losses in the wires are accounted for assuming a strong or weak skin effect. The impedance sheet conditions are formulated in the time-domain using the convolution integral, which is evaluated recursively in FDTD. Numerical examples and comparisons with analytical results are provided to verify the proposed techniques.     

Analysis of the coupling of an incident wave with a wire inside a cavity using an FEM in frequency and time domains

This paper presents a numerical method based on finite elements in both the frequency and time domains for modeling the coupling of an incident wave with a conducting wire placed inside a metallic cavity having a small aperture. The method uses edge elements on tetrahedra for the electric field representation. The formulation can take into account thin wires as well as lumped elements. In the time-domain approach, the time derivatives are discretized by the Newmark method, which allows obtaining an unconditionally-stable scheme with second-order accuracy. Numerical results are provided to validate the presented method.     

Electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body

The method of moments technique for analyzing electromagnetic scattering from an arbitrarily shaped three-dimensional homogeneous chiral body is presented based on the combined field integral equations. The body is assumed to be illuminated by a plane wave. The surface equivalence principle is used to replace the body by equivalent electric and magnetic surface currents. These currents radiating in unbounded free space produce the correct scattered field outside. The negatives of these currents produce the correct total internal field, when radiating in an unbounded chiral medium. By enforcing the continuity of the tangential components of the total electric and magnetic fields on the surface of the body, a set of coupled integral equations is obtained for the equivalent surface currents. The surface of the body is modeled using triangular patches. The triangular rooftop vector expansion functions are used for both equivalent surface currents. The coefficients of these expansion functions are obtained using the method of moments. The mixed potential formulation for a chiral medium is developed and used to obtain explicit expressions for the electric and magnetic fields produced by surface currents. Numerical results for bistatic radar cross sections are presented for three chiral scatterers - a sphere, a finite circular cylinder, and a cube.     

Single integral equation for electromagnetic scattering bythree-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     

On bounding the equivalent radius

The concept of the equivalent radius, first introduced by Hallén, has been useful in the solution of antenna and scattering problems that involve electrically thin wires of arbitrary cross section. Generally, the solution is first calculated for circular wires of an arbitrary radius, and this radius is then replaced by the equivalent radius of the noncircular wire. In this way the original problem is reduced to that of finding the equivalent radius. Here we bound the equivalent radius through the use of certain isoperimetric inequalities so that the bounds are completely described by knowledge of the wire's cross-sectional area and perimeter. For a given cross-sectional area it is shown that the circular wire possesses the smallest equivalent radius. Applications of these results to problems in shielding and scattering are suggested.     

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     

Higher order impedance boundary conditions for sparse wire grids

Higher order impedance boundary conditions designed for modeling wire grids of thin conducting wires are established. The derivation is based on the exact analytical summation of the individual wire fields. This allows one to write an approximate boundary condition on the grid surface, which connects the averaged electric field and the averaged current (or the electric field and the averaged magnetic fields on the two sides of the grid surface). The condition depends on the tangential derivatives of the averaged current (up to the sixth order). This approach provides an extension of the averaged boundary conditions method (well established for dense grids) to sparse grids. Numerical examples demonstrate very good accuracy of the solutions for the field reflected from grids with the wire separation as large as half of the wavelength     

Currents induced in a wire cross by a plane wave incident at an angle

The currents induced in a thin-wire cross with equal mutually perpendicular arms by an incident plane electromagnetic wave are determined when the normal to the wave front is perpendicular to the horizontal wire and is at an anglethetawith respect to the vertical wire; the direction of the electric vector in the wave front is arbitrary. The analysis is formulated in general terms but explicit formulas are obtained only for the zero-order currents which are generally adequate to determine the scattered field of very thin wires. The relatively simple formulas consist of even and odd parts for both the vertical and horizontal wires; they include components due to mutual coupling as well as those excited directly by the incident field.     

Analysis of a four parallel wire antenna system by the spatialFourier transform method

The electromagnetic fields and currents associated with an infinite four parallel wire transmission line are analyzed through the use of the spatial Fourier transform method. The near and far electromagnetic fields and currents that are associated with frill and gap voltage excitations are analyzed by the Fourier transform method. Possible VHF compact range applications of a four parallel wire antenna system are discussed, including the possibility of simulating an off-axis EM plane wave by the appropriate adjustment of the exciting voltage phase on each of the four parallel wires. Comparisons of Fourier transform method solutions with method-of-moments solutions and finite-difference-time-domain solutions are made for an infinite four parallel wire antenna system     

Electromagnetic scattering and radiation from finite microstripstructures

Two techniques are presented for the analysis of electromagnetic radiation and scattering from finite microstrip structures. The two techniques are based on two different formulations, viz. the volume-surface and surface-surface formulations. In the volume-surface formulation the finite-sized dielectric is replaced by an equivalent volume polarization current whereas the conducting plates are replaced by equivalent surface currents. For the surface-surface formulation the surface covering the dielectric volume is replaced by equivalent electric and magnetic currents and the conducting plates by surface electric currents. Both techniques can be utilized for the analysis of arbitrarily shaped finite microstrip structures. The techniques are quite accurate, and they are utilized to validate each other. Typical numerical results are presented to demonstrate the agreement between these two solution techniques     

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     

EM pickup and scattering by a wire

This article treats pickup and scattering by a single wire in free space or over a ground plane. The wire may be uniform or nonuniform and infinite or finite. We only treat the case where wire radius is so small compared to a wavelength and the other problem dimensions that scattering by the wire is independent of azimuth. Solutions based directly on Maxwell's equations are compared with solutions based on the telegrapher's equations; for 1 mm radius Cu wire at 1 GHz, equilibrium CW currents as computed from the two models, for a uniform, infinite wire, differ by 6 dB. In general, the wire-current solutions are separated into a homogeneous part and a particular or driven part. The driven part couples and scatters fields, while,at least on an infinite wire in the far field, the homogeneous part does not     

Analytical aspects of plane wave illuminated thin wires and slits

The paper deals with simple elementary approximations for the current and charge response on different straight wire structures, dipoles and short slits in the receiving case. After proof that transmission line equations are also valid for single wires without discontinuities, these equations are formulated including the incoming wave. They turn out have simple particular solutions that could be expected for the case, when the electric field is parallel to the wire, but holds true for the general case too. Satisfying the boundary condition at discontinuities (wire ends, lumped elements) gives rise to additional waves appearing as solutions of the homogeneous wave equation. The formulation of currents along and voltages across a slit, including an illuminating magnetic field at one side of the screen, leads again to transmission-line type equations and, consequently, to the inhomogeneous wave equation. As slits in screens are usually small in terms of wavelength, an approximative solution for the short slit will do. For this case, even closed-form expressions are possible for the magnetic near field     

The Effect of Cylindrical Ferromagnetic Shells on the Self and Mutual Inductance of Parallel Wires

The effect of ferromagnetic shields on the self and mutual inductances of the wires enclosed by a ferromagnetic shell has been theoretically analyzed. Some theoretical equations based on a simplified model, which assumes that the driving wires and returning wires are located within two separated magnetic shells, are derived. The analysis shows that the effect of the ferromagnetic shells on the inductance of the wires depends strongly on the separation of the two magnetic shells; the closer the two magnetic shells, the stronger the effect. For a configuration of two identical ferromagnetic shells of internal radius 0.65 cm and separated by 10 cm, it is estimated that the self and mutual inductances are increased by about 30 percent for a wire of radius 0.06 cm. The changes of the self and mutual inductances are essentially due to the interactions between the ferromagnetic shells and the induced fields of the current elements.     

Heat Loss of Circular Electric Waves in Helix Waveguides

This paper presents a theoretical calculation of the eddy current losses of circular electric waves in a closely-wound helix waveguide. The wire diameter is assumed large compared to the skin depth, but small compared to the guide diameter and the operating wavelength, so that the fields near the wire are quasistatic and may be determined by conformal mapping. When the wires are in contact, the waveguide wall is effectively a metal surface with grooves of semicircular cross section, the current flow being parallel to the direction of the grooves. The power loss for this case is computed to be about 8.5 per cent higher than in a waveguide with smooth metal walls. When the wires are not in contact, the wall is treated as a grating of parallel, round wires. The increase in power loss over a smooth surface is approximately 22.5 per cent when the wires are separated by a distance equal to their diameter.     

Transient electromagnetic scattering from dielectric objects using the electric field Integral equation with Laguerre polynomials as temporal basis functions

In this paper, we propose a time-domain electric field integral equation (TD-EFIE) formulation for analyzing the transient electromagnetic response from three-dimensional (3-D) dielectric bodies. The solution method in this paper is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Triangular patch basis functions are used for spatial expansion and testing functions for arbitrarily shaped 3-D dielectric structures. The time-domain unknown coefficients of the equivalent electric and magnetic currents are approximated using a set of orthonormal basis function that is derived from the Laguerre functions. These basis functions are also used as the temporal testing functions. Use of the Laguerre polynomials as expansion functions for the transient portion of response enables one not only to handle the time derivative terms in the integral equation in an analytic fashion but also completely separates the space and the time variables. Thus, the time variable along with the Courant condition can be eliminated in a Galerkin formulation using this procedure. We also propose an alternative formulation using a different expansion of the magnetic current. The total computational cost for this new method is similar to that of an implicit marching-on in time (MOT)-EFIE scheme, even though at each step this procedure requires more computations. Numerical results involving equivalent currents and far fields computed by the two proposed methods are presented and compared.