A sheet impedance approximation for electrically thick materialshields

This paper describes a simple extension of the sheet impedance concept to treat electromagnetic (EM) shields that may be thick in terms of material shield wavelengths. For magnetic shields, a simple relation between the equivalent electric and magnetic currents representing the shield is obtained, and the electric current is found as the solution of a single surface integral equation that is shown to be a simple perturbation of that for a perfect electric conducting (PEC) surface. Finally, it is shown that the computation of the small interior fields of good shields requires the use of the proper PEC interior equivalent problem     

Moment method analysis of the magnetic shielding factor of aconducting TM shield at ELF

This paper presents an integral equation and method of moments (MoM) solution to the problem of TM transmission by a metallic conducting shield at extremely low frequencies (ELF). In order to accurately compute the total fields interior to the shield, equivalent problems are formulated which avoid the numerically difficult problem of computing the total fields as the sum of the incident plus scattered fields. In particular, the total electric field on the interior surface of the shield is obtained by a volume current equivalent problem, and then the total magnetic field interior to the shield is formulated in terms of equivalent magnetic surface currents flowing on the interior surface of the shield replaced by a perfect conductor     

An Equivalent Surface Source Method for Computation of the Magnetic Field Reduction of Metal Shields

A numerical method for computation of the resultant quasi-static magnetic field in the vicinity of parallel wires and metal shields is presented. The primary magnetic field source is time-harmonic currents in wires. This field is modified by conducting magnetic and/or nonmagnetic shields. The material is assumed to be linear under the applied source field. The shielding effectiveness can be estimated by a comparison between the primary and the resultant field. The reaction magnetic field is expressed by a sum of fields caused by equivalent single- and double-layer sources distributed on the shield surface. Integral equations for unknown distributions of these equivalent sources are derived from the Green's second identity implemented inside and outside the shields. These equations are coupled integral equations, and are solved by the moment method. Numerical results of the resultant (shielded) magnetic field obtained with the proposed method are compared with the results of: 1) analytically solvable problems; 2) measurements; and 3) two different numerical methods.      

On the boundary conditions at surface current distributions described by the first derivative of Dirac's impulse

Boundary conditions at surface distributions of doublets of electric current are considered in this work. It is shown that such current distributions can be treated as the superposition of a double plus a single layer of electric current, the latter being equivalent to a simple layer of magnetic current. Accordingly, it is shown that proper distributions of purely electric current can be specified over any given closed surface so that no fields are excited inside the volume bounded by the surface.     

On the attenuation of transient fields by imperfectly conducting spherical shells

Exact formulas for the electric and magnetic fields at any arbitrary point within a cavity region completely enclosed by a conducting spherical shell of arbitrary size are derived under the assumption that the exciting electromagnetic field is a linearly polarized, monochromatic, plane wave falling on the external surface of the shell. It is shown that the polarization of the electromagnetic field at the center of the cavity is the same as the polarization of the incident wave. From a knowledge of this steady-state solution, the time history of the electromagnetic field at the center of the cavity is calculated for the case where the incident wave is a Gaussian pulse. Numerical information on the effectiveness of the aluminum and copper shields under steady-state and transient conditions is provided for several pulse durations, shield sizes, and wall thicknesses.     

Electromagnetic coupling to and from shielded cables-optimizingfactors

Judging the shielding effectiveness of shielded cables often means in practice that only the transfer impedance is considered. The transfer impedance essentially characterizes the coupling via the magnetic field; the coupling via the electric field, the transfer admittance, is mostly neglected. This may be correct for shields with high optical coverage but for optimized single braided shields (coverage ≈0.8 . . . 0.9), the transfer admittance has to be taken into account. In practice, the cable shields are mostly grounded or open-ended at the line ends. With regard to the shield connections, the electromagnetic coupling to a cable by a plane wave and coupling from a cable are investigated. From the results, optimizing factors for the coupling parameters of shielded cables are deduced. By means of these optimizing factors the coupling to and from a cable can be minimized in certain applications     

Geometrical aspects of magnetic shielding at extremely lowfrequencies

The magnetic shielding effectiveness for closed and open shield structures is studied at extremely low frequencies. Analytical solutions are used for simple geometries, while more complex structures are evaluated using a finite-element method. Both highly conductive and ferromagnetic materials are studied, and their different shielding behavior is shown. Ferromagnetic shields give good results for small and closed shields and they also give a large field attenuation at close range to the source for open shield geometries. Highly conductive materials, on the other hand, are found to be suitable for large shield sizes. The attenuation is, however, reduced in the close vicinity of the source. Comparisons of numerical results with analytical calculations and measurements confirmed the high accuracy of the finite-element model     

介质体电磁散射分析中的等效偶极矩法

在介质体电磁散射分析中,提出了一种基于等效偶极矩法的快速矩阵生成技术。该方法以矩量法和RWG基函数为基础,将源点处的电(磁)流等效为电(磁)偶极子,因而阻抗矩阵元素可以认为是源点电(磁)偶极子所产生的近区场与场点电流基函数之间的相互作用。这样等效偶极矩法避免了格林函数二重积分,使得阻抗矩阵元素的生成速度明显提高。数值结果表明该方法有较高的计算效率和精度。     

A simple theory for optimizing finite width ELF magnetic fieldshields for minimum dependence on source orientation

The effectiveness of single layer, finite width, planar extremely low frequency (ELF) magnetic field shields is strongly dependent upon the orientation of the field sources. Since source information is difficult to obtain, the issue of designing shields which are independent of source orientation is important. Here, a simple analytic model for shielding by multiple layer, finite width, planar shields constructed from perfect electric and perfect magnetic material is presented. This is augmented by a study of conditions for which the perfect material approximation is valid. The simple model is used to determine strategies for designing shields which are independent of source orientation. It is found that two layer perfect electric/magnetic shields perform significantly better than single layer shields     

Geometrical Effects on Shielding Effectiveness at Low Frequencies

A frequent approach to computing the magnetic shielding effectiveness of enclosures is to consider the effect of a plane wave impinging on a sheet of infinite extent. This permits an analysis based on a transmissionline characterization. However, when the wavelength is large compared to the dimensions of the enclosure, other analytical approaches provide better results. It has been shown that the current distribution on a box-like object scattering in the Rayleigh region tends to concentrate at the edges and corners of the box. This leads to concentrations of the magnetic field in the vicinity of edges and corners both inside and outside the enclosure. Since the effects of the current concentrations are localized, the magnetic shielding problem can be simplified by assuming a uniform current distribution on the exterior of the enclosure. Under this assumption the socalled ?circuit approach? can be applied. The box-like enclosure is characterized as a series of shorted turns which shield a sensor within the enclosure. Based on the geometry, the mutual and leakage impedances between the source and sensor are used to compute the magnetic shielding effectiveness. This approach yields valid results for shields constructed of either wire mesh or sheet metal. It can also be extended to account for degradation due to bad bonds. A comparison of results, both transient and steady state, of the circuit approach and scattering theory show close agreement for spherical enclosures.     

The equivalence of the electric and magnetic surface current approaches in microstrip antenna studies

It is shown that the fields produced by the electric surface currents on the conducting patch of a microstrip antenna are equivalent to those produced by a magnetic surface current sheet bounding the patch in the substrate only when dyadic Green's functions for the two-layer stratified medium are used.     

Transient electromagnetic field propagation through infinite sheets, into spherical shells, and into hollow cylinders

Gaussian electromagnetic field pulses of several durations are propagated through infinite sheets into the interior of hollow cylinders and into the interior of spherical shells. The plates, spheres and cylinders are made of aluminum and contain no slots. The time history of the propagated pulses is computed. Finally, the time sequence of the electric field is calculated in the interior of a cylinder of finite length when connected at its ends by wires to a generator delivering a current pulse of Gaussian shape. The dimensions of the cavities are assumed to be sufficiently small so that resonances are not excited by the highest significant frequency contained in the shortest pulse considered. The numerical study is restricted to thin-walled aluminum shields 1/32 inch, 1/16 inch, 1/8 inch and 1/4 inch thick. The half-amplitude widths of the pulses employed lie in the range14 musec to2400 musec. It is shown that the resultant Gaussian pulse electric fields defined on the surface of the plates and cylinders are propagated with little diminution in amplitude. This is understandable due to the requirement that the tangential fields are continuous across the interfaces, and to the fact that skin effect is almost nonexistent at low frequencies. The incident (as contrasted to resultant) field pulse undergoes reflection at the boundary surface. Hence, the attenuation sustained by the incident field is great, since reflection is the chief mechanism of attenuation of fields at low frequencies. Thin spherical shells form effective magnetic shields. The electric field is small in the interior of thin-walled cylinders carrying extremely large transient 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&oarr;_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&oarr;_s for a small, square aperture loaded with a number of impedance sheets of practical interest. These values of M&oarr;_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     

On Reducing the Lightning Transients in Buried Shielded Cables Using Follow-On Earth Wire

This paper investigates the importance of a follow-on buried bare earth wire for the lightning protection of buried shielded cables. The use of follow-on bare wires for lightning protection of communication towers was suggested as a recommendation in certain standards, without being complemented either by theory or experiments. When lightning transients couple to the cable shields, it induces large currents (depending on the type of coupling) causing transient overvoltages between the inner conductors and the shield. It is shown by simulations based on multiconductor transmission line theory that if the follow-on bare earth conductor is placed in parallel with the shielded cable with the bare earth wire connected to the shield at the current injection end, then the shield current, and thereby, the internal transient voltages of the cable are reduced considerably.     

An improved near- to far-zone transformation for thefinite-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     

A Nonmodal Formulation for Electromagnetic Transmission through a Filled Slot of Arbitrary Cross Section in a Thick Conducting Screen

This paper considers the two-dimensional problem of electromagnetic transmission through a filled slot of arbitrary cross section in a thick perfectly conducting screen. The equivalence principle is used to divide the original problem into three isolated parts where postulated equivalent sources radiate into unbounded, homogeneous media. These equivalent electric and magnetic currents are chosen to ensure continuity of the tangential components of electric and magnetic fields at each aperture. An integral equation is written for each of the three parts with the equivalent currents as unknowns. The resulting set of coupled integral equations is solved by the method of moments. It is shown in the Appendix that this set of equations has a unique solution. The primary quantities computed are the equivalent magnetic and electric currents on each aperture and the electric current on the remaining portions of the slot cross section. These results are compared with those obtained from a modal solution, where the fields in the slot cross section are expressed in terms of parallel-plate waveguide modes.     

A measure of coupling efficiency for antenna penetrations

The electromagnetic penetration into a shielded enclosure through an antenna connected to a receiver inside the shield is discussed. Reciprocity is used to relate the far-zone fields to the short circuit current in the transmission line. Using a Norton equivalent circuit, a measure of coupling efficiency is derived, relating the electric field incident on the antenna to the current incident on the receiver. It is shown that the coupling efficiency can be determined from standard electromagnetic measurements. As a first example, an open-ended coaxial waveguide is considered. As a second example, a transmission line connected to a receiver inside the shield and to a center-fed dipole antenna outside the shield is discussed. Numerical results are presented for the dipole for various receiver bandwidths and transmission line characteristics. The results are given both in the frequency domain and in the time domain for a pulse incident field     

Integral equation modeling of the scattering and absorption ofmultilayered doubly-periodic lossy structures

Previously, the scattering and absorption of a doubly-periodic array of pyramidal absorbers were analyzed using a surface integral equation (SIE) approach. This method is now extended to multilayered absorbers with arbitrarily shaped surfaces between the layers. The developed method is verified on planar stratified absorbers, on wedge absorbers, and rectangular absorbers showing the capability of the method to handle such structures as well. It is also shown that convergence depends critically on the discretization of the equivalent electric and magnetic current     

A stable integral equation for electromagnetic scattering fromhomogeneous dielectric bodies

It is shown that a previously derived integral equation for electromagnetic scattering from a homogeneous dielectric body (see ibid., vol.AP-32, p.166-172, Feb. 1984) does not have a unique solution at resonant frequencies of the cavity formed by making the surface S of the body perfectly conducting and filling the region internal to S with the external medium. This integral equation was formulated so that an equivalent electric current radiates in the presence of the homogeneous external medium to produce the scattered field external to the body. A combination of equivalent electric and magnetic currents is used to formulate an integral equation whose solution is always unique