A sheet impedance approximation for electrically thick multilayered shields

This paper describes an extension of the sheet impedance concept to treat inhomogeneous or multilayered shields that may be thick in terms of material shield wavelengths. For shields with magnetic materials, a simple relation between the equivalent electric and magnetic currents representing the shield is obtained. This allows the magnetic current to be treated as a dependent unknown and the electric current to be found as the solution of a single surface integral equation shown to be a perturbation of that for a perfect electric conducting (PEC) surface. By using the proper interior equivalent problem, it is shown that the method produces accurate and stable results for shielding by a rectangular box.     

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.      

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.     

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 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     

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.     

A simple hybrid method for ELF shielding by imperfect finite planar shields

A simple method is described for calculating the shielding performance of a two-dimensional (2-D) thin finite-width shield made of imperfect material in the presence of the magnetic field from line source conductors. First, solutions to two canonical problems with closed-form simple analytic formulas are presented; shielding by reflection from and absorption in thin planar shields of infinite extent and shielding by perfect conductor shields of finite width. Then the method for calculation of magnetic-field shielding by perfect conductor finite-width shields is extended using the simple interpolation method, to thick shields made of imperfect material. Finally, the hybrid solution is developed by adding the two results in quadrature. The result is a simple theory for shielding by finite-width shields made of any real shielding material of arbitrary thickness. Its accuracy has been validated by comparison to finite-element method solutions and existing measurements.     

The field equivalence principle: illustration of the establishmentof 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     

A fictitious domain method for conformal modeling of the perfectelectric conductors in the FDTD method

We present a fictitious domain method to avoid the staircase approximation in the study of perfect electric conductors (PEC) in the finite-difference time-domain (FDTD) method. The idea is to extend the electromagnetic field inside the PEC and to introduce a new unknown, the surface electric current density to ensure the vanishing of the tangential components of the electric field on the boundary of the PEC. This requires the use of two independent meshes: a regular three-dimensional (3-D) cubic lattice for the electromagnetic field and a triangular surface-patching for the surface electric current density. The intersection of these two meshes gives a simple coupling law between the electric field and the surface electric current density. An interesting property of this method is that it provides the surface electric current density at each time step. Furthermore, this method looks like FDTD with a special model for the PEC. Numerical results for several objects are presented     

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     

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.     

Image theory for electromagnetic sources in chiral medium above thesoft and hard boundary

The classical image theory valid for electromagnetic (EM) sources in an isotropic medium above a planar perfect electric conductor (PEC) or perfect magnetic conductor (PMC) surface was extended to involve the planar soft-and-hard surface (SHS) boundary that can be realized with tuned corrugations. The image principle is now generalized to EM sources in isotropic chiral medium above an SHS boundary. The problem is solved by two consecutive decompositions of the sources reducing the problem to four classical ones involving electric and magnetic sources above PEC and PMC boundaries; each involving an isotropic nonchiral medium and possessing a known image solution. One of the decompositions is based on the fact that the two eigenwaves of a chiral medium do not couple at a soft-and-hard surface; and, the other one, on the eigenpolarizations of the reflection dyadic     

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     

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     

Fast RCS computation over a frequency band using method of momentsin conjunction with asymptotic waveform evaluation technique

The method of moments (MoM) in conjunction with the asymptotic waveform evaluation (AWE) technique is applied to obtain the radar cross section (RCS) of an arbitrarily shaped three-dimensional (3-D) perfect electric conductor (PEC) body over a frequency band. The electric field integral equation (EFIE) is solved using the MoM to obtain the equivalent surface current on the PEC body. In the AWE technique, the equivalent surface current is expanded in a Taylor's series around a frequency in the desired frequency band. The Taylor series coefficients are then matched via the Pade approximation to a rational function. Using the rational function, the surface current is obtained at any frequency within the frequency range, which is in turn used to calculate the RCS of the 3-D PEC body. A rational function approximation is also obtained using the model-based parameter estimation (MBPE) method and compared with the Pade approximation. Numerical results for a square plate, a cube, and a sphere are presented over a frequency bandwidth. Good agreement between the AWE and the exact solution over the bandwidth is observed     

Field analysis of penetrable conductive shields by thefinite-difference time-domain method with impedance network boundaryconditions (INBCs)

Impedance network boundary conditions (INBCs) are implemented in the finite-difference time-domain (FDTD) method to analyze the electromagnetic field around penetrable shield structures. The shield region is eliminated from the computational domain and the INBCs are applied on the new boundary surfaces, i.e., shield surfaces, to take into account the field discontinuity produced by the shield. The INBCs represent an important extension of the well-known surface impedance boundary conditions (SIBCs) since the INBCs model accurately the coupling of the electromagnetic fields through penetrable shields and lead to a significant reduction of the number of the FDTD unknowns. The INBC expressions are given analytically in both frequency and time domains, and the INBC implementation in a FDTD code is discussed. The proposed INBC-FDTD method is numerically efficient because the resulting convolution integrals are recursively solved. Furthermore, approximate time-constant INBCs are proposed which are valid for many practical applications. The analysis of transient electromagnetic fields around penetrable conductive shields in simple test configurations are presented and compared with the analytical solutions     

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     

Magnetostatic simulations for design of superconducting magneticshields

A magnetostatic approach to numerical simulations of magnetic field attenuation by superconducting shields is demonstrated on simple geometries. Comparisons to published measurements and analytic calculations show that results are accurate for simulation of a shield in the shape of a cylindrical tube. The capabilities of the method are shown by simulations which close the cylinder with end caps having access ports or gaps. With end caps having cylindrical ports, the simulated attenuation transits smoothly between the analytical results for semi-infinite tubes of the two radii. Radial gaps between solid end caps and the cylinder allow little flux leakage for time-varying fields, but significant leakage for static fields