Shielding effectiveness of a rectangular enclosure with arectangular aperture

An analysis is presented of the shielding effectiveness (SE) of a rectangular enclosure with an aperture in one face. The enclosure is treated as a length of rectangular waveguide and the aperture as a length of coplanar strip transmission line. Theoretical values of SE agree with measurements for a range of enclosures, apertures and frequencies. The variation of SE with position in the enclosure is also correctly predicted     

A hybrid FD-MoM technique for predicting shielding effectiveness of metallic enclosures with apertures

In this paper, a hybrid technique combining the finite-difference (FD) method and the method of moments (MoM) in the frequency domain is proposed to predict the shielding effectiveness of rectangular conducting enclosures with apertures under external illumination. The interior and exterior regions of the enclosure are analyzed separately by employing the field equivalence principle. Internal electromagnetic fields are discretized using the (FD) method, while external fields are formulated by the MoM. Enforcement of continuity of the tangential magnetic field over the aperture surface gives the desired equation to solve for electromagnetic fields everywhere. Numerical results for the shielding effectiveness of a rectangular cavity with apertures calculated by the new hybrid technique are presented and validated by comparing with experimental data.     

Shielding effectiveness of metallic enclosures at oblique and arbitrary polarizations

Shielding effectiveness of metallic enclosures with apertures when illuminated by an oblique incidence arbitrary polarized plane wave has been studied by using an efficient hybrid modal/moment technique. Shielding effectiveness of rectangular enclosures with one, two, and four apertures at multiple points inside the enclosures for various frequencies has been calculated when the illuminating source flies by the front of the enclosure. The work shows that the shielding effectiveness is seriously affected by frequency, angle of incidence and polarization of the illuminating field; the number and orientation of apertures; and the location inside the cavity. It has been shown that the usual assumption about the normal incidence being the worst-case scenario for shielding effectiveness values may not be valid when there is more than one aperture in the cavity. The paper emphasizes the need for the statistical investigation of shielding effectiveness problem of metallic enclosures with apertures.     

EMI from cavity modes of shielding enclosures-FDTD modeling andmeasurements

Electromagnetic interference (EMI) from slots and apertures resulting from coupling of interior sources through enclosure cavity modes in a rectangular test enclosure is reported. EMI from a specially designed test enclosure with slots or apertures excited by interior sources was studied experimentally and with finite-difference time-domain (FDTD) modeling. The measurements and FDTD modeling agree well. The results indicate that radiation at cavity mode resonances through slots and apertures of nonresonant dimensions can be as significant as the radiation at aperture or slot resonances. The agreement between the FDTD modeling and measurements demonstrates the usefulness of FDTD for investigating aspects of shielding enclosure design such as coupling to slots and apertures and slot interactions     

EMI from airflow aperture arrays in shieldingenclosures-experiments, FDTD, and MoM modeling

Aperture arrays designed to provide airflow through shielding enclosures can provide part of the coupling path from interior sources to external electromagnetic interference (EMI). In this work, radiation through aperture arrays is investigated numerically and experimentally. FDTD modeling is compared with measurements on aperture arrays in a test enclosure. The method of moments (MoM) is also utilized to study radiation from apertures and to investigate the mutual coupling between apertures in an infinite conducting plane. A simple design equation for the relation between aperture size and number and shielding effectiveness is proposed     

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     

Diffusive electromagnetic penetration into metallic-enclosures

The physics of shielding by a metallic enclosure is discussed. Simple engineering formulas in the frequency and time domains are deduced from a rigorous formulation to calculate the cavity fields for certain canonical enclosure shapes. These simple formulas are generalized so as to be applicable to enclosures of arbitrary shape. The great difference in shielding effectiveness between enclosures and planar slabs is pointed out.     

An EMI estimate for shielding-enclosure evaluation

A relatively simple, closed-form expression has been developed to estimate the EMI from shielding enclosures due to coupling from interior sources through slots and apertures at the enclosure cavity modes. A power-balance method, Bethe's (1944) small-hole theory, and empirically developed formulas for the relation between radiation, and slot length and number of slots, were employed to estimate an upper bound on the radiated EMI from shielding enclosures. Comparisons between measurements and estimated field strengths suitably agree within engineering accuracy     

Review of Circuit Approach to Calculate Shielding Effectiveness

The shielding effectiveness of an enclosure at low frequencies can be readily computed using a circuit approach. Not only does this technique include the effects of the properties of the shield material, but it also includes the details of the geometry of the enclosure. Furthermore, this approach allows a nonempirical consideration of mesh enclosures and the effects of resistive seams in enclosure walls. By working with the circuit analogue, penetration by transient fields can also be computed. Essentially the enclosure is viewed as an antenna. In the case of magnetic shielding effectiveness, the enclosure is viewed as a short circuited loop antenna. In the case of electric field penetration, the enclosure is viewed as a fat electric dipole. Using this characterization and exact solutions where available, the current distribution on the outside of the enclosure is first determined. Then, based on the current distribution, the penetrating fields are computed. The equations are developed in such a way as to preserve a lumped circuit analogue for the low-frequency region. The basic circuit equations for magnetic field penetration are rederived from a rigorous solution. Rules to estimate the rise-time, fall-time, and peak magnitudes of transient penetrating fields are developed. The electric shielding effectiveness is developed in a similar manner. In both cases the results of the circuit approach agree well with those based on rigorous solutions of the electromagnetic boundary conditions. The results also agree with published experimental data on both large and small enclosures.     

Equivalent circuit parameters of an aperture coupled open resonatorcavity

In this paper, we use modified form of Bethe's small hole coupling theory to compute equivalent circuit parameters of an aperture coupled open resonator cavity. The open resonator cavity is composed of spherical mirrors of circular cross section. The cavity is coupled to a rectangular waveguide by means of a common hole in the mirror and the shorted end wall of the rectangular waveguide. Closed form expressions have been obtained for the equivalent circuit parameters. Experiments conducted in the W-band frequency range show good agreement with theory when an experimentally estimated correction to the transmission coefficient is applied for the thickness of the coupling holes     

Electromagnetic Pulse Penetration Through Small Apertures

The electromagnetic field penetration through small apertures is discussed for general aperture shapes. Approximnate analytical expressions are obtained for the penetration fields. In particular the fields that penetrate a small aperture into the region between two parallel, perfectly conducting plates are determined and some numerical results are obtained.     

Use of Reverberation Chambers to Determine the Shielding Effectiveness of Physically Small, Electrically Large Enclosures and Cavities

With the proliferation of small electric devices in recent years, along with various other applications, there is a growing need to test and determine the shielding properties or shielding effectiveness (SE) of physically small (but electrically large) enclosures or cavities. In this paper, we discuss how a reverberation chamber technique can be used to measure the SE of such enclosures. The approach consists of placing the small enclosure inside a reverberation chamber and using frequency stirring to excite the reverberation chamber. A small surface probe (i.e., a monopole) is mounted on the inside wall of the small enclosure to measure the power level inside the small enclosure. We present measured data from various other reverberation chamber approaches obtained from various enclosure configurations. The data from these other reverberation chamber approaches are used to validate the proposed approach. We also compared measured data to theoretical calculations of the SE for two small enclosures with circular apertures. These various comparisons illustrate that the proposed technique is a valid approach for determining the SE of physically small (i.e., cubic enclosure dimensions of the order of 0.1 m and smaller), but electrically large enclosures (that support several modes at the lowest frequency of interest).      

Survey of Techniques for Measuring RF Shielding Enclosures

An intensive literature survey has been conducted to review existing techniques for measuring the effectiveness of RF shielding enclosures. Prevalent methods of measuring E- and H-field components and for sensing the total field are discussed and evaluated. The procedures described in the literature are tabulated into groups determined by their similarities in method or theory and are compared by listing the advantages and disadvantages inherent in each. (A weighting system is devised to aid in evaluating each of the principal methods discussed.) Also discussed are the theoretical considerations underlying each of the methods listed, as applicable to the measurement of shielding effectiveness. Among these are the concepts of the resultant wave impedance of the E-M field at a point inside a shielded enclosure and the relationship of low-impedance and high-impedance fields in the near field regions of antenna systems. Techniques for extending the frequency and intensity of illuminating fields are also discussed, as well as the insertion loss method of determining leakage from a shield. Limitations and deficiencies of this latter procedure are noted.     

A mode-matching technique for mode coupling in a gyrotron cavity

The mode-matching technique (MMT) is used to compute the electromagnetic fields, stored energy, and input admittances of a gyrotron cavity coupled to one or more waveguides. The method is based on matching the cavity and waveguide eigenmodes across the cavity apertures and accommodates cavity walls of finite conductivity. The MMT is used in the gyrotron problem because fields in and near the aperture must be computed accurately, and because the eigenmode decomposition is advantageous for inclusion of an electron beam. Irrotational modes are part of the complete set of orthogonal vectors required to expand an H-field in an open cavity, but were excluded in most gyrotron literature; here, this is corrected. The MMT is numerically implemented for cavities of rectangular and circular cross section. Coupling between different modes in a gyrotron cavity through external and ohmic losses is demonstrated. A coupled (complex) cavity gyrotron design is analyzed using MMT. The energy and modal spectra of the cavity are computed, demonstrating the mode selective properties of the design     

Broad-band modeling of a realistic power converter shield forelectric vehicle applications

This paper deals with the broad-band modeling of a realistic power converter shield used in an electric vehicle. To validate such a model, comparisons between computation and measurements are required. As it is not practical to characterize experimentally the true radiation of a power converter through its enclosure, a reciprocal approach has been defined in which the enclosure is illuminated by a plane wave (receiving configuration). The associated experimental setup has been carefully defined and tested. At low frequency, the model is based on radiation through apertures in a simple cavity. At higher frequency, the Aseris-BE code, which is based on the boundary integral equations technique, has been used for computation. An optimal and realistic mesh of the enclosure suitable for the Aseris-BE code has been built by making numerous comparisons between computation and measurements, which have shown how to improve the mesh     

Design criteria for linearly polarized waveguide arrays

The influence of the waveguide aperture size on the admittance variation with scan angle of a waveguide phased array is presented. It is shown that certain size waveguide apertures can cause zero radiation directions. Design criteria which yield the maximum waveguide size to minimize or eliminate this condition are derived.     

Coupling phenomena in concentric multi-applicator phased arrayhyperthermia systems

The coupling between the waveguide applicators of a four-element phased array hyperthermia system irradiating a three-layered cylindrical tissue model of circular cross section is analyzed theoretically. The fields inside the tissue layers are expressed in terms of cylindrical vector wave functions satisfying the corresponding wave equations, while the fields inside each waveguide are expanded in terms of guided and evanescent normal modes. Then, by implementing the appropriate boundary conditions, a system of four coupled integral equations is derived in terms of the unknown electric field distributions on the open waveguide apertures. This system is solved by expanding the unknown electric field on each aperture into waveguide normal modes and by applying a Galerkin's procedure. The self reflection coefficient and the mutual coupling coefficients are then determined and numerical results for a four-element phased array hyperthermia system are computed and presented for different waveguide applicator sizes and settings     

On the aperture and pattern space factors for rectangular and circular apertures

A consequence of a recently discovered edge condition for planar apertures is that all planar aperture distributions are separable physically into a product of an edge factor and an aperture space factor, analogous to the way in which the radiation pattern separates into a product of an element factor and a pattern space factor. An exact relationship between these aperture and pattern space factors for physically realizable vector fields is derived here for rectangular and for circular apertures. For rectangular apertures it leads to a two-dimensional set of doubly orthogonal functions that are characteristic of the aperture geometry. Characteristic functions for circular apertures, however, are shown to exist only if the vector fields are circularly symmetric, although for scalar fields they exist for completely arbitrary aperture distributions with arbitrary edge taper. For rectangular apertures the characteristic functions consist of products of spheroidal functions and for circular apertures they are obtained from a generalization of the spheroidal functions. Some of the properties of these generalized spheroidal functions are developed here.     

Parfum-CW: A program to analyze radiated fields using minimization in terms of circular waveguide modes

A program for the interpretation of far field radiation patterns of oversized circular apertures is described. It allows to determine, from amplitude measurements only, the relative amplitude and phase at the aperture of the modes propagating in the waveguide. It best-fits the data with a set of waveguide modes chosen by the user.     

Analytical formulation for the shielding effectiveness ofenclosures with apertures

An analytical formulation has been developed for the shielding effectiveness of a rectangular enclosure with an aperture. Both the magnetic and electric shielding may be calculated as a function of frequency, enclosure dimensions, aperture dimensions and position within the enclosure. Theoretical values of shielding effectiveness are in good agreement with measurements. The theory has been extended to account for circular apertures, multiple apertures, and the effect of the enclosure contents