Spatial Filter Housing for Enhancement of the Shielding Effectiveness of Perforated Enclosures with Lossy Internal Coating : Broadband Characterization

is work is concerned with studying and enhancement of the electromagnetic shielding effectiveness of open metallic enclosures with openings over a wide range of the frequency including the UHF band. e suggested methods depend on the suppression of the excessive power penetrating the enclosure cavity especially at its resonances by a variety of methods that include increasing aspect ratio of the rectangular aperture, splitting the opening into a number of apertures, coating the internal walls of the metallic enclosure with a multilayered lossy material of the appropriate conductivity pro�le, and, �nally, placing the metallic enclosure inside a spatial �lter housing. A minimum value of 20 dB is achieved for the shielding effectiveness using the suggested methods. e present work also provides a study to investigate the effect of the direction and polarization of the incident plane wave on the shielding effectiveness of the enclosure.


Introduction
Metallic shielding is one of the major means to prevent electronic equipment from electromagnetic interference in electromagnetic compatibility (EMC) design [1][2][3].e shielding efficiency of a metallic enclosure is characterized by its shielding effectiveness (SE), which is de�ned as the ratio of the electromagnetic �eld without the presence of the enclosure to the �eld with the presence of the enclosure at the same observation point.However, the integrity of these enclosures is oen compromised by apertures and slots used to accommodate visibility, ventilation, or access to interior components.Such openings allow exterior electric and magnetic �elds to penetrate to the interior space, where they may couple onto printed circuit boards (PCBs) thus inducing currents and voltages on interior conductors.It is important to study the EM shielding effectiveness of shielding enclosures in the presence of these apertures.
Calculated shielding effectiveness depends on the position inside the enclosure where the �elds are calculated.For walls of the enclosure that are considered to be perfectly conducting, the penetration of �elds is only through the apertures.ere is a variety of modeling techniques associated with EMC, such as Method of Moments (MoM) [4][5][6], Finite Element Method (FEM) [7], and Finite-difference Time-domain method (FDTD) [8,9].Different modeling techniques are suited to different problems.In the present work, the FDTD technique is preferable, since it is an effective time-domain volume-based method.
e maximum penetration of the electromagnetic power occurs when the plane wave is normally incident on the aperture plane with the electric �eld parallel to the same plane and normal to the longer side of the rectangular aperture.Of course, this is the worst case regarding electromagnetic shielding requirements.erefore, the determination of the shielding effectiveness is usually achieved by considering a plane wave at a normal angle of incidence.Nevertheless, the effect of considering other angles of incidence and polarization has been proven to be signi�cant [4].
Improvement of the shield effectiveness of the rectangular enclosure at the cavity resonant frequency [6] can be obtained by using lossy internal coating to the enclosure walls, thus absorbing some of the internal �elds, which leads to the reduction of the -factor of the cavity and, hence, reducing its ability to store electromagnetic energy.Additional improvement of the shielding effectiveness is achieved in the present work by placing a planar band-stop spatial �lter in front of the aperture such that most of the incident power is �ltered out before penetrating the cavity.�f course the spatial �lter is designed so that its stop band is centered on the cavity resonant frequency.
Another suggestion to improve the shielding effectiveness of such an enclosure is by splitting the single aperture to multiple apertures arranged in rows and columns such that the total area of the multiple apertures is the same as that of the original one.Splitting an aperture into multiple smaller apertures has the effect of decreasing the coupling between the exterior and interior of the enclosure cavity due to the additional vertical and horizontal metallic strips between the small apertures.
e above three approaches for increasing the shielding effectiveness are combined together, and the resulting improvement in the shielding effectiveness of the enclosure is investigated over a wide frequency range.

Shield Design
A rectangular metallic enclosure with a single or multiple apertures in one of its side walls is shown in Figure 1.e enclosure has the dimensions     .e rectangular aperture has the dimensions   .
Like all cavities, the interior of a conducting rectangular box has discrete resonance modes.ese internal modes are obtained as the solutions of source-free Maxwell's equations in the region bounded by the walls of the rectangular box.ese modes can exist in an empty rectangular cavity if the largest cavity dimension is greater than or equal to one half a free space wavelength.Below this cutoff frequency, the cavity resonance cannot exist.
e resonant frequencies can be calculated for a rectangular box-shaped enclosure using the following expression [7]: where   is the speed of EM waves in free space and , , and  represent the mode integers (one of which can be zero).It is obvious that the frequency of a resonance mode is inversely proportional to the related enclosure dimension.For the present case, the rectangular enclosure is designed such that its smallest dimension is that along the -coordinate, so the resonance modes of the lowest frequencies are those modes with  = , and, hence, the resonance mode of the lowest frequency is the TE 11 mode.
To improve the shielding effectiveness of such an open metallic rectangular box it is suggested to modify its design by (1 increasing the aspect ratio of the rectangular aperture, (2 splitting the aperture into small-sized multiple apertures whose total area is the same as the original aperture, (3 using multilayered lossy coating on the inner walls of the rectangular box, and (4 placing an external band-stop spatial �lter in front of the aperture.e evaluation of the proposed design will be discussed in detail in the remaining of the paper.

Evaluation of the Shielding Effectiveness
Using FDTD e shielding effectiveness is de�ned as where   refers to the total electric �eld computed at the calculation or measurement point inside the cavity and   refers to the incident electric �eld computed at the same location in the absence of the enclosure.e metallic enclosure is subjected to an incident plane wave.e direction of incidence and polarization of the plane wave are as indicated in Figure 2.
An incident plane wave has its direction of propagation determined by the angles   and   as shown in Figure 2. Another angle,   , is the angle between the projection of the electric �eld vector on the - plane and the -axis.us, knowing the direction of propagation, the angle   determines the direction of the electric �eld, and hence it is called the polarization angle.e FDTD method [10][11][12] is applied with an absorbing boundary condition to truncate the solution space whilst simulating free space.A computer memory efficient formulation of the split-�eld perfectly matched layer (P��) proposed by Berenger [13] is utilized throughout the present work.e metallic walls are considered as perfectly electric conductor (P�C) by enforcing the parallel electric �eld components to vanish on these walls.e total �eld�scattered �eld (TF�SF) formulation [11] is utilized to calculate the �elds inside the enclosure and, hence, the shielding effectiveness.Two forms of the plane waves are used: the �rst is a sinusoidal (continuous) plane wave, which is utilized to calculate the shielding effectiveness at a single frequency.e other plane wave is Gaussian pulsed and is used to calculate the shielding effectiveness over a speci�c frequency range.e detailed expressions for the continuous and Gaussian-pulsed plane wave are given as follows.
3.1.Continuous Plane Wave.According to the above description of the plane wave, one can write the following expressions for the incident �elds of a continuous (sinusoidal) plane wave: where    is the amplitude of the incident electric �eld,   ,   , and   are the wavenumbers in , , and  directions, respectively, and are given as   =  sin   cos   ,   =  sin   sin   , and   =  cos   , and  is the total wavenumber in free space.One can note that  =  2     2    2  .

Gaussian-Pulsed Plane
Wave.For a Gaussian-pulsed plane wave, the incident �elds can be written as follows: where the time period  determines the Gaussian pulse width and   is the time at which the Gaussian pulse reaches its maximum value.

Results and Discussions
e following presentations and discussions are concerned with the frequency response of the shielding effectiveness of a rectangular box enclosure with single or multiple rectangular apertures as well as the improvement of this response by different methods.Some of the results are concerned with the dependence of the shielding effectiveness of such enclosures on the size and the aspect ratio of the aperture in case of an enclosure with a single aperture.Other results concerned with the effect of the arrangement and number of apertures in the case of an enclosure with multiple apertures are presented and discussed.e other parameters affecting the shielding effectiveness such as the direction of incidence and the polarization of the incident plane wave are discussed, and the related results are presented.e results concerned with the improvement of the shielding effectiveness using lossy coating on the inner walls of the enclosure and�or a spatial band-stop �lter which is placed in front of the aperture are presented and discussed.
It may be worth noting that the results presented in this section are obtained by applying the FDTD method as described above through a computer program developed using C++ language.For the sake of investigating the validity of the developed program, some of the results obtained here are compared with other published ones.center of the enclosure over the frequency range of 100 MHz to 1 GHz.e FDTD method is applied for this purpose by dividing the three dimensional space including the metallic enclosure into 180 × 180 × 180 cubic cells each of dimensions 0.5 × 0.5 × 0.5 cm.e enclosure wall thickness is one cell of perfect conductivity.e total/scattered �eld formulation is used with a perfectly matched layer (PML) of 8-cell thickness as absorbing boundary conditions.

Characterization of the Shielding Effectiveness of a
Gaussian-pulsed plane wave is applied, and the discrete Fourier transform is applied.e results are shown in Figure 3 and compared with those obtained using the multilevel fast multiple moment method (MLFMM) [14].As shown in the �gure, there is a good agreement between the results, which insures the validity of the applied FDTD algorithm.
More comparisons can be achieved among the results concerning the same enclosure with an aperture of dimensions 30 × 12 cm 2 obtained using different methods.e SE is calculated over the frequency range of interest and compared with that obtained in [5].e comparison is presented in Figure 4 showing good agreement among the results.

Effect of the Aperture Width on the Shielding Effectiveness of an
Enclosure with a Single Aperture.It may be important to investigate the effect of the aperture width (horizontal dimension) on the SE of the enclosure while keeping the aperture vertical dimension unchanged.One may expect that by decreasing the aperture width the SE increases as the area through which the electromagnetic power can penetrate into the enclosure cavity is reduced.Figure 5 shows a plot for the SE against the frequency with varying the aperture width from 5 to 30 cm while keeping the aperture height at 10 cm.An   -polarized plane wave is assumed to be normally incident on the aperture.As shown in Figure 5, the SE decreases rapidly when the frequency approaches the internal resonance of the cavity.Two resonances appear in the �gure: the �rst one is related to the resonant mode TE 101 (at about 707 MHz for the closed cavity) and the second is related to TE 102 mode (at about 1118 MHz for the closed cavity).For an open cavity the resonant frequencies for internal modes decrease with increasing the aperture width; this is noticeable in the SE/frequency plot of Figure 5.
It is shown in the �gure that as the aperture gets narrower, the SE shows very sharp minimum of high amplitude at the TE 101 resonant mode.As the aperture is getting wider, the minimum of the SE at TE 101 becomes less sharp, has lower amplitude, and occurs at a lower frequency.

Effect of Direction of Incidence of the Plane Wave on the
Shielding Effectiveness of an Enclosure with a Single Aperture.e shielding effectiveness of a conducting rectangular box with a rectangular aperture depends on the direction of propagation of the incident plane wave.Figures 6 and 7 show the dependence of the shielding effectiveness on the elevation angle of incidence   at different frequencies.According to the coordinate system shown in Figure 2 the plane wave is normally incident on the aperture plane when   = 0; this gives the lowest value of the shielding effectiveness.e maximum value of the shielding effectiveness is obtained when the plane wave direction is parallel to the aperture plane (  = 90 ∘ ).It is clear, in Figures 6 and 7, that the shielding effectiveness obtained when the plane wave is incident on the back of the shielding enclosure (  = 180 ∘ ) is slightly larger than that obtained when the plane wave is incident directly on the aperture face (  = 0 ∘ ).In Figure 6, the results obtained in the present work are compared to those obtained in [5] using the commercial soware package FEKO and those obtained through measurements.e comparison shows good agreement.
Figure 7 shows the dependence of the shielding effectiveness on the elevation angle of incidence   for different values of the operating frequency.e results ensure that, at all the frequencies, the minimum shielding effectiveness is obtained when the plane wave direction is normal to the aperture plane, whereas the maximum shielding effectiveness is obtained when the plane wave direction is parallel to the aperture plane.

Effect of Polarization of the Incident Plane Wave on the
Shielding Effectiveness of an Enclosure with a Single Aperture.e orientation of the electric �eld of the incident plane wave affects the shield effectiveness of a box-shaped enclosure with a rectangular cavity.e results presented in Figure 8 demonstrate the dependence of the shielding effectiveness on the polarization angle   .As shown in the �gure, the minimum value of the shielding effectiveness is obtained when the electric �eld is parallel to the larger edge of the slot, whereas the maximum value is obtained when the incident electric �eld is normal to this edge of the slot.In this example, the plane wave is normally incident on the slot plane, and hence the incident electric �eld lies in the slot plane.

Improvement of the Shielding Effectiveness of a Rectangular
Enclosure with a Rectangular Aperture.In the following, a variety of methods are presented to improve the shielding effectiveness of a rectangular metallic box with an aperture.Some of these methods depend mainly on preventing most of the incident power from entering the cavity while the other methods depend on suppressing the power penetrating into the cavity.

Improvement of the Shielding Effectiveness of the Enclosure by
Increasing the Aspect Ratio of the Aperture.Let us de�ne the aspect ratio of the rectangular aperture as the ratio between the length of the vertical side and that of the horizontal side.According to the plot shown in Figure 9, the shielding effectiveness increases with increasing the aspect ratio except at the resonant frequency of the enclosed cavity.
For further investigations of the effect of the aspect ratio on the shielding effectiveness, Figure 10 shows a comparison among the values of the shielding effectiveness of an enclosure of a single slot for three different values of the aspect ratio.It is clear in the �gure that the shield effectiveness increases with increasing the aspect ratio over the entire frequency range except at the frequency corresponding to the internal resonance.

Improvement of the Shielding Effectiveness by Using
Multiple Apertures instead of Single Aperture.If the single aperture on one of the rectangular enclosure is split into multiple apertures whose total area is the same as that of the original aperture, the shielding effectiveness may be improved.In other words, the single slot is replaced by a number of smaller slots arranged in a planner array as rows and columns.is leads to increase the shielding effectiveness of the shielding enclosure.Figure 11 shows a comparison between the shielding effectiveness of an enclosure with a single slot and that of two slots arranged in one row and two columns, where the two slots together have the same area of the single slot.It is shown in the �gure that splitting the single slot into two adjacent slots results in increasing the shielding effectiveness except at the resonant frequency of the enclosure cavity.For further investigations of the effect of splitting the slot area into a larger number of smaller slots, Figure 12 shows a comparison among the shielding effectiveness of an enclosure of a single slot to that of an enclosure with four slots arranged as 2 × 2 array and that of an enclosure with eight slots arranged as 2 × � array.It is clear in the �gure that as the number of slots increases, the shield effectiveness increases provided that the total area of the multiple slots is the same as that of the single slot.To ensure this result, a third case is presented in Figure 13 from which we can arrive at the same conclusion.

Improvement of the Shielding Effectiveness of Open Enclosures at Internal Resonance Using Lossy Coating on the
Internal Walls.e electromagnetic power coupling from an incident wave to the interior of a rectangular cavity is enhanced at the internal resonances of the cavity.Consequently, the shielding effectiveness may be very low over narrow frequency bands around the internal resonance.e shield effectiveness of an open rectangular enclosure can be improved by diminishing or reducing the internal �eld at such resonance.is can be achieved by coating the walls of the rectangular cavity by an absorbing material, which causes the internally generated �elds to be partially absorbed into the wall coating, and hence the internal region of the enclosure seems to be surrounded by a free space region rather than a conducting boundary.In other words, the absorbing coating on the internal walls leads to reduce the -factor of the cavity and, hence, to reduce its ability to store electromagnetic energy.Figure 14 shows a comparison between the shielding effectiveness of an open box-shaped enclosure with an internal absorbing coating and that of the same enclosure without such coating.e results show that the shielding effectiveness is improved at the internal resonances corresponding to the TE 101 and TE 102 modes of the rectangular cavity; however, a slight reduction of the shielding effectiveness occurs over the low frequency range.is can be attributed to that the lossy coating on the internal wall has better absorption of the excessive electromagnetic power at the higher frequencies than its absorption at lower frequencies.On the other hand, the thickness of the coating layer results practically in reducing the inner dimensions of the enclosure cavity leading to a bad effect on the shielding effectiveness at lower frequencies.
It should be noted that to get a good absorbing coating, it is constructed up from several layers that achieve a speci�c conductivity pro�le.e improvement obtained in the case presented in Figure 14 is achieved using conductivity pro�le: 0.01, 0.0316, 0.1, 0.316, 1, and 3.16 ohm −1 ⋅m −1 arranged from the outer layer to that touching the internal conducting walls of the enclosure.
If the single aperture (10 × 10 cm 2 ) is split into four apertures (each 5 × 5 cm 2 ) arranged in two rows and two columns, the internal coating has more considerable improvement of the shielding effectiveness of the rectangular enclosure over a wide frequency band.is is clear in Figure 15, where the minimum value is about 20 dB over the entire frequency band of operation (0-1 GHz).Even for higher frequencies, the internal coating in this case is still capable of preserving the shielding effectiveness of the rectangular enclosure above 20 dB.

Improvement of the Shielding Effectiveness of Open
Enclosures at Internal Resonance Using External Spatial Filter.e severe degradation of the shielding effectiveness of the open enclosure occurs in narrow band intervals around the frequencies corresponding to the internal resonances of the enclosure cavity.If a band-stop spatial �lter �15] is placed outside the shield in front of the aperture such that most of the incident power at a cavity resonant frequency is �ltered out before penetrating the cavity, this will considerably improve its shielding effectiveness at this frequency.Of course the, spatial �lter will be designed so that its stop band is centered on the resonant frequency of the shield cavity.According to previous discussions, the worst value of the shielding effectiveness of a rectangular enclosure of the dimensions 30 × 12 × 30 cm with aperture of dimensions 10 × 10 cm is obtained at about 0.7 GHz.A band-stop �lter can be constructed up as a planner array of conducting strips as shown in Figure 16.e frequency response of this �lter is shown in Figure 17.As shown in this �gure, the stop band of this �lter is centered on 0.78 GHz.
Figure 18 shows the variation of the shielding effectiveness of an open enclosure with a spatial �lter screen placed in front of its aperture, as shown in Figure 16 over the operating frequency band compared with that of the same enclosure without the spatial �lter screen.It is clear that the shielding effectiveness is improved at the resonant frequency and over the higher frequency band such that it is almost kept greater than 0 dB over the entire frequency range (0-1.0GHz).

Improvement of Shielding Effectiveness of Open Enclosures by Combination of Multiple Methods.
We can combine more than one technique of those previously discussed for further improvement of the shielding effectiveness of open enclosures.Figure 19 shows the effect of using a lossy coating and, at the same time, placing a spatial �lter screen in front of the aperture of an open rectangular metallic enclosure on the shielding effectiveness over the operating frequency range compared with that of the original enclosure.It is obvious that this con�guration gives better shielding at the resonant frequency, considering a 30 × 12 × 30 cm enclosure with 10 × 10 cm aperture, than that obtained using the internal coating or the �lter screen alone.Figure 20 shows a comprehensive comparison for some possible combinations of shielding improvement techniques.Now, let us summarize the methods presented throughout the previous discussions to improve the shielding effectiveness of rectangular metallic enclosures with rectangular apertures; these include (i) increasing aspect ratio of the rectangular aperture with keeping its area, (ii) splitting the apertures into a larger number of apertures with keeping the same opening area, (iii) coating the internal walls of the metallic enclosure with a multilayered lossy material with the appropriate conductivity pro�le, and, �nally, (iv) placing an external electromagnetic �lter screen at the proper distance in front of the aperture of the metallic enclosure.If all these methods are used together to get a combined solution, the resulting shielding effectiveness, as a function of the frequency, will be like that shown in Figure 21 compared to that of the original enclosure.It is clear that this solution is the best for a 30 × 12 × 30 cm enclosure with a 10 × 10 cm aperture as regarding the shielding effectiveness over the entire frequency range and at the internal resonances as well.F 20: Shielding effectiveness versus frequency at the center of a 30 × 12 × 30 cm 3 enclosure with a 10 × 10 cm 2 aperture illuminated by a plane wave at normal incidence.F 21: Shielding effectiveness versus frequency of a 30 × 12 × 30 cm 3 enclosure with a single 10 × 10 cm 2 aperture and without internal coating and without a spatial �lter compared to that of an internally coated enclosure with four 5 × 5 cm 2 apertures and with a spatial �lter of 3 × 5 conducting strips, placed 4 cm away from the apertures when both are illuminated by a plane wave at normal incidence.

Conclusion
are studied over a wide range of the frequency.It is shown that the shielding effectiveness is severely degraded at the internal resonances of the enclosure cavity and may decrease below −40 dB.A variety of methods are suggested to improve the shielding effectiveness of rectangular enclosures with rectangular apertures over a wide frequency range and at the internal resonances of the metallic enclosure.e suggested methods include increasing aspect ratio of the rectangular aperture with keeping its area, splitting the opening into a number of apertures with keeping the same opening area, coating the internal walls of the metallic enclosure with a multilayered lossy material of the appropriate conductivity pro�le, and, �nally, placing an e�ternal electromagnetic band-stop frequency selective screen at the proper distance in front of the aperture of the metallic enclosure.It is shown that any of these methods when applied alone lead to a signi�cant improvement of the shielding effectiveness.Also it is shown that various combinations of more than one method of those suggested in the present work result in further improvements of the shielding effectiveness.A combination of all these methods (applied together) leads to a minimum shielding effectiveness of 20 dB over the operating frequency band.e results concerning the effect of the angle of incidence and polarization of the incident plane on the shielding effectiveness of the enclosure over the entire frequency range are presented.

F 1 :
Geometry of a rectangular metallic enclosure with rectangular apertures.

F 2 :
De�nition of angle of incidence and polarization of the incident plane wave.

F 3 :
Comparison among the values of the SE obtained using three different methods for a box-shaped enclosure of dimensions 30 × 12 × 30 cm 3 with rectangular aperture of dimensions 20 × 3 cm 2 illuminated with   -polarized plane wave.

10 F 4 :F 5 :
Comparison among the values of the SE obtained using three different methods for a box-shaped enclosure of dimensions 30 × 12 × 30 cm 3 with rectangular aperture of dimensions 30 × 12 cm 2 illuminated with   -polarized plane wave.Shielding effectiveness versus frequency at the center of a box-shaped enclosure of dimensions (30 × 12 × 30 cm 3 ) with rectangular aperture of different dimensions.

F 6 :F 7 :
Shielding effectiveness of a box-shaped enclosure (30 × 12 × 30 cm 3 ) with a rectangular aperture (20 × 3 cm 2 ) against the elevation angle of incidence of the plane wave (  ),    MHz.Shielding effectiveness of a box-shaped enclosure (30 × 12 × 30 cm 3 ) with a rectangular aperture (20 × 3 cm 2 ) against the elevation angle of incidence of the plane wave (  ) for different frequencies.

F 8 :
Shielding effectiveness versus polarization angle (  ) of the incident plane wave for a 30 × 12 × 30 cm 3 box-shaped enclosure with 20 × 3 cm 2 aperture at different frequencies.

F 9 : 7 . 8
Shielding effectiveness versus frequency for a box-shaped enclosure of dimensions 30 × 12 × 30 cm 3 with a single slot for different values of the aspect ratio and having the same area.cm × 7.8 cm aperture 15 cm × 4 cm aperture 20 cm × 3 cm aperture F 10: Shielding effectiveness versus frequency for a boxshaped enclosure of dimensions 30 × 12 × 30 cm 3 with a single slot for different values of the aspect ratio and having the same area.

F 11 :F 12 :
20 cm × 3 cm) Two apertures (each 10 cm × 3 cm) Shielding effectiveness versus frequency for a boxshaped enclosure of dimensions 30 × 12 × 30 cm 3 with a single slot as that with two slots.Shielding effectiveness versus frequency for a boxshaped enclosure of dimensions 30 × 12 × 30 cm 3 with a different number of rectangular apertures.

F 13 :
Shielding effectiveness versus frequency for a boxshaped enclosure of dimensions 30 × 12 × 30 cm 3 with different number of rectangular apertures having the same total area.

F 14 :
Shielding effectiveness versus frequency of a 30 × 12 × 30 cm 3 box-shaped enclosure with a 10 × 10 cm 2 aperture illuminated by a plane wave at normal incidence in the presence and absence of a lossy internal coating of 1.5 cm thickness.

F 15 :F 16 :
× 5 cm apertures without coating Four 5 cm × 5 cm apertures with internal coating Shielding effectiveness versus frequency of a 30 × 12 × 30 cm 3 box-shaped enclosure with four 5 × 5 cm 2 apertures arranged in two rows and two columns, illuminated by a plane wave at normal incidence in the presence and absence of a lossy internal coating of 1.5 cm thickness.Housing the open enclosures in frequency selective walls.

F 17 :F 18 :
Frequency response of the band-stop �lter composed of planner array of strips.Shielding effectiveness versus frequency for a 30 × 12 × 30 cm 3 enclosure with a 10 × 10 cm 2 aperture illuminated by a plane wave at normal incidence with a spatial �lter of 3 × 5 conducting strips, placed 4 cm away from the aperture.

F 19 :
e characteristics of the electromagnetic shielding effectiveness of a metallic enclosure with a rectangular aperture Shielding effectiveness versus frequency for an internally coated 30 × 12 × 30 cm 3 enclosure with a 10 × 10 cm 2 aperture illuminated by a plane wave at normal incidence with a spatial �lter of 3 × 5 conducting strips, placed 4 cm away from the aperture.