On the Evaluation of the Shielding Effectiveness of an Electrically Large Enclosure

The shielding effectiveness (SE) has become a fundamental step in testing active or passive electric devices. The Reverberating Chamber (RC) is a wellestablished method for determining the SE since has the advantage to expose the material to a more realistic environment. In this paper the SEe of electrically large enclosures with a metallic mesh grid in a RC is evaluated. Enclosures made with metallic mesh are considered. In particular, it is shown that the SE of a material is unable to provide complete information for the SEe of an electrically large enclosure made with the same material. Moreover, this latter one is related to the loading conditions within the enclosure itself. Measurements accomplished at RC of the Università di Napoli Parthenope (formerly Istituto Universitario Navale, IUN) confirm the physical soundness of the proposed approach.


Introduction
The importance of electromagnetic interference (EMI) and electromagnetic compatibility (EMC) in daily environment arises from the fact that the environment is electromagnetically hostile.The increasing use of electronic devices makes the EMI and EMC issues of great relevance in such environments in which more devices are used in disparate contexts.The enclosure are great of importance for controlling the emission of such electronic systems.On the other hand, they increase immunity of the devices subject to strong electromagnetic interference.A measure of the efficiency of an enclosure is the shielding effectiveness (SE e ), i.e. the ability of attenuating the sources of electromagnetic disturbance.Usually, the nested reverberating chamber (RC), with the mode-stirred method, is employed to characterize the enclosures [1][2].Nested RCs have been used in the past to determine the SE of material [3].The RC is an electrically large chamber which uses several stirring techniques to randomize the input electromagnetic field in order to expose the device under test to a more realistic environment [1].
The SE e of an enclosure is defined as follows [1][2] SE e = −10 log 10 where P in is the power received by the receiving antenna placed in RC and P out is the power received by a receiving antenna placed in the enclosure.Therefore, the SE e relates the interior fields to the external incident field.The SE e is a fundamental step in establishing the EMC of active or passive devices.Among the different enclosures used to shield the electronic devices, the metallic meshes are potentially attractive as electromagnetic shield enclosure because of their reduced weight per unit area compared to metallic box.However, the metallic mesh often forms parts of enclosures, as it allows the aeration of the electronic circuits, which are shielded by enclosures themselves.The electromagnetic behavior of wire meshes has been previously addressed in [4][5].
In this paper, an electrically large enclosure is placed in an RC and measurements of the SE e are accomplished.This type of configuration is essentially a nested RC [3,6].
Clearly, the walls of the enclosure are regarded as reciprocal walls.In Fig. 1 is shown a sketch of the measurement set-up.The field within the RC is well randomized by three stirrers.The set-up includes two antennas in the RC and a small monopole probe, which is placed on one interior wall of the enclosure.In Section 3, the experimental set-up is further discussed.Being the walls made of metallic mesh, the enclosure within the RC has no stirrers inside since all points into the enclosures statistically have the same fields level; The enclosure within the RC has no paddles since its mode density is quite high.As long as the SE e is weak or moderate , the Q of all enclosure modes is low and each of those modes is randomly excited from the RC field.Therefore the internal field, is sum of all enclosure modes, is effectively randomized.In other words, the RC mode stirrers act as mode stirrer also for the enclosure.Following the mathematical model developed in [7] this paper shows that the SE e of the enclosure is smaller than that obtained by the same material exposed to an RC electromagnetic field.Further, the SE e is dependent on the loading conditions of the enclosure.Measurements accomplished at RC of the Università di Napoli Parthenope (formerly Istituto Universitario Navale, IUN) confirm the physical soundness of the proposed approach and its applicability from an operational point of view.

Mathematical Model
In this section, two equivalent mathematical models for SE e , based on power balance, are shown.An approach followed for measuring the SE e of electrically large enclosure is based on the RC technique.It is assumed that the field is uniform and isotropic inside and outside the enclosure.Following the power balance theory, the SE e of an electrically large enclosure can be expressed as follows [1][2] SE e = 10 log 4πV where V and Q are the volume and the quality factor of the enclosure, respectively, λ is the working wavelength, and σ t is the average transmission cross section (TCS) of the enclosure walls.〈 〉 represents the averaged over an incident angle of 4π steradians and over all polarizations.From power balance it can be written [7]: whence [7] , , e SE t w i a i e out in t A P P σ σ σ σ where S i and S o are the incident power density inside and outside the enclosure, respectively; σ w,i is the total average absorption cross section (ACS) of the enclosure wall when the field impinges from the inner, σ a,i is the average ACS of the load, A e is the effective area of the receiving antenna inside the enclosure [2], and σ t is the one in eq. ( 2).It is important to note that in (4) SE e is defined to be greater than 1 as in [1].
It must be noted that the trend of SE e given by eq. ( 2), for different frequency range is not straightforward to draw, particularly for enclosure where σ t is very sensitive to the frequency changes.Further, Q factor in eq. ( 2) is inversely proportional to σ t .Equation ( 4) improves the comprehension of the SE e of an enclosure; by setting σ ae,i = σ w,i + σ a,i + A e (5) eq. ( 4) becomes , e SE .
If the enclosure is unload, i.e. σ a,i = 0, then In the case of a metallic mesh enclosure, the behavior of SE e can be simply described by observing that the transmission cross section grows more rapidly with increasing of the frequency respect to σ ae,i .In particular, at low frequencies, σ t is smaller than σ ae,i ,.Hence, a SE e greater than 1 is expected.On the other hand, as the frequency gradually increases, the transmission cross section increases faster than σ ae,i .Therefore, a value of SE e about equal to 1 (0 dB), is obtained.Accordingly, a decreasing trend of SE e , with frequency is expected.In [7], it is shown that SE e can be expressed as follows where σ a,i has been assumed equal to zero; SE is the shielding effectiveness of the wall material; R is the reflectivity of the enclosure walls when the field impinges from the inner of the enclosure [8].σ t can be expressed as follows [7] σ t = σ t,gA SE (9) where σ t,gA is the TCS of the total geometric area of the wall enclosure when they are considered perfectly transmitting; clearly, σ t is attendant to the same geometric area.The SE can be achieved as follows [7]: where σ a,gA is the total geometric area of the enclosure walls when they are considered perfectly absorbing [7].It is important to note that σ a,gA≡ σ t,gA =S g /2 where S g is the surface area of enclosure walls.One specifies that in (9) SE is defined to be greater than 1.
Although the losses were negligible by setting σ w,i =0 in eq. ( 10), pioneering results about R (SE) of metallic mesh grids have been carried out in [9].In this paper, initial results of SE e are predicted by using ( 8)-( 10) and R measurements [9]; a comparison with measured SE e is shown as well.

Experiment Results
In this section, a meaningful set of experimental results is shown.Before that, a brief description of the calibration procedure is first summarized.For the evaluation of SE e , the power levels in the enclosure are monitored by a small probe placed on one of the enclosure wall.Hence, large reflection at the antenna terminal can occur due to the mismatch between the probe and the coaxial cable used to deliver the field to the probe terminal.In order to validate the theoretical model with the proposed procedure, two different-size enclosures of metallic grid, have been employed.Both the enclosures are cubic boxes of 49 cm side size.The first enclosure is made with metallic grid and its mesh size is 5 mm, see Fig. 3; the second is made with metallic fabric and its mesh size is 1 mm: the latter has a foam structure as a support, see Fig. 2.
They have been placed on foam support within the RC during the measurements; the clearance from the chamber floor is 50 cm.This approach is essentially a nested RC.
The stirrers within RC accomplish the randomization of the electromagnetic field.Hence, the uniformity and isotropy of the field inside the enclosure can be assumed since it is uniformly and randomly excited from all sides.In any case, when SE e values increase until 10 dB about, a conventional stirrer must be placed within the enclosure; by experience, this concept is very more stringent for monopole mismatch measurements.It is important to note that for such measurements the enclosure is excited by monopole itself and that for the frequency points where the mismatch is very strong, the residual error about S 22 parameter, can significantly affect the achieved SE e , see eq. ( 11).The losses inside the enclosure reduce the impedance mismatch of the probe monopole.In any case, if the assumed hypothesis of uniformity and isotropy of the field deteriorates, then the quality of expected results deteriorates as well.In particular, this problem occurs at lower frequencies in the employed frequency range, where the modal behavior of the enclosure is not negligible.In Fig. 4 is shown the SE e obtained with the enclosure made with a mesh size of 5 mm.The SE e of the enclosure with the correction due to mismatch of the probe (blue line) and without it (black line) is shown.As expected, according to the theoretical model, the SE e shows a decreasing behavior with the frequency.It must be noted that when the black and blue line have the same value, i.e. around 3 GHz and from 6 to 8 GHz, the return loss on the receiving antenna is always smaller than 10 dB, see Figure 5.A visual comparison with the results obtained in [9] shows a value of SE e smaller than SE, to witness that a shielding reduction is obtained when an enclosure is employed.In Fig. 6 is shown the SE e obtained with the enclosure made with a mesh size of 1 mm.
Figure 4: SE e from measurements of 5 mm mesh size enclosure.
In conclusion, the SEe of an enclosure with wall of metallic grids decreases with the increasing of the frequency.Moreover, the SE e is smaller than the corresponding one obtained with the same material of which the enclosure is made [9].The SE e of an enclosure tends to the one of a metallic grid if a load is placed within the enclosure, see next Figs.8 and 9 in section 4.
In Fig. 7 is shown a comparison between the shielding effectiveness of the enclosure made with metallic mesh of 1 mm with a piece of absorber (blue line) and without it (black line).
Figure 5: Return Loss, enclosure built with metallic mesh whose side is 5 mm.
Figure 6: SE e from measurements of 1 mm mesh size enclosure.
The absorber is of the Emerson-Cuming, its dimensions are 9 cm x 9 cm x 9 cm, and it is place on a foam support, see Fig. 3.As expected, the loading effect improves the SE e of the enclosure that increases from 2 to about 10 dB.In particular, apart from the effect due to the mismatch of the monopole, at lowest frequency, σ t becomes smaller than σ ae,i ; also, σ w,i is negligible with respect to σ t , but it has no zero value.

Comparisons and Discussion
In this Section, the comparison between the expected results of SE e and the measured ones is discussed.The former are achieved according to ( 8)- (10); the experimental measurements of R (SE), reported in Figs. 8  and 9, are the same as in [9].One specifies that those measurements were available for the paper, and that the frequency step is 1 GHz.However, in [9] SE was simply achieved as 1-R (so it turned out to be less than 1), while it here is calculated according to (10), by estimating σ a,gA, and σ w,i ; the latter was estimated as specified below.For the enclosure with mesh size of 5 mm, the expected SE e is about zero dB over the whole frequency range from 1 to 18 GHz.This agrees well with experimental results in Fig. 4, in particular from 2 GHz up.Fig. 10 shows the expected results for σ w,i +A e (black line) and σ w,i (blue line).In Fig.
11 SE e for the enclosure with mesh size of 1 mm is shown.The calculation of A e takes into account the developing of the model ( 6) [7].
The estimate of σ w,i has been simplified; indeed, it has been estimated by considering the solid part of inner total area of the wall enclosure.Clearly, the losses have been estimated by considering a field uniform and isotropic [7], [10].For the enclosure with mesh size of 1 mm, the ratio between solid area and surface total area is equal to 0.6, and the metal type is aluminum.σ w,i has been estimated by means of the average absorption coefficient of the solid part of the enclosure walls.In other words, the solid area of inner total area of the enclosure is assimilated to a metallic plate with equivalent surface area.For a metallic plate with ordinary thickness one can write: which represents the average absorption coefficient of the solid part, can be expressed in the following analytical form: where k 0 is the free-space wavenumber, δ is the skin depth, f is the frequency, s w is the conductivity of the metal forming the grid or the fabric, ε 0 represents the free-space permittivity.
In short, by also considering (10), one can write: where C 1 is a constant equal to the ratio between solid area and surface total area.( 16) has been used to estimate σ w,i .
For the enclosure with mesh size of 1 mm, C 1 = 0.6, as said above, and s w =3.8e+7 S/m.By considering (10) and the results in Figs. 8 and 10, it can be noted that σ w,i has a negligible effect on SE of a metallic fabric with mesh size of 1 mm as well, and that A e can have a significant effect on SE e at low frequencies.Results in Fig. 11 shown that the expected SE e appreciably differs from measured one from 1 to 5 GHz, and the result mismatch decreases as the frequency increases.The authors think that the mismatch of the results at lower frequencies in the employed frequency range is due to the fact that the modal behavior of the enclosure is not negligible, so that the necessary property of uniform and isotropy of the field are no more fully satisfied.Uniformity and isotropy of the field can be improved by a mechanical stirred installed inside the enclosure; however, at frequencies where the modal density is inadequate, it is not possible to obtain field uniformity and isotropy within the enclosure.would turn out to be affected; however, at lower frequencies the effective area of the monopole is significantly greater than σ w,i , and it can assume appreciably values higher from the expected ones.Also, at the frequency points where the mismatch is very strong, the correction in eq. ( 11) can turn out been affected.Finally, another reason for mismatch of the results can be the accuracy of the R (SE) measurements.Both models ( 2) and ( 7) have been developed under conditions of uniformity and isotropy of the field; in principle, they could be applied in different field conditions as well; but that is very difficult, as the estimates of the parameters requires the accurate knowledge of the field structure inside an enclosure.
It is well known that the leakage for an enclosure can be low, but it cannot be zero.Therefore, it is important to note that an enclosures must be made with material having both high SE and low R [11], where the latter refers to internal side of the enclosure walls.

Uncertainty Measurements
When SE e is equal to about 0 dB, a slightly negative value can be measured, as it can be clearly noted in Figs. 4. It is due to imperfect field isotropy and uniformity, which causes a measurement uncertainty.The field conditions of uniformity and isotropy depend on effectiveness of the stirrers; for our RC used in the experiments, a field uniformity within ±0.5 dB was measured at 1 GHz with unloaded chamber [12].This already justifies the SE e slightly negative which has been measured.In any case, for further information, an estimate of the SE e overall measurement uncertainty is here performed, by measuring it in 10 different configurations of the measurement setup.Each independent measurement configuration is achieved by changing the location of the enclosure and/or horn antennas and/or their polarization.
The results are shown in Figs. 12 and 13, where are illustrated SE e uncorrected and corrected, respectively.In order to save time, 1000 independent samples are acquired at each frequency point, in a frequency range from 1 GHz to 12 GHz with step frequency of 200 Mhz.
Figure 12: Uncorrected SE e from measurements of 5 mm mesh size enclosure; 10 independent measurement configurations; 1000 independent samples at each frequency point.
Figure 13: Corrected SE e from measurements of 5 mm mesh size enclosure; 10 independent measurement configurations; 1000 independent samples at each frequency point.
Therefore, the standard deviation of SE e is estimated for 10 independent measurement configurations.Fig. 14 shows the standard uncertainty [14] of corrected SE e ; the standard uncertainty (in dB) is expressed relative to the mean.It is important note that the standard uncertainty was estimated in conditions absolutely realistic; that is, it was actually calculated in the same conditions of measurement (with enclosure inside the chamber).The estimated uncertainty includes the degrade of the calibration of the VNA which due to the repeated connections which were necessary between a measure and the other (two-port VNA) and the time taken to make the measures.This in particular affects the mismatching measurements, as one can note in Figs.
12, 13 and 14.In fact, a high deviation of the SE e is noted at 1.2 GHz for corrected results only.On the other hand, the monopole probe is strongly mismatched at that frequency, see Fig. 5 as well.It is specified that the tests were performed on a time of six hours about included warm-up and calibration procedure.However, the max of the standard uncertainty of SE e is less than 1 dB, except the value of 2.2 dB at 1.2 GHz.The estimate uncertainty is conservative with respect to the measures shown in Fig. 4, where 3000 points are acquired for each frequency, and because it is based only on 10 independent measurement configurations; moreover it includes the degrade of the calibration as specified above.However, it is consistent with results shown in [12] and is adequate to the experience and confirms the conclusions drawn here.

Conclusions
In this paper a different form of the SE e of an enclosure made with metallic grids has been proposed and successfully tested by measurements accomplished at IUN RC.Measurements have been accomplished for the first time on enclosure totally made with square metallic mesh and they have been proved that the SE e of an enclosure is always smaller than the SE of a material.Further, the SE e of such enclosures is decreasing with the increasing of frequency.Finally, by loading the enclosure with absorbing material, it has been noted that the SE e tends to the one of the wall metallic grid.

Figure 1 :
Figure 1: Illustration of the RC set-up measurements

Figure 2 :
Figure 2: A sketch of the IUN RC with a particular of the enclosure made with mesh size of 1 mm.

Figure 3 :
Figure 3: 5 mm metallic mesh enclosure used for the experiments.

Figure 7 :
Figure 7: Enclosure made with metallic mesh of 1 mm side dimension.Difference between the SE e with the absorber (blue line) and without it (black line) inside the enclosure.

Figure 8 :
Figure 8: Reflectivity (black line) and SE (red line) vs. frequency of a 1 mm side dimension mesh grid.

Figure 9 :
Figure 9: Reflectivity (black line) and SE (red line) vs. frequency of a 5 mm side dimension mesh grid.

Figure 10 :
Figure 10: Expected results in dBsq.m. for σ w,i +A e (black line) and σ w,i , (blue line) for the enclosure with mesh size of 1 mm

Figure 11 :
Figure 11: Expected SE e for the enclosure with mesh size of 1 mm

Figure 14 :
Figure 14: Standard uncertainty of corrected SE e in dB In Fig.2a sketch of the inner of the IUN RC with a particular of the enclosure employed in the measurements, is shown.In all experiments the transmitting and the receiving antenna used in the RC are both Ets-Lindgren doubleridged waveguide horn certified to work in the 1 -18 GHz frequency range.An Agilent Technologies Vector Network Analyzer (VNA) is used in experimental tests.Measurements by shifting the measuring frequency in the designed frequency range (1 -18 GHz) by steps of 200 MHz are accomplished.3000 independent samples are acquired at each frequency point.It must be noted that the statistically independence of the acquired samples, provided by the vibration of IUN RC walls that add up to the mechanical stirring, has been verified by the autocorrelation function (not shown to save space).The scattering coefficient S 21 is measured and an off-line data analysis is accomplished.The software used to acquire and to off-line analyze the data is developed in LabVIEW, a graphical development environment of the National Instruments (NI).
In order to circumvent this drawback, a correction of the SE e is accomplished.As matter of fact, two separate calibrations were performed (in the continuous stirring chamber case): a transmission one and a reflection procedure.The two measurements are taken in two separate steps.Hence, the scattering coefficients ɺ S 21 and ɺ S 22 are measured.Port1 is permanently connected to the horn antenna in RC.Port2 is in succession connected to the horn antenna in RC (hornhorn, hh) and to monopole antenna on the enclosure wall (horn-monopole, hm) according to Fig.1.Therefore, SE the entrance door.The S3 stirrer has bars of 1.20mx0.18msize and it is placed in the ceiling.The S1, S2 and S3 stirrers work in continuous mode with a maximum speed of 190, 390 and 320 rate per minute (rpm), respectively.