a wide-frequency model of metal foam for shielding applications

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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010 75 A Wide-Frequency Model of Metal Foam for Shielding Applications Onofrio Losito, Member, IEEE, Domenico Barletta, and Vincenzo Dimiccoli Abstract—The use of metal foam continues to grow in terms of research and application. Recently, new developments in the electromagnetic (EM) environment, such as shielding applications, have been proposed. A model of metal foam shielding is devel- oped and discussed in this paper to characterize and simulate the EM shielding behavior. More specifically, the EM characteriza- tion has been considered, and experimental shielding effectiveness measurements have been performed. These new double wire-mesh screens, obtained as a development of previously planar shields, al- low the design of metal foam EM shields, showing good agreement results among this model, some prototype of this model, and metal foams. The good agreements among data pave the way to improve the model for the low-frequency metal foams behavior. Index Terms—Double shielding, metal foams, shielding effec- tiveness (SE), wire-mesh screens. I. INTRODUCTION M ETAL foams have attracted engineers worldwide for decades because of their incomparable combination of lightweight structure, good acoustic and thermal isolation prop- erties, strong impact absorption, and vibration damping capa- bilities [1]. Recently, new developments in the electromagnetic (EM) environment, such as shielding applications, will hope- fully trigger the development of new applications and/or im- provement of the existing ones. Fig. 1 shows an example of an open cell aluminium foam. We can note that its low apparent density and its capability to allow both light and air transmission can be useful in several applications. The analysis of the shielding properties of different kinds of metal foams discussed in [2] has shown that metal foams are complex and random structures, which require sophisticated numerical models that are computationally onerous, challenging the development of metal foam analytical models. From the rigorous and exhaustive overview of the most adopted processes to make metal foams described in [1], we have reported only a few, such as “gas-injection,” the easiest to implement with aluminium alloy. Another interesting set of Manuscript received December 4, 2008; revised May 10, 2009 and August 11, 2009. First published January 29, 2010; current version published February 18, 2010. This work was supported by POR 2002–2006, Regione-Puglia, Italy (Axis III, measured 3.12 act. A, int. sp. A.1). O. Losito was with ITEL Telecomunicazioni S. r. l., Ruvo di Puglia, Bari 70033, Italy. He is now with the Electromagnetics Fields Group, Department of Electrotechnics and Electronic, Politecnico di Bari, Bari 70125, Italy (e-mail: [email protected]). D. Barletta and V. Dimiccoli are with ITEL Telecomunicazioni S. r. l., Ruvo di Puglia, Bari 70033, Italy (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEMC.2009.2035109 Fig. 1. Example of open cell aluminium foam. manufacturing methodologies is based on liquid-state process- ing or metal deposition on cellular platform. Apart from the adopted processes, the most important param- eters of metal foam are the relative density and the pore size. Relative (or apparent) density is the volume of foam material relative to the volume of material in a solid block of the base material, and it influences foam stiffness, strength, and both electrical and thermal conductivity. Pore size represents instead the pore dimension and is strongly connected to the number of pores per linear inch (PPI), an important characteristic for optical capacity, specific surface area, and fluid flow resistance. Varying the values of PPI and relative density, it is possible to obtain a different EM characteristics property. The planar wire-mesh screen model, developed by Casey [3] and compared with a commercial aluminium shield, perforated periodically with apertures was a first step to solve the EM problem in rigorous evaluation of the metal foam’s shielding effectiveness (SE) [4]. Encouraged by the results, we have im- proved the previously planar model and developed a new EM model. Therefore, the EM shielding behavior of a metal foam slab was investigated considering a shield model with double wire-mesh layers, separated by an air space. The single screen, whose meshes are assumed to be square is described by an equivalent sheet impedance operator as mentioned in [3]. The agreement of both experimental and theoretical data is a chal- lenge to optimize this model. In the following section, we have described the metal foams model developed to predict their EM shielding behavior. In Section IV, results obtained by CST Microwave Studio (CST MS) simulations are described, in order to validate our model. Section V describes the results given for experimental mea- surements of a metal foam slab and the theoretical new model. Finally, conclusions are drawn in Section VI. 0018-9375/$26.00 © 2010 IEEE

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Page 1: A Wide-Frequency Model of Metal Foam for Shielding Applications

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010 75

A Wide-Frequency Model of Metal Foamfor Shielding Applications

Onofrio Losito, Member, IEEE, Domenico Barletta, and Vincenzo Dimiccoli

Abstract—The use of metal foam continues to grow in termsof research and application. Recently, new developments in theelectromagnetic (EM) environment, such as shielding applications,have been proposed. A model of metal foam shielding is devel-oped and discussed in this paper to characterize and simulate theEM shielding behavior. More specifically, the EM characteriza-tion has been considered, and experimental shielding effectivenessmeasurements have been performed. These new double wire-meshscreens, obtained as a development of previously planar shields, al-low the design of metal foam EM shields, showing good agreementresults among this model, some prototype of this model, and metalfoams. The good agreements among data pave the way to improvethe model for the low-frequency metal foams behavior.

Index Terms—Double shielding, metal foams, shielding effec-tiveness (SE), wire-mesh screens.

I. INTRODUCTION

M ETAL foams have attracted engineers worldwide fordecades because of their incomparable combination of

lightweight structure, good acoustic and thermal isolation prop-erties, strong impact absorption, and vibration damping capa-bilities [1]. Recently, new developments in the electromagnetic(EM) environment, such as shielding applications, will hope-fully trigger the development of new applications and/or im-provement of the existing ones.

Fig. 1 shows an example of an open cell aluminium foam.We can note that its low apparent density and its capability toallow both light and air transmission can be useful in severalapplications.

The analysis of the shielding properties of different kindsof metal foams discussed in [2] has shown that metal foamsare complex and random structures, which require sophisticatednumerical models that are computationally onerous, challengingthe development of metal foam analytical models.

From the rigorous and exhaustive overview of the mostadopted processes to make metal foams described in [1], wehave reported only a few, such as “gas-injection,” the easiestto implement with aluminium alloy. Another interesting set of

Manuscript received December 4, 2008; revised May 10, 2009 and August11, 2009. First published January 29, 2010; current version published February18, 2010. This work was supported by POR 2002–2006, Regione-Puglia, Italy(Axis III, measured 3.12 act. A, int. sp. A.1).

O. Losito was with ITEL Telecomunicazioni S. r. l., Ruvo di Puglia, Bari70033, Italy. He is now with the Electromagnetics Fields Group, Department ofElectrotechnics and Electronic, Politecnico di Bari, Bari 70125, Italy (e-mail:[email protected]).

D. Barletta and V. Dimiccoli are with ITEL Telecomunicazioni S. r. l., Ruvodi Puglia, Bari 70033, Italy (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TEMC.2009.2035109

Fig. 1. Example of open cell aluminium foam.

manufacturing methodologies is based on liquid-state process-ing or metal deposition on cellular platform.

Apart from the adopted processes, the most important param-eters of metal foam are the relative density and the pore size.Relative (or apparent) density is the volume of foam materialrelative to the volume of material in a solid block of the basematerial, and it influences foam stiffness, strength, and bothelectrical and thermal conductivity. Pore size represents insteadthe pore dimension and is strongly connected to the numberof pores per linear inch (PPI), an important characteristic foroptical capacity, specific surface area, and fluid flow resistance.Varying the values of PPI and relative density, it is possible toobtain a different EM characteristics property.

The planar wire-mesh screen model, developed by Casey [3]and compared with a commercial aluminium shield, perforatedperiodically with apertures was a first step to solve the EMproblem in rigorous evaluation of the metal foam’s shieldingeffectiveness (SE) [4]. Encouraged by the results, we have im-proved the previously planar model and developed a new EMmodel. Therefore, the EM shielding behavior of a metal foamslab was investigated considering a shield model with doublewire-mesh layers, separated by an air space. The single screen,whose meshes are assumed to be square is described by anequivalent sheet impedance operator as mentioned in [3]. Theagreement of both experimental and theoretical data is a chal-lenge to optimize this model.

In the following section, we have described the metal foamsmodel developed to predict their EM shielding behavior. InSection IV, results obtained by CST Microwave Studio (CSTMS) simulations are described, in order to validate our model.Section V describes the results given for experimental mea-surements of a metal foam slab and the theoretical new model.Finally, conclusions are drawn in Section VI.

0018-9375/$26.00 © 2010 IEEE

Page 2: A Wide-Frequency Model of Metal Foam for Shielding Applications

76 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010

Fig. 2. Geometry of an individual square wire-mesh. The wire junctions areassumed to be bonded.

II. WIRE-MESH SCREEN MODEL

The analysis of complex foam structures is not possible withsimple numerical models and algorithms. Moreover, an accurateanalysis with numerical models is computationally onerous. Apossible solution to improve the time of the computational anal-ysis of foams is the development of an analytical model, whichdescribes their EM behavior in a simple way.

The first step to develop the new model of metal foams for ourpurposes is to modify a planar wire-mesh screen with boundedjunction as mentioned in [4], using the same dimensions ofthe ligaments and pore of a thin metal foam slab. The screengeometry is shown in Fig. 2.

This laminated shield can be described electromagneticallyby an equivalent sheet impedance operator Zs , when the meshdimensions are small compared to wavelength [3]. The operatorZs relates the tangential electric field Es to the surface currentdensity on the screen as

Es = Zs × Js. (1)

The equivalent sheet impedance for a screen with squaremeshes of dimension as × as is

Zs = (Zw as + jωLs)(I − nn) +jωLs

2K0εr∇s ×∇s (2)

where Zw is the internal impedance per unit length of the meshwire, K0 is the free-space wavenumber, and ∇s denotes thesurface del operator. I is the idem factor or identity dyadic, n isa unit vector normal to the surface occupied by the mesh, andLs the sheet inductance parameter is

Ls =µ0as

2πln

(1 − e−2πrw /as

)−1(3)

where rw is the radius of the mesh wires.If we consider a plane wave, in order to evaluate the effec-

tiveness of a planar mesh screen, it is necessary to evaluate thetransmission coefficient.

Fig. 3. Complete SE equation compared with the planar (2-D) model.

In the case where the mesh wires are perfectly conducting,we have [3]

SE = −20 log10(2ωLs/Z0)√

1 + (2ωLs/Z0)2

(4)

where Z0 is the free-space characteristic impedance.Consider the equation for SE [6]

SEdB = AdB + RdB + BdB . (5)

We know that A is the absorption loss of the wave for a screenthickness much greater than a skin depth, which becomes

AdB = 8.686αl (6)

where l is the thickness of the screen. For a wire-mesh screen,α is equal to

α =2π

λc

√1 −

(f

fc

)2

. (7)

Moreover, R is the reflection loss term, and according to [6]it is equal to

RdB = 20 log10

∣∣∣∣∣(1 + K)2

4K

∣∣∣∣∣ (8)

where K = Ls/Z0 for a wire-mesh screen.Finally, B represents the multiple-reflection loss term and as

mentioned in [7] is equal to

BdB = 20 log10

∣∣1 − e−2αle−j2β l∣∣ . (9)

In the previous planar model implementation, the B termhad been neglected because it was assumed that most of the EMfield attenuation was due to the absorption and reflection (screenthickness is much greater than the skin depth). In fact, Fig. 3shows good agreement between the planar (2-D) SE (4), andthe complete equation of SE (8). Therefore, it can be inferredthat the planar model represents a good approximation of thegeneral SE equation.

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LOSITO et al.: WIDE-FREQUENCY MODEL OF METAL FOAM FOR SHIELDING APPLICATIONS 77

Fig. 4. New model obtained from double wire-mesh screen sheets.

Nevertheless, the SE values of the planar model greatly under-estimate the SE of metal foam, as described in [8]. Therefore, wehave proposed a simple new model to approximate the shield-ing behavior of a metal foam slab, considering the slab as ashield with double wire-mesh layers, separated by an air space(see Fig. 4). In this new model, l1 and l3 are the thickness of aplanar wire-mesh screen which correspond to the radius of themesh wires, while l2 , the air space, is equal to the thickness ofmetal foam slab. The radius of the planar wire-mesh screen, canbe obtained for a different kinds of metal foams by approxi-mate formulas mentioned in [1], using the relative (or apparent)density and the number of PPI of metal foam

ρ

ρs

∼= 3r2w

a2s

(10)

PPI × as + (PPI + 1) rw = 25.4. (11)

The SE of a “good conductor” is given by [5]

SEsingle ∼= 4η0

ηe

tδ . (12)

Considering a model with double shielding layers separatedby an air space, the thickness of each is equal to t/2. If wedisregard multiple reflections in this air space, the total SE isgiven by [9]

SEdouble ∼=[4η0

ηe

t2 δ

]2

=[4η0

η

]2

etδ . (13)

Thus, the “interface mismatched” contribution for a doubleslab is the square of a single slab. Translating this result to ametal foam slab, we have a new SE model, which was givenin [9]

SE = −40 log102ωLs/Z0√

1 + (2ωLs/Z0)2. (14)

Therefore, the SE for a double layer shield can be written as

SEdouble = 2SEsingle . (15)

Fig. 5. SE (E-field) of the theoretical model with and without the B2 factor,compared with experimental data of metal foam slab Type I described in Table I.

Remembering (5), if we consider the B factor for a doublewire-mesh layers shield it can be written as [6]

Bdouble = B1 + B2 + B3 (16)

where B1 and B3 represent the multiple reflections, which occurin the two screens of thickness l1 and l3 , respectively, that are ofthe same value because they are made with the same material.As said before, for a screen thickness much greater than the skindepth, B1 and B3 can be neglected.

Moreover, B2 , the thickness of the air space between the twoscreens cannot be neglected, therefore, considering (8) for adouble layers shield we can obtain, as shown in [6]

B2 = 20 log10

∣∣∣∣1 −(

1 − 4η

Zw

)(cos 4π

l2λ0

− j sin 4πl2λ0

)∣∣∣∣(17)

where l2 is the air space thickness, η is the screen impedance(equal to Ls for our wire-mesh screen), and Zw = Z0 is thefree-space characteristic impedance (377 Ω).

Considering the B2 factor, our final model becomes

SE = −40 log10(2ωLs/Z0)√

1 + (2ωLs/Z0)2

+ B2 . (18)

It is clear, as shown in (14) that B2 is a periodic factor, whichallows to see in detail the frequency resonance of metal foamslab that is not visible in the equation of SE (14), as we can notein Fig. 5.

Increasing the number of PPI in our model, from (10) and(11), we can note a reduction of a square wire-mesh dimen-sion, and from (3) and (4), we can deduce, especially for highfrequency, a decrease in the SE value, as shown in Fig. 6.

The good results of this model for high frequency encourageus to use this double wire-mesh screen as an approximate modelto predict the SE for low frequency magnetic shield. Naturally,the EM shielding behavior of a metal foam at a low frequencyis different. In fact, in this case we can define the magnetic-field

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78 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010

Fig. 6. SE (E-field) of the theoretical model with PPI = 10 (low PPI) and PPI= 20 (high PPI).

Fig. 7. Parallel mesh shielding geometry.

shielding transfer function as [3]

Tm (jω) =magnetic field in the shielded region

magnetic field in the absence of shield. (19)

Considering a plane wave, (19) can be written as [7]

Tm (jω) =(

1 +jωµ0

nZs

)−1

(20)

where

n = 1 for the parallel-mesh geometry;n = 2 for the cylindrical geometry;n = 3 for the spherical geometry.

For our purpose, we can consider the parallel-mesh geometry,as show in Fig. 7, because it can be compared with our model(see Fig. 4).

It is clear that the quantity a/n is simply the volume-to-surfaceratio, therefore, (20) becomes

Tm (jω) =(

1 +jωµ0Ve

ZsSe

)−1

(21)

where Ve and Se indicate the volume and the surface area of theenclosure.

Now assuming that the mesh wires are sufficiently thin(Z ′

w as∼= Rs), Tm (jω) can be written as

Tm (jω) ∼= Rs + jωLs

Rs + jωµ0Ve/Se(22)

where Rs = as/πr2w σw . Defining τs = Ls/Rs (a time constant

characteristic of the mesh), and τe = µ0Ve/(SeRs) (a time con-

Fig. 8. EMC box implemented with CST software.

Fig. 9. Shielded EMC box implemented with CST software designed withdouble wire-mesh geometry with as = 3 mm, rw = 0.4 mm, and l2 = 14 mm.

stant characteristic of the enclosure), with τe τs , we have

Tm (jω) =(

1 + jωτs

1 + jωτe

). (23)

To sum up the analytical model of a magnetic-field SE enclo-sure, SEm can be defined as [3]

SEm = −20 log10 |Tm (jω)| . (24)

SEm is nearly zero at frequencies below ω = 1/τe and prac-tically uniform at frequencies above ω = 1/τs .

Between these two frequencies, SEm increases at 20 dB perdecade. As described previously for a double wire-mesh screen,we can write (15) so that our new model becomes

SEm double = −20 log10

[1 + (ωτs)2

1 + (ωτe)2

](25)

where τe is a double of a single shielding.

III. NUMERICAL SIMULATION

The first step for the validation of our new model consistedof the simulation of a double wire-mesh screen with CST MS.An EMC box (40 cm × 30 cm × 35 cm) opened on one sidewas simulated and excited with a coaxial cable (see Fig. 8).

The SE was calculated as the difference between E far-fieldwithout a double wire-mesh screen and E far-field with a doublewire-mesh screen on the other side of the EMC box implementedused for the screen as the geometry shown in Fig. 2, with as

and rw obtained for different kinds of metal foams by (10) and(11). The thickness of the air space l2 is equal to the thicknessof metal foam slab tested (see Fig. 9).

The SE was evaluated at 30 cm from the end of the boxsource and at 1 m from the source. These simulated values werecompared with our new model, obtaining good agreement, asshown in Fig. 10.

Page 5: A Wide-Frequency Model of Metal Foam for Shielding Applications

LOSITO et al.: WIDE-FREQUENCY MODEL OF METAL FOAM FOR SHIELDING APPLICATIONS 79

Fig. 10. Simulated and estimated SE (E-field) compared with experimentaldata of metal foam slab Type I described in Table I.

The main difference among our model, full-wave CST model,and the experimental data (see Fig. 10) is essentially in theapproximation of the random structure of metal foam, especiallyfor wider dimensions of metal foams with higher porosity thatalso requires more computational time for CST simulation.

Moreover, low-frequency simulations have not been madewith CST MS, because of the onerous computational cost of thetiny dimension of the new model compared with the wavelengthof the frequency range simulations. However, there is no reasonwhy our model cannot be applied to lower frequencies below800 MHz. This in conclusion leads to prefer our model to theCST model.

Finally, the agreement between theoretical and simulated be-havior of SE and the simplicity of our new model paved the wayto make a physical double wire-mesh screen model. This op-portunity led to compare the SE measurements of this physicaldouble screen with the SE of the metal foam slabs.

IV. EXPERIMENTAL RESULTS

In this section, we show the results of the measurements madeon different kinds of metal foams that were compared with ourmodel and with its physical model. Fig. 11 shows the electric-field SE related to four open cell slabs 30 cm × 30 cm of 1.4 cmthickness, while varying some structural properties accordingto data summarized in Table I [2]. More specifically, Type I–IVdata have been experimentally obtained and measurements per-formed in the range 10 kHz–20 GHz.

As commonly accepted, three different frequency rangeshave been identified (namely “low frequency,” “resonance,”and “high frequency”), and in each one appropriate sourceshave been used. The aluminium foam slabs have been carefullyadapted to an aperture of a shielding room and measurementsperformed according to IEEE Standard 299-1997.

It is clear from Fig. 11 that all the studied slabs show goodshielding capability in the whole frequency range and especiallyfor frequencies up to 2 GHz. As expected, a SE reduction has

Fig. 11. SE measurements (E-field) for the aluminium foam slabs describedin Table I.

TABLE IDUOCEL ALUMINIUM FOAMS TESTED

been found for higher frequencies, because of the effects ofthe open cell nature of the considered aluminium foams. More-over, some values of measured data were characterized of somedecibels of uncertainty.

To investigate the causes of uncertainly, we can considerthe unstable measure of the E field inside the shielding roomdue to the small dimension of metal foam slabs tested, andthe different properties of different kind of antennas used inthe experimental measurement. More closely, by comparing theSE values of aluminium foam slabs of Type II with those ofType IV (see Fig. 12), it is apparent that for metal foams withthe same apparent density, shielding capabilities increase if PPIincreases. Moreover, when comparing slabs with the same PPIbut different relative density (Type III and Type IV, respectively),lower shielding performance is measured for lower density slabs(see Fig. 13).

This is in agreement with that shown for mechanicalproperties; i.e., increasing porosity for most properties, in-cluding strength, stiffness, and conductivity increases thenexponentially.

The previous results were compared with our new modelresults (see Fig. 14) using the same total thickness of metalfoam slab for our model.

We can see the agreement of the EM behavior of metal foamswith our model. Moreover, it is clear how this model can ac-curately predict the worst SE results at the first resonance ofthe EMC box (just over 8 GHz). It is known that smaller boxesresonate at higher frequency, therefore, making the box small

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80 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 52, NO. 1, FEBRUARY 2010

Fig. 12. SE measurements (E-field) for the aluminium foam slabs Type II andType IV described in Table I.

Fig. 13. SE measurements (E-field) for the aluminium foam slabs Type IIIand Type IV described in Table I.

Fig. 14. SE measurements (E-field) for the aluminium slabs described inTable I compared with the theoretical model.

Fig. 15. Physical implementation of our model.

Fig. 16. SE measurements (E-field) for iron and brass double wire-meshscreens compared with theoretical values of the our model and with metal foamType II.

enough to push the first resonance above the upper limit of thetest frequency range. The physical realization of our model wasmade by using a wooden support (30 × 30 × 1.4 cm), cov-ered by a double wire-mesh grid with as and rw of 3 mm and0.4 mm, respectively [see Fig. 15(a)–(b)].

Two screens were created by covering the wooden supportfirst with an iron double wire-mesh grid and second with a brassdouble wire-mesh grid. The experimental measures of thesephysical models were compared with metal foam Type II, andour model, using the same geometrical parameter of the physicaldouble wire-mesh grid, showing good agreement as shown inFig. 16.

It is also clear from Fig. 16 that the EM performance of ametal foam slab is comparable with a physical double wire-meshscreen, so the prototypes of our model can be considered as per-forming an analytical characterization of metal foams. Finally,we compared the experimental magnetic SE of our prototypeswith the first approach for a low-frequency model described in(25), obtaining the results shown in Fig. 17.

We can see that our low-frequency model has the same trendas the experimental SEm results of metal foam slab Type II,but are not completely in agreement, because the analyticalmodel is the first approximation of the low-frequency behaviorof metal foam. However, from Fig. 17 we can also see the good

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LOSITO et al.: WIDE-FREQUENCY MODEL OF METAL FOAM FOR SHIELDING APPLICATIONS 81

Fig. 17. SE measurements (H-field) for iron and brass double wire-meshscreens compared with theoretical values of the low-frequency model and withmetal foams Type II.

agreement of the metal foam slab Type II, with iron and brassdouble wire-mesh screens. This paves the way to improve theanalytical study of the model for low frequency.

V. CONCLUSION

We have considered a variety of relevant topics to understandthe problem of the EM characterization of metal foams fortheir use in radio-frequency EM shields and for low-frequencyshields. We have discussed the experimental results about theSE of some specific types of open cell aluminium foam slabs,showing good shielding properties over a large frequency range.Moreover, to describe the analytical behavior of metal foams, wehave presented a new double wire-mesh screen model, obtainedas a development of the model proposed by Casey and discussedin [4]. The proposed model was validated by numerical simula-tions that is obtained by using CST MS. The possibility to easilyobtain a physical model of the analytical one, led us to makea prototype of a double wire-mesh screen by using a woodensupport covered by two kinds of metallic grid, i.e., iron andbrass. The theoretical data of our model compared with experi-mental results show strong agreement between metal foams anddouble wire-mesh screens. The same agreement was seen be-tween experimental and theoretical results for metal foams andprototypes of our model, so that these prototypes can be con-sidered as performing an analytical characterization of metalfoams. Finally, the good agreement of our model theoreticaldata, compared with experimental results for SE at low frequen-cies, encourages the optimization of this model, requiring ananalytical improvement.

REFERENCES

[1] M. F. Ashby, A. G. Evans, N. A. Fleck, L. J. Gibson, J. W. Hutchinson,and H. N. G. Wadley, Metal Foams: A Design Guide. London, U.K.:Butterworth-Heinemann, 2000.

[2] L. Catarinucci, O. Losito, L. Tarricone, and F. Pagliara, “High added-value EM shielding by using metal-foams: Experimental and numericalcharacterization,” in Proc. IEEE Int. Symp. Electromagn. Compat. (EMC2006), Aug., vol. 2, pp. 285–289.

[3] K. F. Casey, “Electromagnetic shielding behavior of wire-mesh screens,”IEEE Trans. Electromagn. Compat., vol. 30, no. 3, pp. 298–306, Aug.1988.

[4] L. Catarinucci, O. Losito, and L. Tarricone, “On the use of metalfoams in EM shielding applications,” in Proc. Mediterr. Microw. Symp.(MMS’2006), Genova, Italy, Sep., pp. 240–245.

[5] C. R. Paul, Introduction to Electromagnetic Compatibility, 2nd ed. NewYork: Wiley, 2006, ch. 10.

[6] R. B. Schultz, V. C. Plantz, and D. R. Brush, “Shielding theory andpractice,” IEEE Trans. Electromagn. Compat., vol. 30, no. 3, pp. 187–201, Aug. 1988.

[7] K. S. H. Lee, Ed. “EMP interation: Principles, techniques, and referencedata,” Air Force Weapons Lab. Tech. Rep. TR-79–403, pp. 555–556, Dec.1979.

[8] O. Losito, “An analytical characterization of metal foams for shieldingapplications,” presented at the PIERS 2008, Hyatt Regency, Cambridge,MA, 2–6, Jul.

[9] O. Losito, M. Bozzetti, V. Dimiccoli, and D. Barletta, “An analytical 3Dmodel of metal foams for EM shielding applications,” presented at theEMC Eur. 2008, Hamburg, Germany, 8–12, Sep.

Onofrio Losito (M’08) was born in Molfetta, Bari,Italy. He received the M.Sc. degree in electronic en-gineering from the Politecnico di Bari, Bari, in 2002,and the Ph.D. degree in information engineering fromthe Universita del Salento, Leece, Italy, in September2007.

Since 1999, he has been engaged in the tech-niques of installation for systems of telecommunica-tions and measures of electromagnetic (EM) fieldswith the high schools as an outside expert. In 2007,he joined ITEL Telecommunication S. r. l., Ruvo di

Puglia, Bari, as a Researcher in the ITEL Laboratory of Electromagnetic Com-patibility. He is currently with the Electromagnetics Fields Group, Departmentof Electrotechnics and Electronic, Politecnico di Bari. His research interestsinclude the analysis and design of 1-D and periodic leaky wave antennas, mi-crowave filters, and EM shieldings, for radio frequency.

Domenico Barletta was born in Canosa di Puglia,Bari, Italy, on January 7, 1971. He received the M.Sc.degree in electronic engineering from the Politecnicodi Torino, Torino, Italy, in 1998.

In 1999, he joined ITEL Telecomunicazioni S. r.l., Ruvo di Puglia, Bari, as a Research Engineer in theITEL Laboratory of Electromagnetic Compatibility,where he became Manager of Prevention and Protec-tion, in 2006 and Quality Assurance/EnvironmentalHealth and Safety Manager in 2008. He has been co-ordinating projects and operative activity in 30 coun-

tries in the area of shielding for magnetic resonance and tests of electromagneticcompatibility and electrical safety.

Vincenzo Dimiccoli was born in Barletta, Italy, onApril 7, 1972. He received the M.Sc. degree in elec-tronic engineering from the Politecnico di Bari, Bari,Italy, in 1999.

In 1999, he joined ITEL Telecomunicazioni S. r.l., Ruvo di Puglia, Bari, a company set up in 1982with diversified activities in various sectors related toelectromagnetic (EM) impact, shielding for magneticresonance for civil and military purposes, and tests ofEM compatibility and electrical safety, as a ProjectEngineer and became Engineering Division Manager

in 2006. He has been coordinating research projects with several Italian univer-sities and industrial districts, increasing its scientific publications.