IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011 579

Shielding Effectiveness of a Thick MultilayeredPanel in a Reverberating Environment

Domenico Alessandro Lampasi, Member, IEEE, and Maria Sabrina Sarto, Fellow, IEEE

Abstract—This paper presents and discusses different ap-proaches for the measurements of the shielding effectiveness ofthick multilayered panels, based on the use of nested reverber-ation chambers. In particular, it is considered the case of thickmultilayered panels, characterized by one highly reflecting face,like a protected composite laminate or a protected glazing window.The paper proposes a novel test procedure, which allows one toestimate from the measurement of a finite dimension panel, theshielding performance of an infinite material sheet against a re-verberating field. The method is validated by comparison with theresults of analytical simulations and provides accurate results ina wide frequency range, above the lowest-usable frequency of theouter chamber.

Index Terms—Electromagnetic shielding, high intensity radi-ated field (HIRF), multilayered electromagnetic shields, reverber-ation chambers.

I. INTRODUCTION

ADVANCES in material technology and development ofnew multifunctional materials combining electrical, elec-

tromagnetic, mechanical, and structural properties, with thermalcontrol capability and eventually specific optical performances,pose new challenges in the development of methods for theexperimental characterization of the electromagnetic shieldingeffectiveness (SE) at radio frequency (RF). Multilayered mate-rials and laminates are widely used in different fields of engi-neering to combine the structural properties with the functionalones. Examples are sandwich panels in spacecraft and aircraftstructures, or laminated shielding and thermal-control glazingwindows in architectural, automotive, and aerospace applica-tions. Such laminated materials can have thickness ranging fromsome millimeters to a few centimeters, thus resulting electricallythick in the RF above a few gigahertz. The proper electromag-netic design and installation of a laminated structure in a realcomplex environment would require the characterization of theshielding performance of the material. In case of thick samples,such characterization may be very demanding in terms of set-updimensions and data processing algorithms [1].

Manuscript received April 23, 2010; revised December 5, 2010; acceptedFebruary 18, 2011. Date of publication May 2, 2011; date of current versionAugust 18, 2011. This work was supported by the European Union within theproject HIRF-SE under Grant Agreement no. 205294.

D. A. Lampasi is with the National Agency for New Technologies, Energyand Sustainable Economic Development (ENEA), Frascati, Italy.

M. S. Sarto is with the Department of Astronautics, Electrical and Ener-getic Engineering of Sapienza University of Rome, 00184 Rome, Italy. (e-mail:mariasabrina.sarto@uniroma1.it).

Digital Object Identifier 10.1109/TEMC.2011.2132723

The coaxial waveguide method, described in the standardASTM-D4935 for the frequency range up to 1.5 GHz [2] andextended in [3] to the range 30 MHz–8 GHz, provides the mea-surement of the SE of a planar sample of material against a nor-mally incident plane wave. The method is limited to the testingof isotropic materials, and is particularly suitable in case of thinspecimen with at least one external conducting face [2]. In caseof thick laminates, which are the objective of the present study,the technique is limited by the excitation of spurious modespropagating in the radial direction, between the two faced wave-guide flanges [3]. Moreover, for material operating in complexsystems, like an aircraft, the shielding performance in presenceof an electromagnetic field (EMF) propagating from any direc-tion and with any polarization could be more significant thanthe SE provided by the ASTM-D4935 method, in the hypothe-sis of plane wave with normal incidence. In particular, the SEof a thick laminated, measured in a reverberating environment,represents a sort of worse-case performance.

The IEC 61000–4-21 standard [4] describes the use of thenested reverberating chamber (NRC) approach for the measure-ment of the SE of materials and panels. The main issue with thisapproach is to obtain an SE measurement that is independentof the test set-up configuration and, in particular, of the paneland aperture dimensions, of the cavity characteristics, of thechamber loading effect, and of the bonding condition. Differ-ent procedures have then been proposed in the literature, basedon the definition of the SE either in terms of received poweror aperture transmission cross-section [5]–[15]. The problemof correlating experimental measurements performed applyingthe NRC method with the results of full wave numerical sim-ulations has been discussed in [16], in which a full-wave 3-Dmethod based on the finite-difference time-domain techniquehas been applied. The reverberating field has been modeled andsimulated considering the superposition of incident plane waveshaving any angle of incidence and polarization [17]. However,the correlation between the SE measurements obtained using theNRC approach and those obtained applying the ASTM-D4935standard is still an open issue. A further problem is that the min-imum frequency at which the NRC-based measurements arereliable is limited by the size of the inner test cavity and, there-fore, is generally much higher than the lowest useable frequency(LUF) of the outer chamber [4]. Some studies have also beendone in order to solve the problem of the effect of contact be-tween the test enclosure and the loading panel. To this purpose,a near-field test set-up has been proposed in [18].

The scope of this paper is to propose a measurement pro-cedure that provides an accurate estimation of the shield-ing performance of a thick laminate screen using NRCs. The

0018-9375/$26.00 © 2011 IEEE

580 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011

developed method provides an SE measurement that is not af-fected neither by the shape of the test specimen nor by the innerchamber configuration, but it is representative of the SE of ascreen having infinite dimensions illuminated by a reverberat-ing EMF. The effect of the panel bonding on the SE measure-ment is investigated and a method to correct the effect of thenon-reciprocity of the NRC test method is proposed.

The results of the proposed test procedure are validated bycomparison with the SE measured using the ASTM-D4935method on thin shielding materials and with analytical calcula-tions. The good agreement between the measured and the com-puted data confirms the validity of the proposed approach, evenin the frequency range where the inner reverberating chamberis undermoded.

The paper is organized as follows: At first, a short reviewof the SE measurement methods based on the use of the NRCapproach is presented. The expressions of the SE as a function ofthe scattering parameters are reported to facilitate the applicationof the different methods. Then, the analytical model of the SEof a thick laminate having infinite dimensions and illuminatedby a reverberating field is developed. Finally, the results of theproposed test method are presented and compared with coaxialwaveguide measurements and analytical calculations.

II. EXPERIMENTAL PROCEDURE

A. Received Powers and Quality Factors

The test method considered in this paper is based on the useof two NRCs, as sketched in Fig. 1(a) or (b) [3]. The innerchamber (IC) consists of an aluminum box whose top lid has arectangular aperture that can host the planar sample under test.The outer chamber (OC) produces a stirred field incident on theIC and on the sample to be tested. The use of the hybrid modestirring (HS) approach that combines the mechanical stirring(MS) and the frequency stirring (FS) techniques ensures goodreverberating properties in both the chambers [10], [11], [13].

Due to the statistical characteristics of the EMF inside an RC,all the measurements derive from ensemble averages, indicatedby the symbols 〈·〉, which are calculated over both the paddlepositions and the frequency bandwidth.

The average scalar power density 〈S〉 in a RC for a givenwavelength λ can be derived from the average root mean squareelectric field as [19]

〈S〉 =〈|E|2〉

η0=

λQ

2πV〈PT〉 (1)

in which η0 is the free-space impedance, V is the chamber usefulvolume, Q is the chamber quality factor, and 〈PT〉 is the averagepower transmitted in the chamber by the transmitting antennas.The average power received by any matched lossless antenna inthe RC is given by [19]

〈PR〉 =λ3Q

16π2V〈PT〉 . (2)

The power transmitted in the IC through the aperture is ex-pressed as a function of the aperture cross-section 〈σa〉 averagedover all the incidence angles (2π steradians) and polarizations,

Fig. 1. Sketch of the NRC measurement set-up using either a 2-port (a) ora 4-port (b) VNA. Tx is the (horn) transmitting antenna in the OC, Rx isthe (short monopole) receiving antenna in the IC, Txaux and Rxaux are theadditional transmitting and receiving antennas used to correct the chamber Q-factor variations.

of the scalar power density 〈SO 〉 incident from the OC to the IC,and of the average power transmitted in the IC 〈PTI〉 [5]:

〈σa〉 = 2〈PTI〉〈SO 〉

. (3)

If the power penetrating through the IC walls is negligible, theaverage power 〈PRI〉 received by an antenna located in the ICcan be expressed as a function of the average power 〈PTO 〉transmitted by an antenna in the OC by using (2) combined with(3) and (1):

〈PRI〉 = 〈σa〉λ4QIQO

64π3VIVO〈PTO 〉 (4)

in which the subscripts “O” and “I” indicate a quantity relatedto the OC and IC, respectively.

B. Shielding Effectiveness Measurements

Different definitions and methods have been presented in thepast in order to characterize the SE performances of a screenusing scattering parameter measurements in NRCs. In the fol-lowing, the different methods are reviewed and a novel approachable to correct the effects of the nonreciprocity of the test set-upand of the finite size of the specimen under test is presented.

1) Basic Method (BM): The BM uses the test-set up ofFig. 1(a) and uses only the two antennas: Tx, connected tothe VNA port 1, and Rx, connected to the port 2

In the BM, the SE of the test sample is defined as [8]

SEBM = 10 log10〈PRIr〉〈PRI〉

(5)

LAMPASI AND SARTO: SHIELDING EFFECTIVENESS OF A THICK MULTILAYERED PANEL IN A REVERBERATING ENVIRONMENT 581

in which 〈PRI〉 is the average power measured in the IC withthe panel covering the IC aperture and the subscript “r” denotesthe reference configuration without the panel under test. Thosepowers are estimated assuming the hypotheses

〈PRIr〉 ≈ 〈PRVNAr〉 =⟨|S21r |2

⟩〈PTVNAr〉 (6a)

〈PRI〉 ≈ 〈PRVNA〉 =⟨|S21 |2

⟩〈PTVNA〉 (6b)

in which 〈PRVNA〉 and 〈PTVNA〉 are respectively the averagepower transmitted and received by the VNA and S21 is the trans-mission coefficient between the VNA port 1 and port 2. More-over, it is considered that the efficiencies of all the antennas areconstant for the loaded and unloaded aperture configurationsand that the power transmitted by the VNA in the load and ref-erence configuration is unchanged, i.e., 〈PTVNAr〉 ≈ 〈PTVNA〉.Therefore, SEBM in (5) yields

SEBM = 10 log10

⟨|S21r |2

⟩⟨|S21 |2

⟩ . (7)

2) Standard Method (SM): The SM uses only the two antennasTx and Rx of the test set-up of Fig. 1(a), like in the BM, butintroduces a correction for the antenna mismatches [11]. TheSE is defined by (5) by assuming the following expressions forthe powers in the load and reference configurations

〈PRIr〉 ≈〈PRVNAr〉

1 − |〈S22r〉|2, 〈PRI〉 ≈

〈PRVNA〉1 − |〈S22〉|2

(8a)

〈PTVNAr〉 ≈〈PTOr〉

1 − |〈S11r〉|2, 〈PTVNA〉 ≈

〈PTO 〉1 − |〈S11〉|2

(8b)

in which S11 and S22 are the reflection coefficients at the VNAports 1 and 2, respectively, and 〈PTOr〉 ≈ 〈PTO 〉 is the averagepower in the OC, which is considered to be unchanged in theload and reference configurations.

By introducing the conditions (8a) and (8b) in (5), the SEmeasured with the SM yields [11]

SESM = SEBM

+ 10 log10

[ (1 − |〈S11〉|2

1 − |〈S11r〉|2

) (1 − |〈S22〉|2

1 − |〈S22r〉|2

)].

(9)

3) Advanced Method (AM): The AM makes use of all the4 antennas appearing in the test set-up of Fig. 1(a) or (b) [8]:Txaux is an auxiliary antenna transmitting in the IC, Rxaux is anauxiliary antenna receiving in the OC. In order to account forthe effect of the scattering from the aperture, the SE is definedas the ratio of the aperture cross-sections in the unloaded andloaded configurations [8]

SEAM = 10 log10〈σar〉〈σa〉

. (10)

Using (3) 〈σar〉 and 〈σa〉 can be expressed as functions of thepowers 〈PTO 〉 and 〈PTOr〉 transmitted in the OC with the loaded

and unloaded aperture, and of the corresponding powers 〈PRI〉and 〈PRIr〉 received in the IC. Considering again (8a) and (8b),SEAM can be rewritten as

SEAM=10 log10〈PRIr〉QIQO

〈PRI〉QIrQOr= SESM + 10 log10

QIQO

QIrQOr.

(11)The ratio between the Q-factors of the IC in the load and

reference configurations can be estimated using (2) as functionof the measured scattering parameters using the 2-port VNA, assketched in Fig. 1(a)

QI

QIr=

〈PRI〉 〈PTIr〉〈PRIr〉 〈PTI〉

=

⟨|S21I |2

⟩ (1 − |〈S11Ir〉|2

)(1 − |〈S22r〉|2

)⟨|S21Ir |2

⟩ (1 − |〈S11I〉|2

)(1 − |〈S22〉|2

) . (12)

In the previous expression PTI is the power transmitted in theIC by the Txaux antenna, and PRI , S11I , S21I , and S22 are thepower and scattering parameters measured in the IC when theTxaux antenna is the transmitting one and Rx is the receivingone. A similar expression can be written for the ratio QO /QOr

QO

QOr=

〈PRO 〉 〈PTOr〉〈PROr〉 〈PTO 〉

=

⟨|S21O |2

⟩ (1 − |〈S11r〉|2

) (1 − |〈S22Or〉|2

)⟨|S21Or |2

⟩ (1 − |〈S11〉|2

) (1 − |〈S22O 〉|2

) . (13)

in which PTO is the power transmitted by the Tx antenna, andPRO , S11 , S21O , and S22O are the power and scattering param-eters measured in the OC when Tx is the transmitting antennaand Rxaux is the receiving one. Hence, SEAM yields

SEAM = SEBM

+ 10 log10

⎡⎣

⎛⎝

⟨|S21O |2

⟩

1 − |〈S22O 〉|2

⎞⎠

⎛⎝

⟨|S21I |2

⟩

1 − |〈S11I〉|2

⎞⎠

⎤⎦

− 10 log10

⎡⎣

⎛⎝

⟨|S21Or |2

⟩

1 − |〈S22Or〉|2

⎞⎠

⎛⎝

⟨|S21Ir |2

⟩

1 − |〈S11Ir〉|2

⎞⎠⎤⎦ .

(14)

Using a 4-port VNA as sketched in Fig. 1(b), SEAM can berewritten in the following equivalent form

SEAM = SEBM

+ 10 log10

⎡⎣

⎛⎝

⟨|S41 |2

⟩

1 − |〈S44〉|2

⎞⎠

⎛⎝

⟨|S23 |2

⟩

1 − |〈S33〉|2

⎞⎠

⎤⎦

− 10 log10

⎡⎣

⎛⎝

⟨|S41r |2

⟩

1 − |〈S44r〉|2

⎞⎠

⎛⎝

⟨|S23r |2

⟩

1 − |〈S33r〉|2

⎞⎠

⎤⎦ .

(15)

582 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011

4) Enhanced Method (EM): The EM uses all the 4 antennasappearing in the test set-up of Fig. 1(a) or (b) and aims to takeinto account the multiple interactions between the IC and theOC and the nonreciprocity of the samples and to the measure-ment set-up [14]. Following [14] in the hypothesis of reciprocalsamples, the aperture cross-section can be calculated as

〈σa〉 = 1 − 〈PROI〉2

〈PTO 〉2· 〈PTI〉〈PRII〉

· 〈PTO 〉〈PROO 〉

. (16)

Considering a similar expression for 〈σar〉, the definition (10)of SE yields

SEEM = SEAM + 10 log10

(1 − 〈PROI〉2

〈PTO 〉2· 〈PTI〉〈PRII〉

· 〈PTO 〉〈PROO 〉

)

− 10 log10

(1 − 〈PROIr〉2

〈PTOr〉2· 〈PTIr〉〈PRIIr〉

· 〈PTOr〉〈PROOr〉

)

(17)

that can be rewritten in terms of the scattering parameters asfollows:

SEEM = SEAM + 10 log10

⎛⎜⎝1 −

⟨|S21 |2

⟩2

⟨|S21I |2

⟩ ⟨|S21O |2

⟩⎞⎟⎠

− 10 log10

⎛⎜⎝1 −

⟨|S21r |2

⟩2

⟨|S21Ir |2

⟩ ⟨|S21Or |2

⟩⎞⎟⎠ . (18)

5) Combined Method (CM): The CM combines the nestedreverberation approach with the measurement of the SE of areference sample (ref) characterized by a known SE (SEref ).Starting from (5), it results

SECM = 10 log10〈PRIr〉〈PRI〉

= SEref + 10 log10〈PRIref 〉〈PRI〉

. (19)

Considering (7) it yields

SECM = SEref + 10 log10

⟨|S21ref |2

⟩⟨|S21 |2

⟩ (20)

which can be expressed also in terms of the SEBM given in (7)

SECM = SEBM + CF. (21)

In the previous expression CF is the correction factor in dB:

CF = SEref − SEBMref (22)

in which SEBMref is the SE of the reference sample measuredusing the BM.

Notice that the estimation of SE using (19) is accurate ifthe reference sample is characterized by a reflection coeffi-cient similar to that of the specimen under test. In the nextSection III-B, it is demonstrated that for an electrically thinconducting sheet, the SE against a plane wave with normal in-cidence is coincident with the SE estimated in a reverberatingenvironment. This means that if the reference sample is a thin

Fig. 2. Schematic configuration of an M-layer panel of infinite dimensionsilluminated by a TE and a TM polarized plane waves.

Fig. 3. Number of modes in the IC and OC as a function of the frequency.The indicated LUFs are those providing at least 60 excited modes [4].

conducting sheet, SEref in (22) can be obtained applying theASTM-D4935 method [2].

III. MODELING

A. Thick Multilayer Panel

The effect produced by a reverberating environment on themultilayered panel sketched in Fig. 3 is simulated consideringan infinite set of plane waves impinging on the infinite surfaceof the screen, with all the possible incidence and polarizationangles, ϑ0 and ϕ0 , respectively.

It is considered that for each incident angle (0≤ ϑ0 < 90◦) theimpinging wave is decomposed in a TE and in a TM polarizedplane wave. Due to the infinite planar dimensions of the panel,the analysis of the configuration is the performed applying thetransmission line method.

The m-th layer of the panel is characterized by its thicknessdm , relative permittivity εrm , relative permeability μrm , andelectrical conductivity σm . The incidence angle at the mth inter-face between layers (m–1) and m, i.e., ϑm , can be derived fromϑ0 using the Snell law

sin ϑm =sinϑ0√

μrm (εrm + σm /jωε0). (23)

LAMPASI AND SARTO: SHIELDING EFFECTIVENESS OF A THICK MULTILAYERED PANEL IN A REVERBERATING ENVIRONMENT 583

Notice that the angle ϑm can be a complex number in case ofdissipative media. The complex propagation constant is

γm = jkm = jω

√μrm μ0

(εrm ε0 + σm

jω

)cos ϑm . (24)

The characteristic impedances for the TE and TM polarizedwave are respectively,

ηTEm =

ηm

cos ϑm(25a)

ηTMm = ηm cos ϑm (25b)

in which ηm is the intrinsic impedance of the m-th layer in caseof normal incidence

ηm =

√jωμrm μ0

σm + jωεrm ε0. (26)

Accordingly, the input-to-output transmission matrix of themth layer assumes different expressions for the TE and TMincident waves. For the TE wave it yields

ΦTEm =

[Φm11 ΦTE

m12

ΦTEm21 Φm22

]

=

⎡⎣

cosh (γm dm ) −ηTEm sinh (γm dm )

− sinh (γm dm )ηTE

m

cosh (γm dm )

⎤⎦ . (27)

Notice that the proper coefficients of the transmission matrix areindependent of the wave polarization. The transmission matrixfor the TM polarization, i.e., ΦTM

m , is obtained by replacing ηTEm

in (27) with ηTMm .

The total input-to-output transmission matrix of the multilay-ered panel is given by the product of the single-layer matrices.For the TE mode, it yields

ΦTE =[

ΦTE11 ΦTE

12

ΦTE21 ΦTE

22

]=

M −1∏m=0

[Φ(M −m )11 ΦTE

(M −m )12

ΦTE(M −m )21 Φ(M −m )22

].

(28)The field attenuation factor for the TE wave, i.e., ΨTE , is

defined as the ratio of the transmitted and incident electric fieldcomponents, ETE

tz and ETE0z , and is expressed as function of the

coefficients of the transmission matrix in (28)

ΨTE =2

Φ11 + Φ22 − η0ΦTE21 − ΦTE

12

/η0

(29)

in which η0 is the vacuum characteristic impedance. For theTM wave, the field attenuation factor is defined as the ratio ofthe transmitted and incident electric field components ETE

tz andETE

0z , and is obtained from (29) by replacing the TE quantitieswith the ones computed for the TM polarization.

The electric field transmitted through the panel is given bythe sum of the TE and TM contributions

EIC = ETMt + ETE

t = ETMtx x + ETM

ty y + ETEtz z (30)

in which

ETMtx = ETM

ty tan ϑ0 (31a)

ETMty = ΨTMETM

0y (31b)

ETEtz = ΨTEETE

0z . (31c)

The incident tangential field components appearing in (30) and(31 a–c) are expressed as function of the incident field amplitudeand of the incidence and polarization angles

ETM0y = E0 cos ϕ0 cos ϑ0 (32a)

ETE0z = E0 sin ϕ0 . (32b)

In a reverberating environment, the SE is defined referring tothe normalized average of the square module of (30), namely

SERE = 10 log10E2

0⟨|EIC |2

⟩ (33)

in which the average is intended with respect to 0 ≤ ϑ0 < 90◦

and with respect to –90◦ ≤ ϕ0 < 90◦. Since the field attenuationfactors are only function of the incidence angle, the average onthe polarization angle can be computed analytically, and (33)can be rearranged in the form

SERE = 10 log102⟨

|ΨTM |2⟩

+⟨|ΨTE |2

⟩ (34)

in which the average is intended with respect to 0 ≤ ϑ0 < 90◦.

B. Thin Conducting Screen

For a thin conducting screen, having thickness d, conductiv-ity σ, relative permittivity εr and relative permeability μr , thefield attenuation factors for the TE and TM waves assume thefollowing simplified expressions in the hypothesis σ � ωε0εr

ΨTE =2

η0σd cos2 ϑ(35a)

ΨTM =2

η0σd(35b)

in which cosϑ can be expressed as function of the incidenceangle ϑ0 in free space using Snell’s law

cos2 ϑ = 1 − sin2 ϑ0

μr [εr + σ/(jωε0)]. (36)

Thus, SERE in (34) assumes the following approximated ex-pression:

SERE = SE0 − 10 log10

⎛⎝1

2+

1

2⟨|cos2 ϑ|2

⟩⎞⎠ (37)

in which the average is intended with respect to 0 ≤ ϑ0 < 90◦,SE0 is the low-frequency value of the SE of a thin conductingfilm against a plane wave with normal incidence

SE0 = 45.51 + 20 log10 (σd) (38)

and

∣∣cos2 ϑ∣∣2 =

1 + (ωε0/σ)2 (εr − sin2 ϑ0

/μr

)2

1 + (ωε0εr/σ)2 . (39)

584 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011

TABLE IPARAMETERS USED FOR THE SIMULATION OF THE THICK PANELS

Notice that the condition σ � ωε0εr results in having |cosϑ|2

≈ 1 in (39) and SRE ≈ SE0 in (37). This demonstrates that foran electrically thin conducting shield, the SE measuremed in anRC, where all incidence angles and polarizations are averaged,is coincident with its SE against a plane wave with normalincidence.

IV. RESULTS AND DISCUSSION

A. Test Set-up Configuration

The NRC set-up is sketched in Fig. 1(a) and (b). The OChas dimensions (3.52 m × 2.95 m × 2.49 m) and is made ofpainted stainless steel. The IC consists of an aluminum cubicbox, with side of 70 cm, whose top lid has a rectangular aperturewith dimensions (24.2 cm × 15.5 cm), hosting the planar sam-ple under test. The frequency range 0.5–6 GHz is explored bysweeping the two-port VNA over 500 MHz-wide sub-intervals.This leads to 11 measurement intervals with 1601 measured fre-quencies corresponding to 17 611 total measured frequencies.The measurement process is automated by a LabVIEW-basedprogram that manages the VNA settings and the stirrer step-by-step rotation. A full two-port VNA calibration is applied. TheMS is implemented in mode-tuning [4] with N = 50 steps. Thereceived signals are averaged over a complete stirrer rotationdivided in the N positions (for the MS) and over a 200 MHzagility bandwidth (for the FS) [11].

The OC and IC LUFs are estimated considering the graph ofFig. 3 representing the number of excited modes as a functionof the frequency. It results that the OC LUF is about 200 MHz,whereas the IC LUF is much higher (about 1.9 GHz) becauseof the smaller dimensions and of the cubic shape.

The two sandwich panels having the configurations reportedin Table I are considered. Sandwich S1 is the glazing windowshown in Fig. 4, having a total thickness of about 19 mm, pro-tected by a thin transparent conducting film having an effectiveconductivity of 914.8 S/m and total thickness of 60 μm. Thesecond panel S2 consists of two thick dielectric layers having atotal thickness of 19 mm, and of a thin conducting film 50 μmin thickness with effective conductivity of 742.2 S/m.

B. SE Measurement of Thin Conducting Films

First, the shielding performances of the single thin films F1and F2 of Table I are measured using both the NRC approach,

Fig. 4. Transparent film F1 applied on the multilayered glazing window S1.

with the different definitions described in Section II, and thedouble flanged coaxial waveguide (DFCW) method [2], [3].The obtained results are reported in Fig. 5(a) and (b).

Notice that, for the considered films and measurement con-ditions, the BM leads nearly to the same results of the SM, aswell as the AM leads nearly to the same results of the EM.

Moreover, for frequencies above 2 GHz, i.e., in case the ICis reverberating, SEAM and SEEM well approximate the curvemeasured using the DFCW method. This suggests that the AMand EM are able to correct the effects of the finite size of thetest sample and of the test box.

Fig. 5(b) also shows the estimated CF defined by (22), con-sidering the film F2 as reference material. The expression (21)is then applied to estimate SECM for the film F1, as shown inFig. 5(a). Notice that the curve obtained with the CM well ap-proximates the SEAM curve but is less affected by the resonancesappearing at frequencies lower than 2 GHz, due to the under-moded excitation of the IC and related to the IC and aperturedimensions [20].

C. SE Measurement of Thick Panels: The Effect of Bonding

The SE of the thick panels S1 and S2 is measured using onlythe NRC approach, since the DFCW method is not applicablein these cases. Both multilayers are electrically thick and arecharacterized by only one highly reflecting face.

In order to assess the effect of bonding on the SE perfor-mances, the measurements are performed considering the panelsmounted over the IC aperture in the four different configurationssketched in Fig. 6(a)–(d): 1) film F1 or F2 upwards, and panelbonded to the metallic wall with a copper tape; 2) film F1 orF2 upward, and panel floating; 3) film F1 or F2 downward, andpanel bonded to the metallic wall with a copper tape; 4) film F1or F2 downward, and panel floating.

Fig. 7 shows the frequency spectra of the SE measured withthe AM (SEAM ) and with the CM (SECM ) in the differentbonding configurations sketched in Fig. 6(a)–(d). Notice thatthe effect of bonding is particular evident in the configurationwith the conducting film F1 upward: The bonding produces an

LAMPASI AND SARTO: SHIELDING EFFECTIVENESS OF A THICK MULTILAYERED PANEL IN A REVERBERATING ENVIRONMENT 585

Fig. 5. SE of the transparent films F1 (a) and F2 (b), measured with the NRCsapproaches BM, SM, AM, EM, CM, or using the coaxial waveguide test-fixture(DFCW), and frequency spectrum of the correction factor CF for film F2.

Fig. 6. Sketches of the considered test configurations: (a) conducting filmupward and panel bonded to the IC wall, (b) film upward and floating panel,(c) film downward and bonded panel, and (d) film downward and floating panel.

increase of the SE because it prevents the direct coupling ofthe EMF through the thick border to the panel. On the contrary,when the film F1 is downward, the SE measured with the float-ing panel is slightly higher that the one obtained with the panelbonded. This is because the conducting tape around the thickborder of the panel, as shown in Fig. 6(c), behaves as a pick-uploop for the parasitic currents that, after being generated by the

Fig. 7. SEAM and SECM of sandwich S1, measured in the configurationssketched in Fig. 6.

Fig. 8. SEAM and SECM of sandwich S2, with the conducting film up andpanel border bonded, or with the conducting film down and the panel borderfloating.

EMF in the OC, are induced directly on the conducting surfaceof the panel, and radiate an additional scattered field in the IC.

It is then concluded that only the two configurations (a) and(d) of Fig. 6 should be considered to minimize the effect of thedirect EMF coupling through the thick panel border. Therefore,the SE measurements of the sandwich S2 were performed onlyin the two best bonding configurations: film upward bonded andfilm downward floating. Fig. 8(a) and (b) shows the frequencyspectra of SEAM and SECM measured in those two configura-tions, respectively.

D. Measurement Validation by Comparison With Model Results

The SEs of the sandwiches S1 and S2 are computed applyingthe simulation models described in Section II, considering areverberating incident field, and a TE or TM plane wave, withnormal (ϑ0 = 0◦) or oblique (ϑ0 = 60◦) incidence. The obtainedfrequency spectra are reported in Fig. 9(a)–(d).

Figs. 10 and 11 show the comparison between the frequencyspectra of the SE of panels S1 and S2, computed in case ofnormal incidence (ϑ0 = 0◦) and in a reverberating environment

586 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011

Fig. 9. Computed SE of the sandwiches S1 and S2 against different excitationfields: a reverberating field, a TE or TM plane wave with normal (ϑ0 = 0◦) oroblique (ϑ0 = 60◦) angle of incidence.

Fig. 10. Computed SE of the sandwich S1, against a reverberating field(SERE ) or a plane wave with normal incidence (ϑ0 = 0◦), and measuredones applying the AM (SEAM ) and the CM (SECM ). The measurements areperformed with the conducting film upward and bonded border (a) or conductingfilm downward and floating border (b).

Fig. 11. Computed SE of the sandwich S2, against a reverberating field(SERE ) or a plane wave with normal incidence (ϑ0 = 0◦), and measuredones applying the AM (SEAM ) and the CM (SECM ). The measurements areperformed with the conducting film upward and bonded border (a) or conductingfilm downward and floating border (b).

(SERE ), and measured using the AM and CM methods (SEAMand SECM , respectively) in the configurations of Fig. 6(a) and(d). It can be observed that both the AM and the CM mea-surements generally tends to overestimate SERE in the caseof film upward and bonded panel, whereas the measurementsperformed with the conducting face down and floating panelsprovide an underestimate of the computed SERE . Moreover, be-low the LUF of the IC, i.e., in the frequency range where theAM is not valid, the CM gives a satisfactory estimate of SEREfor both S1 and S2.

In conclusion, the best fitting of the computed SERE is ob-tained by applying the CM in the frequency range below theLUF of the IC and the AM above.

In particular, the fitting can be improved by considering theaverage between the values of SE measured in the configurationswith the film upward bonded and the film downward floating.These results are summarized in Fig. 12(a) and (b) for the mul-tilayers S1 and S2, respectively: It is demonstrated that, usingthe proposed procedure, it is possible to accurately estimate the

LAMPASI AND SARTO: SHIELDING EFFECTIVENESS OF A THICK MULTILAYERED PANEL IN A REVERBERATING ENVIRONMENT 587

Fig. 12. Computed and measured SE of the sandwiches S1 (a) and S2(b) against a reverberating field: The CM is applied in the range below theLUF of the IC, and the AM above.

shielding performance of a thick panel independently of thepanel size and IC dimensions, in the whole frequency rangeabove the LUF of the OC.

V. CONCLUSION

The NRC method is applied to the measurement of the shield-ing effectiveness of conducting panels, considering in particularthe case of electrically thick multilayered shields having onehighly reflecting external surface. Measurement procedures,basing on different expressions of the SE, are discussed andcompared, in order to define the approach that allow to correlatethe results of the measures with the ones of simulation models.

It is demonstrated that in case of an electrically thin conduct-ing shield the SE against a plane wave with normal incidence,measured using the DFCW method, is coincident with the oneobtained in a reverberating environment, measured by applyingthe NRC approach as function of the aperture cross-section ofthe unloaded and loaded IC. In case of a thick panel having oneconducting external surface, it is shown that the effect of theun-perfect bonding in the NRC test set-up can be minimizedconsidering the average between the values of the SE measuredwith the conducting face upward bonded and with the conduct-ing face down ward floating.

Finally, the range of validity of the NRC approach is extendedfor frequencies below the LUF of the IC, but above the LUFof the OC, considering the method that combined the NRCtechnique with the measurement of the SE of a reference samplehaving known properties.

In conclusions, the proposed procedure allows one to estimatefrom NRC measurements the SE of an infinite planar sampleof material against an incident reverberating field, in a widefrequency range, above the LUF of the outer test cavity.

The obtained results well correlate with the ones obtained fora thin conducting film using the double-flanged test set-up, thusconfirming the validity of the proposed approach.

ACKNOWLEDGMENT

The authors thank Dr. Alessio Tamburrano for supporting inthe measurements of the SE of the thin conducting films usingthe DFCW method.

REFERENCES

[1] W. C. Stone, “Electromagnetic signal attenuation in construction materi-als,” NIST, Gaithersburg, MD, NIST Construction Automation ProgramReport No. 3, Oct. 1997.

[2] ASTM, “Standard test method for measuring the electromagneticshielding effectiveness of planar materials,” ASTM-D4935, WestConshohocken, Pennsylvania, USA, Sep. 1989.

[3] M. S. Sarto and A. Tamburrano, “An innovative test method for the shield-ing effectiveness measurement of conductive thin films in a wide frequencyrange,” IEEE Trans. Electromagn. Compat., vol. 48, no. 2, pp. 331–341,May 2006.

[4] IEC 61000–4-21, “Electromagnetic compatibility (EMC) – Part 4–21:Testing and measurements techniques – Reverberation chamber test meth-ods,” Geneva, Switzerland, May 2005.

[5] D. A. Hill, M. T. Ma, A. R. Ondrejka, M. L. Crawford, and R. Johnk,“Aperture excitation of electrically large, lossy cavities,” IEEE Trans.Electromagn. Compat., vol. 36, no. 3, pp. 169–178, Aug. 1994.

[6] M. O. Hatfield, “Shielding effectiveness measurements using mode-stirredchambers: a comparison of two approaches,” IEEE Trans. Electromagn.Compat., vol. 30, no. 3, pp. 229–238, Aug. 1988.

[7] T. A. Loughry and S. H. Gurbaxani, “The effects of intrinsic test fixtureisolation on material shielding effectiveness measurements using nestedmode-stirred chambers,” IEEE Trans. Electromagn. Compat., vol. 37,no. 3, pp. 449–452, Aug. 1995.

[8] C. Holloway, D. A. Hill, J. Ladbury, G. Koepke, and R. Garzia, “Shieldingeffectiveness measurements of materials using nested reverberation cham-bers,” IEEE Trans. Electromagn. Compat., vol. 45, no. 2, pp. 350–356,May 2003.

[9] C. L. Holloway, D. A. Hill, J. M. Ladbury, and G. Koepke, “Require-ments for an effective reverberation chamber: unloaded or loaded,”IEEE Trans. Electromagn. Compat., vol. 48, no. 1, pp. 187–194, Feb.2006.

[10] C. L. Holloway, J. Ladbury, J. Coder, G. Koepke, and D. A. Hill, “Measur-ing shielding effectiveness of small enclosures/cavities with a reverbera-tion chamber,” in Proc. IEEE 2007 Int. Symp. EMC, Honolulu, HI, 8–13Jul. 2007.

[11] S. Greco and M. S. Sarto, “New hybrid mode-stirring technique for SEmeasurement of enclosures using reverberation chambers,” in Proc. IEEEInt. Symp. EMC, Honolulu, HI, 8–13 Jul. 2007.

[12] R. De Leo, G. Gradoni, A. Mazzoli, F. Moglie, G. Moriconi, and V. MarianiPrimiani, “Shielding effectiveness evaluation of densified-small-particles(DSP) cement composite,” in Proc. IEEE 2008 Int. Symp. EMC, 8–12Sep. 2008, pp. 1–6.

[13] C. L. Holloway, D. A. Hill, M. Sandroni, J. M. Ladbury, J. Coder,G. Koepke, A. C. Marvin, and Y. He, “Use of reverberation chambers to de-termine the shielding effectiveness of physically small, electrically largeenclosures and cavities,” IEEE Trans. Electromagn. Compat., vol. 50,no. 4, pp. 770–782, Nov. 2008.

[14] A. Gifuni and M. Migliaccio, “Use of nested reverberating chambers tomeasure shielding effectiveness of nonreciprocal samples taking into ac-count multiple interactions,” IEEE Trans. Electromagn. Compat., vol. 50,no. 4, pp. 783–786, Nov. 2008.

[15] D. A. Lampasi, “EMC tests of artificial satellites in loaded nested rever-beration chambers,” in Proc. 2009 Eur. Space Agency (ESA) WorkshopAerospace EMC, Florence, Italy, 30 Mar.–1 Apr. 2009.

[16] V. Mariani Primiani, F. Moglie, and A. P. Pastore, “Field penetrationthrough a wire mesh screen excited by a reverberation chamber field:FDTD analysis and experiments,” IEEE Trans. Electromagn. Compat.,vol. 51, no. 4, pp. 883–891, Nov. 2009.

[17] D. A. Hill, “Plane wave integral representation for fields in reverberationchambers,” IEEE Trans. Electromagn. Compat., vol. 40, no. 3, pp. 209–217, Aug. 1998.

[18] A. C. Marvin, L. Dawson, I. D. Flintoft, and J. F. Dawson, “A method forthe measurement of shielding effectiveness of planar samples requiring nosample edge preparation or contact,” IEEE Trans. Electromagn. Compat.,vol. 51, no. 2, pp. 255–262, May 2009.

[19] J. Ladbury, G. Koepke, and D. Camell, “Evaluation of the NASA Lan-gley research center mode-stirred chamber facility,” U.S. Department ofCommerce, NIST, Boulder, CO, NIST Tech. Note 1508, 1999.

[20] M. P. Robinson, T. M. Benson, C. Christopoulos, J. F. Dawson, M. D.Ganley, A. C. Marvin, S. J. Porter, and D. W. P. Thomas, “Analyticalformulation for the shielding effectiveness of enclosures with apertures,”IEEE Trans. Electromagn. Compat., vol. 40, no. 3, pp. 240–248, Aug.1998.

588 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 53, NO. 3, AUGUST 2011

Domenico Alessandro Lampasi (S’99–M’06) re-ceived the M.Sc. degree in electronic engineering andthe Ph.D. degree in electrical engineering from theUniversity of Rome Sapienza, Rome, Italy, in 2002and 2006, respectively.

He is currently with the Italian National Agencyfor New Technologies, Energy, and Sustainable Eco-nomic Development (ENEA), Frascati, Italy. He pre-viously worked for Research Center for Nanotech-nology Applied to Engineering (CNIS) of Universityof Rome, for the Department of Electrical Engineer-

ing of University of Rome, for ABB Energy Automation, and for Italian PublicHigh School. His research interests include modeling and measurement tech-niques in the field of electromagnetic compatibility, nanotechnology, and powersystems. For ENEA, he is involved in several experimental projects concerningnuclear fusion.

Maria Sabrina Sarto (F’10) received the Laurea,summa cum laude, and the Ph.D. degrees in electricalengineering from the University of Rome Sapienza,in 1992 and 1997, respectively.

Since 2005, she has been Full Professor of elec-trotechnics and electromagnetic compatibility at theFaculty of Engineering of Sapienza University ofRome, where she has been also Director of the Re-search Center for Nanotechnology Applied to En-gineering of Sapienza since 2006, Director of theElectromagnetic Compatibility Laboratory of the

Department of Electrical Engineering since 1998, of the Joint Lab onMicro/Nanotechnologies for industrial applications of Sapienza InnovationConsortium since 2007, of the Nanotechnology and Nanoscience Laboratoryat Sapienza University since 2010. She has published more than 100 papers inthe field of electromagnetic compatibility (EMC), numerical electromagnetics,and advanced materials for EMC. Her current research interest includes carbonnanotube interconnects modeling and design, carbon nanotube and graphene-based nanomaterials for EMC, and EMC in aerospace. She has been AssociateEditor of the IEEE EMC TRANSACTIONS since 1998, and Cochair of theIEEE EMC Society TC11 on “Nanotechnology and Advanced Materials.”

Prof. Sarto was Distinguished Lecturer of the IEEE EMC Society in 2001–2002, member of the Advisory Board of the IEEE Council on Nanotechnol-ogy, Chair of the working group IEEE STD 299.1 of IEEE EMC Society. Shereceived several awards from IEEE EMC Society and Society of AutomotiveEngineers (SAE).