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EVALUATION OF SHIELDING EFFECTIVENESS OF RECTANGULAR ENCLOSURE

WITH MULTIPLE APERTURES USING TRANSMISSION LINE MODEL

G. KAMESWARI, P. V. Y. JAYASREE& V. GOPI

Department of ECE, GIT, Gitam University, Visakhapatnam, Andhra Pradesh, India

ABSTRACT

The electrical and magnetic shielding effectiveness of a metallic shield perforated with numerous apertures is

evaluated in this work using the Transmission Line Method (TLM). Here an appropriate admittance that takes the mutual

coupling between the apertures into account is considered as to represent the array of apertures. The fundamental formulas

are included to deal with the case of a rectangular enclosure with numerous small rectangular apertures in this model.

The electric and magnetic shielding effectiveness are compared in this paper. The observation points are taken along one of

the rectangular enclosure dimension i.e., depth of the enclosure and then observed the each point for the shielding

effectiveness of both electric and magnetic fields. Shielding effectiveness is calculated for the oblique incidence of single

and multiple apertures. Simulation results demonstrate that: lower frequencies display better shielding than higher

frequencies; the effectiveness of shielding of a single hole is worse than of a multi-hole for identical areas. The electric

shielding effectiveness increases continuously with the angle of incidence and the magnetic shielding effectiveness

decreases continuously with the angle of incidence.

KEYWORDS: Electromagnetic Interference, Shielding Effectiveness, Transmission Line Method (TLM), PerforatedWall with Numerous Apertures, Oblique Incidence

INTRODUCTION

With the gradual advance and application of electronic technology, the electromagnetic interference problem

becomes more and more threatening. Electromagnetic interference causes degradation of system performance or

equipment. To control or suppress EMI and achieve EMC there are many methods like shielding, grounding and filtering

etc. It is well known that shielding is the most important technique used to control the EMI. Shielding effectiveness (SE)

can be defined as the ratio of magnitude between the electric or magnetic field which is present on the barrier and that of

the electric or magnetic field which is transmitted through the barrier. Wave penetration through apertures and slots used to

accommodate visibility, weight ratio, ventilation, or access to interior components affects SE primarily and drastically.

Several analytical and Numerical techniques are suggested to estimate SE of an enclosure with apertures. Analytical

methods are accurate but can just be applied to very simple geometries with some approximations. A simple analytical

method based on transmission-line parameters have been introduced by Robinson et al [2].In this method, the rectangular

enclosure and the aperture is modeled by a short-circuited rectangular waveguide and a coplanar strip transmission line,

respectively. The electric and magnetic SE is obtained by using the voltage and the current at a point in the equivalent

circuit. This straightforward approach is limited to center aperture and the incident plane wave can only have one

polarization direction of travel and ignores the mutual admittance between apertures. There are numerous numerical

techniques such as finite-difference time-domain (FDTD) method [3], finite element method [4], transmission-line matrix

International Journal of Electronics, Communication &

Instrumentation Engineering Research and

Development (IJECIERD);

SSN (P): 2249-684X; ISSN (E): 2249-7951Vol. 4, Issue 6, Dec 2014, 1-12

TJPRC Pvt. Ltd.


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2 G. Kameswari, P. V. Y. Jayasree& V. Gopi

Impact Factor (JCC):4.9467 Index Copernicus Value (ICV): 3.0

method [5] and hybrid [6] methods that offer good accuracy over a broad frequency band but at the cost of large memory

and CPU time. Hence, numerical techniques are severely limited in analyzing realistic enclosures that have large numbers

(hundreds) of small holes. The available time-domain methods include TLM and FDTD. TLM is a well-established

technique, suitable for the prediction of transient in electromagnetic applications. Moreover, TLM is simple, explicit, andunconditionally stable. So, TLM is preferred here. In this work, for an enclosure with many rectangular openings, we

present more accurate aperture array admittance [1] for use in behavior the waveguide equivalent circuit model of

Robinson et al [2]. While the enclosure is modeled as a short-circuited waveguide, the aperture array is characterized by

admittance [7], [8].

EQUIVALENT CIRCUIT MODEL OF A RECTANGULAR ENCLOSURE

Rectangular cabinet with a rectangular aperture is shown in figure 1.

Figure 2 Shows An Equivalent Circuit of Robinson Et Al [2] Which Is A Rectangular Shaped Aperture Within An

Empty Enclosure of The Same Shape. The Longer Side of The Slot Is Shown Normal to The E-field, Which Is The Worst

Case for Shielding.

Figure 1: Rectangular Cabinet with a Rectangular Aperture.

The Observation Point is P and the Wall Thickness is T .

Figure 2: Equivalent Circuit of Enclosure

The electric shielding at a distance p from the slot is obtained from the voltage at point p in the equivalent

circuit, while the current at pgives the magnetic shielding. In Figure 2, the source of radiation is represented by voltage

V0and the impedance Z0=377. The typical impedance and the propagation constant of the enclosure by the shorted wave

guide are represented asgZ and gK .We proceed by first finding equivalent impedance for the slot and then using simple

transmission line theory to transform all the voltages and impedances to point P.

Slot Impedance

The aperture is represented as a length of coplanar strip transmission line, shorted at each end. The total width is


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Evaluation of Shielding Effectiveness of Rectangular Enclosure with Multiple Apertures Using Transmission Line Model 3


equal to the height of the enclosure b and the separation is equal to the width of the slot w. Its characteristic impedance is

given by [9] as

1120 ( / ) ( / )os e eZ k w b k w b= (1)

Where kand 1k are elliptic integrals. The effective width weis given by

5 41 l n

4e

t ww w

t

= +

(2)

Where, t is the thickness of the enclosure wall.

If we b/ 2(which is true for most practical apertures) then, according to [9] the following approximation may

be used:

( )

( )

124

2

24

1 1 /1 2 0 ln 2

1 1 /

e

o s

e

w bZ

w b

+ =

(3)

To calculate the aperture impedance Zap, we transform the short circuits at the ends of the aperture through a

distance l/2 to the center. This is represented by pointA in the equivalent circuit. It is mandatory here to include a factor l/a

to account for the coupling between the aperture and the enclosure

01 t a n2 2

a p o s

k llZ j Z

a

=

(4)

This accounts for the connection between transmission line and waveguide.

ELECTRIC AND MAGNETIC SHIELDING EFFECTIVENESS

According to Thevenins theorem fusing Z0, V0and Zapresults in an equivalent voltage.

0

1

0

a p

a p

V ZV

Z Z=

+

(5)

And source impedance1 0 0/ap apZ Z Z Z Z= +

(6)

For the TE10mode of propagation, the waveguide has characteristic impedance:

2

0/ 1 ( / 2 )gZ Z a= (7)

And propagation constant:2

0 * 1 ( / 2 )gK K a= (8)

Where0 02 /K =

Note thatgZ and gK are imaginary at frequencies below the cutoff (equal to c0/2a). Then V1, Z1and the short

circuit at the terminal of the wave guide to P are transformed by attributing an equivalent voltage V2, source impedance Z2

and load impedanceZ3.


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12

1( ) ( / ) s in ( )g g g

VV

C o s k P j Z Z k p=

+

(9)

1

21

t a n ( )

1 ( / ) t a n ( )

g g

g

Z j Z k pZ

j Z Z g k p

+

=

+

(10)

3 tan ( )g gZ jZ k d p= (11)

The voltage at Pis now 2 3 2 3/ ( )pV V Z Z Z = + (12)

And the current at P is 2 2 3I / ( )p V Z Z= + (13)

When the enclosure is absent, the load impedance at premains simply asZ0.The voltage at pis VP1= V0/2 and

the current is IP1= V0/2Z0.

The electric and magnetic shielding are, therefore, given by

10 020 log 2 / pSE V V =

(14)

10 0 020log 2 Z / pSM I V =

(15)

Rectangular Enclosure with Multiple Apertures

For correct estimation of shielding, it is essential to consider the mutual coupling between the apertures.

Figure 3: Wall of an Enclosure Partially Perforated by a Centered Array of Rectangular

For array of apertures given in Figure3, the normalized shunt admittance is ([10], [11]) is given by

2 2 2 2 2013 2

0 00

3 288. ( / / ) ( )ah h v

m v n h

m nom odd n odd

Y d dj j n d m d J X

Y d d

= =

= + +

(16)

Where 0and Y0are the free-space wavelength and intrinsic admittance respectively, dvand dhare the vertical and

horizontal separations between the holes and d is the diameter of circular hole.

The argument of the Bessel function is


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( )

1/22 2 2 2

5/ 22 2 2 2

( / / ) / 2

/ /

h v

h v

d m d n d X

m d n d

=

+

(17)

Where d = 0.636(h + s) for rectangular holes (18)

Here h is length of small rectangular hole ands is width of small rectangular hole.

2sd d= For square holes (19)

Heres

d is side length of the small square hole and the primes denote summation on even integers only, J1is the

Bessel function of the first kind of the first order, and m, n=1 if m, n = 0 and 2 if m, n 0. The second term in (16) can be

neglected when dv, dh and d are much less than the wavelength. The impedance Zah =1 /Yah models the array of small

rectangles linking the free space with the waveguide [6], [7]. Figure 3 depicts an enclosure wall partially perforated by an

array of rectangles; its effective wall impedance Zah1is a fraction of Zah. Using an impedance ratio concept, Zah

1becomes

1

ah ah

w lZ Z

a b

=

(20)

Where length l and width w of the array are

( )12 2

h hh

d dl m d= + + (21)

( )12 2

v vv

d dw n d= + +

(22)

Here, m and n are the number of small holes in length and width of the array, respectively.

Angle of Incidence

We know that an electromagnetic wave consists of magnetic and electric fields which are always perpendicular to

each other. When the electric field along the y-direction and magnetic field along the x-direction then the wave propagated

along the z-direction. To any polarization angle , incident wave can be decomposed into two orthogonal components, of

which electric strength is cosE

and sinE

respectively. This can result in the source voltage cosoV

and

sino

V in the equivalent circuit.

RESULTS

Single Aperture

Electric Shielding Effectiveness

We consider a rectangular box of size (300X120X300) mm3, whose walls are perforated with rectangular slots.

The box is assumed to be excited by a plane wave with normal incidence forstudying

the SE of a rectangular box with

perforatedwalls. Figure 4 shows the variation of the electric shielding effectiveness as a function of frequency by using

TLM method. The calculations show that the enclosure resonates at approximately 700MHZ frequency and SE decreases

with frequency below the resonant frequency.


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Figure 4: Calculated Se Using Transmission Line Formulation in 300x120x300mm3 Box With 100x5mm2 Apertures

Figure 5 shows the calculated SE at three different positions within the (300X120X300) mm3enclosure with an

(100X5) mm2aperture. The calculations show that the enclosure resonates at approximately 700MHz. below the resonant

frequency SE decreases with frequency and increases with distance from the aperture.

Figure 5: Calculated Se at Three Positions in 300x120x300mm3 Box with 100x5mm2 Aperture

Figure 6 shows calculated SE at center in 300X120X300 mm3with two different apertures of sizes 100X5mm

2

and200X30 mm2

. It is observed that the shielding of larger aperture at lower frequencies is worse than that of the smaller.

Figure 6: Calculated Se at Center in 300x120x300mm3 Box with Two 100x5mm 2 and 200x30mm2

Apertures

Figure 7 shows the calculated SE at the centre of the boxes of (222X55X146) mm3, (480X120X480) mm

3with

the same aperture (100X5) mm2. It can be observed from these figures that the small box does not resonate below 1GHz,

while the big box shows resonances at 440 and 980MHz.


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Figure 7: Calculated Se of 222x55x146mm3 and 480x120x480mm3 Boxes with the Same Aperture of 100x5 Mm2

Size

Magnetic Shielding Effectiveness

We consider a rectangular box of size (300X120X300) mm3, whose walls are perforated with rectangular slots.

The box is assumed to be excited by a plane wave with normal incidence for studying the SM of a rectangular box with

perforated walls.

Figure 8: Calculated Sm Using Transmission Line Formulation In 300x120x300mm3 Box With 100x5mm2

Aperture

Figure 8 shows the variation of the magnetic shielding effectiveness as a function of frequency by using TLM

method. Figure 8 shows that the SM is almost independent of frequency.

Figure 9 shows SM of the 300X120X300mm3box with 100X5mm

2aperture, calculated at p=30, 150 and 270mm.

The box resonance at 700MHz can be seen at p=30mm and p=270mm but is not occur at the center of the box due to the

mode structure of the resonance. SM increases with distance from the aperture at lower frequencies, but is almost

independent of frequency.

Figure 9: Calculated Sm at Three Positions in 300x120x300mm3 Box with 100x5mm2 Aperture


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Figure10 shows calculated SM at center in 300X120X300 mm3with two different apertures of sizes 100X5mm

2

and 200X30 mm2. It is observed that the shielding of larger aperture at lower frequencies is worse than that of the smaller.

Figure 10: Calculated Sm at Center in 300x120x300mm3 Box with Two 100x5mm 2 and 200x30mm2

Apertures

Figure 11 shows the calculated SM at the centre of the boxes of (222X55X146) mm3, (480X120X480) mm

3with

the same aperture (100X5) mm2. It can be observed from these figures that the small box does not resonate below 1GHz,

while the big box shows resonances at 440 and 980MHz.

Figure 11: Calculated Sm of 222x55x146mm3 and 480x120x480mm3 Boxes with the Same Aperture of 100x5 Mm2

Size

Rectangular Enclosure with Multiple Apertures

Figure 12 shows the electrical SE results for the same box dimensions 300X120X300mm 3but different arrays of

(2X2), (4X4), (6X6) rectangular apertures with 40mm vertical and horizontal separation, in each case the total area was

same. The transmission line formulation predicts that SE is increased by increasing the number of apertures while keeping

the total area the same.

Figure 12: Comparison of Electrical Se for the Same Box Dimensions 300x120x300mm3 but Different

Arrays of (2x2), (4x4), (6x6) Rectangular Apertures


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Figure 13 shows the magnetic SE results for the same box dimensions 300X120X300mm3but different arrays of

(2X2), (4X4), (6X6) rectangular apertures with 40mm vertical and horizontal separation, in each case the total area was

same. The transmission line formulation predicts that magnetic SE is increased by increasing the number of apertures while

keeping the total area the same and it is almost independent of frequency.

Figure 13: Comparison of Magnetic Se for the Same Box Dimensions 300x120x300mm3 but Different Arrays of

(2x2), (4x4), (6x6) Rectangular Apertures

Angle of Incidence

Figure 14 Shows The Electric Shielding Effectiveness Verses Angle of Incidence. It Can Be Observed That The

Electric Shielding Effectiveness Increases Continuously With The Angle of Incidence.

Figure 14: Electric Shielding Effectiveness versus Angle of Incidence

Figure 15 Shows The Magnetic Shielding Effectiveness Verses Angle of Incidence. It Can Be Observed That The

Magnetic Shielding Effectiveness Decreases Continuously With The Angle of Incidence.


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Figure 15: Magnetic Shielding Effectiveness verses Angle of Incidence

CONCLUSIONS

In this paper, analysis was carried out with a very efficient analytical approach based on waveguide equivalent

circuit model to determine SE of rectangular box with numerous small apertures. The array of numerous apertures is

substituted with a proper equivalent admittance in the modified circuit model.

The calculation of electric and magnetic shielding depends on the frequency and applied fields polarization and

the enclosures dimensions and aperture(s), the quantity and position of the apertures within the enclosure. Though, the

further work is needed to characterize this factor for typical electronic equipment, the formulation will be of use to

designers of shielded enclosures.

ACKNOWLEDGMENTS

We thank the management of GITAM University for all the support and encouragement rendered in this work.

We also extend our thanks to the Vice Chancellor and Registrar of GITAM University for providing the required facilities

for carrying out this work.

REFERENCES

1.

A. Boutar et al (2009) Transmission line model for shielding effectiveness estimation of a rectangular

enclosure with apertures CNCEM-09.

2. Robinson et al (1998) Analytical formulation for the shielding effectiveness of enclosures with apertures,

IEEE Transactions on Electromagnetic compatibility, Vol. 40, pp240-248.

3.

M. Li et al (2000) EMI from cavity modes of shielding enclosures FDTD modeling and measurements.

IEEE transactions on electromagnetic compatibility, Vol. 42, no.1, pp 29-38.

4. S. Benhassine et al (2002) An efficient finite-element time-domain method for the analysis of the coupling

between wave and shielded enclosure IEEE transactions on electromagnetic compatibility, vol. 38, no.2,

pp 709-712.

5.

P. Argus et al (2000) Efficient modeling of apertures in thin conducting screens by the TLM method in proc.

IEEE Int. Symp. Electromagn.Compat., vol. 1, pp 101-106.

6. S. Tharf et al (1994) A hybrid finite element- Analytical solutions for in-homogeneously filled shielding


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enclosures IEEE transactions on electromagnetic compatibility, vol. 36, no.4, pp 380-385.

7.

Dehkhoda et al (2007) An efficient shielding effectiveness calculation (A rectangular enclosure with numerous

apertures). IEEE International Symposium on electromagnetic compatibility.

8. Dehkhoda et al (2008) An efficient and reliable shielding effectiveness evaluation of a rectangular enclosure

with numerous apertures IEEE transactions on electromagnetic compatibility, vol. 50, no.1, pp 208-212.

9.

K.C. Gupta et al (1979) Micro strip lines and slotlines. Norwood, MA: Artech House, Chapter 7.

10. T.Y. Otoshi (1972) A study of microwave leakage through perforated flat plates IEEE Trans. Microw. Theory

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