Comparative Study of the Shielding Properties of Slotted Enclosure with Inner or Outer Excitations Using FEM

doi:10.4236/ojapps.2013.32B009

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Open Journal of Applied Sciences, 2013, 3, 47-50

doi:10.4236/ojapps.2013.32B009 Published Online June 2013 (http://www.scirp.org/journal/ojapps)

Comparative Study of the Shielding Properties of Slotted

Enclosure with Inner or Outer Excitations Using FEM

Baolin Nie, Pingan Du

School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, China

Email: [email protected]

Received 2013

ABSTRACT

Finite element method (FEM) is employed in this paper to conduct the comparative study of the shielding properties of

enclosure with outer and inner excitations. Plane wave is adopted for the outer excitation case while coaxial cable is

utilized to model the inner excitation source. Moreover, the resonance phenomena of slotted enclosure under different

excitation are studied in detail. Finally, some conclusions with regard to the relationships and distinctions between the

inner and outer excitations for the same enclosure are proposed.

Keywords: FEM; Plane Wave; Shielding; Wave Port

1. Introduction

The penetration of electromagnetic fields through slot

has been of considerable interest because of its crucial

influence on the shielding performance. As a result, nu-

merous approaches have been proposed to quantify the

shielding properties of enclosures with aperture and slot.

One class of approaches uses outer excitation [1-3]. Usu-

ally, plane wave is adopted as source to excite the entire

system. These approaches become prevalent mainly be-

cause they are simple and easy to implement. Another

class of approaches utilizes inner excitation such as wave

port or current probe to excite the system [4,5]. These

approaches are more complicated because the electro-

magnetic radiation properties of excitation source are

dependent on the position of observation point.

In this paper, the well-established FEM [6] is em-

ployed to investigate the shielding properties of enclo-

sure with outer or inner excitation. The resonance phe-

nomena of slotted enclosure are studied in detail. Finally,

some conclusions which are useful for shielding design

are proposed.

2. Shielding Models and FEM Description

2.1. Shielding Model

The geometrical model from Reference [4] is taken in

this study for comparison and validation purpose. The

geometry of the enclosure with a slot is shown in Figure

1. The enclosure is excited by coaxial cable with charac-

teristic impedance of 50 . The center conductor of the

coaxial cable extends to span the width of the cavity with

a 0.16-cm-diameter wire and terminated on the opposite

cavity wall with a 47



resistor. The enclosure is con-

structed of five pieces of 0.635-cm-thick metal, and one

plate of 0.05-cm-thick metal for the side containing the

slot. The interior dimensions of the enclosure are 22 14

 30 cm. The coaxial cable at x = 17 cm, z = 15 cm, with

a center conductor along y axis, is employed as an exci-

tation source. A 12  0.1 cm slot located on the front

plate is 0.2 cm away from the bottom edge.

2.2. Brief FEM Description

For simplicity, let us consider an electromagnetic prob-

lem defined in a volume denoted by and bounded by

perfect conducting surface (PEC), waveguide port boundary

condition (WPBC) and absorbing boundary condition

(ABC). Besides, lumped resistor has to be incorporated

into FEM to appropriately model the inner excitation

source. By applying Galerkin’s method, the correspond-

ing weak-form solution of the boundary-value problem

Figure 1. Shielding enclosure with a slot residing on one of

its sides and excited by coaxial cable.

B. L. Nie, P. G. Du

described above is given as

inc2 inc1

1()()

ˆˆ

()()

1()

jrj

jknn dS

PdS

dS dS



























 









 



NENE

NU NU

(1)

where



inc1inc1 inc

inc2inc2 inc

2TEM TEMTEM

00 0

TEM

ˆ()().

ˆˆ

()( )

()

2ln /

Pjknn







 



 





UEE

EeeE

and

N denote testing functions. Expanding the electric

field as

(,) ()





rNr (2)

with N denoting the total number of unknowns.

The physical meanings of the variables in the above

equations are shown in Table 1. For the plane wave

source case, the excitation applies on the ABC surface.

We have , and

2inc2

() 0PE Uinc

has the uniform

plane wave form. While for the wave port source case,

the excitation applies on the port surface. We have

, and

inc1 0Uinc

is set to be the same with .

For simplicity, we have omitted the spatial dependant

factor in equations (1)-(4), all the vectors should be func-

tion of position vector , and this abbreviation method

applies in the following sections.

TEM

Table 1. Variables and their meaning.

Variable Meaning



Relative permittivity of the medium



Relative permeability of the medium



Relative permeability of the medium filled in wave

port

k Wave number of coaxial cable



 Propagation constant of coaxial cable

n Unit vector normal to boundary surface



Unit vector in radial direction of coaxial cable

a Inner radius of the coaxial cable

b Outer radius of the coaxial cable

inc

For plane wave source, it is plane wave. For wave

port source case, it is the same as .

TEM

By substituting (2) into (1), we obtain

1, 2,,

ij ji

Ebi N





 (3)

where



TEM TEM

TEM inc1

1()( )

()( )

ijrij

iij

jk dS

jk dS dS

bdS





























 

NN NN

eN eN

eN NU

This formulation is called Galerkin’s formulation since

the same functions are used for both expansion and test-

ing. Equation (3) can be written compactly as

{}

K

Eb (4)

which can be solved for {}

. Because the elemental

interactions in (3) are local in nature,

is a sparse and

symmetric matrix that can be solved efficiently using a

sparse matrix solver. Once {}

is obtained, the field

everywhere in V can be calculated using (2), from

which other parameters, such as the input impedance and

radiation patterns, can be computed.

3. Results

For the plane wave excitation case, the shielding per-

formance is measured by shielding effectiveness (SE)

int

ext

SE(dB)20 log （

） (5)

where int

is the electric field at a given point inside

the enclosure and ext

is the field at the same point in

absence of the enclosure.

For the coaxial cable excitation case, the power deliv-

ered to the enclosure is related to the reflection coeffi-

cient as







(6)

where

V is the source voltage and 0

is the source

impedance. In this study, the source voltage is 1 V and

the source impedance equals the characteristic imped-

ance of the coaxial cable (50 ), so the maximum

power available at the source terminal is 2.5 . Scat-

tering parameter at the coaxial cable port can be

extracted as

11 2

()

inc inc

inc

SdS







-EE E

E (7)

B. L. Nie, P. G. Du 49

Figure 2 shows the power delivered to the enclosure.

The measurement result from [4] is also presented here

for validation purpose. It can be seen from the figures

that the FEM simulation results agree with measurement

results well in general. This guarantees the correctness of

the following simulations.

Figure 3 shows the resonance points and their attrib-

utes of enclosure with the slot. Figure 4 shows the SE

and resonance points of the enclosure for -polarized

plane wave excitation. Figure 5 shows the SE and reso-

nance points of the enclosure for

-polarized plane

wave excitation. The value of their resonance points are

listed in Table 2, Table 3, and Table 4, respectively.

By comparing Figure 3 and Figure 4 we can see that

the TEM resonance at 1.08 GHz due to probe half wave-

length resonance disappears when we change the excita-

tion source from coaxial cable to plane wave. At the

same time, TEy012 mode is excited while TMy111 mode

and TMy201 mode are suppressed. Besides, the reso-

nance frequency of TMy101 mode decreases since the

terminated feed probe is removed. The slot resonance is

due to the half wavelength resonance since the length of

slot equals to half wavelength at about 1.2 GHz. So this

resonance remains for both configurations. It also shows

that the same enclosure can have very different reso-

nance behavior when it is excited by different sources.

One should keep this in mind when involved in the de-

sign of shielding enclosures because the resonance is the

most crucial part in this process.

By comparing Figure 4 and Figure 5 we can see that

the SE of the enclosure increases significantly when we

change the excitation source from Y-polarized plane

wave to Z-polarized plane wave. This is because the ap-

erture greatly cuts into the path of induced current and

breaks the integrality of shielding for Y-polarized case. It

can be deduced form Table 3 and Table 4 that the slot

Figure 2. Delivered power into rectangular enclosure with

the slot.

Figure 3. Resonance point of the enclosure excited by coax-

ial cable.

Figure 4. SE of rectangular enclosure with the slot for

Y-polarized plane wave excitation.

Figure 5. SE of rectangular enclosure with the slot for

Z-polarized plane wave excitation.

B. L. Nie, P. G. Du

Table 2. Resonance points of the enclosure with inner exci-

tation.

Modes Frequency (GHz)

101

TM 0.89

TEM 1.08

cavity-slot 1.12

slot 1.23

111

TM 1.37

201

TM 1.43

cavity-slot 1.53

Table 3. Resonance points of the enclosure with outer -

polarized plane wave excitation.

Modes Frequency (GHz)

101

TM 0.84

cavity-slot 1.16

slot 1.25

cavity-slot 1.40

012

TE 1.47

Table 4. Resonance points of the enclosure with outer -

polarized plane wave excitation.

Modes Frequency (GHz)

101

TM 0.84

cavity-slot 1.16

102

TM 1.21

110

TE 1.27

cavity-slot 1.40

012

TE 1.47

resonance is absent when the excitation source is

Z-polarized plane wave. But the two resonance points

associated with coupling of cavity and slot exist. More-

over, TMy102 mode and TEy110 mode are excited.

4. Conclusions

In this paper, the FEM is employed to investigate the

shielding properties of slotted enclosure with outer or

inner excitation. The resonance phenomena of slotted

enclosure are studied in detail for both inner and outer

excitations. Different polarization configurations of inci-

dent plane wave for the outer excitation case are also

investigated, especially for their resonance behavior. It

also shows that the same enclosure can have very differ-

ent resonance behavior when it is excited by different

sources, Which could be helpful for shielding enclosure

design.

5. Acknowledgements

The authors thank the National Natural Science Founda-

tion of China (Grant No. 51175068), the China Scholar-

ship Council (CSC), and the Fundamental Research

Funds for the Central Universities of China for their

supporting.

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