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
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
V
22
x
y
z
14
30
Figure 1. Shielding enclosure with a slot residing on one of
its sides and excited by coaxial cable.

B. L. Nie, P. G. Du
48
described above is given as
2
0
0
2
inc2 inc1
1()()
ˆˆ ()()
1()
1
p
p
jrj
r V
j
S
j
rg S
jj
S
rg S
kd
jknn dS
PdS
dS dS
















 




 


NENE
NE
NE
NU NU
V
(1)
where

inc1inc1 inc
inc2inc2 inc
1
0
2TEM TEMTEM
00 0
TEM
0
ˆ()().
ˆ()().
ˆˆ ()( )
()
11
ˆ
2ln /
p
S
nP
nP
Pjknn
P
ba



 
 

 


UEE
UEE
EE
EeeE
e
d S
and
j
N denote testing functions. Expanding the electric
field as
1
(,) ()
N
ii
i
tE


E
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
E
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
E
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
0
e
r
Table 1. Variables and their meaning.
Variable Meaning
r

Relative permittivity of the medium
r

Relative permeability of the medium
rg

Relative permeability of the medium filled in wave
port
g
k Wave number of coaxial cable
0g
jk   Propagation constant of coaxial cable
ˆ n Unit vector normal to boundary surface
ˆ

Unit vector in radial direction of coaxial cable
a Inner radius of the coaxial cable
b Outer radius of the coaxial cable
inc
E
For plane wave source, it is plane wave. For wave
port source case, it is the same as .
TEM
0
e
By substituting (2) into (1), we obtain
1
1, 2,,
N
ij ji
j
K
Ebi N


 (3)
where

2
0
0
TEM TEM 0
00
TEM inc1 0
0
1()( )
()( )
2
pp
p
ijrij
r
V
ij
S
ij
SS
rg
iij
SS
rg
kd
jk dS
jk dS dS
jk
bdS

















 
 
NN NN
NN
eN eN
eN NU
V
dS
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
{}
ij
K
K
Eb (4)
which can be solved for {}
E
. Because the elemental
interactions in (3) are local in nature,
K
is a sparse and
symmetric matrix that can be solved efficiently using a
sparse matrix solver. Once {}
E
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 （
E
E
） (5)
where int
E
is the electric field at a given point inside
the enclosure and ext
E
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

2
2
11
0
1
8
s
V
P
Z


S (6)
where
s
V is the source voltage and 0
Z
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
mW
11
S
11 2
()
.
p
p
inc inc
S
inc
S
dS
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
Y
Z
-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
50
Table 2. Resonance points of the enclosure with inner exci-
tation.
Modes Frequency (GHz)
101
y
TM 0.89
TEM 1.08
cavity-slot 1.12
slot 1.23
111
y
TM 1.37
201
y
TM 1.43
cavity-slot 1.53
Table 3. Resonance points of the enclosure with outer -
polarized plane wave excitation.
Y
Modes Frequency (GHz)
101
y
TM 0.84
cavity-slot 1.16
slot 1.25
cavity-slot 1.40
012
y
TE 1.47
Table 4. Resonance points of the enclosure with outer -
polarized plane wave excitation.
Z
Modes Frequency (GHz)
101
y
TM 0.84
cavity-slot 1.16
102
y
TM 1.21
110
y
TE 1.27
cavity-slot 1.40
012
y
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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