416
I. Introduction
Pollution by electromagnetic radiation is becoming more
and more serious with increasing use of electrical devices
such as TVs, computers, mobile phones, and radios in our
daily lives. It is increasingly affecting the normal life of
people, animals, and has imperceptible side effect on animals
and humans (Bhattacharjee, S., 2014). Metals are the most
common materials for Electromagnetic Interference (EMI)
shielding. They function mainly by reflection due to the free
electrons in them. Metal sheets are bulky, so metal coating
made by electroplating, electroless plating, or vacuum depo-
sition are commonly used for shielding (Chung, D.D.L., 2000).
The use of electromagnetic shielding technology to elimi-
nate or reduce the hazards of electromagnetic radiation has
gained significant meaning (Yan-Jun, S. et al., 2015; Tipa,
R.S. et al., 2008).
In science education, the properties of electromagnetic
waves such as reflection, refraction, diffraction etc. are
taught in secondary physics education or undergraduate
physics class at university level using microwaves as well as
those of light. Furthermore, the reflection or absorption of
EM waves is a topic in engineering education from the view
point of the Electromagnetic Compatibility (EMC) technology
as described above. Hence the electromagnetic shielding
effect by metals or some other materials can be an issue for
science and engineering education. In our daily lives, the
microwave oven or Induction heater (IH) are home electronics
products; the EM shielding is utilized in the protection from
microwave radiation.
As microwave shielding materials, we have selected the
Metal Wire Array (MWA), which is used as the metal wire
grid in the transparent front door of a microwave oven. To
prevent the emission of harmful microwaves from the radia-
tion source, very low transmission and high reflection or
absorption characteristics are required for electromagnetic
shielding materials.
In this study, we investigated the reflection and trans-
mission of a microwave through Metal Wire Array (MWA)
composite structures composed of thin metal wires and a
Polyethylene Terephthalate (PET) film to prepare experiments
Research Article
Demonstration of Electromagnetic Shielding Using Metal Wire Array Composite Structures
Takanori TSUTAOKA*1,2, Uswatun HASANAH*2, Aiko TSURUNAGA*1, Takashi UMEDA*1, Kinya SHIMIZU*2
*1Department of Science Education, Graduate School of Education, Hiroshima University *2Division of Natural Science, Graduate School for International Development and Cooperation,
Hiroshima University
AbstractReflection and transmission of electromagnetic (EM) waves by a Metal Wire Array (MWA) composite structure were
studied for a demonstration of electromagnetic shielding. Metal wire array composites have a layered structure consisting of a cross section paper, an array of thin copper wires and Polyethylene Terephthalate (PET) film. A simple experimental apparatus was constructed for the measurement of the reflection coefficient Γ and the transmission one T of the MWA composites with different intervals of metal wires. The electromagnetic shielding effect was evaluated by the calculation of Γ and T using the transmission line theory. The experimental results indicated a good agreement with the theoretical calculation; it can be considered that the microwave transmission and reflection experiments using MWA composite structures can be utilized as an experimental teaching material to learn radio wave shielding.
Key words: electromagnetic shielding, transmission and reflection coefficients, metal wire array
科学教育研究 Vol. 41 No. 4(2017) 417
for the demonstration of the EM shielding with metal wire
array or grid and its composite structures. The complex
transmission and reflection coefficients, T and Γ have been
calculated as a function of wire distance by transmission
line theory; the experiments were carried out using the
10.5 GHz microwave. In this report, the experimental and
theoretical results of the transmission and reflection of
the EM wave through the MWA composite structure will
be presented; the effect of EM shielding by the MWA com-
posite will be discussed from the viewpoint of physics or
engineering education.
II. Electromagnetic properties of metal wire array
and its composite structure
We consider a simple model of a thin metal wire array
having a diameter d and the distance among the wires x in
the configuration as shown in Fig. 1. We assume that a
plane wave having the electric field E and magnetic field H
propagates along the wave vector k. When the distance x is
smaller than several cm, radio waves with a frequency up to
several 100 MHz cannot pass through the MWA; the radio
wave can be shielded by the metal wire structures (array or
grid) even when there exists a free space between wires.
When the radio waves arrive at the MWA, the polarization
of free electrons is induced by the electric field E along the
metal wire. This polarization produces an electric field Ei
along the opposite direction of E; E will be canceled out by
Ei. This concept is taught in high school or undergraduate
physics class as well as undergraduate engineering educa-
tion. As is known, since the transmission and reflection
characteristics of EM waves through the MWA will change
depending on the polarization direction of the incident
wave, it is required to consider the polarization axis in the
theoretical and experimental treatments.
The electromagnetic properties of metal wire array can
be described by transmission line theory using equivalent
circuit analysis; the reflection or transmission of the plane
waves through an electromagnetic medium can be presented
by the following matrix representation (Pozer, D.M., 2005),
E A B EH C D H 2 1
2 1
. (1)
where, E1, H1 and E2, H2 are the electric and magnetic fields
at the anteroposterior position of the medium, respectively.
The matrix [A, B, C, D] is called transmission matrix. When
a plane wave passes through the medium with the thickness
d, the formula (1) can be written as
cosh sinh
sinh cosh
d Z dE EH Hd d
Z
2 1
2 11
, (2)
where γ and Z are the propagation constant and impedance
of the medium, respectively.
In the case of metal wire array as shown in Fig. 1, the
Fig. 1. Structure of the Metal Wire Array. The inset indicates the equivalent circuit.
Demonstration of Electromagnetic Shielding Using Metal Wire Array Composite Structures418
equivalent circuit can be described by an inductance L which
is inserted parallel to the transmission line as shown in the
inset of Fig. 1; the transmission matrix can be described by
(Decker, M.T., 1959; Lewis, E.A. et al., 1952)
wgg
A Bj YC D jXL
1 01 0 1 011 1 11
. (3)
Xg indicates the reactance of the metal wire array. When we
set d and x as the diameter of metal wires and the distance
between them, respectively, the Xg is given as follows
(Rotman, W., 1962),
lngZ x x
Xd
0
0
, (4)
where λ0 and π are the wavelength of the plane wave in the
free space and the ratio of the circumference of a circle to its
diameter, respectively. In the matrix (3), the element C can be
represented by the admittance of the wire array Ywg,
wgg
Y jX
1
. (5)
The transmission and reflection coefficients of the medium
can be calculated from the input impedance of this medium
Zin; the Zin is given by,
in
BA
E AE BH ZZDH CE DH CZ
2 1 1 0
2 1 1
0
. (6)
Hence the reflection coefficient Γ and the transmission one T
are written as
r in
i in
BA CZ D
E Z Z ZBE Z Z A CZ DZ
00 0
00
0
(7)
and
t t
i i
E E ET
E E E 2
2
ZBAZ B A CZ DZ
0
00
0
21
, (8)
where Ei, Er and Et are the electric field of incident, reflected
and transmitted EM waves, respectively. By using (3) to (5)
we can get the Γ and T of the metal wire array as follows,
wg
wg
Z YZ Y
0
02
(9)
and
wg
TZ Y
0
22
. (10)
The calculated absolute values of the reflection and trans-
mission coefficients Γ and T are shown in Fig. 2 ((a) reflection
coefficient, (b) transmission one) as a function of the distance
x. 2.45 GHz is the operating frequency of a commercially
available microwave oven; 10.5 GHz indicates the operating
frequency of this study. The microwave generator at 10.5 GHz
can be fabricated using a gun diode; commercially available
microwave experimental equipment can be used in the phys-
ics class (Microwave Optics Systems, 2016). The thickness
of wires is 0.1 mm. As is shown in Fig. 2(b), T is zero up to
about x=0.1 cm indicating the both microwaves cannot
pass through the MWA. Γ is unity in this distance range;
it is indicated that the microwaves at 2.45 and 10.5 GHz can
be shielded by the metal wire array or grid having 1 mm
distance. Γ starts to decrease from about x=0.2 cm and
becomes zero at about x=100 cm for the 2.45 GHz wave.
Simultaneously, T increases with x in this distance range.
For the 10.5 GHz microwave, the shielding frequency shifts
to a smaller distance.
In this study, we made a laminated structure consisting of
the MWA and a PET film as shown in Fig. 3(a). The parallel
straight copper wires were aligned with the y-axis as shown
in Fig. 3(b). The distance between wires is defined by x. The
two types of copper wire with diameter d of 0.1 and 0.3 mm
were used. The equivalent circuit of this composite struc-
ture is shown in Fig. 4. The MWA is sandwiched between a
PET film with the thickness of b and a cross section paper.
The metal wire array part can be represented by the Z0 with
the thickness of d/2 and the lumped admittance Ywg. In this
structure, the PET film has a larger permittivity than that
of vacuum, ε0; the permittivity value of the cross section
paper is almost the same as ε0. Hence the impedance of PET
film Zw should be taken into account.
科学教育研究 Vol. 41 No. 4(2017) 419
Fig. 3. Schematic diagram of the metal wire array composite
structure (a) and a photograph of the metal wire array on the
cross-section paper (b).
Fig. 4. Structure of the metal wire array composite (MWAC) and
the equivalent circuit.
Fig. 2. Theoretical calculation results of reflection (a) and transmission (b) coefficients for the metal wire array as a function of the distance
between wires x at different frequencies, 2.45 and 10.5 GHz.
Demonstration of Electromagnetic Shielding Using Metal Wire Array Composite Structures420
The element C of the transmission matrix (3) of the metal
wire array composite structure (MWAC) can be represented
by (Hatakeyama, K. et al., 2015; Yamamoto, S. et al., 2015)
wgm
C Y jZ b d
0
2
, (11)
where εm is the electric permittivity of the PET film. Δb and
Δd are defined by,
bb
0
22
(12)
and
dd
0
22
. (13)
The transmission and reflection coefficients of the MWAC
can be calculated from (7) and (8) using the transmission
matrix with C as (11); Γ and T are given by
Z YZ Y
0
02
(14)
and
TZ Y
0
22
(15)
with
wgm
Y Y jZ b d
0
2
. (16)
Furthermore, we can consider the electric permittivity of
this MWA composite structure; by use of the given parameters,
the relative permittivity εr of the MWAC can be represented
by (Yamamoto, S. et al., 2015)
' "
ln
mr r r
b dj
xb d x b dd
20 1
2
. (17)
Since the wavelength λ0 can be represented by λ0=c/f (c is the
speed of light), the frequency fp at which the εr’ crosses zero
from negative to positive is given by
lnp
m
cf
xb d xd
22 1 1
2
. (18)
The fp is called plasma frequency; the εr’ becomes negative
below this frequency. In the formula (17), if εm is real number
(εr”=0: no loss), εr has only the real part εr’. Since the magnetic
permeability of the MWA and MWAC is positive in the
whole frequency range, EM waves with a frequency below fp
cannot propagate in this medium. The shielding effect of the
MWA is attributed to the plasmonic property of metal grids
which is produced by the plasma oscillation of conduction
electrons in metal wires (Rotman, W., 1962), the effective
permittivity becomes negative in the plasmonic state below
plasma frequency fp. This is the physical reason that the EM
waves can be shielded by the plasma medium. The frequency
dependence of εr’ then can be represented by
' pmr
fb db d f
2
21
. (19)
When the frequency is fixed, εr’ can be obtained as a function
of wire array distance x from (17). The variation of εr’ with
frequency for the MWA at several wire array distances has
been studied so far; good agreements between theoretical
calculations and experimental results for the MWA structure
were reported (Tsutaoka, T. et al., 2004). Furthermore, it has
been reported that the plasma frequency fp of MWA shifts
to a higher frequency range as x decreases. The calculated
electric permittivity εr’ of the MWAC is shown in Fig. 5 as a
function of the wire distance x at several fixed frequencies.
Fig. 5. Relative permittivity εr’ of the metal wire array as a
function of distance x at several frequencies.
科学教育研究 Vol. 41 No. 4(2017) 421
We can define the plasma distance xp at which the εr becomes
negative below this distance for the MWA or MWAC. At
10.5 GHz, the xp locates at about 5.6 cm.
III. Experimental apparatus and setup
In this study, basic research was carried out for the
development of experimental teaching materials to observe
electromagnetic wave shielding by metal wire array. A metal
wire grid having an array of thin metal lines as shown in
Fig. 3(b) was prepared using thin copper wires with a diam-
eter d of 0.1 mm. The distance between wires x was adjusted
to be several values from 1.0 to 30 mm. As described above,
to keep the MWA in the right position, a composite structure
in which the MWA was sandwiched by the two layers of
cross section paper and PET film was prepared. The thick-
ness of the PET film is 100 μm with a relative permittivity
value εm=3.2.
We constructed simple experimental setups for the trans-
mission and reflection measurements. A schematic diagram
of the transmission experiment for the MWA is shown in
Fig. 6(a). As the transmitter of the 10.5 GHz microwave, a
commercially available microwave experimental apparatus
(Uchida TE-4) was used. This type of microwave experi-
mental apparatus is common in commercially available
teaching materials for physics education. This equipment
contains the signal generator and antenna in a box. The
Fig. 6. Experimental setup for the transmission coefficient measurement.
Demonstration of Electromagnetic Shielding Using Metal Wire Array Composite Structures422
transmitted wave was detected by the receiver which contains
the antenna and detecting circuits inside. The appropriate
distance between transmitter and MWA or MWAC and
receiver was selected considering the apertural area of
antenna and receiver where the microwave becomes the far
field plane wave at the sample position. In this experiment,
we set z1 as the distance from the top surface of the transmit-
ting antenna to the metal wire array and z2 as the distance
between the MWA and the antenna of the receiver; z1 and z2
are 48.8 cm and 37.4 cm, respectively.
A photograph of the transmission experiment setup is
shown in Fig. 6(b). The EM absorber was placed beside the
sample to eliminate the diffracted waves. The direction of the
electric field E from the transmitter was set to be parallel to
the metal wire array direction; the plane wave with the wave
vector k was made incident vertically to the MWAC plane.
The amplitude of the received signal was recorded using a
voltmeter. The transmission coefficient was determined
from the amplitude ratio in which the obtained signal voltage
V was normalized by the voltage V0 which is measured
without the sample between transmitter and receiver as
VT
V
0
, (20)
where T changes from zero (no transmission) to unity (100%
transmission).
In the reflection measurement, transmitter and receiver
were placed on the same side from the MWAC sample; the
microwave was diagonally entered into the surface of the
MWAC sample as shown in Fig. 7. The incident angle θ was
set to 40°. The reflection coefficient Γ was determined by
the same procedure using the normalized voltage V0 as the
reflected signal by a metal copper plate, Γ=V/V0. In this
case, Γ changes from unity (100% reflection by the metal
plate) to zero (no reflection).
IV. Results and discussion
The experimental results of the transmission and reflec-
tion coefficients, T and Γ, of the metal wire array composite
structure are shown in Fig. 8 ((a) transmission coefficient T
and (b) reflection one Γ) as a function of the distance x. In
Fig. 8(a), the solid lines are the theoretical curves of T calcu-
lated from (15) for the MWA only and the MWA+PET film
(MWAC), respectively. The solid circles indicate the experi-
mental results of the setup for the transmission measurement.
When the interval x is 10 mm or above, the transmission
coefficient T is close to unity indicating that the MWAC is
transparent to the 10.5 GHz microwave. Meanwhile, T
changes significantly when x is between 5 and 10 mm; the
microwave cannot pass through the MWAC below about
1 mm. Hence it is shown that the distance between wire s
should be at least 1.0 mm to shield the 10.5 GHz microwave
with the MWAC structure. As shown in this figure, the cal-
culation curve for the MWAC has a good agreement with the
current measurement.
The reflection coefficient Γ of the MWAC and the MWA is
Fig. 7. Experimental setup for the reflection coefficient measurement.
科学教育研究 Vol. 41 No. 4(2017) 423
shown in Fig. 8(b) as a function of the distance x. The solid
lines are the calculated curves; the solid circles indicate the
experimental results. When the interval among the metal
wires x is below about 0.1 cm, the reflection coefficient Γ is
almost unity; Γ rapidly decreases between x=0.1 and 1.0 cm.
A fairly good agreement between the calculated results of
the MWAC and the measurements was obtained.
The difference of the calculated transmission coefficient
T between the MWA and the MWAC is not so large compared
to that for the reflection coefficient. This result indicates that
the transmission characteristic of the microwave through
the MWAC is mainly determined by the metal wire array;
the PET film does not have an important role in the trans-
mission. On the other hand, the PET film decreases the
shielding effect of the microwave; since Γ at the 1.0 cm
distance is 0.4 for the MWA, Γ at the same x is almost zero.
The plasma distance xp is also indicated in the figures. At
the xp, T is unity and Γ is zero; 0% shielding can be achieved
at the plasma distance.
From the results indicated above, it can be concluded that
the characteristics of the microwave shielding by metal wire
array or grid can be demonstrated by a simple experiment
using a metal wire array composite combined with numerical
calculations by the transmission line theory. As an example
for a practical application, it can be shown that the EM wave
from the microwave oven can be shielded by the metal wire
grid with several mm of aperture; hence the object in the
oven is visible through the front door. Simultaneously, a low
frequency plasmonic state which can be achieved by the
metal wire array composite structure can be demonstrated
from the view point of material science as well.
V. Conclusions
We investigated the demonstration of microwave shield-
ing by a simple experimental setup using metal wire array
sheets as well as a theoretical calculation of the transmis-
sion and reflection coefficients. A commercially available
experimental apparatus using a 10.5 GHz microwave was
employed as transmitter and receiver. The transmission and
reflection coefficients of the metal wire array composite
structure were measured as a function of the distance x;
good agreements between theoretical and experimental
results for the transmission and reflection coefficients have
been obtained. Hence this experiment can be utilized as
an experimental teaching material to observe microwave
shielding by metal wire array in undergraduate physics or
engineering education as well as advanced study for second-
ary physics education.
Acknowledgements
This work was supported by a grant-in-aid for scientific
research (A) No. 17H00820) from the Japan Society for the
Fig. 8. The reflection coefficient Γ and transmission coefficient T of the metal wire array composite at 10.5 GHz as a function of the wire
distance x. Solid lines indicate the theoretical calculation results and solid circles show the experimental results.
Demonstration of Electromagnetic Shielding Using Metal Wire Array Composite Structures424
Promotion of Science and the Indonesia Endowment Fund
for Education Scholarship (LPDP).
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(Received July 6, 2017; Accepted September 11, 2017)
Takanori TSUTAOKA
Department of Science Education, Graduate School of Education,
Hiroshima University
1-1-1 Kagamiyama, Higashi-Hiroshima 739-8524, Japan