Demonstration of Electromagnetic Shielding Using Metal ...

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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.


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.


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.


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

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