Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
4
,
No
. 3,
J
une
2
0
1
4
,
pp
. 44
1~
44
6
I
S
SN
: 208
8-8
7
0
8
4
41
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
A Modified Fractal Bow Tie Antenna for an RFID Reader
Chaouki Gues
mi, Abdelhak
Ferchichi, Ali
Ghar
sallah
Unit of r
e
sear
ch
Circuits
and
El
ectronics S
y
stems High Frequ
e
ncy
F
acult
y
of S
c
i
e
n
ce,
Univers
i
t
y
El
M
a
nar
,
Tun
i
s
,
T
unis
i
a
Article Info
A
B
STRAC
T
Article histo
r
y:
Received
Ja
n 21, 2014
Rev
i
sed
May 10
, 20
14
Accepted
May 26, 2014
In this paper
,
fractal Bowtie
antenna
s are proposed. To validate o
u
r structur
e
and to develop an analy
t
ic metho
d
to
determ
ine t
h
e geom
etr
y
p
a
r
a
m
e
ters, the
Lumped theor
y
is used. The
proposed
structure is simulated using CST
Microwave Stud
io and
then Com
p
ared
to
th
e electrical M
odel. Th
e
proposed
circu
it has
th
e s
a
m
e
res
onant as
pect when
com
p
aring to th
e Bo
wtie ant
e
nna
with a much reduced simulation
time.
The Bowtie antenn
a has a
box with a
size of
44 *80 *
1
.5 mm
3
. This
a
n
tenna
will
be d
e
s
i
gned
to an
R
F
ID Reader
that resonates on
2.45
GHz.
Keyword:
Bo
wtie An
ten
n
a
Fractal
Lum
p
ed elem
e
n
ts
RFID Read
er
Copyright ©
201
4 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ab
del
h
a
k
Ferc
hi
chi
,
Uni
t
of
resea
r
c
h
C
i
rc
ui
t
s
an
d
El
ect
roni
cs
Sy
st
em
s Hi
gh
F
r
e
que
ncy
,
Facu
lty of Scien
ce,
Un
iv
ersity
El Mana
r, T
unis, Tunisia,
Em
a
il: ab
d
e
lh
ak
ferch
i
ch
i@yah
o
o
.
fr
1.
INTRODUCTION
The
best
i
d
e
n
t
i
f
i
cat
i
on t
e
c
h
n
o
l
o
gy
wi
rel
e
ss so
n t
h
e
seco
nd
w
o
rl
d
wa
r i
s
radi
o
fre
que
ncy
id
en
tificatio
n
RFID. Co
m
p
aring
with
b
a
r co
d
e
s tech
no
l
o
g
y
RFID tech
no
log
y
is
m
o
re efficien
t for m
a
n
y
reason
s, su
ch
as read
i
n
g
d
i
stan
ce, track
i
ng
cap
ab
ility al
so
is
m
o
re rob
u
st. To
d
a
y RFID is u
s
ed
in
sev
e
ral
areas, s
u
ch as
electronic toll collecti
o
n
,
an
ti-th
eft system i
n
m
a
ll, track
i
ng o
f
ani
m
al and pat
i
e
nt
an
d v
e
hi
cl
e
secu
r
ity [1
].
Acco
r
d
i
n
g t
o
t
h
e o
p
e
r
at
i
ng
fr
eque
ncy
o
f
t
h
e
reade
r
, RF
ID
syste
m
s can be
classified into: 125 KHz
l
o
w fre
q
u
ency
ban
d
,
1
3
.
5
6
M
H
z hi
g
h
f
r
e
que
ncy
ba
n
d
, 8
6
0
M
H
z
(
U
l
t
r
a Hi
gh
Fre
q
uen
c
y
)
UH
F ban
d
a
n
d 2.
45
-
5.
8G
Hz
m
i
crowave ban
d
. U
H
F
an
d
m
i
crowave RFID s
y
ste
m
have se
veral adva
ntage com
p
ared L
F
/HF
syste
m
. Especially, the commercial use of
m
i
cro-wa
ve
RFID system
in
th
e supp
ly ch
ain
an
d
i
d
en
tifyin
g
pers
o
n
s ha
ve
b
ecom
e
very
po
pul
a
r
, w
h
i
c
h gi
ves t
h
e
read
e
r
several
t
y
pe
w
o
r
k
i
n
g i
n
t
h
i
s
f
r
eq
ue
ncy
ba
nd
whi
c
h
i
s
becom
i
ng i
n
creasi
ngl
y
i
m
port
a
nt
. The
im
port
a
nt
re
q
u
i
r
em
en
ts fo
r
th
is typ
e
s o
f
read
ers is sm
a
ll size
ant
e
n
n
a, l
i
ght
wei
g
ht
an
d l
o
w
pr
ofi
l
e
whi
c
h a
r
e feat
ures
o
f
m
i
crost
r
i
p
a
n
t
e
nna.
The
ope
rating pri
n
ciple of t
h
e RFID syste
m
can be
e
xpl
ained as
foll
owing: when a
trans
p
onder
appea
r
s in the ope
ration range of reade
r
, it starts receivi
ng bot
h energy and data fr
om
the reader. The rectify
cir
c
u
it in
th
e tr
an
sp
ond
er
co
ll
ects an
d
stor
es th
e en
erg
y
f
o
r p
o
w
e
r
i
n
g
th
e
o
t
h
e
r
cir
c
u
it in th
e tr
an
sp
onder
[
3
-
4
]
. After co
llectin
g
en
oug
h en
erg
y
th
e tran
sp
ond
er can ope
r
a
te
a
n
d
se
nd b
a
ck
p
r
e-
s
t
or
ed
d
a
ta
to r
e
ad
er
,
lik
e
electronic a
r
ticle code
or tag ID code. The
reade
r
t
h
en
passed
t
h
e
rece
ived res
p
onse data
to
a server for
syste
m
ap
p
licatio
n
,
su
ch
as th
e
requ
est
o
f
price and
man
u
f
act
u
r
e in
fo
rm
atio
n
of co
m
i
d
ities, o
r
u
s
er
au
th
en
ticatio
n
[2
].
For
hei
g
ht
gai
n
and wi
de ba
nd
wi
dt
h
,
fract
al
t
echni
que
is effectiv
e fo
r th
ese resu
lts. It is co
m
b
in
atio
n
of ante
nna technology and fractal ge
om
etry [5]. The fra
ctal antenna is
the sa
m
e
symmetric geom
e
t
ry that
r
e
p
eats ov
er the en
tir
e
sur
f
a
ce. Ind
eed, th
is techn
i
qu
e
w
a
s a
v
e
r
y
b
r
o
a
d
f
o
cu
s
of
r
e
search
.
Th
e b
e
st known
fractal techniques a
r
e: Koc
h
curve,
Hi
l
b
e
r
t
cur
v
e, Hel
i
x
, Si
erpi
nski
ca
r
p
et
/
g
asket
a
n
d
M
i
nkw
os
ki
R
i
ng
[
6
]
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
44
1 – 4
4
6
44
2
[7].
We ca
n sa
y that the ante
nna
s fractal ge
om
etry are ve
ry co
m
p
licated
an
d d
i
fficu
lt to m
a
d
e
, as to
the p
a
st
few years th
ere h
a
v
e
b
een no n
e
w fractal stru
ctures.
Wh
ile bo
wtie an
tennas in
ad
d
ition
t
o
ligh
t
wei
g
h
t
, ease
o
f
fab
r
ication
an
d reliab
ility po
ssess a
wid
e
an
d u
ltras wi
d
e
b
a
nd
.
The m
a
nagem
e
nt
of c
o
m
m
u
n
i
cat
i
on i
n
var
i
ous a
pp
lication
s
req
u
i
res a very ad
v
a
n
c
ed
id
en
tification
syste
m
. Th
at is wh
y th
ere are
h
a
v
i
n
g
d
i
fficu
lty fo
r sim
p
lify
th
e id
en
tificatio
n pro
cess.
In
rece
nt
y
ear
s, m
a
ny
st
udi
es ha
ve
bee
n
devel
ope
d
t
o
pr
o
v
i
d
e a
n
i
m
po
rt
ant
a
n
t
e
n
n
a
f
o
r
R
F
I
D
applications. In
our case, we
foc
u
s on
t
h
e RFID
Rea
d
er
ant
e
n
n
a w
h
e
r
e
we nee
d
t
o
p
r
ovi
de a m
i
ni
aturi
z
e
d
structure with
acceptable pa
ra
m
e
ters. Th
e publications tha
t
have worked
on
this goal are
m
a
ny we cite so
me
one t
h
at we
us
ed as a re
fere
nce: First, S-
Kokici
an
d E-
Ko
rkm
az desi
gn a
n
d o
p
t
i
m
ize of B
o
w
-
t
i
e
opt
i
c
a
l
an
tenn
as, in
t
h
eir wo
rk
, t
h
e o
p
tical an
ten
n
a
s were illu
m
i
n
a
ted
b
y
a lin
early p
o
l
arized
p
l
an
e wav
e
perpe
ndic
u
lar t
o
the s
u
rface
of the
optical antennas
.
T
h
e
sim
u
la
tions fre
quency
ra
nge
is 250-650
T
H
z, [8]. In
[
9
],
D
an Y
a
ng, H-
ch
- Y
a
ng
,
J-
Zh
an
g, an
d
Y
-
Li
p
r
es
e
n
t
A no
vel
c
r
o
sse
d bo
wt
i
e
d
i
po
le (CBD) an
tenn
a, t
h
e
st
ruct
u
r
e i
s
des
i
gne
d t
o
Inm
a
rsat
appl
i
cat
i
o
n
s
, t
h
e
pol
a
r
i
zat
i
on
was ci
rc
ul
arl
y
. Thi
r
d,
D
a
ot
i
e
Li
, an
d J
u
n
-fa
-
M
a
o, p
r
o
p
o
se
d
a novel
Koc
h
-l
i
k
e fract
al
cu
rve t
o
t
r
a
n
s
f
o
r
m
ul
t
r
a-wi
de
b
a
nd
(U
WB
)
b
o
w
-
t
i
e
i
n
t
o
so
cal
l
e
d
Koc
h
-l
i
k
e si
de
d
fract
al
b
o
w
-t
i
e
di
p
o
l
e
,
[1
0]
.
Th
is p
a
p
e
r is
o
r
g
a
n
i
zed
as fo
llo
w, in
th
e first sectio
n
we will d
e
scrib
e
an
bo
wtie an
ten
n
a
for an
RFID
reade
r
.
In the sec
o
nd s
ection,
a fractal b
o
wtie an
tenn
a is d
e
sign
ed an
d
sim
u
lated
b
y
th
e co
mmercial
soft
ware (C
ST
M
W
S).
In the
third pa
ra
gra
p
h we b
u
ild
a
n
electrical
m
odel to the
tw
o
str
u
ctur
es of
bow
tie
ant
e
n
n
a.
Fi
nal
l
y
,
we c
o
ncl
u
de
o
u
r
pa
per
an
d
we s
u
g
g
est
so
m
e
pers
pect
i
v
e
s
.
2.
BOW TIE
AN
TENN
A
F
O
R
AN
RF
ID
RE
ADE
R
Al
t
h
o
u
gh t
h
e
R
F
ID t
a
g a
n
d
reader
s ha
ve
m
a
rked a su
ccess ei
t
h
er i
n
i
ndust
r
i
e
s or
i
n
sci
e
nt
i
f
i
c
p
u
b
licatio
n
s
, bu
t
th
e g
a
in
of
an
tenn
as rem
a
in
s
v
e
ry
lo
w,
which
li
m
its th
e max
i
m
u
m
read rang
e
o
f
at least two
m
e
t
e
rs. In ad
di
t
i
on, t
h
e
ban
d
w
i
d
t
h
s are n
o
t
so b
r
oa
d t
o
c
o
ver
ban
d
s
UH
F and m
i
crowa
v
e. I
n
ad
di
t
i
o
n
,
som
e
desi
g
n
s
can
n
o
t
ad
j
u
st
t
h
e
i
m
peda
nce
o
f
t
h
e ant
e
nna
. s
o
we
nee
d
t
o
de
vel
o
p R
F
I
D
t
a
gs a
n
d
reade
r
s
w
h
o
pos
sess a
n
t
e
n
n
a
wh
ose
gai
n
i
s
great
e
r
t
h
a
n
a wi
dt
h
o
f
cl
assi
c ban
d
a
nd
wh
ose
ope
rat
i
on ca
n c
ove
r t
h
e U
H
F
and m
i
crowave ba
nds i
n
the
world entier.de
m
o
re,
have
a
mechanism
enables a
d
justm
e
nt
of
t
h
e i
m
ped
a
nce
t
o
increase t
h
e
de
gree
of
free
d
om
.
To
so
lv
e th
e
pro
b
l
em
s
m
e
n
tio
n
e
d abov
e, tech
no
log
y
b
o
wtie an
tenn
a
was
a
m
o
n
g
th
e
b
e
st
so
l
u
tio
n
s
.
2.
1.
Bow Tie An
ntenna
Two
a
n
tennas are placed face
to f
ace from
their summ
it with a gap be
twe
e
n them is
the pri
n
ciple of
bo
wt
i
e
ant
e
nna
s. T
h
e
per
f
o
r
m
a
nce
of t
h
e
bo
wt
i
e
ant
e
n
n
as
depe
n
d
s
on
se
veral
ge
om
et
ric par
a
m
e
t
e
rs, such
a
s
bowtie size, a
p
ex angle, and ga
p si
ze
[
11]
-
[
1
2
]
.
B
o
wt
i
e
a
n
t
e
n
n
a
pol
a
r
i
zat
i
on ca
n
be l
i
near
o
r
ci
rc
ul
a
r
, t
h
e
im
pedance
of t
h
e b
o
wt
i
e
ant
e
nna ca
n be cal
cul
a
t
e
d t
h
e
o
ret
i
cal
l
y
by
t
r
ans
m
i
ssi
on l
i
n
e t
h
eory
[
13]
, a
nd
can be
chan
ge
d
by
va
r
y
i
ng t
h
e
fl
ar
e a
ngl
e,
w
h
i
c
h
m
a
y
chan
ge t
h
e
re
son
a
nt
wa
vel
e
ngt
h sl
i
g
ht
l
y
[1
4]
.
M
o
re
preci
sel
y
, i
n
o
u
r a
r
t
i
c
l
e
we p
r
op
ose
a bo
w
tie an
ten
n
a
fo
r RFID
read
e
r
that ca
n sol
v
e the
pr
o
b
l
e
m
s
m
e
nt
i
one
d
2.
2.
Geome
t
ry
The sc
hem
a
t
i
c
of t
h
e
bo
wt
i
e
a
n
t
e
n
n
a
gi
ve
n i
n
ou
r a
r
t
i
c
le is sh
own
in Figure 1
.
It is a p
l
anar an
tenn
a
consisting
of t
w
o m
e
tal layer
s
is pri
n
ted
on
each
one
of t
h
e
listed FR4
subs
trate with
permittivity
ε
r
= 4.3 a
n
d
lo
ss tang
en
t (t
an
g
δ
) = 0.025
. On
e of
t
h
e layer
s
is pr
in
ted th
e
m
i
crowav
e radi
at
i
o
n m
e
m
b
er and t
h
e
ot
he
r t
o
the UWB element. T
h
e m
i
crow
ave
com
p
o
n
e
n
t
i
s
ba
sed
o
n
t
w
o
i
s
oscel
es t
r
i
a
ngl
es
whi
c
h
are pl
ace
d i
n
f
r
ont
of
th
eir top
con
n
e
cted
to
each
o
t
h
e
r
b
y
th
e RFID ch
ip
In
term
e
d
iate.
Wh
ile the UW
B
is a m
o
d
i
fied
v
e
rsion o
f
th
e
C
r
osse
d E
x
p
o
n
ent
i
a
l
Tape
re
d Sl
ot
ant
e
nna
(XET
S) p
r
op
ose
d
i
n
[1
5]
,
[1
6]
.T
hi
s l
a
st
st
ruct
u
r
e gi
ve
n g
o
o
d
resul
t
s
fo
r
U
W
B
.
The t
w
o
pa
rt
s o
f
t
h
e m
i
crowa
v
e a
n
d U
W
B
ant
e
nn
a
m
u
st
be
m
a
de wi
t
h
great
pre
c
i
s
i
on
s
o
that m
i
nimizes
the m
u
tual
in
fluence. T
h
us, the two elem
ents are aligne
d s
o
t
h
at
t
h
e hol
e
s
of p
o
w
e
r eac
h si
de
of
t
h
e s
u
bst
r
at
e
sh
ow
n i
n
Fi
g
u
r
e
1.
During
th
e si
m
u
la
tio
n
we
used
a d
i
screte p
o
rt with
an
im
p
e
d
a
n
ce equal to
5
0
Ω
i
n
p
u
t fo
r
U
W
B
.
Microwa
v
e
for ha
rbor we
use
d
a l
u
m
p
ed ele
m
ent that
r
e
p
r
esen
ts an
RFI
D
I
C
in
ou
r pr
opo
sed
an
tenn
a.
The
geom
etry bowtie RFID ele
m
ent
m
i
cr
owa
v
e
vi
ew i
n
Figure 2 consists
of two
trian
g
l
es. In
ad
d
ition
,
th
e t
w
o
elem
en
ts o
f
o
u
r an
ten
n
a
m
u
st b
e
v
e
ry clo
s
e; in
fact, th
e lin
es th
at con
n
ect the RFID
micro
w
av
e elemen
t with
th
e ch
ip
are
v
e
ry
th
in
,
v
e
ry
na
r
r
o
w
a
n
d
p
o
si
t
i
one
d i
n
a m
a
nne
r t
h
at
m
i
ni
m
i
zes
in
terferen
c
e wi
th
XETS an
tenn
a
o
n
th
e
op
posite sid
e
.
For m
a
xim
u
m
po
wer t
r
a
n
s
f
e
r
t
o
2.
4
5
G
H
z
,
t
h
e ant
e
n
n
a
im
pedance R
F
ID m
u
st
be equal
t
o
t
h
e
conjugate
of the chip Z
(antenna)
=R x +
j Lx.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
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7
0
8
A Mod
ified
Fra
c
ta
l Bo
w Tie
An
tenna
fo
r an RFID Read
er
(Ab
d
e
lha
k
Ferch
i
ch
i)
44
3
Fi
gu
re
1.
E
xpl
ode
d
vi
ew
o
f
t
h
e a
n
t
e
n
n
a s
h
o
w
i
n
g
bot
h R
F
I
D
a
n
d
U
W
B
fa
ces i
n
a
d
di
t
i
on
t
o
t
h
e c
o
m
m
on
substrate
Fi
gu
re
2.
Ge
o
m
et
ry
B
o
wt
i
e
of
t
h
e R
F
I
D
fa
ce o
f
t
h
e
hy
bri
d
a
n
t
e
n
n
a,
desi
gne
d
wi
t
h
C
S
T
M
i
cro
w
ave
St
udi
o.
Tab
l
e
1
.
Param
e
ter Val
u
es
o
f
th
e RFID Elemen
t in
Milli
m
e
t
e
rs
C
sub
L
sub
T
c
T
b
Q
ou
t
80
44
40
40
35
Q
in
C
s
L
s
P
32
3
2
2
C
sub
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I
S
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:
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08
IJEC
E V
o
l
.
4, No
. 3,
J
u
ne 2
0
1
4
:
44
1 – 4
4
6
44
4
Figu
re
3.
Para
m
e
ters defi
nin
g
the
U
W
B Ele
m
ent
2.
3.
Simula
ti
o
n
Results
As ca
n
be see
n
, i
n
t
h
e si
m
u
l
a
ti
on
res
u
l
t
s
,
we
obt
ai
n
a
reso
na
nt
f
r
eq
ue
ncy
e
qual
t
o
2.
45
G
H
z
whi
c
h i
s
an
RFI
D
fr
equen
c
y. Th
e
g
a
in is abou
t 2.85
dB wh
ich
is accep
tab
l
e
for
o
u
r
ap
p
lication
.
Fi
gu
re 4.
The
R
e
t
u
rn
L
o
ss of
t
h
e pr
o
pose
d
a
n
t
e
n
n
a
Fi
gu
re 5.
The
Gai
n
o
f
ou
r
a
n
t
e
nna
3.
A
PR
OPSED
FR
AC
TA
L BOW
TIE READER ANTENNA
3.
1.
F
r
a
c
ta
l Techniq
u
e
Fract
al
geom
etri
es have
bee
n
appl
i
e
d i
n
seve
ral
t
echnologies. Indee
d
, any
self-sim
ilar confi
g
urati
on
can take
the
na
me fractal ge
ometry. Th
e
pr
o
p
ert
y
o
f
t
hum
b i
s
t
o
t
a
ke t
h
e
sam
e
characteristics of the
ge
neral
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
A Mod
ified
Fra
c
ta
l Bo
w Tie
An
tenna
fo
r an RFID Read
er
(Ab
d
e
lha
k
Ferch
i
ch
i)
44
5
stru
cture
for each
sub
section
wh
ic
h
was
well exp
l
ain
e
d b
y
Man
d
e
l
b
rot in
17
[1
975
].
W
e
can will re
m
a
k
e
several
fractal ge
om
etries as sierpens
ki
Koc
h
, Mi
nk
owsk
i,
Hilb
ert. Th
e RF
ID
s
y
ste
m
s and m
i
crowave
devi
ces
wel
l
us
i
ng
fract
al
ge
o
m
et
ri
es t
o
i
m
prove
t
h
ei
r
cha
r
a
c
t
e
ri
st
i
c
s.
3.
2.
Geome
t
ry
Th
is fractal Bo
w-tie an
tenn
a is p
r
op
o
s
ed
at
th
e b
e
g
i
nn
ing o
f
a
coup
le of si
m
ilar iso
s
celes trian
g
l
es
by facing the
summit,
made fractalisation
is subt
rac
ting
a central inve
rted triangl
es
of each the
pri
n
cipals
trian
g
l
es. After sub
t
raction
,
t
h
r
ee e
qual t
r
iangles stay on ea
ch si
de
of t
h
e s
t
ructure
[18].
Whi
c
h ca
n
be
m
o
re gene
ral
i
zed
by
ap
pl
y
i
ng
t
h
e si
er
pe
ns
ki
t
echn
o
l
o
gy
, i
n
deed
, t
h
e
sam
e
p
r
oce
d
ure i
s
rep
eated
to th
e
rem
a
in
in
g
triang
les. Th
e
nu
mb
er of
t
r
i
a
ngl
es
N
n
, l
e
ngt
h
of
a si
de
of
t
r
i
a
n
g
l
e Ln a
n
d t
h
e
fractional area
An can be
calc
u
lated
after every iteratio
n [19
]
:
N
n
=
3
n
L
n
= 1/
2
n
A
n
= L
n
N
n
2
=
(3/
4
)
n
Fi
gu
re
(6
) s
h
o
w
s
fract
al
a
n
t
e
nn
B
o
wt
i
e
ant
e
nna
w
h
i
c
h
u
s
ed t
w
o i
t
e
rat
i
o
ns
of
Si
er
pe
ns
ki
w
h
i
c
h
i
s
m
ount
ed o
n
s
u
bst
r
at
e FR
4 a
m
a
t
e
ri
al
havi
n
g
a t
h
i
c
k
n
ess
h
= 1.5 m
m
, a
di
el
ect
ri
c cons
t
a
nt
ε
r = 4.
3 a
nd l
o
ss
t
a
nge
nt
(t
a
n
g
δ
) = 0.025
.
Fi
gu
re
6.
B
o
wt
i
e
Fract
al
A
n
t
e
nna
3.
3.
Simula
ti
o
n
Results
The si
m
u
l
a
t
i
o
n
res
u
l
t
s
o
f
t
h
e
pr
o
pose
d
fract
al
ant
e
n
n
a
gi
v
e
us
a
res
ona
nt
f
r
eq
ue
ncy
e
qual
t
o
2.
4
5
GHz
w
h
i
c
h
i
s
an R
F
ID
f
r
eq
u
e
ncy
an
d a
gai
n
a
b
out
2.
9
3
d
B
whi
c
h i
s
acc
ept
a
bl
e
fo
r
ou
r
appl
i
cat
i
o
n.
Fi
gu
re 7.
The
R
e
t
u
rn
L
o
ss
of the Fractal ant
e
nna
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I
S
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:
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08
IJEC
E V
o
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.
4, No
. 3,
J
u
ne 2
0
1
4
:
44
1 – 4
4
6
44
6
Figure 8.
The
Gain of
fractal antenna
4.
CO
NCL
USI
O
N
A B
o
wt
i
e
frac
t
al
ant
e
nna i
s
devel
ope
d a
n
d
pr
op
ose
d
i
n
t
h
i
s
pa
per. T
h
e
ant
e
n
n
a i
s
de
si
gne
d t
o
a
n
RFID Reade
r
and it presents
m
a
ny advant
ageous
com
p
aring to a class
i
cal Bowtie antenna. T
h
e
use
of
a
sim
p
le and an
efficient circ
ui
t
m
odel wa
s very use
f
ul
an
d
h
e
lp
s u
s
to
do
a go
od
an
alytic stud
y. Besides, th
e
sim
u
l
a
t
i
on t
i
m
e
was
re
duce
d
whi
c
h m
eans a
fast
t
o
ol
s
of
si
m
u
l
a
t
i
on.
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r
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m
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