I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
E
lec
t
r
ical
an
d
Com
p
u
t
e
r
E
n
gin
e
e
r
in
g
(
I
JE
CE
)
Vol.
12,
No.
1,
F
e
br
ua
r
y
2022,
pp.
983
~
996
I
S
S
N:
2088
-
8708
,
DO
I
:
10
.
11591/
ij
e
c
e
.
v12
i
1
.
pp
9
83
-
996
983
Jou
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M
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C
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:
M
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dha
l
B
ha
r
a
thr
a
j
Kuma
r
De
pa
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tm
e
nt
of
E
lec
tr
onics
a
nd
C
omm
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ti
on
E
n
ginee
r
ing,
S
h
r
i
Dha
r
mas
thala
M
a
njuns
thes
hwa
r
a
I
ns
ti
tut
e
of
T
e
c
hnology
Dha
r
mas
thala
R
d,
ne
a
r
S
iddhava
na
,
Ujir
e
,
Ka
r
na
ta
ka
574240,
I
ndia
E
mail:
bha
r
a
th
r
a
jkum
a
r
100@gmail.
c
om
1.
I
NT
RODU
C
T
I
ON
Now
a
da
ys
,
the
wide
ba
nd
a
ntenna
s
a
r
e
wide
ly
us
e
d
a
s
a
n
e
no
r
mous
a
ppli
c
a
ti
on
in
wi
r
e
les
s
c
omm
unica
ti
on
s
ys
tems
due
to
it
s
higher
im
pe
da
nc
e
ba
ndwidth
a
nd
s
im
ple
s
tr
uc
tur
e
[
1]
.
C
ons
e
que
ntl
y,
the
ult
r
a
wide
ba
nd
(
UW
B
)
tec
hnology
is
c
ons
ider
e
d
a
s
the
s
igni
f
ica
nt
s
olut
ion
f
or
f
utur
e
wir
e
les
s
c
omm
unica
ti
on
ba
s
e
d
on
it
s
huge
f
r
e
que
nc
y
s
pe
c
tr
um
f
r
om
3
.
1
GH
z
to
10.
6
GH
z
[
2
]
-
[
4]
.
I
n
de
ve
lo
ping
the
c
omm
unica
ti
on
s
ys
tem,
the
a
ntenna
is
r
e
quir
e
d
t
o
be
de
s
igned
with
les
s
powe
r
c
ons
umpt
ion,
inexpe
ns
ive,
low
pr
o
f
il
e
,
les
s
e
r
c
ompl
e
xit
y,
highe
r
p
r
e
c
is
ion
r
a
nging,
li
gh
t
we
ight
,
a
nd
e
a
s
e
o
f
i
mpl
e
menta
ti
on
[
5
]
-
[
7]
.
T
he
UW
B
tec
hnology
is
us
e
d
in
d
if
f
e
r
e
nt
a
ppl
ica
ti
ons
s
uc
h
a
s
high
-
a
c
c
ur
a
c
y
r
a
da
r
s
,
medic
a
l
im
a
ging
s
ys
tems
,
high
-
da
ta
r
a
te
wir
e
les
s
c
omm
unica
ti
ons
,
r
e
mot
e
s
e
ns
ing,
medic
a
l
moni
tor
ing
,
a
nd
medic
a
l
s
e
ns
or
da
ta
c
oll
e
c
ti
on
s
ys
tems
[
8
]
-
[
9]
.
T
he
s
e
UW
B
a
ntenna
s
a
r
e
c
ons
tr
uc
ted
in
dif
f
e
r
e
nt
de
s
igns
s
uc
h
a
s
dipol
e
a
nd
monopol
e
/l
oga
r
it
hmi
c
a
ntenna
.
I
n
UW
B
a
ppli
c
a
ti
ons
,
the
monopol
e
a
ntenna
s
a
r
e
c
ons
ider
e
d
d
ue
to
it
s
va
r
ious
a
dva
ntage
s
s
uc
h
a
s
s
im
ple
s
tr
uc
tur
e
,
e
a
s
y
f
a
br
ica
ti
on,
good
r
a
diation,
a
nd
ult
r
a
-
wide
ba
nd
f
r
e
que
nc
y
[
10
]
-
[
11]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
12
,
No.
1,
F
e
br
ua
r
y
2
022:
983
-
996
984
T
he
f
r
a
c
tal
ge
ometr
y
s
ha
pe
is
us
e
d
a
s
a
ntenna
s
ha
pe
s
ins
tea
d
of
the
e
uc
li
de
a
n
ge
ometr
ies
be
c
a
us
e
of
it
s
s
pa
c
e
f
il
li
ng
pr
ope
r
ty,
a
ls
o,
thi
s
f
r
a
c
tal
ge
ometr
y
is
us
e
d
to
obtain
the
mul
ti
-
ba
nd
ope
r
a
ti
on
a
nd
mi
niatur
iza
ti
on
[
12
]
-
[
14]
.
T
he
p
r
ope
r
ty
of
s
pa
c
e
f
il
li
ng
in
a
s
mall
a
r
e
a
im
pr
ove
s
the
e
lec
tr
ica
l
pa
th
length
of
the
de
s
igned
a
ntenna
[
15]
.
Ge
ne
r
a
ll
y,
the
f
r
a
c
tal
ge
ometr
y
is
a
ppli
e
d
int
o
the
pa
tch
a
nd
it
is
a
dde
d
in
the
a
ntenna
f
or
de
s
igni
ng
the
f
r
a
c
tal
a
ntenna
whic
h
is
us
e
d
to
obtain
the
c
ompac
t,
s
mall
s
ide
lobe
a
r
r
a
ys
a
nd
higher
ga
in
a
e
r
ials
[
16
]
-
[
17]
.
How
e
ve
r
,
the
f
r
a
c
tal
a
ntenna
s
ha
ve
dif
f
e
r
e
nt
c
ha
ll
e
nge
s
s
uc
h
a
s
r
a
diation
pa
tt
e
r
n
e
nha
nc
e
ment,
a
r
bit
r
a
r
y
f
r
e
que
nc
y
r
a
ti
o,
unif
or
mi
ty
of
im
pe
da
nc
e
,
polar
iza
ti
on
in
mul
ti
b
a
nd
a
nd
dir
e
c
ti
vit
y
[
18]
.
T
he
S
ier
p
ins
ki
f
r
a
c
tal
a
ntenna
is
c
ons
ider
e
d
a
s
a
n
e
nor
mous
s
tr
uc
tur
e
be
twe
e
n
th
e
f
r
a
c
tal
a
ntenna
s
.
I
n
the
de
s
ign
o
f
e
lec
tr
omagne
ti
c
ba
n
d
-
ga
p,
the
S
ier
pins
ki
c
ur
ve
is
de
ve
loped
to
a
v
oid
the
s
im
ult
a
ne
ous
s
witching
nois
e
ove
r
hig
h
-
s
pe
e
d
c
ir
c
uit
s
.
T
his
S
ier
p
ins
ki
a
ntenna
is
us
e
d
to
obtain
th
e
mul
ti
-
ba
nd
pe
r
f
or
manc
e
,
but
the
dif
f
iculty
oc
c
ur
s
while
de
s
igni
ng
the
a
ntenna
f
or
the
de
s
ir
e
d
f
r
e
que
nc
y
[
1
9
]
-
[
20]
.
T
he
main
c
ontr
ibut
ions
of
thi
s
pa
pe
r
a
r
e
given
a
s
f
oll
ows
:
T
he
s
ier
pins
ki
c
a
r
pe
t
f
r
a
c
tal
monopol
e
a
ntenna
(
S
C
F
M
A)
de
s
ign
is
de
ve
loped
unti
l
two
it
e
r
a
ti
ons
to
obtain
maxi
mum
ba
ndwidth.
T
he
r
e
f
or
e
,
the
maximum
ba
ndwidth
is
obtaine
d
ba
s
e
d
on
the
s
pa
c
e
f
il
li
ng
a
nd
s
e
lf
-
s
im
il
a
r
f
e
a
tur
e
s
.
M
or
e
ove
r
,
the
r
e
duc
ti
on
in
monopol
e
pa
tch
s
ize
is
pr
opos
e
d
to
mi
nim
ize
a
r
e
a
of
the
ove
r
a
ll
a
ntenna
s
tr
uc
tur
e
.
He
r
e
,
the
pa
tch
a
nd
the
gr
ound
a
r
e
de
ve
loped
us
ing
the
c
oppe
r
a
s
we
ll
a
s
F
R
4
is
us
e
d
a
s
a
s
ubs
tr
a
te
with
los
s
tange
nt
o
f
0.
02
a
nd
r
e
lative
pe
r
mi
tt
ivi
ty
of
4.
4
.
T
he
ove
r
a
ll
or
ga
niza
ti
on
of
the
pa
p
e
r
a
r
e
given
a
s
f
oll
ows
:
T
he
li
ter
a
tur
e
s
ur
ve
y
a
bout
the
r
e
c
e
nt
f
r
a
c
tal
s
ha
pe
-
ba
s
e
d
a
ntenna
s
tr
uc
tur
e
s
is
s
ur
ve
ye
d
in
s
e
c
ti
on
2.
T
he
im
pleme
ntation
of
S
C
F
M
A
de
s
ign
up
to
two
it
e
r
a
ti
ons
a
long
with
it
s
dim
e
ns
ions
a
r
e
m
e
nti
one
d
in
s
e
c
ti
on
3.
T
he
r
e
s
ult
s
a
nd
dis
c
us
s
io
n
of
the
S
C
F
M
A
de
s
ign
is
de
s
c
r
ibed
in
s
e
c
ti
on
4.
F
inally,
t
he
c
onc
lus
ion
is
made
in
s
e
c
ti
on
5.
2.
L
I
T
E
RA
T
UR
E
S
UR
VE
Y
T
ha
ka
r
e
[
21
]
a
na
lyze
d
the
ba
ndwidth
im
pr
ove
m
e
nt
of
pr
int
e
d
c
i
r
c
ular
plana
r
f
r
a
c
tal
monopol
e
a
ntenna
with
a
nd
without
the
pr
oxim
it
y
c
oupli
ng
.
T
he
f
e
e
d
tec
hniques
of
c
oa
l
pyr
o
lys
is
wa
s
tew
a
te
r
(
C
P
W
)
a
nd
mi
c
r
os
tr
ip
li
ne
we
r
e
us
e
d
to
im
pr
ove
the
mul
t
iband
ba
ndwidt
h
in
the
f
r
a
c
tal
monopol
e
a
ntenna
de
s
igned
with
the
c
oupled
pr
oxim
it
y
r
ing
.
He
r
e
,
the
f
e
e
d
tec
hnique
wa
s
us
e
d
due
to
the
pr
ope
r
ti
e
s
o
f
s
e
lf
-
s
im
il
a
r
it
y
in
the
it
e
r
a
ti
ve
f
r
a
c
tal
a
ntenna
.
T
his
wor
k
f
a
il
e
d
to
a
n
a
lyze
the
ga
in
va
lue
of
the
f
r
a
c
tal
monopo
le
a
nte
nna
f
or
a
ll
it
s
f
our
it
e
r
a
ti
ons
.
Gupta
a
nd
M
a
thur
[
22]
de
s
igned
the
s
qua
r
e
s
ha
pe
d
UW
B
f
r
a
c
tal
a
ntenna
a
long
with
the
r
igh
t
a
ngled
is
os
c
e
le
s
(
R
I
T
)
Koc
h
in
the
mar
gin
o
f
the
pa
tch.
T
he
c
ir
c
le
s
ha
pe
wa
s
de
ve
loped
in
the
c
e
nter
of
the
pa
tch
to
obtain
the
c
ir
c
u
lar
polar
iza
ti
on
in
the
r
e
s
ona
nt
f
r
e
que
nc
ies
.
How
e
ve
r
,
the
r
e
tur
n
los
s
wa
s
im
pr
o
ve
d
only
whe
n
the
a
ppr
opr
iate
matc
hing
wa
s
done
in
thi
s
f
r
a
c
tal
a
ntenna
.
Va
r
a
mi
ni
e
t
al.
[
23
]
pr
e
s
e
nted
the
mi
c
r
os
tr
ip
a
ntenna
with
S
ier
pins
ki
c
a
r
pe
t
(
M
ASC
)
to
e
nha
nc
e
the
matc
hing
a
nd
ba
ndwidth
a
nd
the
M
inkows
ki
f
r
a
c
tal
wa
s
us
e
d
to
maximi
z
e
the
a
ntenna
a
r
e
a
.
T
he
pe
r
mea
bil
it
y
a
nd
pe
r
mi
tt
iv
it
y
we
r
e
obtaine
d
to
s
pli
t
r
ing
r
e
s
ona
tor
(
i.
e
.
,
meta
mate
r
ial
)
by
us
ing
the
r
e
f
lec
ti
on/t
r
a
n
s
mi
s
s
ion
method.
T
he
f
e
a
tur
e
of
r
e
c
onf
igur
a
bil
it
y
w
a
s
a
c
hieve
d
by
a
c
c
ompl
is
hing
the
junction
in
the
meta
mate
r
ial
laye
r
.
T
he
f
ir
s
t
a
ntenna
wa
s
obtaine
d
two
d
if
f
e
r
e
n
t
r
e
s
ona
nc
e
s
s
uc
h
a
s
3.
2
a
nd
4.
5
GH
z
whe
r
e
a
s
the
s
e
c
ond
a
ntenna
wa
s
obtaine
d
two
mo
r
e
r
e
s
ona
nc
e
s
s
uc
h
a
s
3.
5
a
nd
5.
8
GH
z
by
va
r
ying
the
meta
mate
r
ial
la
ye
r
.
T
his
wor
k
a
na
lyze
d
the
a
ntenna
ga
in
a
nd
e
f
f
icie
nc
y
on
l
y
f
or
the
indoo
r
a
ppli
c
a
ti
on.
S
ha
r
ma
a
nd
S
ha
r
ma
[
24]
pr
e
s
e
nted
the
two
-
hybr
id
f
r
a
c
tal
s
lot
f
or
de
s
igni
ng
the
m
icr
os
tr
ip
pa
tch
a
ntenna
(
M
P
A)
.
I
n
thi
s
a
ntenna
,
the
Koc
h
c
ur
ve
w
a
s
us
e
d
in
the
f
ir
s
t
s
lot
a
s
we
ll
a
s
the
c
ombi
na
ti
on
of
Koc
h
c
ur
ve
with
M
inkows
ki
wa
s
us
e
d
to
de
ve
lop
the
s
e
c
ond
s
lot
.
T
his
hyb
r
id
f
r
a
c
tal
s
lot
wa
s
de
s
igned
with
the
pa
r
ti
a
l
g
r
ound
plane
to
ob
tain
the
wide
ba
nd
a
ppli
c
a
ti
ons
.
T
he
a
ntenna
’
s
ga
in
a
nd
ba
ndwidth
we
r
e
o
pti
mi
z
e
d
by
va
r
ying
the
length
of
pa
r
ti
a
l
gr
ound
plane
.
Ho
we
ve
r
,
the
ga
in
o
f
the
hybr
id
f
r
a
c
tal
s
lot
a
ntenna
wa
s
les
s
in
the
wide
ba
nd
a
ppli
c
a
ti
ons
.
Aw
a
n
e
t
al.
[
25]
de
ve
loped
the
ul
tr
a
-
thi
n
f
lexible
pa
tch
a
ntenna
f
or
I
ndian
s
umm
e
r
mons
oon
(
I
S
M
)
a
ppli
c
a
ti
ons
.
T
he
uti
li
z
a
ti
on
of
f
r
a
c
tal
pa
tche
s
w
a
s
r
e
duc
e
d
the
s
ize
up
to
30
%
a
c
c
or
ding
to
the
typi
c
a
l
qua
dr
il
a
ter
a
l
pa
tch.
Ne
xt,
a
r
e
c
tangula
r
s
tub
wa
s
u
s
e
d
in
the
f
e
e
dli
ne
to
mi
n
im
ize
the
ha
r
moni
c
s
.
He
nc
e
,
thi
s
ult
r
a
-
thi
n
f
lexible
pa
tch
a
ntenna
wa
s
us
e
d
to
ob
tain
c
ompac
t
s
ize
,
wide
ba
ndwidth,
a
nd
moder
a
te
ga
in.
How
e
ve
r
,
the
r
e
s
ona
ti
ng
f
r
e
que
nc
y
of
the
a
ntenna
wa
s
a
f
f
e
c
ted
be
c
a
us
e
of
the
s
tub
us
e
d
in
the
f
r
a
c
tal
pa
tch.
J
indal
e
t
al.
[
26]
p
r
e
s
e
nted
the
M
inkows
ki
a
n
d
mea
nde
r
c
ur
ve
-
ba
s
e
d
hybr
id
f
r
a
c
tal
a
ntenna
(
M
M
F
HA
)
f
or
the
mobi
le
de
vice
s
.
He
r
e
,
the
mobi
le
de
vice
s
we
r
e
us
e
d
in
va
r
ious
c
omm
unica
ti
on
a
ppli
c
a
ti
ons
s
uc
h
a
s
mobi
le
a
d
hoc
ne
twor
ks
,
de
lay
tol
e
r
a
nt
ne
twor
ks
a
nd
wir
e
les
s
s
e
ns
or
ne
twor
ks
.
I
n
thi
s
M
M
F
HA
,
a
n
im
pe
da
nc
e
ba
ndwidth
wa
s
e
nha
nc
e
d
by
M
e
a
nde
r
c
ur
ve
a
s
we
ll
a
s
mul
ti
ba
nd
wa
s
a
c
hi
e
ve
d
by
us
ing
the
M
inkows
ki
c
ur
ve
s
.
How
e
ve
r
,
the
i
mpeda
nc
e
wa
s
a
f
f
e
c
ted
with
the
notch
a
t
the
gr
ound
plane
of
M
M
F
HA
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Sier
pins
k
i
c
ar
pe
t
fr
ac
tal
monopole
antenna
for
ult
r
a
-
w
ideband
appli
c
ati
o
ns
(
M
e
dhal
B
har
athr
aj
K
umar
)
985
3.
S
CF
M
A
DE
S
I
GN
I
n
thi
s
S
C
F
M
A
de
s
ign,
the
ba
ndwidth
of
the
a
nte
nna
is
mi
nim
ize
d
by
im
pleme
nti
ng
the
s
ier
pins
ki
c
a
r
pe
t
up
to
two
it
e
r
a
ti
ons
.
T
he
s
ize
of
monopol
e
pa
tch
is
opti
mi
z
e
d
f
o
r
r
e
duc
ing
the
ove
r
a
ll
a
r
e
a
o
f
a
ntenna
de
s
ign.
I
nit
ially
,
th
is
S
C
F
M
A
de
s
ign
c
ons
ider
s
the
r
e
c
tangle
s
ha
pe
pa
tch
a
nd
then
the
s
qua
r
e
s
ha
pe
d
s
lot
s
a
r
e
r
e
moved
in
the
ba
s
e
c
a
s
e
,
f
ir
s
t
i
ter
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on.
T
he
pr
oc
e
s
s
of
thi
s
S
C
F
M
A
de
s
ign
ha
s
two
major
s
teps
whic
h
a
r
e
a
ntenna
de
s
ign
c
onf
igur
a
ti
o
n
a
nd
pa
r
a
met
r
ic
s
tudy
of
the
S
C
F
M
A
de
s
ign.
T
he
a
ntenna
de
s
ign
c
onf
igur
a
ti
on
s
hows
the
ba
s
e
c
a
s
e
,
f
ir
s
t
it
e
r
a
ti
o
n
a
nd
s
e
c
ond
it
e
r
a
ti
on
a
ntenna
de
s
ign
a
long
with
it
s
dim
e
ns
ion.
T
he
pa
r
a
met
r
ic
s
tudy
de
s
c
r
ibes
the
e
f
f
e
c
t
of
f
r
a
c
tal
s
ha
pe
s
in
mi
c
r
os
tr
ip
pa
tch.
T
he
de
s
ign
pr
oc
e
s
s
of
the
S
C
F
M
A
is
de
s
c
r
ibed
in
the
f
oll
owing
s
e
c
ti
o
n.
3.
1.
S
ier
p
in
s
k
i
f
r
ac
t
al
an
t
e
n
n
a
T
he
de
s
ign
of
S
ier
pins
ki
c
a
r
pe
t
is
ge
ne
r
a
ll
y
a
plane
f
r
a
c
tal
whic
h
is
de
ve
loped
by
the
W
a
c
ław
S
ier
pińs
ki
in
1916
.
T
he
method
of
pa
r
ti
ti
on
ing
the
s
ha
pe
int
o
s
maller
c
opies
of
it
s
e
lf
,
e
li
mi
na
ti
ng
one
or
mor
e
r
e
pli
c
a
s
a
nd
is
r
e
c
ur
s
ively
pr
olonged
to
other
s
ha
p
e
s
.
I
n
thi
s
S
ie
r
pins
ki
c
a
r
pe
t
s
tr
uc
tur
e
,
the
mi
ddle
r
e
c
tangle
is
r
e
moved
in
the
ba
s
e
c
a
s
e
a
nd
it
is
r
e
pe
a
ted
f
or
n
e
xt
two
it
e
r
a
ti
ons
to
obtain
the
wide
ba
nd
f
r
e
que
nc
y
r
a
nge
.
3.
1.
1.
S
ier
p
in
s
k
i
c
ar
p
e
t
I
n
thi
s
pr
opos
e
d
de
s
ign,
the
s
tr
uc
tur
e
o
f
S
ier
pins
ki
c
a
r
pe
t
i
s
ini
ti
a
li
z
e
d
wi
th
r
e
c
tangle
s
tr
uc
tur
e
.
T
he
r
e
c
tangle
s
tr
uc
tur
e
is
divi
de
d
int
o
9
c
or
r
e
s
ponding
s
ub
-
r
e
c
tangle
s
in
a
3
-
by
-
3
gr
id.
T
he
c
e
ntr
a
l
s
ub
-
r
e
c
tangle
r
e
moved
the
ba
s
e
c
a
s
e
a
nd
thi
s
pr
oc
e
dur
e
is
r
e
pe
a
ted
in
f
ir
s
t
it
e
r
a
ti
on
f
or
the
r
e
maining
s
ub
-
r
e
c
tang
les
.
Additi
ona
ll
y,
the
s
a
me
pr
oc
e
dur
e
is
e
xtende
d
in
s
e
c
ond
it
e
r
a
ti
on
f
o
r
a
ll
the
8
s
ub
-
r
e
c
tangle
s
of
the
m
icr
os
tr
ip
a
ntenna
.
T
he
de
s
ign
of
mi
c
r
os
tr
ip
a
ntenna
c
ont
a
ins
the
s
pe
c
if
ic
pa
r
a
mete
r
s
s
uc
h
a
s
r
e
s
ona
nt
f
r
e
que
nc
y
a
ntenna
width,
e
f
f
e
c
ti
ve
diele
c
tr
ic
c
ons
tant,
e
f
f
e
c
ti
ve
a
ntenna
length,
length
e
xtens
ion,
a
nd
pa
tch
leng
th.
a.
Ante
nna
width
(
)
A
pr
a
c
ti
c
a
l
width
(
W
)
is
c
a
lcula
ted
f
or
a
n
e
f
f
e
c
ti
v
e
mi
c
r
os
tr
ip
a
ntenna
whic
h
lea
ds
to
obtain
be
tt
e
r
r
a
diation
pa
tt
e
r
n.
T
he
e
xpr
e
s
s
ion
to
c
a
lcula
te
the
a
ntenna
width
is
given
in
the
(
1)
.
=
2
√
2
+
1
(
1)
W
he
r
e
,
is
r
e
pr
e
s
e
nted
a
s
ve
locity
of
the
li
ght
(
3
×
10
8
/
)
,
r
e
lative
pe
r
mi
t
ti
vit
y
is
r
e
pr
e
s
e
nted
a
s
a
n
d
r
e
s
ona
ti
ng
f
r
e
que
nc
y
is
r
e
p
r
e
s
e
nted
a
s
.
b.
E
f
f
e
c
ti
ve
diele
c
tr
ic
c
ons
tant
(
)
T
he
e
f
f
e
c
ti
ve
d
iele
c
tr
ic
c
ons
tant
of
the
mi
c
r
os
tr
ip
a
ntenna
is
c
a
lcula
ted
us
ing
the
f
oll
owing
(
2
)
.
=
+
1
2
+
−
1
2
[
1
+
12
(
ℎ
/
]
−
1
/
2
(
2)
c.
Ante
nna
length
(
)
Ge
ne
r
a
ll
y,
the
width
a
nd
length
of
mi
c
r
os
tr
ip
a
nt
e
nna
is
identif
ied
by
s
e
lec
ti
ng
the
s
ub
s
tr
a
te.
T
he
e
qua
ti
on
(
3)
s
hows
the
e
f
f
e
c
ti
ve
length
of
the
pa
tc
h
us
e
d
in
the
a
ntenna
de
s
ign.
=
2
√
(
1
)
(
3)
d.
L
e
ngth
e
xtens
ion
(
∆
)
T
he
f
ields
in
the
pa
tch
e
dge
e
xpe
r
ienc
e
s
the
f
r
ingi
ng
while
de
s
igni
ng
the
a
ntenna
.
T
he
length
o
f
the
pa
th
is
incr
e
a
s
e
d
by
∆
on
both
s
ides
of
the
pa
tch,
b
e
c
a
us
e
of
the
f
r
ingi
ng
f
ields
a
long
the
pa
tch
lengt
h.
T
he
e
xtens
ion
of
the
length
is
given
in
the
(
4)
.
∆
=
0
.
412
ℎ
[
(
+
0
.
3
)
(
ℎ
+
0
.
264
)
(
−
0
.
258
)
(
ℎ
+
0
.
8
)
]
(
4)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
12
,
No.
1,
F
e
br
ua
r
y
2
022:
983
-
996
986
e.
P
a
tch
length
(
)
T
he
a
c
tual
pa
tch
length
is
de
ter
mi
ne
d
by
us
ing
the
(
5)
.
=
−
2
∆
(
5)
T
he
monopol
e
a
ntenna
ope
r
a
tes
a
t
the
W
ideba
nd
f
r
e
que
nc
y
but
r
e
tur
n
los
s
of
monopol
e
a
ntenna
is
low
that
a
f
f
e
c
ts
the
ove
r
a
ll
e
f
f
icie
nc
y.
T
he
r
e
f
or
e
,
the
de
s
ign
of
S
C
F
M
A
is
pr
opos
e
d
in
monopol
e
a
ntenna
to
im
pr
ove
the
ba
ndwidth.
3.
2.
De
s
ign
c
on
f
ig
u
r
at
ion
s
T
he
s
tr
uc
tur
e
of
S
ier
pins
ki
c
a
r
pe
t
f
r
a
c
tal
a
ntenna
i
s
de
s
igned
f
r
om
the
r
e
gular
M
icr
os
tr
ip
pa
tch
a
nd
it
is
ope
r
a
ted
thr
ough
dif
f
e
r
e
nt
it
e
r
a
ti
ons
to
ge
ne
r
a
te
the
mul
ti
ba
nd
c
ha
r
a
c
ter
is
ti
c
s
.
T
he
r
e
c
tangle
p
a
tch
s
ize
f
or
the
ba
s
e
c
a
s
e
is
20×
25
2
a
nd
the
mi
ddle
s
ub
-
s
qu
a
r
e
s
lot
in
the
s
ize
of
7×
7
mm
2
is
r
e
moved
a
s
s
hown
in
the
F
igur
e
1
.
Ne
xt
,
thi
s
S
ier
p
ins
ki
c
a
r
pe
t
f
r
a
c
tal
a
ntenna
is
mount
e
d
on
the
s
ubs
tr
a
te
with
the
th
ickne
s
s
of
1.
6
mm
F
R
4
s
ubs
t
r
a
te
a
nd
thi
s
F
R
4
s
ubs
tr
a
te
ha
s
los
s
tange
nt
(
)
of
0.
02
a
nd
r
e
lative
pe
r
mi
tt
ivi
ty
(
)
o
f
4.
4.
M
or
e
ove
r
,
the
pa
tch
a
nd
gr
ound
a
r
e
de
s
igned
by
us
ing
the
c
oppe
r
a
nd
the
gr
ound
plane
is
c
r
e
a
ted
with
the
s
ize
of
30×
7
mm
2
a
s
s
hown
in
F
igur
e
2.
T
hi
s
S
C
F
M
A
a
n
tenna
us
e
s
the
mi
c
r
os
tr
ip
f
e
e
d
li
ne
with
the
width
of
2.
5
mm
a
nd
length
of
10
mm
be
twe
e
n
th
e
pa
tch
a
nd
gr
ound
plane
.
M
or
e
ove
r
,
the
width
a
n
d
length
of
f
e
e
d
ins
e
t
f
or
the
mi
c
r
os
tr
ip
f
e
e
d
a
r
e
0.
5
mm
a
nd
3
mm
r
e
s
pe
c
ti
ve
ly.
F
igur
e
1.
S
t
r
uc
tur
e
o
f
S
C
F
M
A
f
o
r
ba
s
e
c
a
s
e
F
igur
e
2.
S
t
r
uc
tur
e
o
f
gr
ound
plane
W
he
r
e
,
the
length
a
nd
width
of
the
pa
tch
a
r
e
a
nd
;
the
length
a
nd
width
of
the
gr
ound
a
r
e
a
nd
;
the
length
a
nd
width
of
the
s
ubs
tr
a
te
a
r
e
a
nd
;
the
length
a
nd
width
of
the
f
e
e
d
a
r
e
a
nd
;
the
length
a
nd
width
of
the
f
e
e
d
ins
e
t
a
r
e
a
nd
;
the
length
a
nd
width
of
the
r
e
moved
s
lot
1
a
r
e
1
a
nd
1
.
I
n
the
f
i
r
s
t
i
ter
a
ti
on
of
S
C
F
M
A,
the
8
s
ub
-
r
e
c
tangle
s
of
the
S
C
F
M
A
a
r
e
a
ga
in
divi
de
d
int
o
9
s
ub
r
e
c
tangle
s
.
S
im
il
a
r
to
the
ba
s
e
c
a
s
e
,
the
mi
ddl
e
s
ub
s
qua
r
e
s
lot
s
a
r
e
r
e
moved
f
r
om
a
ll
8
s
ub
-
r
e
c
tangle
s
of
pa
tch
de
s
ign.
T
he
r
e
moved
s
lot
ha
s
the
s
ize
of
2×
2
2
ove
r
the
S
C
F
M
A
d
e
s
ign
whic
h
is
us
e
d
to
obtain
t
he
mul
ti
ba
nd
f
r
e
que
nc
y.
T
he
s
tr
uc
tur
e
of
S
C
F
M
A
f
o
r
f
i
r
s
t
it
e
r
a
ti
on
is
s
hown
in
F
igur
e
3
.
W
he
r
e
,
the
length
a
nd
width
o
f
the
r
e
moved
r
e
c
tan
gle
s
lot
2
a
r
e
2
a
nd
2
.
I
n
s
e
c
ond
it
e
r
a
ti
on
o
f
S
C
F
M
A,
the
8
s
ub
r
e
c
tangle
s
f
r
om
the
f
i
r
s
t
it
e
r
a
t
ion
a
r
e
a
ga
in
divi
de
d
int
o
9
s
ub
r
e
c
tangle
s
.
S
im
il
a
r
to
the
ba
s
e
c
a
s
e
,
the
mi
ddle
s
ub
s
qua
r
e
s
a
r
e
r
e
moved
f
r
om
a
ll
the
8
s
ub
r
e
c
tangle
s
of
pa
tch
de
s
ign.
T
he
r
e
moved
s
lot
ha
s
the
s
ize
of
0
.
8×
0.
8
mm
2
ove
r
the
S
C
F
M
A
de
s
ign
whic
h
is
us
e
d
to
ob
tain
the
mul
ti
ba
nd
f
r
e
que
nc
y.
T
he
s
tr
uc
tur
e
of
S
C
F
M
A
f
or
s
e
c
ond
it
e
r
a
ti
on
is
s
hown
in
F
igur
e
4.
W
he
r
e
,
the
length
a
nd
widt
h
of
the
r
e
moved
r
e
c
tangle
s
lot
3
a
r
e
3
a
nd
3
.
Addit
ionally,
t
he
f
a
br
ica
ted
de
s
ign
o
f
S
C
F
M
A
a
ntenna
is
s
hown
in
F
igur
e
5.
T
he
pa
r
a
mete
r
va
lues
of
the
pr
opos
e
d
de
s
ign
a
r
e
given
in
T
a
ble
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Sier
pins
k
i
c
ar
pe
t
fr
ac
tal
monopole
antenna
for
ult
r
a
-
w
ideband
appli
c
ati
o
ns
(
M
e
dhal
B
har
athr
aj
K
umar
)
987
F
igur
e
3.
S
t
r
uc
tur
e
o
f
S
C
F
M
A
f
o
r
f
ir
s
t
it
e
r
a
ti
on
F
igur
e
4.
S
t
r
uc
tur
e
o
f
S
C
F
M
A
f
o
r
s
e
c
ond
it
e
r
a
ti
on
(
a
)
(
b)
(
c
)
(
d)
F
igur
e
5.
F
a
br
ica
ted
S
C
F
M
A
a
ntenna
:
(
a
)
ba
s
e
c
a
s
e
,
(
b
)
f
i
r
s
t
it
e
r
a
ti
on
,
(
c
)
s
e
c
ond
it
e
r
a
ti
on
,
a
nd
(
d)
ba
c
k
view
T
a
ble
1.
P
a
r
a
mete
r
va
lues
of
S
C
F
M
A
de
s
ign
P
a
r
a
me
te
r
V
a
lu
e
P
a
r
a
me
te
r
V
a
lu
e
P
a
r
a
me
te
r
V
a
lu
e
25
mm
20
mm
7
mm
30
mm
45
mm
30
mm
1.6
mm
10
mm
2.5
mm
3
mm
0.5
mm
1
7
mm
1
7
mm
2
2
mm
2
2
mm
3
0.8
mm
3
0.8
mm
-
-
3.
3.
M
icr
os
t
r
ip
li
n
e
f
e
e
d
I
n
mi
c
r
os
tr
ip
l
ine
f
e
e
d
,
the
c
onduc
ti
ng
s
tr
ip
o
f
mi
c
r
os
tr
ip
pa
tch
is
dir
e
c
tl
y
c
onne
c
ted
to
the
e
dge
of
mi
c
r
os
tr
ip
pa
th
a
s
s
hown
in
F
igur
e
4.
T
he
length
a
nd
width
o
f
the
mi
c
r
os
tr
ip
li
ne
f
e
e
d
c
onne
c
ted
with
the
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
12
,
No.
1,
F
e
br
ua
r
y
2
022:
983
-
996
988
S
C
F
M
A
a
r
e
10
mm
a
nd
2.
5
mm
r
e
s
pe
c
ti
ve
ly.
T
he
main
a
dva
ntage
of
us
ing
the
mi
c
r
os
tr
ip
li
ne
f
e
e
d
is
that
the
f
e
e
d
a
nd
mi
c
r
os
tr
ip
a
r
e
a
tt
a
c
he
d
in
the
s
a
me
a
nd
it
is
us
e
d
to
de
s
ign
f
lat
s
tr
uc
tu
r
e
.
3.
4.
P
ar
a
m
e
t
r
ic
s
t
u
d
y
of
t
h
e
S
CF
M
A
d
e
s
ign
T
he
de
tailed
inf
o
r
mation
of
the
S
C
F
M
A
de
s
ign
a
n
d
wide
ba
nd
c
ha
r
a
c
ter
is
ti
c
s
a
r
e
a
na
lyze
d
us
ing
thi
s
pa
r
a
metr
ic
s
tudy.
T
he
ge
ometr
ica
l
a
nd
e
lec
tr
ica
l
pr
ope
r
ti
e
s
a
f
f
e
c
t
the
c
ha
r
a
c
ter
is
ti
c
s
of
the
wide
ba
nd
a
ntenna
.
T
he
c
ons
tant
pa
r
a
mete
r
s
in
the
S
C
F
M
A
de
s
ign
a
r
e
the
dim
e
ns
ions
of
pa
tch,
gr
ound
,
s
ubs
tr
a
te,
f
e
e
d,
a
nd
f
e
e
d
li
ne
.
I
n
thi
s
S
C
F
M
A,
the
f
r
a
c
tal
s
tr
uc
tur
e
s
a
r
e
d
e
ve
loped
to
obtain
the
wide
ba
nd
f
r
e
que
nc
ies
.
He
nc
e
,
the
dis
s
im
il
a
r
it
ies
in
the
S
C
F
M
A
de
s
ign
c
r
e
a
tes
the
c
ha
nge
s
in
the
r
e
tur
n
los
s
,
v
o
lt
a
ge
s
tanding
wa
ve
r
a
ti
o
(
VSWR
)
a
nd
im
pe
da
nc
e
mi
s
matc
hing
pr
ope
r
ti
e
s
a
s
s
hown
in
F
igur
e
2
to
F
igu
r
e
4
.
M
or
e
ove
r
,
the
r
e
t
ur
n
los
s
is
im
pr
ove
d
in
highe
r
f
r
e
que
nc
ies
a
nd
we
a
ke
ne
d
lowe
r
f
r
e
que
nc
y
due
to
the
inc
r
e
ment
in
r
e
lative
pe
r
mi
tt
ivi
ty.
T
he
r
e
lative
pe
r
mi
tt
ivi
ty
is
s
e
lec
ted
a
s
4.
4
f
o
r
S
C
F
M
A
de
s
ign
be
c
a
us
e
of
it
s
be
tt
e
r
r
e
tur
n
los
s
in
higher
f
r
e
que
nc
ies
.
T
he
higher
it
e
r
a
ti
ons
of
S
ie
r
pi
ns
ki
C
a
r
pe
t
f
r
a
c
tal
s
tr
uc
tur
e
a
r
e
us
e
d
in
the
m
icr
os
tr
ip
pa
th
a
ntenna
f
or
incr
e
a
s
ing
the
ope
r
a
ti
ng
ba
ndwidth
of
the
S
C
F
M
A
de
s
ign.
T
he
r
e
f
o
r
e
,
the
S
C
F
M
A
de
s
ig
n
obtains
UW
B
f
r
e
que
nc
ies
ba
s
e
d
on
the
thr
e
e
di
f
f
e
r
e
nt
de
s
igns
s
uc
h
a
s
ba
s
e
c
a
s
e
,
f
ir
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
i
ter
a
ti
on.
T
he
e
lec
tr
ic
a
nd
magne
ti
c
f
ield
f
or
the
th
r
e
e
de
s
igns
of
S
C
F
M
A
a
r
e
given
in
the
F
igur
e
s
6
a
nd
7
r
e
s
pe
c
ti
ve
ly.
(
a
)
(
b)
(
c
)
F
igur
e
6.
E
lec
tr
ic
f
ield
f
o
r
S
C
F
M
A
de
s
ign
:
(
a
)
b
a
s
e
c
a
s
e
,
(
b)
f
ir
s
t
it
e
r
a
ti
on,
a
nd
(
c
)
s
e
c
ond
it
e
r
a
ti
on
(
a
)
(
b)
(
c
)
F
igur
e
7.
M
a
gne
ti
c
f
ield
f
or
S
C
F
M
A
de
s
ign
:
(
a
)
ba
s
e
c
a
s
e
,
(
b)
f
i
r
s
t
it
e
r
a
ti
on
,
a
nd
(
c
)
s
e
c
ond
it
e
r
a
ti
on
4.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
T
he
r
e
s
ult
s
a
nd
dis
c
us
s
ion
of
the
pr
opos
e
d
S
C
F
M
A
de
s
ign
is
dis
c
us
s
e
d
in
thi
s
s
e
c
ti
on.
T
he
pr
opos
e
d
S
C
F
M
A
im
pleme
ntation
a
nd
s
im
ulation
a
r
e
c
a
r
r
ie
d
out
us
ing
the
high
-
f
r
e
que
nc
y
s
tr
uc
tu
r
e
s
im
ulator
(
HFS
S
)
whic
h
is
ope
r
a
ted
in
a
W
indows
8
ope
r
a
ti
ng
s
ys
tem
with
I
ntel
c
or
e
i3
p
r
oc
e
s
s
or
a
nd
4
GB
R
A
M
.
T
his
pr
opos
e
d
S
C
F
M
A
de
s
ign
is
a
c
c
ompl
is
he
d
in
thr
e
e
dif
f
e
r
e
nt
de
s
igns
s
uc
h
a
s
ba
s
e
c
a
s
e
,
f
i
r
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
a
s
we
ll
a
s
the
dim
e
ns
ions
of
thi
s
S
C
F
M
A
de
s
ign
is
given
in
the
T
a
ble
1
.
T
he
pe
r
f
or
manc
e
of
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Sier
pins
k
i
c
ar
pe
t
fr
ac
tal
monopole
antenna
for
ult
r
a
-
w
ideband
appli
c
ati
o
ns
(
M
e
dhal
B
har
athr
aj
K
umar
)
989
the
S
C
F
M
A
de
s
ign
is
a
na
lyze
d
in
te
r
ms
of
r
e
tu
r
n
los
s
,
VSWR
,
r
a
diation
pa
tt
e
r
n
a
nd
g
a
in
.
M
or
e
ove
r
,
the
r
e
s
ult
s
of
the
S
C
F
M
A
de
s
ign
a
r
e
a
na
lyze
d
us
ing
both
the
s
im
ulation
a
nd
f
a
b
r
ica
ti
on
whic
h
a
r
e
de
s
c
r
ibed
a
s
f
oll
ows
:
4.
1.
Re
s
u
lt
s
f
r
om
s
im
u
la
t
ion
T
his
s
e
c
ti
on
s
hows
the
r
e
s
ult
s
take
n
f
r
om
the
s
im
ulation
us
ing
HFS
S
s
of
twa
r
e
.
He
r
e
,
the
r
e
s
ult
s
a
r
e
given
f
or
S
C
F
M
A
de
s
ign
with
ba
s
e
c
a
s
e
,
f
i
r
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
.
4.
1.
1.
Re
t
u
r
n
los
s
R
e
tur
n
los
s
is
the
r
e
f
lec
ti
on
of
s
ignal’
s
powe
r
whe
n
the
s
ignal
r
e
f
lec
ti
on
is
e
nter
e
d
in
the
tr
a
ns
mi
s
s
ion
li
ne
a
nd
thi
s
r
e
tur
n
los
s
is
e
xpr
e
s
s
e
d
in
the
(
6
)
:
11
=
−
20
log
|
Γ
|
(
6
)
w
he
r
e
the
r
e
f
lec
ti
on
c
oe
f
f
icie
nt
is
r
e
pr
e
s
e
nted
a
s
Γ
that
is
the
r
a
t
io
be
twe
e
n
incide
nt
wa
ve
’
s
a
mpl
it
u
de
a
nd
r
e
f
lec
ted
wa
ve
’
s
a
mpl
it
ude
.
T
he
r
e
tur
n
los
s
f
or
the
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
,
f
i
r
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
a
r
e
s
hown
in
the
F
igur
e
s
8,
9
a
nd
10
r
e
s
pe
c
ti
ve
ly.
T
he
r
e
s
ona
nt
f
r
e
que
nc
y
of
the
S
C
F
M
A
de
s
ign
in
ba
s
e
c
a
s
e
is
3.
4
GH
z
with
a
ba
ndwidth
of
2.
6
-
4.
0
GH
z
f
or
the
r
e
tur
n
los
s
va
lue
-
16.
0931
dB
.
S
im
il
a
r
ly,
the
r
e
s
ona
nt
f
r
e
que
n
c
y
of
the
S
C
F
M
A
de
s
ign
in
f
ir
s
t
it
e
r
a
ti
on
is
3.
2
GH
z
with
a
b
a
ndwidth
of
2.
5
-
4.
3
GH
z
f
o
r
the
r
e
t
ur
n
los
s
va
lue
-
21.
0295
dB
.
How
e
ve
r
,
the
S
C
F
M
A
de
s
ign
in
s
e
c
ond
it
e
r
a
ti
on
a
c
hieve
s
two
dif
f
e
r
e
nt
r
e
s
ona
nt
f
r
e
que
nc
ies
whic
h
a
r
e
2.
8
GH
z
a
nd
3.
8
GH
z
in
t
he
ba
ndwidth
o
f
2
.
4
-
4.
4
GH
z
.
T
he
r
e
tur
n
los
s
of
S
C
F
M
A
de
s
ign
in
s
e
c
o
nd
it
e
r
a
ti
on
obtains
two
di
f
f
e
r
e
nt
r
e
tur
n
los
s
with
r
e
s
pe
c
t
to
the
two
f
r
e
que
nc
ies
-
48.
4897
dB
a
nd
-
46.
7584
dB
.
F
igur
e
s
8
to
10
s
how
the
r
e
tur
n
los
s
of
ba
s
e
c
a
s
e
whic
h
is
le
s
s
whe
n
c
ompar
e
d
to
the
other
de
s
igns
s
uc
h
a
s
f
ir
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
.
F
igur
e
8.
R
e
tur
n
los
s
of
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
F
igur
e
9.
R
e
tur
n
los
s
of
S
C
F
M
A
a
t
f
ir
s
t
it
e
r
a
ti
on
F
igur
e
10.
R
e
tur
n
los
s
of
S
C
F
M
A
a
t
s
e
c
ond
it
e
r
a
ti
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
12
,
No.
1,
F
e
br
ua
r
y
2
022:
983
-
996
990
4.
1.
2.
VSWR
VSWR
is
the
r
a
ti
o
be
twe
e
n
the
maximum
volt
a
ge
(
)
a
nd
mi
nim
um
volt
a
ge
(
)
of
the
a
ntenna
whic
h
is
e
xpr
e
s
s
e
d
in
the
(
7
)
.
=
=
|
1
+
Γ
|
|
1
−
Γ
|
(
7)
F
igur
e
s
11,
12
a
nd
13
s
hows
the
VSWR
of
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
,
f
ir
s
t
it
e
r
a
ti
on
a
n
d
s
e
c
ond
it
e
r
a
ti
on
r
e
s
pe
c
ti
ve
ly.
T
he
VSWR
f
o
r
the
p
r
opos
e
d
S
C
F
M
A
in
ba
s
e
c
a
s
e
a
nd
f
ir
s
t
it
e
r
a
ti
on
a
r
e
1.
5
a
nd
1.
8
r
e
s
pe
c
ti
ve
ly.
How
e
ve
r
,
the
S
C
F
M
A
in
s
e
c
ond
it
e
r
a
ti
on
c
r
e
a
tes
two
dif
f
e
r
e
nt
VSWR
whic
h
a
r
e
1.
7
a
nd
1.
6
.
F
igur
e
11
to
F
igur
e
13
s
hows
that
the
V
S
W
R
of
a
ll
3
de
s
igns
of
S
C
F
M
A
a
r
e
les
s
than
2
whic
h
s
hows
that
it
pr
ovides
be
tt
e
r
r
a
diation
pa
tt
e
r
ns
.
He
nc
e
,
the
pr
op
os
e
d
S
C
F
M
A
obtains
be
tt
e
r
VSWR
ba
s
e
d
on
a
n
e
f
f
e
c
ti
ve
matc
hing
be
twe
e
n
the
f
r
a
c
tal
a
ntenna
a
nd
mi
c
r
o
s
tr
ip
f
e
e
d
l
ine
a
s
we
ll
a
s
the
les
s
e
r
VS
W
R
im
p
r
ove
s
the
f
r
e
que
nc
y
a
nd
mi
nim
ize
s
the
los
s
in
the
t
r
a
ns
mi
tt
e
d
powe
r
.
F
igur
e
11.
VSWR
of
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
F
igur
e
12.
VSWR
of
S
C
F
M
A
a
t
f
ir
s
t
it
e
r
a
ti
on
F
igur
e
13.
VSWR
of
S
C
F
M
A
a
t
s
e
c
ond
it
e
r
a
ti
on
4.
1.
3.
Radi
a
t
ion
p
at
t
e
r
n
T
he
r
a
diation
pa
tt
e
r
n
is
c
ons
ider
e
d
a
s
one
of
t
he
main
pa
r
a
mete
r
s
in
the
a
ntenna
de
s
ign
that
il
lus
tr
a
tes
the
r
a
ti
o
o
f
powe
r
r
a
diate
d
to
input
po
we
r
.
T
h
is
r
a
diation
pa
tt
e
r
n
a
ls
o
c
ons
ider
s
diele
c
tr
ic
los
s
e
s
a
nd
c
onduc
ti
on.
T
he
r
a
diation
pa
tt
e
r
n
of
the
S
C
F
M
A
f
or
ba
s
e
c
a
s
e
,
f
i
r
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
a
r
e
s
hown
in
the
F
igur
e
14,
15
a
nd
16
r
e
s
pe
c
ti
ve
ly.
He
r
e
,
the
r
a
diation
pa
tt
e
r
n
is
c
a
lcula
ted
by
va
r
ying
the
a
ngle
(
)
f
r
om
-
180
°
to+180
°
.
T
he
r
a
diation
pa
tt
e
r
n
p
r
e
s
e
nted
in
the
F
igur
e
s
14,
15
a
nd
16
s
hows
that
the
S
C
F
M
A
a
c
hieve
s
the
be
tt
e
r
r
a
diation
pa
tt
e
r
n
in
the
ba
ndw
idt
h
r
a
nge
of
2
.
6
-
4.
0
GH
z
,
2
.
5
-
4.
3
GH
Z
a
nd
2
.
4
-
4.
4
GH
z
r
e
s
pe
c
ti
ve
ly.
T
he
c
a
lcula
ted
r
a
diation
pa
tt
e
r
n
s
hows
t
ha
t
the
S
C
F
M
A
de
s
ign
obtains
a
r
e
li
a
ble
omni
dir
e
c
ti
ona
l
r
a
diation
pa
tt
e
r
n
in
both
the
lowe
r
a
nd
higher
f
r
e
que
nc
ies
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
Sier
pins
k
i
c
ar
pe
t
fr
ac
tal
monopole
antenna
for
ult
r
a
-
w
ideband
appli
c
ati
o
ns
(
M
e
dhal
B
har
athr
aj
K
umar
)
991
F
igur
e
14.
R
a
diation
pa
tt
e
r
n
of
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
F
igur
e
15.
R
a
diation
pa
tt
e
r
n
of
S
C
F
M
A
a
t
f
i
r
s
t
it
e
r
a
ti
on
F
igur
e
16.
R
a
diation
pa
tt
e
r
n
of
S
C
F
M
A
a
t
s
e
c
ond
it
e
r
a
ti
on
4.
1.
4.
Gai
n
T
he
r
a
t
io
be
twe
e
n
the
a
ntenna
’
s
output
powe
r
a
n
d
a
ntenna
’
s
tot
a
l
input
powe
r
is
de
f
ined
a
s
ga
in.
T
he
input
powe
r
to
the
a
ntenna
is
the
tot
a
l
powe
r
whic
h
include
s
ove
r
a
ll
los
s
e
s
powe
r
a
nd
r
a
diate
d
powe
r
.
T
he
ga
in
o
f
the
a
ntenna
is
e
xpr
e
s
s
e
d
in
the
(
8
)
.
=
ℎ
ℎ
(
8)
F
igur
e
s
17,
18
a
nd
19
s
hows
the
ga
in
o
f
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
,
f
ir
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
r
e
s
pe
c
ti
ve
ly.
F
igur
e
s
17,
18
a
nd
19
s
hows
that
the
va
lue
of
ga
in
a
r
e
1
.
97
dB
,
1
.
90
dB
a
nd
2.
94
dB
r
e
s
pe
c
ti
v
e
ly.
T
he
a
ntenna
with
highe
r
ga
in
is
us
e
d
to
incr
e
a
s
e
the
l
in
e
of
s
ight
pa
th.
He
nc
e
,
the
S
C
F
M
A
de
s
ign
pr
ovide
s
higher
ba
ndwidth
s
uc
h
a
s
2.
6
-
4.
0
GH
z
,
2.
5
-
4.
3
GH
Z
a
nd
2.
4
-
4.
4
GH
z
f
or
ba
s
e
c
a
s
e
,
f
ir
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
r
e
s
pe
c
ti
ve
ly.
4.
2.
Re
s
u
lt
s
f
r
om
f
ab
r
ica
t
ion
F
igur
e
s
20,
21
a
nd
22
s
hows
the
r
e
tu
r
n
los
s
f
or
t
he
f
a
br
ica
ted
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
,
f
i
r
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
r
e
s
pe
c
ti
ve
ly.
T
he
r
e
tur
n
los
s
f
or
the
f
a
br
ica
ted
S
C
F
M
A
de
s
ign
a
t
ba
s
e
c
a
s
e
a
nd
f
ir
s
t
it
e
r
a
ti
on
is
-
16.
0931
dB
a
nd
-
21.
0295
dB
r
e
s
pe
c
ti
ve
ly.
Addi
ti
ona
ll
y,
thi
s
f
a
br
ica
ted
S
C
F
M
A
de
s
igned
f
or
the
s
e
c
ond
it
e
r
a
ti
on
gives
two
dif
f
e
r
e
nt
r
e
tur
n
los
s
e
s
whic
h
a
r
e
-
48.
4897
dB
a
nd
-
46.
7584
dB
.
T
his
r
e
tur
n
los
s
a
na
lys
is
pr
ove
s
that
the
f
a
br
ica
ted
S
C
F
M
A
de
s
ign
is
s
im
il
a
r
to
the
s
im
ulation
r
e
s
ult
s
.
T
he
r
e
s
ult
s
t
a
k
e
n
f
r
om
the
f
a
br
ica
ti
on
de
s
ign
is
a
na
lyze
d
in
th
is
s
e
c
ti
on.
H
e
r
e
,
the
r
e
s
ult
s
a
r
e
a
na
lyze
d
in
ter
ms
of
r
e
tur
n
los
s
,
VSWR
a
nd
r
a
diation
pa
tt
e
r
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
12
,
No.
1,
F
e
br
ua
r
y
2
022:
983
-
996
992
F
igur
e
17.
Ga
in
o
f
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
F
igur
e
18.
Ga
in
o
f
S
C
F
M
A
a
t
f
ir
s
t
it
e
r
a
ti
on
F
igur
e
19.
Ga
in
o
f
S
C
F
M
A
a
t
s
e
c
ond
it
e
r
a
ti
on
F
igur
e
20.
R
e
tur
n
los
s
of
f
a
br
ica
ted
S
C
F
M
A
a
t
ba
s
e
c
a
s
e
F
igur
e
21.
R
e
tur
n
los
s
of
f
a
br
ica
ted
S
C
F
M
A
a
t
f
i
r
s
t
it
e
r
a
ti
on
F
igur
e
22.
R
e
tur
n
los
s
of
f
a
br
ica
ted
S
C
F
M
A
a
t
s
e
c
ond
it
e
r
a
ti
on
T
he
VSWR
r
e
s
pons
e
of
f
a
br
ica
ted
S
C
F
M
A
a
t
b
a
s
e
c
a
s
e
,
f
ir
s
t
it
e
r
a
ti
on
a
nd
s
e
c
ond
it
e
r
a
ti
on
a
r
e
s
hown
in
the
F
igur
e
s
23,
24
a
nd
25
r
e
s
pe
c
ti
ve
ly.
T
he
F
igur
e
s
23
to
25
s
hows
that
the
VSWR
f
or
the
ba
s
e
c
a
s
e
a
nd
f
i
r
s
t
it
e
r
a
ti
on
of
the
f
a
br
ica
ted
S
C
F
M
A
a
r
e
1.
5
a
nd
1
.
8
r
e
s
p
e
c
ti
ve
ly.
Ne
xt,
the
s
e
c
ond
it
e
r
a
ti
on
o
f
f
a
br
ica
ted
S
C
F
M
A
c
r
e
a
tes
two
dif
f
e
r
e
nt
VSWR
r
a
nge
s
s
uc
h
a
s
1.
7
a
nd
1.
6
.
F
r
om
thi
s
VSWR
a
n
a
lys
is
,
it
c
onc
luded
that
the
VSWR
is
les
s
than
2
f
or
a
ll
the
thr
e
e
ba
ndwidth
va
lues
that
a
r
e
2.
6
-
4.
0
GH
z
,
2
.
5
-
4.
3
GH
z
a
nd
2.
4
-
4.
4
GH
z
whic
h
he
lps
to
a
void
the
int
e
r
f
e
r
e
nc
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.