T
E
L
KO
M
N
I
KA
T
e
lec
om
m
u
n
icat
ion
,
Com
p
u
t
i
n
g,
E
lec
t
r
on
ics
an
d
Cont
r
ol
Vol.
18
,
No
.
4
,
Augus
t
2020
,
pp.
1719~1730
I
S
S
N:
1693
-
6930,
a
c
c
r
e
dit
e
d
F
ir
s
t
G
r
a
de
by
Ke
me
nr
is
tekdikti
,
De
c
r
e
e
No:
21/E
/KP
T
/2018
DO
I
:
10.
12928/
T
E
L
KO
M
NI
KA
.
v18i4.
14988
1719
Jou
r
n
al
h
omepage
:
ht
tp:
//
jour
nal.
uad
.
ac
.
id/
index
.
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E
L
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OM
N
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S
imu
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io
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ech
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q
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,
A
l
-
E
s
raa
U
n
i
v
ers
i
t
y
Co
l
l
e
g
e,
Iraq
Ar
t
icle
I
n
f
o
AB
S
T
RA
CT
A
r
ti
c
le
h
is
tor
y
:
R
e
c
e
ived
De
c
13
,
2019
R
e
vis
e
d
J
a
n
6,
2020
Ac
c
e
pted
J
a
n
19,
2020
In
t
h
i
s
p
ap
er,
a
t
u
n
eab
l
e
r
ect
a
n
g
u
l
ar
m
i
cro
s
t
r
i
p
p
at
c
h
a
n
t
e
n
n
a
(MPA
)
i
s
s
i
mu
l
a
t
ed
an
d
o
p
t
i
m
i
zed
t
o
o
p
era
t
e
i
n
f
o
u
r
freq
u
en
c
y
b
an
d
s
o
f
t
h
e
n
ex
t
g
en
era
t
i
o
n
o
f
w
i
rel
e
s
s
c
o
mmu
n
i
ca
t
i
o
n
s
y
s
t
em
s
.
T
h
e
p
r
o
p
o
s
e
d
d
e
s
i
g
n
i
n
c
o
rp
o
rat
e
s
a
co
p
p
er
rad
i
a
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i
n
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p
at
ch
w
i
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fo
u
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mp
l
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ed
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rap
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s
t
r
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p
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fo
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t
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g
p
u
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p
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h
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reco
n
f
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g
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ra
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l
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rface
i
m
p
ed
a
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o
f
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h
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e
can
eas
i
l
y
b
e
al
t
ere
d
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p
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g
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l
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p
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ed
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l
t
a
g
e
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e
t
h
e
o
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erat
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cy
b
a
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d
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f
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p
o
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ed
a
n
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ech
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l
o
g
y
(CS
T
)
m
i
cro
w
av
e
s
t
u
d
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o
(MW
S).
Freq
u
e
n
cy
s
e
l
ect
i
v
e
s
u
rfaces
(FSSs
)
are
i
n
t
r
o
d
u
ced
i
n
o
r
d
er
t
o
i
m
p
ro
v
e
t
h
e
rad
i
at
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o
n
p
arame
t
ers
o
f
t
h
e
a
n
t
en
n
a.
T
h
e
o
p
era
t
i
n
g
freq
u
e
n
cy
b
a
n
d
o
f
t
h
e
t
u
n
eab
l
e
rect
a
n
g
u
l
ar
MPA
i
n
creas
e
s
d
i
rec
t
l
y
as
t
h
e
ap
p
l
i
ed
D
C
v
o
l
t
a
g
e
b
i
a
s
i
s
i
n
creas
e
d
.
Bas
ed
o
n
t
h
e
s
i
mu
l
a
t
i
o
n
res
u
l
t
s
,
a
t
u
n
ea
b
l
e
rec
t
an
g
u
l
ar
MPA
p
l
ace
d
b
et
w
een
t
w
o
F
SSs
i
s
p
ro
p
o
s
ed
fo
r
fi
ft
h
-
g
e
n
erat
i
o
n
ap
p
l
i
ca
t
i
o
n
s
.
K
e
y
w
o
r
d
s
:
5G
60
GH
z
FSS
s
G
r
a
phe
ne
M
icr
os
tr
ip
p
a
tch
a
ntenna
T
une
a
ble
a
ntenna
Th
i
s
i
s
a
n
o
p
en
a
c
ces
s
a
r
t
i
c
l
e
u
n
d
e
r
t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e
.
C
or
r
e
s
pon
din
g
A
u
th
or
:
Nida
l
Qa
s
e
m,
De
pa
r
tm
e
nt
of
E
lec
tr
onics
a
nd
C
omm
unica
ti
ons
E
nginee
r
ing,
F
a
c
ult
y
of
E
nginee
r
ing
,
Al
-
Ahliyya
Amman
Unive
r
s
it
y,
Z
ip
-
c
ode
(
P
os
tal
Addr
e
s
s
)
:
19328,
Amman,
J
or
da
n.
E
mail:
Ne
.
qa
s
e
m@a
mm
a
nu.
e
du.
jo
1.
I
NT
RODU
C
T
I
ON
E
nor
mous
de
ve
lopm
e
nts
in
c
omm
unica
ti
on
tec
hnology,
e
s
p
e
c
ially
in
wir
e
les
s
c
omm
unica
ti
on,
ha
ve
take
n
plac
e
in
r
e
c
e
nt
de
c
a
de
s
.
W
it
h
thes
e
c
ha
nge
s
in
mi
nd
,
the
ne
twor
k
ope
r
a
tor
s
ha
ve
int
r
oduc
e
d
a
dva
nc
e
d
ge
ne
r
a
ti
ons
f
r
om
ti
me
to
ti
me
.
F
oll
owing
the
f
i
r
s
t
-
ge
ne
r
a
ti
on
mobi
le
ne
twor
k
in
the
1980s
,
the
s
e
c
ond
ge
ne
r
a
ti
on
a
ppe
a
r
e
d
in
the
1990s
,
the
thi
r
d
i
n
2001,
a
nd
the
f
ou
r
th
in
2010
.
T
he
ne
xt
t
a
r
ge
t
is
the
im
pleme
ntation
of
the
f
if
th
-
ge
ne
r
a
ti
on
ne
twor
k
,
whic
h
is
e
xpe
c
ted
to
be
gin
in
2020
[
1]
.
W
it
h
the
incr
e
a
s
e
in
ne
twor
k
a
ppli
c
a
ti
ons
a
nd
de
mand
f
o
r
higher
da
ta
r
a
t
e
s
,
s
witching
to
higher
f
r
e
que
nc
ies
is
the
on
l
y
opti
on
f
or
a
voidi
ng
da
ta
c
onge
s
ti
on
that
r
e
mains
to
wir
e
les
s
tec
hnology
ope
r
a
tor
s
.
Highe
r
f
r
e
que
nc
y
ba
nds
of
f
e
r
higher
da
ta
r
a
tes
togethe
r
with
the
s
pe
c
tr
a
l
e
f
f
icie
nc
y
that
is
c
ur
r
e
ntl
y
r
e
quir
e
d
.
I
t
is
e
xpe
c
t
e
d
to
r
e
a
c
h
r
e
a
l
gigabyte
s
bit
r
a
te
in
the
mi
ll
im
e
t
r
e
-
wa
ve
(
mm
-
wa
ve
)
s
pe
c
tr
um
in
a
r
a
nge
be
twe
e
n
30
a
nd
3
00
GH
z
.
I
n
the
mm
-
wa
ve
r
a
nge
,
the
pr
os
pe
c
t
o
f
us
ing
the
u
nli
c
e
ns
e
d
f
r
e
que
nc
y
ba
nd
f
r
om
57
to
64
GH
z
f
or
I
ndus
tr
ial,
S
c
ientif
ic,
a
nd
M
e
dica
l
(
I
S
M
)
a
ppli
cat
ions
is
pr
om
is
ing
[
2,
3]
.
T
his
f
r
e
que
nc
y
ba
nd
ha
s
a
tt
r
a
c
ted
incr
e
a
s
e
d
int
e
r
e
s
t
a
nd
a
tt
e
nti
on
in
the
r
e
s
e
a
r
c
h
c
omm
unit
y
be
c
a
us
e
of
it
s
pos
s
ibl
e
pr
a
c
ti
c
a
l
a
dva
ntage
s
f
or
f
utur
e
a
ppli
c
a
ti
ons
.
T
he
c
r
e
a
ti
on
of
ne
w
tec
hnologi
e
s
in
thi
s
f
r
e
que
nc
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1719
-
1730
1720
ba
nd
ha
s
r
e
s
u
lte
d
in
many
high
-
s
pe
e
d
wir
e
les
s
innovations
,
including
high
-
de
f
ini
ti
on
video
s
t
r
e
a
mi
ng,
high
-
s
pe
e
d
int
e
r
ne
t,
high
-
de
f
ini
ti
on
mul
ti
media
int
e
r
f
a
c
e
s
,
wir
e
les
s
gigabit
E
the
r
ne
t,
a
nd
a
utom
o
ti
ve
r
a
da
r
[
4
]
.
T
he
pr
im
a
r
y
c
ha
ll
e
nge
in
the
mm
-
wa
ve
r
e
gim
e
is
i
nc
r
e
a
s
e
d
pa
th
los
s
e
s
,
whic
h
mea
n
that
the
s
ignal
is
e
a
s
il
y
a
tt
e
nua
ted
;
the
s
ignal
may
a
l
s
o
f
a
de
dur
ing
r
a
inf
a
ll
.
T
he
r
e
f
or
e
,
mm
-
wa
ve
s
a
r
e
pr
e
f
e
r
e
nti
a
ll
y
us
e
d
to
pr
ovide
high
da
ta
tr
a
ns
f
e
r
r
a
tes
in
s
hor
t
dis
tanc
e
c
omm
unica
ti
on.
A
c
r
it
ica
l
e
leme
nt
f
o
r
s
uc
h
a
ppli
c
a
tio
ns
is
a
c
ompac
t
a
ntenna
,
whic
h
s
hould
be
a
ble
to
pr
o
vide
r
e
a
s
ona
ble
ga
in,
high
r
a
diation
e
f
f
icie
nc
y,
a
nd
wide
ope
r
a
ti
ng
f
r
e
que
nc
y
ba
ndwidth
[
5,
6
]
.
M
a
ny
tec
h
niques
c
a
n
be
us
e
d
to
a
c
hieve
tunea
ble
a
ntenna
s
,
i
nc
ludi
ng
r
a
dio
f
r
e
que
nc
y
m
icr
oe
lec
tr
omec
ha
nic
a
l
s
ys
tem
s
witche
s
,
va
r
a
c
tor
s
witche
s
,
P
I
N
diodes
,
f
ield
e
f
f
e
c
t
tr
a
ns
is
tor
s
witche
s
,
li
ght
-
a
c
ti
va
ted
s
witche
s
,
or
tunea
ble
mate
r
ials
,
whic
h
may
be
tuned
by
a
pplyi
ng
the
a
pp
r
opr
i
a
te
li
ght,
magne
ti
c
,
mec
ha
nica
l,
t
he
r
mal
,
o
r
e
lec
tr
ica
l
bias
[
7
]
.
Gr
a
phe
ne
,
a
c
onj
uga
ted
c
a
r
bon
s
he
e
t
s
tr
uc
tur
e
d
in
a
two
-
dim
e
ns
ional
he
xa
gona
l
latti
c
e
,
e
na
bles
mul
ti
-
f
unc
ti
ona
l
s
ignal
e
mi
s
s
ion,
t
r
a
ns
mi
s
s
ion,
mo
dulation,
a
nd
de
tec
ti
on
by
de
vice
s
that
f
e
a
tur
e
hig
h
s
pe
e
d,
s
mall
s
ize
,
a
nd
pa
r
ti
c
ular
ly
low
los
s
.
Gr
a
phe
ne
po
s
s
e
s
s
e
s
a
r
e
c
onf
igur
a
ble
s
ur
f
a
c
e
i
mpeda
nc
e
that
c
a
n
b
e
va
r
ied
by
a
pplyi
ng
a
DC
volt
a
ge
b
ias
to
the
g
r
a
phe
ne
s
he
e
t,
whic
h
c
a
n
be
us
e
d
a
s
a
n
a
lt
e
r
na
ti
ve
to
e
l
e
c
tr
onic
c
omponents
in
de
s
igni
ng
tunea
ble
a
ntenna
s
.
An
a
n
tenna
may
be
tuned
by
c
ha
nging
it
s
e
lec
tr
ic
a
l
lengt
h,
whic
h
c
a
n
be
a
c
c
ompl
is
he
d
by
incr
e
a
s
ing
or
de
c
r
e
a
s
ing
the
c
ur
r
e
nt
dis
tr
ibut
ion
ove
r
the
r
a
diating
pa
tch
of
the
a
ntenna
.
Alter
na
ti
ve
ly
,
the
phys
ica
l
length
o
f
the
a
ntenna
may
be
inc
r
e
a
s
e
d
by
a
dding
a
n
a
ddi
ti
ona
l
s
ha
pe
dir
e
c
tl
y
c
oupled
with
the
ra
diating
a
ntenna
pa
tch
us
ing
gr
a
phe
ne
a
s
a
s
witch
to
c
onne
c
t
or
dis
c
onne
c
t
the
e
xtens
ion
to
the
a
ntenna
r
a
diating
pa
tch.
T
he
tunea
ble
a
ntenn
a
is
us
e
f
ul
f
or
a
ddr
e
s
s
ing
the
is
s
ue
of
the
na
r
r
ow
ba
ndwidth
in
mi
c
r
os
tr
ip
pa
tch
a
ntenna
s
(
M
P
As
)
[
8
-
10
].
F
r
e
que
nc
y
S
e
lec
ti
ve
S
u
r
f
a
c
e
s
(
F
S
S
s
)
a
r
e
plana
r
pe
r
iodi
c
s
tr
uc
tur
e
s
whos
e
r
e
f
lec
ti
on
or
tr
a
ns
mi
s
s
ion
pr
ope
r
ti
e
s
va
r
y
with
f
r
e
que
nc
y.
A
f
r
e
que
nc
y
s
e
lec
ti
ve
s
ur
f
a
c
e
(
F
S
S
)
e
leme
nt
a
c
ts
a
s
a
pa
s
s
ive
e
lec
tr
omagne
ti
c
f
il
ter
that
s
e
lec
ti
ve
ly
r
e
f
lec
ts
or
a
tt
e
nua
tes
the
de
s
ir
e
d
f
r
e
que
nc
y
ba
nd
.
T
he
F
S
S
s
tr
uc
tur
e
e
xhibi
ts
a
hig
h
s
ur
f
a
c
e
im
pe
da
nc
e
that
r
e
f
lec
ts
plane
wa
ve
s
in
pha
s
e
a
nd
s
uppr
e
s
s
e
s
s
ur
f
a
c
e
wa
ve
s
.
I
ntegr
a
ti
ng
a
n
F
S
S
with
a
r
e
c
tangula
r
mi
c
r
os
tr
ip
pa
tch
a
ntenna
(
M
P
A)
c
a
n
e
nha
nc
e
r
a
diation
e
f
f
icie
nc
y,
ba
ndwidth,
a
nd
g
a
in
while
r
e
duc
in
g
s
ide
a
nd
ba
c
k
lobes
in
the
r
a
diation
pa
tt
e
r
n
[
1
1
,
1
2
].
I
n
thi
s
wor
k,
a
de
s
ign
is
pr
opos
e
d
f
or
a
tunea
ble
r
e
c
tangula
r
M
P
A
with
s
uf
f
icie
nt
r
e
c
onf
igur
a
bil
it
y
r
a
nge
to
c
ompens
a
te
f
or
the
na
r
r
ow
ba
ndwidth
o
f
M
P
As
.
S
ince
mm
-
wa
ve
a
ntenna
s
c
ompo
s
e
d
e
nti
r
e
ly
of
gr
a
phe
ne
a
r
e
e
xpe
c
ted
to
ha
ve
low
a
ntenna
pe
r
f
o
r
manc
e
a
nd
a
s
mall
r
e
c
onf
igur
a
bil
it
y
r
a
nge
,
the
p
r
opos
e
d
de
s
ign
us
e
s
a
hybr
id
of
c
oppe
r
a
nd
gr
a
phe
ne
to
a
c
hieve
r
e
a
s
ona
ble
a
ntenna
e
f
f
icie
nc
y
a
nd
ga
in
a
s
w
e
ll
a
s
a
n
a
c
c
e
ptable
tunea
ble
f
r
e
que
nc
y
r
a
nge
.
T
he
de
s
ign
i
s
s
im
ulate
d
a
nd
opti
mi
z
e
d
f
o
r
f
if
th
-
ge
ne
r
a
ti
on
a
pp
li
c
a
ti
ons
.
T
he
pa
pe
r
is
or
ga
nis
e
d
a
s
f
oll
ows
:
s
e
c
ti
on
2
pr
e
s
e
nts
the
s
im
ulation
p
r
oc
e
dur
e
f
o
r
the
r
e
c
tangula
r
M
P
A,
us
ing
M
AT
L
AB
to
obtain
the
a
ntenna
dim
e
ns
ions
a
nd
c
omput
e
r
s
im
ulation
tec
hnology
(
C
S
T
)
mi
c
r
owa
v
e
s
tudi
o
(
M
W
S
)
to
s
im
ulate
the
r
e
c
tangula
r
M
P
A.
S
e
c
ti
o
n
3
p
r
e
s
e
nts
the
s
im
ulation
a
nd
modelli
ng
pr
oc
e
dur
e
f
or
the
pr
opos
e
d
de
s
ign
of
the
tunea
ble
r
e
c
tangula
r
M
P
A.
I
n
S
e
c
ti
on
4
,
the
F
S
S
s
upe
r
s
tr
a
te
laye
r
s
a
r
e
us
e
d
to
e
nha
nc
e
the
tunea
ble
r
e
c
tangul
a
r
M
P
A
ga
in,
r
e
tu
r
n
los
s
,
a
nd
ba
ndwidth
o
f
the
tunea
ble
r
e
c
tangul
a
r
M
P
A.
A
dis
c
us
s
ion
of
the
s
im
ulation
r
e
s
u
lts
obtaine
d
f
r
om
the
ti
me
domain
s
olver
of
C
S
T
-
M
W
S
is
given
in
s
e
c
ti
on
5
.
F
inally
,
s
e
c
ti
on
6
pr
e
s
e
nts
the
c
onc
lus
ions
of
the
wo
r
k.
2.
AN
T
E
NN
A
S
I
M
U
L
AT
I
ON
M
ODE
L
L
I
NG
T
he
de
s
ign
pr
oc
e
dur
e
f
o
r
the
pr
opos
e
d
tunabl
e
a
ntenna
is
s
hown
in
F
igu
r
e
1
.
I
n
de
s
igni
ng
the
r
e
c
tangula
r
M
P
A,
thr
e
e
ke
y
pa
r
a
mete
r
s
mu
s
t
be
s
e
lec
ted:
the
r
e
s
ona
nt
f
r
e
que
nc
y
(
)
,
the
r
e
lative
pe
r
mi
tt
ivi
ty
(
)
,
a
nd
the
s
ubs
tr
a
te
he
ight
(
ℎ
)
.
T
a
ble
1
dis
plays
the
f
unda
menta
l
pa
r
a
mete
r
s
c
hos
e
n
f
or
thi
s
de
s
ign.
F
igur
e
1.
T
he
block
diagr
a
m
of
the
pr
opos
e
d
tunea
ble
r
e
c
tangula
r
M
P
A
de
s
ign
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Simulat
ion
and
opt
imiz
ati
on
of
a
tuneable
r
e
c
ta
ng
ular
mic
r
os
tr
ip
patch
antenna…
(
N
idal
Qas
e
m
)
1721
T
a
ble
1.
F
unda
menta
l
a
ntenna
pa
r
a
mete
r
s
P
a
r
a
me
te
r
V
a
lu
e
O
pe
r
a
ti
ng f
r
e
que
nc
y (
)
60 G
H
z
S
ubs
tr
a
te
r
e
la
ti
ve
pe
r
mi
tt
iv
it
y (
)
2.1
S
ubs
tr
a
te
he
ig
ht
(
h
)
0.1 mm
I
nput
i
mpe
da
nc
e
(
)
50 Ω
T
he
M
P
A
c
a
n
be
powe
r
e
d
us
ing
d
if
f
e
r
e
nt
methods
,
s
uc
h
a
s
a
c
oa
xial
pr
obe
,
a
mi
c
r
os
tr
ip
li
ne
f
e
e
ding
tec
hnique,
or
a
pe
r
tur
e
or
p
r
oxim
it
y
c
oupli
n
g
metho
ds
.
I
n
thi
s
wor
k,
the
ins
e
t
f
e
e
ding
tec
hnique
is
us
e
d
in
or
de
r
to
obtain
the
op
ti
mal
im
pe
da
nc
e
be
twe
e
n
the
a
ntenna
a
nd
the
s
our
c
e
of
the
e
lec
tr
ica
l
wa
ve
.
T
he
input
im
pe
da
nc
e
of
the
ins
e
t
-
f
e
d
r
e
c
tangula
r
M
P
A
de
pe
nds
on
the
f
e
e
d
ins
e
t
(
)
ins
ide
the
pa
tch
a
nd
,
to
a
c
e
r
tain
de
gr
e
e
,
on
the
ga
p
be
twe
e
n
the
f
e
e
d
li
ne
a
nd
th
e
pa
tch
(
)
.
I
n
the
ins
e
t
f
e
e
ding
method
,
the
r
e
s
ona
nc
e
f
r
e
que
nc
y
s
hif
ts
with
va
r
iations
in
a
nd
the
r
e
tur
n
l
os
s
of
the
a
ntenna
c
ha
nge
s
a
s
is
va
r
ied
[
1
3
]
.
T
a
bl
e
2
s
hows
the
dim
e
ns
ions
of
the
g
r
ound
plane
,
s
ubs
tr
a
te,
pa
tch,
a
nd
f
e
e
d
li
ne
of
the
s
im
ulate
d
a
ntenna
,
wh
ich
we
r
e
c
a
lcula
ted
us
ing
the
f
oll
owing
e
qua
ti
ons
[
1
4
,
1
5
]
:
=
2
√
(
+
1
)
2
(
1)
=
+
1
2
+
−
1
2
[
1
+
12
ℎ
]
−
1
2
(
2)
∆
=
0
.
412ℎ
(
+
0
.
3
)
[
ℎ
+
0
.
264
]
(
−
0
.
258
)
[
ℎ
+
0
.
8
]
(
3)
=
2
√
(
4)
=
−
2
∆
(
5)
=
c
os
−
1
(
√
)
(
6)
=
377
2
√
(
7)
=
2
ℎ
{
−
1
−
ln
(
2
−
1
)
+
−
1
2
[
ln
(
−
1
)
+
0
.
39
−
(
0
.
61
)
]
}
(
8)
=
3
.
96
×
(
9)
=
×
4
.
65
×
10
−
9
√
2
(
10)
=
2
×
(
11)
=
2
×
,
(
12)
whe
r
e
is
the
e
f
f
e
c
ti
ve
r
e
lative
pe
r
mi
tt
ivi
ty,
ℎ
is
th
e
he
ight
of
the
d
iele
c
tr
ic
s
ubs
tr
a
te,
is
the
width
of
the
pa
tch
,
is
the
e
f
f
e
c
ti
ve
pa
tch
length,
is
the
a
c
tual
pa
tch
length,
∆
is
the
length
e
xtens
ion
,
is
the
e
quivale
nt
f
e
e
d
li
ne
im
pe
da
nc
e
whic
h
is
50
Ω
,
is
the
r
e
s
ona
nt
input
r
e
s
is
tanc
e
whe
n
the
pa
tch
is
f
e
d
a
t
the
r
a
diating
e
dge
,
is
the
f
e
e
d
li
n
e
width
,
is
the
f
e
e
d
li
ne
length,
is
the
s
ubs
tr
a
te
wid
th,
a
nd
is
the
s
ubs
tr
a
te
length
.
T
he
dim
e
ns
ions
of
the
pa
t
c
h,
s
ubs
tr
a
te,
a
nd
f
e
e
d
li
ne
a
r
e
il
lus
tr
a
ted
in
F
igur
e
2
.
T
he
pa
r
a
mete
r
s
c
a
lcula
ted
f
r
om
the
pr
e
vious
e
qua
ti
ons
we
r
e
im
pleme
nted
in
C
S
T
-
M
W
S
to
s
im
ulate
the
a
ntenna
.
F
igu
r
e
3
il
lus
tr
a
tes
t
he
r
e
c
tangula
r
M
P
A
in
the
C
S
T
-
M
W
S
s
im
ulation
s
of
twa
r
e
.
T
he
opti
mi
s
a
ti
on
pr
oc
e
dur
e
invol
ve
s
mi
nim
is
ing
or
maximi
s
ing
c
e
r
tain
a
ntenna
dim
e
ns
ions
a
nd
other
pa
r
a
mete
r
s
,
s
uc
h
a
s
the
s
u
bs
tr
a
te
thi
c
kne
s
s
or
the
r
e
lative
pe
r
mi
tt
ivi
ty
.
He
r
e
,
the
goa
ls
of
the
opti
mi
s
a
ti
on
a
r
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1719
-
1730
1722
to
im
pr
ove
the
ba
ndwidth
,
r
e
tur
n
los
s
,
a
nd
im
pe
da
n
c
e
matc
hing,
a
s
we
ll
a
s
,
to
f
a
c
il
it
a
te
the
a
ntenna
f
a
b
r
ica
ti
on
pr
oc
e
s
s
whe
r
e
the
las
e
r
mac
hini
ng
a
c
c
ur
a
c
y
in
manuf
a
c
tu
r
ing
the
a
ntenna
is
0.
08
m
m
[
10]
.
Af
ter
the
r
e
c
tangula
r
M
P
A
de
s
ign
wa
s
c
ompl
e
ted,
the
opt
im
is
a
ti
on
pr
oc
e
dur
e
wa
s
c
a
r
r
ied
out
us
ing
tr
ial
a
nd
e
r
r
or
.
T
a
ble
3
p
r
e
s
e
nts
the
opti
mi
s
e
d
pa
r
a
mete
r
s
f
or
a
r
e
c
tangula
r
M
P
A.
F
igur
e
2.
Dimens
ions
of
the
s
ingl
e
r
e
c
tangula
r
M
P
A
a
nd
f
e
e
d
li
ne
F
igur
e
3.
S
im
ulate
d
r
e
c
tangula
r
M
P
A
in
CS
T
-
M
W
S
T
a
ble
2.
C
a
lcula
ted
a
ntenna
pa
r
a
mete
r
s
T
a
ble
3.
Optim
is
e
d
r
e
c
tangula
r
M
P
A
dim
e
ns
ions
P
a
r
a
me
te
r
V
a
lu
e
(
mm
)
P
a
tc
h w
id
th
(
W
)
2.008
P
a
tc
h l
e
ngt
h (
L
)
1.6681
S
ubs
tr
a
te
w
id
th
(
)
4.016
S
ubs
tr
a
te
l
e
ngt
h (
)
3.3362
F
e
e
d l
in
e
i
ns
e
t
(
)
0.58217
F
e
e
d l
in
e
w
id
th
(
)
0.308
F
e
e
d l
in
e
l
e
ngt
h (
)
1.21968
G
a
p be
twe
e
n t
he
f
e
e
d l
in
e
a
nd t
he
pa
tc
h (
)
0.0179
P
a
r
a
me
te
r
V
a
lu
e
(
mm
)
P
a
tc
h w
id
th
(
W
)
2
P
a
tc
h l
e
ngt
h (
L
)
1.625
S
ubs
tr
a
te
w
id
th
(
)
4
S
ubs
tr
a
te
l
e
ngt
h (
)
3.25
F
e
e
d l
in
e
i
ns
e
t
(
)
0.5
F
e
e
d l
in
e
w
id
th
(
)
0.12
F
e
e
d l
in
e
l
e
ngt
h (
)
1.8
G
a
p be
twe
e
n t
he
f
e
e
d l
in
e
a
nd
th
e
pa
tc
h (
)
0.1
3.
GRAP
HE
NE
-
B
ASE
D
T
UN
E
A
B
L
E
RE
C
T
AN
G
UL
AR
M
P
A
T
he
r
e
c
tangula
r
hybr
id
gr
a
phe
ne
-
meta
l
M
P
A
s
tudi
e
d
in
thi
s
wor
k
is
c
ompr
is
e
d
of
a
c
oppe
r
r
a
diating
pa
tch,
in
whic
h
f
ou
r
s
tr
ips
of
g
r
a
phe
ne
a
r
e
im
plan
ted
,
a
nd
a
s
oli
d
c
oppe
r
gr
ound
plane
.
T
he
s
e
c
ond
ke
y
s
tep
in
the
de
s
ign
o
f
the
tu
ne
a
ble
M
P
A
is
the
pos
it
ioni
n
g
of
the
gr
a
phe
ne
s
tr
ips
ove
r
the
r
a
diating
pa
tch.
T
he
idea
l
loca
ti
on
de
pe
nds
on
the
c
ur
r
e
nt
dis
tr
ibut
ion
ove
r
t
he
pa
tch,
whe
r
e
the
gr
a
phe
ne
s
tr
ips
a
r
e
ins
e
r
ted
in
the
good
a
c
c
umul
a
ted
c
ur
r
e
nt
pos
it
ion.
F
igu
r
e
4
il
lus
tr
a
tes
the
s
ur
f
a
c
e
c
ur
r
e
nt
dis
tr
ibut
ion
ove
r
the
r
a
diating
pa
tch
of
the
r
e
c
tangula
r
M
P
A
a
t
the
ope
r
a
ti
ng
f
r
e
que
nc
y
.
F
igur
e
4.
S
ur
f
a
c
e
c
ur
r
e
nt
dis
tr
ibut
ion
ove
r
the
r
a
di
a
ti
ng
pa
tch
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Simulat
ion
and
opt
imiz
ati
on
of
a
tuneable
r
e
c
ta
ng
ular
mic
r
os
tr
ip
patch
antenna…
(
N
idal
Qas
e
m
)
1723
T
he
gr
a
phe
ne
s
tr
ips
s
e
r
ve
a
s
a
c
ontr
oll
e
d
s
witc
h
to
dir
e
c
t
the
c
ur
r
e
nt
f
low
ove
r
the
s
ur
f
a
c
e
of
the
a
ntenna
r
a
diating
pa
tch
.
T
he
e
f
f
e
c
ti
ve
length
of
the
r
a
diating
pa
tch
then
de
pe
nds
on
the
DC
volt
a
ge
bias
(
)
:
in
the
ON
s
tate
it
r
e
mains
c
ons
tant,
whil
e
in
the
OFF
s
tate
the
e
f
f
e
c
ti
ve
length
is
s
hor
ter
than
the
a
c
tual
length
.
T
he
ON
s
tate
c
or
r
e
s
ponds
to
a
lo
w
gr
a
phe
ne
s
ur
f
a
c
e
im
pe
da
nc
e
,
whic
h
a
ll
ows
the
c
ur
r
e
nt
to
f
low
th
r
ough
the
s
tr
ip
,
whe
r
e
a
s
the
OFF
s
tate
c
or
r
e
s
ponds
to
a
high
s
ur
f
a
c
e
im
pe
da
nc
e
,
pr
e
ve
nti
ng
the
f
low
of
the
c
ur
r
e
nt
thr
ough
the
s
tr
ip.
T
he
ON
/OF
F
s
tate
is
de
ter
mi
ne
d
by
the
a
c
r
os
s
the
g
r
a
phe
ne
s
tr
ips
.
c
o
uld
be
a
ppli
e
d
dir
e
c
tl
y
thr
ough
the
f
e
e
d
por
t
if
the
s
a
m
e
volt
a
ge
is
gi
ve
n
to
a
ll
the
gr
a
phe
ne
s
tr
ips
s
o
that
they
a
r
e
a
ll
a
c
ti
va
ted/de
a
c
ti
va
ted
a
t
the
s
a
me
t
im
e
.
P
r
a
c
ti
c
a
l
ly,
c
a
n
be
input
us
ing
a
br
oa
dba
nd
c
omm
e
r
c
ial
bia
s
tee
,
whic
h
is
c
onne
c
ted
be
twe
e
n
the
por
t
of
a
ve
c
tor
ne
twor
k
a
na
lyze
r
a
nd
the
a
ntenna
input
mi
c
r
os
t
r
ip
li
ne
.
T
he
is
then
a
ppli
e
d
be
twe
e
n
the
a
ntenna
g
r
ound
p
lane
a
nd
the
gr
a
phe
ne
s
tr
ips
ins
ide
the
a
ntenna
r
a
d
iating
pa
tch
[
1
6
]
.
I
n
o
r
de
r
to
obtain
the
pr
a
c
ti
c
a
l
va
lues
f
or
the
ON
a
nd
OFF
s
ur
f
a
c
e
im
pe
da
nc
e
s
(
a
nd
),
the
f
oll
owing
e
qua
ti
ons
a
r
e
us
e
d
[
1
7
-
19
]
:
=
(
13)
=
ℏ
√
(
14)
=
4
ℏ
2
ℎ
2
√
2
(
15)
=
ℏ
√
(
16)
=
ℏ
2
(
2
(
)
−
(
+
)
)
2
(
)
[
+
2
(
−
+
1
)
]
,
(
17)
whe
r
e
is
the
s
c
a
tt
e
r
ing
e
f
f
e
c
t,
is
the
r
e
laxa
ti
on
ti
me,
is
the
e
lec
tr
on
mobi
li
ty
(
in
m
2
/Vs
)
,
=
7
.
6
×
10
−
7
is
the
two
-
dim
e
ns
ional
mas
s
de
ns
it
y
of
g
r
a
phe
ne
in
(
in
kg/m
2
)
,
ℎ
=
2.
1×
10
4
m/
s
is
the
ve
locity
of
long
it
udinal
a
c
ous
ti
c
phonons
in
g
r
a
phe
ne
,
is
the
tempe
r
a
tur
e
in
Ke
lvi
n
,
ℏ
is
the
r
e
duc
e
d
P
la
nc
k’
s
c
ons
tant,
i
s
the
B
olt
z
mann
c
ons
tant,
is
the
e
lec
tr
on
c
ha
r
ge
(
in
C
)
,
is
the
g
r
a
phe
ne
c
he
mi
c
a
l
potent
ial
(
in
e
V)
,
=
1
×
10
6
m/
s
is
the
F
e
r
m
i
ve
locity
,
is
the
c
a
r
r
ier
de
ns
it
y
(
in
m
-
2
),
is
the
g
r
a
phe
ne
thi
c
kne
s
s
(
in
m)
,
a
nd
is
the
de
f
o
r
mation
pot
e
nti
a
l
(
in
e
V)
.
F
r
om
r
e
c
e
nt
e
xpe
r
im
e
ntal
s
tudi
e
s
,
~18
e
V
a
ppe
a
r
s
to
be
a
pr
e
va
lent
a
nd
r
e
c
ognize
d
va
lue
f
o
r
gr
a
phe
ne
o
ve
r
a
s
ubs
tr
a
te
[
1
7
]
.
T
he
va
lue
of
/
may
be
de
ter
mi
ne
d
by
incr
e
a
s
ing/
de
c
r
e
a
s
ing
the
c
ha
r
ge
c
a
r
r
ier
de
ns
it
y
a
c
c
or
ding
to
(
13
)
,
T
a
ble
4
il
lus
tr
a
tes
s
e
lec
ted
pa
r
a
mete
r
va
lues
f
or
the
gr
a
phe
ne
s
ur
f
a
c
e
im
pe
da
nc
e
modelli
ng
in
bo
th
the
ON
a
nd
OF
F
s
tate
s
.
Dif
f
e
r
e
nt
va
lues
of
we
r
e
c
hos
e
n
in
or
de
r
to
s
tudy
the
e
f
f
e
c
ts
of
incr
e
a
s
ing
or
de
c
r
e
a
s
ing
on
the
tuni
ng
o
f
the
.
A
lar
ge
va
lue
of
mayn’
t
be
c
hos
e
n
f
or
a
ppli
c
a
ti
ons
with
low
powe
r
c
ons
umpt
ion,
s
uc
h
a
s
mobi
le
phone
s
.
How
e
ve
r
,
the
va
lue
of
is
not
uni
ve
r
s
a
l
a
nd
c
a
n
be
de
c
r
e
a
s
e
d,
de
pe
nding
on
the
a
ppli
c
a
ti
on
a
nd
the
r
e
quir
e
d
ope
r
a
ti
ng
f
r
e
que
nc
y
ba
nd
,
by
s
e
lec
ti
ng
a
thi
n
s
ubs
tr
a
te
wi
th
a
gr
e
a
ter
.
T
he
gr
a
phe
ne
s
tr
ips
we
r
e
s
im
ulate
d
a
nd
modelled
in
C
S
T
-
M
W
S
a
s
a
thi
n
ohmi
c
s
he
e
t
s
ur
f
a
c
e
im
pe
da
nc
e
.
T
a
ble
5
il
l
us
tr
a
tes
the
gr
a
phe
ne
s
tr
ip
di
mens
ions
,
a
nd
F
igur
e
5
s
hows
the
s
im
ulate
d
a
ntenna
in
C
S
T
-
M
W
S
.
I
n
or
de
r
to
de
mons
tr
a
te
the
a
c
t
ivation
or
de
a
c
ti
va
ti
on
pr
oc
e
s
s
f
or
the
gr
a
phe
ne
s
tr
ips
to
c
ha
nge
the
,
F
igur
e
6
il
lus
tr
a
tes
the
s
ur
f
a
c
e
c
ur
r
e
nt
dis
tr
ibut
io
n
ove
r
the
a
ntenna
r
a
diating
pa
tch
a
nd
the
gr
a
phe
ne
s
tr
ips
a
t
60
GH
z
.
W
he
n
the
gr
a
phe
ne
s
tr
ips
a
r
e
in
the
O
F
F
s
tate
,
a
s
mall
c
u
r
r
e
nt
is
a
ll
owe
d
to
p
r
opa
ga
te
a
l
ong
with
the
s
tr
ips
due
to
the
lar
ge
va
lue
of
,
c
ont
r
a
r
y
that
whe
n
the
g
r
a
phe
ne
s
tr
ips
a
r
e
in
the
ON
s
tate
,
s
ubs
tantially
mor
e
c
ur
r
e
nt
is
c
a
pa
ble
to
p
r
opa
ga
te
a
long
the
s
tr
i
ps
due
to
the
s
mall
va
lue
of
.
T
a
ble
4.
S
e
lec
ted
pa
r
a
mete
r
va
lues
f
or
the
gr
a
phe
n
e
modelli
ng
P
a
r
a
me
te
r
V
a
lu
e
S
ta
te
ON
O
F
F
(m
2
/Vs
)
.
2.7
2.7
D
(
e
V
)
4
4
T
(
K
)
295
295
(
V
)
5
20
30
0.5
n
(m
-
2
)
5.8×
10
16
2.32×
10
17
3.48×
10
17
6×
10
14
(
Ω
/
)
27.71 +
j
9.256
11.4 +
j
5.7
8.1 +
j
4.65
2569.6+
j7
4.72
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1719
-
1730
1724
T
a
ble
5.
Gr
a
phe
ne
s
tr
ips
dim
e
ns
ions
S
tr
ip
D
im
e
ns
io
n (
mm
)
S
tr
ip
D
im
e
ns
io
n (
mm
)
1
0.16×
0.53
1
0.65
2
0.16×
0.54
2
0.35
3
0.16×
0.54
3
0
.65
4
0.16×
0.53
4
0.27
5
0.35
6
0.06
7
0.27
8
0.05
(a
)
(b
)
F
igur
e
5.
T
une
a
ble
r
e
c
tangula
r
M
P
A
;
(
a
)
P
r
opos
e
d
de
s
ign
in
C
S
T
-
M
W
S
a
nd
(
b)
Dimens
ions
of
the
g
r
a
phe
ne
s
tr
ips
im
plant
e
d
in
the
r
a
diating
pa
tch
(
a
)
.
(
b)
F
igur
e
6.
S
ur
f
a
c
e
c
ur
r
e
nt
dis
tr
ibut
ion
ove
r
the
r
a
di
a
ti
ng
pa
tch
a
nd
gr
a
phe
ne
s
tr
ips
;
(
a
)
.
ON
s
tate
a
nd
(
b)
OFF
s
tate
4.
DE
S
I
GN
OF
T
HE
F
S
S
S
U
P
E
RST
RA
T
E
L
AY
E
R
T
o
im
p
r
ove
the
a
ntenna
pa
r
a
mete
r
s
,
a
n
F
S
S
s
upe
r
s
tr
a
te
on
the
top
/bot
tom
of
the
tunea
ble
r
e
c
tangula
r
M
P
A,
s
e
pa
r
a
ted
by
a
n
a
i
r
ga
p
,
is
int
r
oduc
e
d.
Us
ing
one
or
mo
r
e
F
S
S
s
upe
r
s
tr
a
tes
,
va
r
ious
r
e
s
ona
nc
e
f
r
e
que
nc
ies
c
a
n
be
a
c
hieve
d,
a
lt
hough
ther
e
a
r
e
l
im
it
a
ti
o
ns
im
pos
e
d
by
the
r
e
quir
e
d
c
ompac
t
a
nte
nna
s
ize
.
I
t
s
hould
be
noted
that
a
n
F
S
S
s
upe
r
s
tr
a
t
e
s
igni
f
ica
ntl
y
r
e
duc
e
s
the
im
pe
da
nc
e
ba
ndwidth.
T
he
c
onf
i
gur
a
ti
on
pr
opos
e
d
he
r
e
f
or
a
tunea
ble
r
e
c
tangula
r
M
P
A
int
e
gr
a
ted
with
a
n
F
S
S
pr
ovides
im
pr
ove
d
pe
r
f
or
manc
e
in
mul
ti
ple
pa
r
a
mete
r
s
,
including
ga
in,
r
e
tur
n
los
s
,
a
nd
ba
ndwidth,
f
or
60
GH
z
a
ppli
c
a
ti
on
s
.
T
he
F
S
S
i
s
uti
li
s
e
d
in
two
wa
ys
:
a
s
a
r
e
f
lec
tor
,
f
o
r
med
by
a
s
top
-
ba
nd
F
S
S
;
a
nd
a
s
a
s
upe
r
s
tr
a
te,
with
a
pa
s
s
-
ba
nd
F
S
S
s
tr
uc
tur
e
.
T
he
pr
opos
e
d
F
S
S
is
de
s
igned
to
op
e
r
a
te
in
the
f
r
e
que
nc
y
r
a
nge
50
-
70
GH
z
,
wi
th
a
r
e
s
ona
nc
e
f
r
e
que
nc
y
of
60
GH
z
.
A
s
qua
r
e
lo
op
(
S
L
)
e
leme
nt,
whic
h
ha
s
the
b
e
s
t
pe
r
f
or
manc
e
a
mongs
t
the
s
im
ple
ge
ometr
ic
s
ha
pe
s
[
20
]
,
is
c
hos
e
n
f
or
both
F
S
S
s
.
T
he
mate
r
ial
us
e
d
is
c
opp
e
r
whic
h
it
s
thi
c
kne
s
s
is
0
.
07
mm
.
T
he
diele
c
tr
ic
m
a
ter
ial
is
Ar
lon
AD
300
whic
h
ha
s
0.
1
m
m
thi
c
kne
s
s
a
nd
it
s
r
e
lati
ve
pe
r
mi
t
ti
vit
y
is
3
.
F
igu
r
e
7
il
lus
tr
a
tes
the
g
e
ometr
y
of
the
S
L
a
r
r
a
y
F
S
S
us
e
d
in
the
s
tudy.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
Simulat
ion
and
opt
imiz
ati
on
of
a
tuneable
r
e
c
ta
ng
ular
mic
r
os
tr
ip
patch
antenna…
(
N
idal
Qas
e
m
)
1725
F
igur
e
7.
T
he
s
top
-
ba
nd
S
L
a
r
r
a
y
F
S
S
e
leme
nt
pa
r
a
mete
r
s
,
with
the
diele
c
tr
ic
s
ubs
tr
a
te
s
hown
in
g
r
e
e
n
a
nd
the
c
on
duc
tor
(
c
oppe
r
)
in
br
own
[
19]
T
he
dim
e
ns
i
ons
of
the
S
L
F
S
S
uni
t
c
e
ll
a
r
e
a
s
f
o
ll
ows
(
a
ll
in
mm
)
:
=
1
.
4
,
=
1
.
2
,
g
=
0
.
2
,
a
nd
=
0
.
1
[
21
]
.
F
igur
e
8
il
lus
tr
a
tes
the
p
r
opos
e
d
c
onf
igu
r
a
ti
ons
f
o
r
a
tunea
ble
r
e
c
tangula
r
M
P
A
with
F
S
S
s
.
T
hr
e
e
layouts
ha
ve
be
e
n
us
e
d:
(
1)
T
he
tunea
ble
r
e
c
t
a
ngular
M
P
A.
(
2)
S
top
-
ba
nd
S
L
a
r
r
a
y
F
S
S
us
e
d
a
s
a
gr
ound
plane
to
r
e
f
lec
t
the
plane
wa
ve
in
pha
s
e
.
(
3)
P
a
s
s
-
ba
nd
S
L
mec
h
-
pa
tch
a
r
r
a
y
F
S
S
us
e
d
a
s
a
s
upe
r
s
tr
a
te
t
o
r
e
duc
e
s
ur
f
a
c
e
wa
ve
s
.
A
pa
s
s
-
ba
nd
S
L
mec
h
-
p
a
tch
a
r
r
a
y
F
S
S
c
a
n
be
r
e
a
li
s
e
d
by
us
ing
the
B
a
binet
dua
ls
in
F
igur
e
7
.
P
r
ovided
that
the
s
tr
uc
tur
e
is
s
ymm
e
tr
ica
l,
B
a
binet’
s
pr
inciple
c
a
n
be
e
mpl
oye
d
to
c
ha
nge
f
r
om
a
s
t
op
-
ba
nd
S
L
a
r
r
a
y
F
S
S
to
a
pa
s
s
-
ba
nd
S
L
mec
h
-
pa
tch
a
r
r
a
y
F
S
S
,
whe
r
e
the
c
onduc
ti
ve
a
nd
non
-
c
onduc
ti
ve
s
pa
c
e
s
a
r
e
r
e
ve
r
s
e
d
[
2
2
].
F
igur
e
8.
A
tu
ne
a
ble
r
e
c
tangula
r
M
P
A
be
twe
e
n
tw
o
F
S
S
s
T
he
r
e
s
ona
nt
he
ight
of
the
F
S
S
s
upe
r
s
tr
a
te
a
ntenna
is
pr
e
dicte
d
with
the
he
lp
o
f
r
e
s
ona
nc
e
e
s
ti
mation,
us
ing
the
s
tanda
r
d
r
a
ytr
a
c
ing
tec
hnique.
T
he
r
e
s
o
na
nc
e
c
ondit
ion
f
or
the
a
ntenna
s
tr
uc
tur
e
a
t
the
b
or
e
s
ight
a
ng
le
a
nd
the
ope
r
a
ti
ng
f
r
e
que
nc
y
a
s
a
f
unc
ti
on
o
f
the
he
ight
of
the
s
upe
r
s
tr
a
te
a
bove
/below
the
s
ubs
tr
a
te
a
r
e
obtaine
d
a
s
[2
3
]:
ℎ
=
2
+
(
(
,
,
)
+
)
4
f
o
r
=
1
,
2
,
3
,
…
…
.
(
18)
whe
r
e
is
a
n
int
e
ge
r
,
is
the
f
r
e
e
-
s
pa
c
e
wa
ve
length
,
(
,
,
)
is
the
r
e
f
lec
ti
on
pha
s
e
a
ngle
of
the
gr
ound
plane
,
a
nd
is
the
r
e
f
lec
ti
on
pha
s
e
a
ngle
of
the
s
upe
r
s
tr
a
te
unit
c
e
ll
.
T
he
va
lu
e
of
(
,
,
)
is
obtai
ne
d
f
r
om
(
19)
;
(
,
,
)
=
−
2
ta
n
−
1
(
t
a
n
(
)
)
(
19)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
1693
-
6930
T
E
L
KO
M
NI
KA
T
e
lec
omm
un
C
omput
E
l
C
ontr
o
l
,
Vol.
18
,
No
.
4
,
Augus
t
2020
:
1719
-
1730
1726
whe
r
e
=
(
√
⁄
)
is
the
c
ha
r
a
c
ter
is
ti
c
im
pe
da
nc
e
of
the
wa
ve
in
the
diele
c
tr
ic
s
ubs
tr
a
te,
is
the
c
ha
r
a
c
ter
is
ti
c
im
pe
da
nc
e
of
the
wa
ve
in
f
r
e
e
s
pa
c
e
,
a
nd
=
(
2
√
)
is
the
pha
s
e
c
ons
tant
of
the
wa
ve
in
the
s
ubs
tr
a
te.
An
e
xpr
e
s
s
ion
f
or
e
s
ti
mating
the
b
or
e
s
ight
dir
e
c
ti
vit
y
,
r
e
lative
to
that
of
the
pr
im
a
r
y
a
ntenna
(
f
e
e
d
a
ntenna
)
ha
s
be
e
n
de
r
ived
in
[
2
4
]
=
1
+
|
(
,
=
0
)
|
1
+
|
(
,
=
0
)
|
(
20)
I
t
c
a
n
b
e
s
e
e
n
f
r
om
(
20
)
that
the
di
r
e
c
ti
vit
y
o
f
the
r
e
c
tangula
r
M
P
A
incr
e
a
s
e
s
a
s
the
magnitude
of
the
r
e
f
lec
ti
on
c
oe
f
f
icie
nt
incr
e
a
s
e
s
.
T
hus
,
in
or
de
r
to
ha
ve
a
pe
r
f
e
c
t
F
S
S
s
upe
r
s
tr
a
te,
the
r
e
qui
r
e
ments
of
a
f
lat
r
e
f
lec
ti
on
pha
s
e
a
nd
a
high
r
e
f
lec
ti
on
magnitude
v
e
r
s
us
f
r
e
que
nc
y
mus
t
be
s
a
ti
s
f
ied
[
2
5
]
.
At
60
GH
z
,
the
F
S
S
r
e
f
lec
ti
on
c
oe
f
f
icie
nt
is
0.
8
a
nd
the
c
or
r
e
s
pondi
ng
r
e
lative
di
r
e
c
ti
vit
y
is
e
s
ti
mate
d
to
be
a
bout
9.
5
dB
i.
T
he
r
e
f
or
e
,
whe
n
the
pr
im
a
r
y
s
our
c
e
a
ntenna
ha
s
5
t
o
7
dB
i
ga
in
(
s
uc
h
a
s
a
r
e
c
tangula
r
M
P
A)
,
plac
ing
t
his
F
S
S
s
upe
r
s
tr
a
te
a
t
a
n
a
ppr
opr
iate
dis
tanc
e
a
bove
/below
the
g
r
ound
plane
c
a
n
incr
e
a
s
e
the
ga
in
to
a
s
m
uc
h
a
s
14
dB
i.
I
nter
e
s
ti
ngly,
thi
s
e
s
ti
mate
d
ga
in
is
in
good
a
gr
e
e
ment
with
the
pr
e
diction
o
f
the
C
S
T
-
M
W
S
model.
T
he
va
r
ious
pa
r
a
mete
r
s
in
(
18)
a
nd
(
19
)
a
r
e
s
um
mar
is
e
d
in
T
a
ble
6.
F
or
the
pr
opos
e
d
c
onf
igur
a
ti
o
n,
the
ga
p
wa
s
va
r
ied
to
obtai
n
the
opti
mum
dis
tanc
e
be
twe
e
n
the
M
P
A
a
nd
F
S
S
.
T
he
idea
l
ga
ps
f
o
r
a
s
ingl
e
r
e
c
tangula
r
M
P
A
we
r
e
f
ound
to
be
2
a
nd
2
.
2
mm
f
or
ℎ
1
a
nd
ℎ
2
,
r
e
s
pe
c
ti
ve
ly,
a
s
s
hown
in
F
igu
r
e
8
.
T
a
ble
6.
P
a
r
a
mete
r
V
al
ue
s
of
(
18
a
nd
19
)
(
)
(
Ω
)
(
−
1
)
(
)
60
377
2
.
2
1
1
.
86
0
.
1
(
Ω
)
(
,
,
)
−
−
(
)
(
)
254
.
17
165
.
6
−
167
−
166
1
.
95
2
.
3
5.
RE
S
UL
T
S
AN
D
DI
S
CU
S
S
I
ON
I
n
thi
s
s
e
c
ti
on,
the
r
e
s
ult
s
obtaine
d
f
r
om
the
a
ntenna
s
im
ulation
in
the
C
S
T
-
M
W
S
s
im
ulation
s
of
twa
r
e
a
r
e
il
lus
tr
a
ted
.
T
he
s
im
ulate
d
r
e
tur
n
los
s
(
11
)
f
or
the
t
une
a
ble
r
e
c
tangula
r
M
P
A
in
the
ON
a
nd
OFF
s
tate
s
f
r
om
the
ti
me
domain
s
olver
o
f
C
S
T
-
M
W
S
is
pr
e
s
e
nted
in
F
igur
e
9
.
I
n
ge
ne
r
a
l,
the
M
P
As
ha
ve
poo
r
ga
i
n;
thi
s
is
be
c
a
us
e
the
a
ntenna
ga
in
is
p
r
opor
ti
ona
l
to
ℎ
a
nd
inver
s
e
ly
pr
opor
ti
ona
l
to
[
23
]
.
F
igur
e
10
s
hows
the
thr
e
e
-
dim
e
ns
ional
r
e
s
ult
s
f
or
the
f
a
r
f
ield
o
f
t
he
tunea
ble
r
e
c
tangula
r
M
P
A
a
t
the
ope
r
a
ti
ng
f
r
e
que
nc
ies
=
52.
35,
59
.
3,
59.
89
,
a
nd
60
GH
z
,
both
with
a
nd
without
F
S
S
s
.
T
he
a
ntenna
ha
s
a
r
e
a
s
ona
ble
ga
in
in
thi
s
ope
r
a
ti
ng
f
r
e
que
nc
y
ba
nd;
howe
ve
r
,
by
us
ing
F
S
S
s
the
a
ntenna
pa
r
a
mete
r
s
a
r
e
e
nha
nc
e
d,
whe
r
e
ga
in
is
s
igni
f
ica
ntl
y
incr
e
a
s
e
d
f
r
om
5
.
7
to
12.
1
dB
i,
ba
ndwith
incr
e
a
s
e
d
f
r
om
2
.
3334
to
3.
18
GH
z
,
a
nd
the
11
de
c
r
e
a
s
e
d
f
r
om
-
42.
4
to
-
54
d
B
at
the
highes
t
va
lu
e
of
(
60
GH
z
)
.
A
s
ingl
e
main
lobe
of
a
r
e
a
s
ona
ble
be
a
m
width
c
ha
r
a
c
ter
is
e
s
the
r
a
diation
pa
tt
e
r
n.
I
n
the
a
z
im
uthal
a
nd
e
leva
ti
on
plane
s
,
the
be
a
m
widths
a
r
e
of
ten
id
e
nti
c
a
l,
r
e
s
ult
ing
in
a
r
e
latively
c
i
r
c
ular
be
a
m,
a
lt
h
ough
thi
s
is
by
no
mea
ns
univer
s
a
l.
T
he
be
a
m
widths
c
a
n
b
e
manipulate
d
to
pr
oduc
e
a
n
a
ntenna
with
highe
r
or
lowe
r
ga
in,
de
pe
nding
on
the
r
e
quir
e
d
a
ppli
c
a
ti
on.
F
igur
e
11
il
lus
tr
a
tes
the
3
-
dB
be
a
m
width
f
or
the
p
r
opos
e
d
a
ntenna
a
t
va
r
ious
ope
r
a
ti
ng
f
r
e
que
nc
y
ba
nds
.
T
he
ba
n
dwidth
is
c
a
lcula
ted
f
r
om
the
r
e
tur
n
los
s
plot
a
t
11
=
-
1
0
dB
.
A
s
umm
a
r
y
of
the
r
e
s
ult
s
a
nd
the
ba
ndwidths
a
r
e
il
lus
tr
a
ted
in
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1727
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Vol.
18
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No
.
4
,
Augus
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2020
:
1719
-
1730
1728
F
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11.
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