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[
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T
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3628
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s
tr
ates
w
it
h
a
C
o
o
p
er
th
ick
n
es
s
o
f
5
0
µ
m
ar
e
co
m
b
in
ed
to
g
e
th
e
r
to
o
b
tain
th
e
b
est
r
esu
lt
s
an
d
d
esig
n
f
o
r
th
e
p
r
o
p
o
s
ed
an
ten
n
a.
A
n
o
p
ti
m
izatio
n
s
tu
d
y
o
f
s
i
ze
an
d
p
er
f
o
r
m
a
n
ce
b
ased
o
n
d
i
f
f
er
e
n
t
s
h
ap
es
f
o
r
th
e
t
w
o
p
ar
asit
ic
p
atch
in
t
h
e
s
ec
o
n
d
a
n
d
t
h
ir
d
la
y
er
s
.
T
h
e
r
esu
l
tin
g
a
n
te
n
n
a
co
n
f
i
g
u
r
atio
n
s
ar
e
p
r
esen
ted
an
d
co
m
p
ar
ed
,
b
etw
ee
n
d
if
f
e
r
e
n
t
s
tr
u
c
tu
r
es
p
r
ese
n
ted
in
t
h
is
w
o
r
k
.
T
h
e
to
tal
s
ize,
ce
n
ter
f
r
eq
u
en
c
y
an
d
b
a
n
d
w
id
th
o
f
ea
ch
ca
s
e
ar
e
s
t
u
d
ied
in
d
etail
to
ac
h
ie
v
e
t
h
e
o
p
tim
a
l
d
esi
g
n
.
T
h
e
an
ten
n
a
p
r
o
p
o
s
ed
w
it
h
cir
cu
lar
ap
er
tu
r
e
an
d
cir
cu
lar
p
a
r
asit
ic
ele
m
e
n
t
is
m
i
n
iat
u
r
ized
f
o
r
o
b
tain
lo
w
r
eso
n
an
ce
f
r
eq
u
en
c
ies b
ased
o
n
th
e
e
f
f
ec
t o
f
le
n
g
th
o
f
t
h
e
f
e
ed
lin
e
an
d
r
ad
iu
s
o
f
ap
er
tu
r
e.
T
h
e
C
ST
MW
s
elec
tr
o
m
a
g
n
etic
s
i
m
u
lato
r
is
u
s
ed
to
p
er
f
o
r
m
th
e
an
te
n
n
a
c
h
ar
ac
ter
is
t
ics.
T
h
ese
p
er
f
o
r
m
a
n
ce
s
d
e
m
o
n
s
tr
ate
t
h
at
th
e
p
r
o
p
o
s
ed
an
ten
n
a
is
g
o
o
d
ca
n
d
id
ate
w
ir
eless
co
m
m
u
n
icat
io
n
s
y
s
te
m
s
o
p
er
atin
g
at
2
.
4
GHz
.
T
h
is
p
ap
er
is
d
iv
id
ed
in
to
f
o
u
r
s
ec
tio
n
s
:
t
h
e
f
ir
s
t
s
ec
tio
n
is
d
ev
o
ted
to
g
iv
e
th
e
g
eo
m
etr
y
d
esi
g
n
o
f
t
h
e
m
u
lti
-
la
y
er
s
p
atc
h
a
n
te
n
n
a
an
d
a
p
r
ef
ac
e
o
f
th
e
i
m
p
o
r
tan
t
p
ar
am
eter
s
in
d
if
f
er
e
n
t
la
y
er
s
d
esi
g
n
s
,
f
o
r
to
p
la
y
er
,
m
id
d
le
la
y
er
a
n
d
b
o
tto
m
la
y
er
.
T
h
e
r
esu
lt
o
b
tain
ed
an
d
t
h
e
d
esig
n
co
n
s
id
er
atio
n
ar
e
d
is
cu
s
s
ed
in
t
h
is
s
ec
tio
n
.
Seco
n
d
s
ec
tio
n
p
r
esen
t
th
e
g
eo
m
etr
y
s
t
u
d
y
o
f
th
is
an
ten
n
a
o
n
th
e
an
ten
n
a
r
esp
o
n
s
es,
b
ased
o
n
e
f
f
ec
t
d
i
f
f
er
en
t
s
h
ap
es
o
f
t
h
e
r
ad
iat
ed
ele
m
e
n
ts
s
u
ch
as
th
e
ap
er
tu
r
e
in
th
e
s
ec
o
n
d
la
y
er
an
d
p
ar
asit
ic
p
atch
i
n
th
e
t
h
ir
d
lay
er
.
T
h
e
s
h
ap
e
s
s
t
u
d
y
o
f
t
h
e
p
ar
asit
ic
p
atch
ar
e
cir
cu
lar
,
f
r
ac
tal
an
d
s
q
u
ar
e
co
m
b
i
n
ed
b
y
cir
cu
lar
,
f
r
ac
tal
an
d
s
q
u
ar
e
f
o
r
m
s
o
f
th
e
ap
er
t
u
r
e
in
t
h
e
m
id
d
le
la
y
er
s
.
A
c
o
m
p
ar
is
o
n
b
et
w
ee
n
all
co
m
b
i
n
atio
n
s
ar
e
p
r
ese
n
te
d
an
d
d
is
c
u
s
s
ed
in
t
h
is
s
ec
tio
n
.
T
h
ir
d
s
ec
tio
n
p
r
esen
t
s
a
n
a
n
ten
n
a
g
eo
m
etr
y
o
f
th
e
ca
s
e
h
a
v
i
n
g
a
g
o
o
d
r
ad
iatio
n
p
r
o
p
e
r
ties
.
Oth
er
t
y
p
e
o
f
an
ten
n
a
m
in
iatu
r
izat
io
n
is
p
r
o
p
o
s
ed
in
th
is
s
ec
t
io
n
.
Fin
all
y
,
a
b
r
ief
c
o
n
cl
u
s
io
n
is
p
r
esen
ted
in
t
h
e
f
o
u
r
th
s
ec
tio
n
.
2.
ANT
E
NNA
D
E
SI
G
N
I
n
th
is
s
ec
tio
n
,
it
is
ex
p
lai
n
e
d
th
e
s
p
ec
if
icatio
n
o
f
t
h
e
g
e
o
m
e
tr
y
d
esi
g
n
o
f
t
h
e
m
u
lti
-
la
y
er
s
p
atch
an
ten
n
a
p
r
o
p
o
s
ed
,
w
e
p
r
o
v
id
e
a
d
escr
ip
tio
n
f
o
r
d
if
f
er
en
t
la
y
er
s
d
esig
n
s
,
a
n
d
a
p
r
ef
ac
e
o
f
t
h
e
r
ad
iated
s
h
ap
es
u
s
i
n
g
in
t
h
i
s
s
t
u
d
y
.
2
.
1
.
M
ultila
y
er
s
p
a
t
ch
a
nte
nn
a
f
o
r
2
.
4
G
H
z
Ou
r
o
b
j
ec
tiv
e
in
th
i
s
p
ap
er
is
to
d
esig
n
a
n
o
v
e
l
v
er
y
s
m
a
ll
an
ten
n
a
b
ased
o
n
w
ir
eless
a
p
p
licatio
n
s
y
s
te
m
s
d
ev
elo
p
ed
p
r
ev
io
u
s
l
y
[
1
0
]
,
[
1
1
]
.
T
h
e
p
r
o
p
o
s
ed
m
u
l
ti
-
la
y
er
s
tr
u
c
tu
r
e
an
t
e
n
n
a
is
c
o
m
p
o
s
ed
b
y
m
u
l
ti
-
la
y
er
s
s
u
b
s
tr
ate
s
an
d
m
u
lti
-
c
o
n
d
u
cto
r
.
A
lo
n
g
d
etai
led
s
t
u
d
y
o
n
th
e
p
ar
a
m
e
ter
an
te
n
n
a
it
w
a
s
ta
k
en
in
to
ac
co
u
n
t
to
m
i
n
iat
u
r
ize
th
e
d
i
m
en
s
io
n
s
o
f
th
e
a
n
te
n
n
a,
p
r
ec
is
el
y
t
h
e
ef
f
ec
t
o
f
t
h
e
s
lo
tted
r
ad
iatin
g
p
atch
a
n
d
s
q
u
ar
e
p
ar
asit
ic
ele
m
e
n
t.
Af
te
r
a
lo
n
g
p
r
o
ce
d
u
r
e
d
esi
g
n
,
a
n
ex
p
lo
d
ed
v
ie
w
o
f
th
i
s
a
n
te
n
n
a
is
ca
n
b
e
s
h
o
w
n
i
n
Fig
u
r
e
1
.
As
a
f
ir
s
t
s
tep
,
th
e
an
ten
n
a
is
i
m
p
le
m
e
n
ted
o
n
FR
4
s
u
b
s
tr
ate
h
av
i
n
g
a
r
elativ
e
p
er
m
itti
v
it
y
o
f
4
.
4
an
d
th
ic
k
n
e
s
s
o
f
1
.
6
m
m
.
T
h
e
g
r
o
u
n
d
p
la
n
e
d
i
m
e
n
s
io
n
s
a
r
e
W
_
g
×
L
_
g
=
6
×
6
m
m
2
.
T
h
e
m
i
cr
o
s
tr
ip
p
atch
i
s
f
ee
d
b
y
m
icr
o
s
tr
ip
o
f
w
id
t
h
p
r
in
ted
o
n
b
o
tto
m
d
ielec
tr
ic
la
y
er
.
T
h
e
f
ee
d
lin
e
an
d
p
ar
tial
g
r
o
u
n
d
p
lan
ar
e
ch
o
s
en
to
b
e
co
p
p
er
w
ith
t
h
ick
n
e
s
s
o
f
0
.
0
5
m
m
,
w
h
ic
h
ar
e
s
ep
ar
ated
b
y
th
e
F
R
4
s
u
b
s
tr
ate
o
f
1
.
6
m
m
.
T
h
e
an
ten
n
a
p
r
ese
n
ted
is
b
ased
in
m
u
lti
la
y
er
s
tech
n
iq
u
es
o
n
t
h
e
FR
4
s
u
b
s
tr
ate
.
I
n
tr
o
d
u
cin
g
s
lo
ts
i
n
r
ad
iati
n
g
p
atch
w
it
h
d
if
f
er
en
t
g
eo
m
etr
y
allo
w
b
i
g
p
er
f
o
r
m
a
n
ce
a
n
d
i
m
p
o
r
ta
n
t
i
m
p
r
o
v
e
m
e
n
t
i
n
s
ize
d
i
m
e
n
s
io
n
s
.
Fi
g
u
r
e
1
p
r
esen
ts
a
d
etailed
in
i
tial
d
esig
n
o
f
2
.
4
GHz
p
r
o
p
o
s
ed
a
n
ten
n
a
-
in
-
P
ac
k
a
g
e.
T
h
e
r
est
o
f
p
ar
a
m
eter
s
o
f
t
h
e
d
esig
n
ed
an
te
n
n
a
ar
e:
=
5
.
1
m
m
,
=
4
.
8
m
m
,
5
.
5
m
m
,
5
.
5
m
m
an
d
tr
ee
la
y
er
s
o
f
an
ten
n
a
h
av
i
n
g
f
ix
ed
v
a
lu
e
s
o
f
x
x
= 6
x
6
x
1
.
6
m
m
3
.
T
h
e
an
ten
n
a
co
n
s
i
s
ts
o
f
t
h
r
ee
la
y
er
s
w
it
h
s
lo
tted
r
ad
iatin
g
p
atch
a
n
d
s
q
u
ar
e
p
ar
asit
ic
lo
ca
t
ed
o
n
t
h
e
m
id
d
le
an
d
to
p
la
y
er
r
esp
ec
ti
v
el
y
.
T
h
e
p
ar
asit
ic
p
atch
is
lo
ca
ted
at
th
e
u
p
p
er
s
id
e
o
f
t
h
e
to
p
d
ielec
tr
ic
la
y
er
i
n
o
r
d
er
t
o
p
r
o
v
id
e
a
m
a
x
i
m
u
m
r
ad
iatio
n
;
A
p
er
tu
r
e
in
t
h
e
m
id
d
le
p
atch
is
u
s
ed
to
r
ad
iate
th
e
p
ar
asit
ic
ele
m
e
n
t.
W
e
p
r
esen
t
t
h
e
an
ten
n
a
r
ad
i
atio
n
b
eh
a
v
io
r
af
ter
s
t
u
d
y
i
n
g
an
d
o
p
ti
m
iz
in
g
all
cr
itical
p
ar
a
m
eter
s
,
Fig
u
r
e
2
s
h
o
w
s
t
h
e
s
i
m
u
lated
r
etu
r
n
lo
s
s
p
er
f
o
r
m
an
ce
o
f
th
e
d
ev
elo
p
ed
an
ten
n
a.
I
t
ca
n
b
e
o
b
s
er
v
ed
t
h
at
th
e
p
r
o
p
o
s
ed
an
ten
n
a
ac
h
ie
v
es
a
b
a
n
d
w
id
th
o
f
1
.
4
to
3
.
5
GHz
.
T
h
e
p
lo
tted
r
esu
lt
i
n
d
icate
s
t
h
at,
at
-
4
8
d
B
r
etu
r
n
lo
s
s
,
th
e
co
m
p
ac
t
an
t
en
n
a
o
p
er
ate
p
er
f
ec
tl
y
at
2
.
4
GHz
.
C
o
n
s
eq
u
en
t
l
y
,
th
e
a
n
te
n
n
a
p
r
esen
ted
b
a
s
ed
i
n
m
u
ltil
a
y
er
s
u
b
s
tr
a
te
s
a
n
d
d
i
m
en
s
io
n
p
ar
a
m
eter
s
tec
h
n
iq
u
e
s
to
r
ed
u
ce
th
e
s
ize,
p
r
o
v
id
es g
o
o
d
r
ad
iatio
n
s
p
r
o
p
er
ties
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8708
Desig
n
S
tu
d
y
o
f
a
Min
ia
tu
r
iz
ed
Mu
lti
-
la
ye
r
ed
A
n
ten
n
a
-
in
-
p
a
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a
g
e
fo
r
2
.
4
GHZ
W
i
r
eles
s
... (
Ja
la
l Na
g
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a
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)
3629
(
a)
(
b
)
Fig
u
r
e
1
.
Geo
m
e
tr
y
o
f
t
h
e
p
r
o
p
o
s
ed
v
er
y
s
m
a
ll a
n
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RE
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I
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I
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
n
t J
E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
8
,
No
.
5
,
Octo
b
er
2
0
1
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:
3
6
2
7
–
3
6
3
5
3634
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RE
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NC
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[1
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Ro
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n
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Co
p
lan
e
r
A
n
ten
n
a
f
o
r
WL
A
N
A
p
p
li
c
a
ti
o
n
s
”
,
IEE
E
T
ra
n
s.
An
ten
n
a
s
Pro
p
a
g
.
,
v
o
l.
5
4
,
n
o
.
1
2
,
p
p
.
3
7
5
5
-
3
7
6
2
,
2
0
0
6
.
[2
]
Zh
ij
u
n
Zh
a
n
g
,
M
a
g
d
y
F
.
Isk
a
n
d
e
r,
Je
a
n
-
Ch
risto
p
h
e
L
a
n
g
e
r
a
n
d
Ji
m
M
a
th
e
w
s,
“
Du
a
l
-
Ba
n
d
W
LA
N
Dip
o
le
A
n
ten
n
a
Usi
n
g
a
n
In
tern
a
l
M
a
tch
i
n
g
Circu
it
”
,
IEE
E
T
ra
n
s.
An
ten
n
a
s
a
n
d
Pr
o
p
a
g
.
,
v
o
l.
5
3
,
n
o
.
5
,
p
p
.
1
8
1
3
-
1
8
1
8
,
2
0
0
5
.
[3
]
K.F
.
T
o
n
g
,
K.M
.
L
u
k
,
K.F
.
L
e
e
a
n
d
S
.
M
.
S
h
u
m
,
“
A
n
a
l
y
sis
o
f
a
b
ro
a
d
b
a
n
d
U
-
slo
t
M
icro
stri
p
A
n
ten
n
a
”
,
1
0
t
h
In
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
n
A
n
te
n
n
a
a
n
d
P
ro
p
a
g
a
ti
o
n
,
n
o.
4
3
6
,
p
p
.
14
-
1
7
,
1
9
9
7
.
[4
]
K.
-
L
.
W
o
n
g
,
Co
m
p
a
c
t
a
n
d
Bro
a
d
b
a
n
d
M
icro
stri
p
A
n
ten
n
a
s,
Jo
h
n
W
il
e
y
&
S
o
n
s,
Ne
w
Yo
rk
,
NY
,
USA
,
p
p
.
1
-
7
,
2
0
0
2
.
[5
]
S
.
P
in
h
a
s
a
n
d
S
.
S
h
tri
k
m
a
n
,
“
Co
m
p
a
riso
n
b
e
tw
e
e
n
C
o
m
p
u
ted
a
n
d
M
e
a
su
re
d
B
a
n
d
w
id
th
o
f
Q
u
a
rter
-
wa
v
e
M
icro
strip
R
a
d
iato
rs
”
,
I
EE
E
T
r
a
n
sa
c
ti
o
n
s
o
n
An
te
n
n
a
s a
n
d
Pro
p
a
g
a
ti
o
n
,
v
o
l
.
3
6
,
n
o
.
1
1
,
p
p
.
1
6
1
5
-
1
6
1
6
,
1
9
8
8
.
[6
]
K.
L
.
W
o
n
g
a
n
d
K.
P
.
Ya
n
g
,
“
S
m
a
ll
d
u
a
l
F
re
q
u
e
n
c
y
M
icro
strip
A
n
ten
n
a
w
it
h
a
C
ro
ss
S
l
o
t
”
,
El
e
c
tro
n
ics
L
e
tt
e
rs
,
v
o
l.
3
3
,
p
p
.
1
9
1
6
-
1
9
1
7
,
1
9
9
7
.
[7
]
Ku
ld
e
e
p
Ku
m
a
r
P
a
ra
sh
a
r,
“
De
si
g
n
a
n
d
A
n
a
l
y
sis
o
f
IS
lo
tt
e
d
Re
c
tan
g
u
lar
M
icro
strip
P
a
tc
h
A
n
ten
n
a
f
o
r
W
irel
e
ss
A
p
p
li
c
a
ti
o
n
”
,
I
n
ter
n
a
t
io
n
a
l
J
o
u
r
n
a
l
o
f
El
e
c
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
o
l.
4
,
n
o
.
1
,
p
p
.
3
1
-
3
6
,
2
0
1
4
.
[8
]
Y.
D.
L
in
a
n
d
T
.
Ito
h
,
“
F
re
q
u
e
n
c
y
-
s
c
a
n
n
in
g
A
n
te
n
n
a
u
sin
g
t
h
e
C
ro
ss
ti
e
o
v
e
rlay
s
lo
w
-
w
a
v
e
S
tru
c
tu
re
s
a
s
T
ra
n
s
m
issio
n
L
in
e
”
,
IEE
E
T
ra
n
s
An
ten
n
a
s P
r
o
p
a
g
.
,
v
o
l.
3
9
,
p
p
.
3
7
7
-
3
8
0
,
1
9
9
1
.
[9
]
S
a
ty
a
n
d
ra
S
in
g
h
L
o
d
h
i
,
P
.
K.
S
i
n
g
h
a
l
a
n
d
V
.
V
.
T
h
a
k
a
re
,
“
De
sig
n
a
n
d
A
n
a
l
y
sis
o
f
T
rip
p
le
Ba
n
d
Ko
c
h
F
ra
c
tal
Ya
g
i
Ud
a
A
n
ten
n
a
”
,
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
Co
mp
u
ter
E
n
g
i
n
e
e
rin
g
,
v
o
l.
3
,
n
o
.
4
,
p
p
.
4
5
6
-
4
6
0
,
2
0
1
3
.
[1
0
]
N.
He
rsc
o
v
ici
a
n
d
M
.
F
.
Os
o
r
io
e
t
a
l
.
,
“
M
in
iat
u
riz
a
ti
o
n
o
f
R
e
c
tan
g
u
lar
M
icro
strip
P
a
tch
e
s
u
sin
g
G
e
n
e
ti
c
A
l
g
o
rit
h
m
s
”
,
IEE
E
An
ten
n
a
s W
ir
e
les
s P
ro
p
a
g
.
L
e
tt
.
,
v
o
l.
1
,
p
p
.
94
-
9
7
,
2
0
0
2
.
[1
1
]
B.
L
e
e
a
n
d
F
.
J.
Ha
ra
c
k
ie
w
icz
,
“
M
in
iatu
re
M
icro
stri
p
a
n
ten
n
a
w
it
h
a
P
a
rti
a
l
ly
F
il
led
h
ig
h
-
P
e
rm
it
ti
v
it
y
S
u
b
stra
te
”
,
IEE
E
T
ra
n
sa
c
ti
o
n
s
o
n
An
te
n
n
a
s a
n
d
Pr
o
p
a
g
a
ti
o
n
,
v
o
l.
5
0
,
n
o
.
8
,
p
p
.
1
1
6
0
-
1
1
6
2
,
2
0
0
2
.
[1
2
]
H.
K.
Ka
n
,
R.
B
.
W
a
terh
o
u
se
,
“
S
m
a
ll
P
ri
n
ted
-
w
in
g
A
n
ten
n
a
S
u
i
tab
le
f
o
r
W
irele
ss
H
a
n
d
se
t
T
e
r
m
in
a
ls
”
,
M
icr
o
wa
v
e
a
n
d
Op
ti
c
a
l
T
e
c
h
n
o
l
o
g
y
L
e
tt
e
rs
,
v
o
l.
3
0
,
n
o
.
4
,
p
p
.
2
2
6
-
2
2
9
,
2
0
0
1
.
[1
3
]
S
h
a
c
k
e
lf
o
rd
,
A
.
K.,
K.
F
.
L
e
e
,
a
n
d
K.
M
.
L
u
k
,
“
De
sig
n
o
f
s
m
a
ll
-
si
z
e
w
id
e
-
b
a
n
d
w
id
th
M
icro
stri
p
-
p
a
tch
A
n
ten
n
a
s
”
,
IEE
E
A
n
ten
.
a
n
d
Pr
o
p
a
.
M
a
g
.
,
v
o
l.
4
5
,
n
o
.
1
,
p
p
.
7
5
-
8
3
,
F
e
b
.
2
0
0
3
.
[1
4
]
R
.
Ch
a
ir,
K.
M
.
L
u
k
,
K.
F
.
L
e
e
,
“
M
in
iatu
re
sh
o
rted
D
u
a
lp
a
tch
A
n
t
e
n
n
a
”
,
IEE
Pro
c
e
e
d
in
g
s
–
M
icr
o
wa
v
e
s,
An
ten
n
a
s
a
n
d
Pro
p
a
g
a
t
io
n
,
v
o
l.
1
4
7
,
n
o
.
4
,
p
p
.
2
7
3
-
2
7
6
,
2
0
0
0
.
[1
5
]
J.
G
.
Jo
sh
i,
S
.
S
.
P
a
tt
n
a
ik
,
S
.
De
v
i
a
n
d
M
.
R.
L
o
h
o
k
a
re
,
“
El
e
c
tri
c
a
ll
y
S
m
a
ll
P
a
tch
A
n
ten
n
a
L
o
a
d
e
d
w
it
h
M
e
tam
a
teria
l
”
,
IET
E
J
o
u
rn
a
l
o
f
R
e
se
a
rc
h
,
v
o
l.
5
6
,
n
o
.
6
,
p
p
.
3
7
3
-
3
7
9
,
2
0
1
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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