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[
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.
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[
5
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d
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An
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6
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in
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an
ten
n
a
ca
p
ab
le
o
f
r
eso
n
atin
g
at
t
w
o
f
r
eq
u
e
n
c
y
b
an
d
s
,
m
ak
i
n
g
it
id
ea
l
f
o
r
ap
p
licatio
n
s
lik
e
W
iMA
X
a
n
d
W
L
AN.
A
d
d
itio
n
a
ll
y
,
a
co
m
p
ac
t,
r
ec
o
n
f
i
g
u
r
ab
le
T
-
s
h
ap
ed
p
lan
ar
an
ten
n
a
[
7
]
is
d
esig
n
ed
f
o
r
p
o
r
tab
le
u
s
e,
p
r
o
v
id
in
g
e
f
f
ici
en
t
an
d
ad
ap
tab
le
p
er
f
o
r
m
a
n
ce
ac
r
o
s
s
m
u
lt
ip
le
f
r
eq
u
en
c
y
b
an
d
s
.
A
Vi
v
ald
i
a
n
ten
n
a
m
en
tio
n
ed
in
t
h
e
liter
a
tu
r
e
[
8
]
o
p
e
r
ates
o
v
er
a
w
id
e
f
r
eq
u
en
c
y
r
a
n
g
e
a
n
d
e
m
p
lo
y
s
a
s
lo
t
-
l
in
e
f
ee
d
to
en
h
an
ce
r
ec
o
n
f
ig
u
r
ab
ilit
y
a
n
d
p
er
f
o
r
m
an
ce
.
B
y
e
m
b
ed
d
in
g
a
p
air
o
f
P
I
N
d
io
d
es
in
to
h
o
r
izo
n
ta
l
an
d
v
er
tical
s
t
r
ip
s
,
in
d
esi
g
n
[
9
]
en
ab
les
s
e
v
er
al
r
ec
o
n
f
ig
u
r
ab
le
f
r
eq
u
e
n
c
y
r
an
g
es
w
i
th
i
n
t
h
e
3
GHz
to
1
0
GHz
r
an
g
e.
C
h
o
u
k
i
k
er
an
d
B
eh
er
a
[
10
]
f
r
eq
u
en
c
y
r
ec
o
n
f
i
g
u
r
ab
le
w
id
e
b
an
d
k
o
tch
s
n
o
w
f
lak
e
f
r
ac
tal
an
ten
n
a
is
an
al
y
ze
d
.
T
h
e
f
r
eq
u
en
c
y
r
ec
o
n
f
i
g
u
r
atio
n
f
o
r
u
ltra
h
ig
h
f
r
e
q
u
en
c
y
(
U
HF
)
f
r
eq
u
e
n
c
y
r
a
n
g
e
ac
h
iev
ed
e
m
p
lo
y
i
n
g
R
F
P
I
N
d
io
d
es
alo
n
g
w
i
th
L
u
m
p
ed
ele
m
e
n
t
li
k
e
ca
p
ac
ito
r
s
an
d
in
d
u
cto
r
s
.
N
g
u
y
e
n
-
T
r
o
n
g
et
a
l.
[
11
]
d
is
cu
s
s
es
a
d
u
al
-
b
an
d
,
c
o
m
p
ac
t
m
o
n
o
p
o
le
an
te
n
n
a
th
at
e
m
p
lo
y
s
v
ar
ac
to
r
d
io
d
es
to
ad
j
u
s
t
f
r
eq
u
e
n
cie
s
.
T
h
e
p
re
-
f
r
ac
tal
s
tr
u
ct
u
r
e
d
escr
ib
ed
in
[1
2
]
allo
w
s
f
o
r
g
r
ea
ter
m
i
n
iat
u
r
izatio
n
w
h
ile
m
ain
ta
in
i
n
g
h
i
g
h
p
er
f
o
r
m
a
n
ce
,
ef
f
ec
ti
v
el
y
ex
p
a
n
d
in
g
th
e
s
u
r
f
ac
e
ar
ea
w
it
h
o
u
t
r
eq
u
ir
in
g
ad
d
itio
n
al
s
p
ac
e,
t
h
r
o
u
g
h
o
p
ti
m
iz
in
g
b
o
th
s
ize
an
d
f
u
n
cti
o
n
alit
y
.
F
u
r
th
er
m
o
r
e,
C
h
ao
u
c
h
e
et
a
l.
[1
3
]
in
tr
o
d
u
ce
s
a
C
P
W
to
p
r
o
v
id
e
a
r
ec
o
n
f
ig
u
r
ab
le
an
ten
n
a
w
it
h
a
cr
escen
t
-
p
atter
n
ed
f
r
ac
tal
d
esig
n
.
I
t
em
p
lo
y
s
R
F
P
I
N
d
io
d
es,
r
esis
to
r
s
,
an
d
in
d
u
cto
r
s
to
en
ab
le
ad
j
u
s
tab
le
s
w
itc
h
i
n
g
ac
r
o
s
s
ei
g
h
t
f
r
eq
u
en
c
y
r
an
g
es,
s
p
an
n
i
n
g
f
r
o
m
1
.
4
6
to
6
.
1
5
GHz
.
A
C
P
W
-
f
ed
tr
ian
g
u
lar
p
atch
an
ten
n
a
[1
4
]
,
lin
k
ed
to
t
w
o
d
i
s
tin
c
t
s
er
p
en
tin
e
s
t
u
b
s
th
r
o
u
g
h
t
w
o
P
I
N
d
io
d
es,
is
p
r
o
p
o
s
ed
to
ac
h
iev
e
r
ad
iatio
n
ac
r
o
s
s
u
p
to
eig
h
t
d
if
f
er
e
n
t
f
r
eq
u
e
n
c
y
b
a
n
d
s
an
d
a
w
id
eb
an
d
s
p
ec
tr
u
m
.
T
h
e
d
esig
n
[1
5
]
-
[1
7
]
d
em
o
n
s
tr
ate
s
a
f
r
eq
u
e
n
c
y
r
ec
o
n
f
ig
u
r
ab
le
an
te
n
n
a
ac
h
ie
v
ed
u
s
in
g
P
I
N
d
io
d
es.
B
ased
o
n
th
e
liter
atu
r
e
s
u
r
v
e
y
,
th
e
f
o
llo
w
i
n
g
cr
itical
f
ac
to
r
s
h
av
e
b
ee
n
d
r
a
w
n
,
w
h
ic
h
in
s
p
ir
e
th
e
p
r
esen
t
w
o
r
k
:
th
e
n
ee
d
f
o
r
m
i
n
i
m
izi
n
g
t
h
e
p
r
o
b
lem
o
f
n
ar
r
o
w
b
an
d
w
i
d
t
h
an
d
lo
w
g
ain
i
n
co
n
v
en
tio
n
al
an
t
en
n
a
s
,
an
d
a
co
m
p
ac
t
an
te
n
n
a
t
h
at
ca
n
w
o
r
k
w
i
th
5G
b
an
d
s
.
T
h
er
ef
o
r
e
,
we
ai
m
to
d
esig
n
an
d
d
ev
elo
p
a
co
m
p
ac
t,
w
id
eb
a
n
d
,
f
r
eq
u
e
n
c
y
-
r
ec
o
n
f
i
g
u
r
ab
le
an
te
n
n
a
o
p
er
atin
g
in
t
h
e
s
u
b
-
6
GHz
s
p
e
ctr
u
m
,
i
m
p
r
o
v
i
n
g
p
er
f
o
r
m
a
n
ce
an
d
f
le
x
ib
ili
t
y
f
o
r
m
o
d
er
n
w
ir
ele
s
s
co
m
m
u
n
i
ca
tio
n
s
y
s
te
m
s
.
T
h
is
m
a
n
u
s
cr
ip
t
p
r
esen
ts
s
ev
er
al
in
n
o
v
ati
v
e
f
ea
tu
r
es,
i
n
cl
u
d
in
g
:
-
T
h
e
p
r
o
p
o
s
ed
an
ten
n
a
co
n
s
i
s
ts
o
f
a
s
i
m
p
le
g
eo
m
etr
ical
co
n
f
i
g
u
r
atio
n
,
t
h
u
s
lead
in
g
to
s
ig
n
i
f
ic
an
tl
y
r
ed
u
ce
d
f
ab
r
icatio
n
er
r
o
r
.
De
s
ig
n
i
n
g
a
co
m
p
ac
t
an
te
n
n
a
t
h
at
in
co
r
p
o
r
ate
P
I
N
d
io
d
es
w
h
ile
m
a
in
ta
in
i
n
g
h
ig
h
p
er
f
o
r
m
a
n
ce
ac
r
o
s
s
v
ar
io
u
s
f
r
eq
u
en
c
y
b
an
d
s
r
e
m
ai
n
s
a
ch
alle
n
g
e.
-
Du
al
-
b
an
d
f
u
n
ctio
n
al
it
y
,
w
h
ic
h
p
r
o
v
id
es
a
g
ai
n
o
f
u
p
to
1
.
9
d
B
at
3
.
9
GHz
an
d
co
v
er
s
a
b
an
d
w
id
t
h
o
f
1
1
3
0
MH
z.
-
T
h
e
an
ten
n
a
ca
n
r
eso
n
ate
at
t
w
o
s
ep
ar
ate
f
r
eq
u
en
c
y
b
a
n
d
s
,
m
a
k
in
g
it
id
ea
l
f
o
r
5
G
f
ix
ed
w
ir
eles
s
ap
p
licatio
n
s
an
d
o
th
er
w
ir
eles
s
n
et
w
o
r
k
in
g
r
eq
u
ir
e
m
e
n
t
s
.
2.
ANT
E
NNA
D
E
SI
G
N
T
h
is
s
ec
tio
n
o
u
tli
n
e
s
th
e
f
u
n
d
am
e
n
tal
s
tr
u
ct
u
r
e
an
d
d
esi
g
n
co
n
ce
p
t
in
r
ef
er
e
n
ce
to
th
e
p
r
o
p
o
s
ed
s
tack
ed
T
-
s
h
ap
ed
an
ten
n
a.
T
h
is
g
eo
m
etr
y
allo
w
s
ea
s
y
in
te
g
r
atio
n
o
f
s
w
itch
e
s
(
e.
g
.
,
P
I
N
d
i
o
d
es)
f
o
r
tu
n
in
g
.
A
m
o
d
i
f
ied
co
n
d
u
cti
v
e
g
r
o
u
n
d
p
lan
e
i
s
u
tili
ze
d
to
e
n
h
a
n
ce
r
ad
i
atio
n
e
f
f
icien
c
y
a
n
d
o
p
ti
m
ize
r
ad
iated
p
atter
n
s
in
th
e
f
ar
f
ie
ld
.
I
n
s
i
m
u
latio
n
s
,
f
r
eq
u
en
c
y
r
ec
o
n
f
ig
u
r
atio
n
i
s
m
an
a
g
ed
u
s
in
g
lu
m
p
ed
R
L
C
co
m
p
o
n
e
n
t
s
,
an
d
a
P
I
N
d
io
d
e
is
in
co
r
p
o
r
ated
in
th
e
f
ab
r
icatio
n
p
r
o
ce
s
s
to
en
ab
l
e
f
r
eq
u
en
c
y
r
ec
o
n
f
ig
u
r
ab
ilit
y
.
Fig
u
r
e
1
d
ep
ict
th
e
p
r
o
p
o
s
ed
an
ten
n
a
f
r
o
m
t
h
e
to
p
an
d
b
o
tto
m
p
er
s
p
ec
tiv
es,
r
e
s
p
ec
tiv
el
y
w
it
h
d
i
m
e
n
s
io
n
s
o
f
1
5
×
2
5
m
m
2
.
T
h
e
an
ten
n
a
is
f
ab
r
icate
d
o
n
a
FR
-
4
s
u
b
s
tr
ate
w
it
h
a
r
elativ
e
d
ielec
tr
ic
co
n
s
tan
t
4
.
4
,
th
ick
n
es
s
1
.
6
m
m
an
d
lo
s
s
tan
g
e
n
t
o
f
0
.
0
2
.
T
h
e
len
g
t
h
o
f
th
e
p
ar
tial
g
r
o
u
n
d
(
L
g
)
i
s
o
p
ti
m
ized
as
s
h
o
w
n
in
Fi
g
u
r
e
s
1
(
a)
an
d
1
(
b
)
.
I
t
also
ch
an
g
es
th
e
r
e
s
o
n
a
n
t
f
r
eq
u
en
c
y
.
B
u
t
to
ac
h
ie
v
e
th
e
d
esire
d
f
r
eq
u
en
c
y
w
i
th
t
h
e
s
a
m
e
a
n
ten
n
a
d
i
m
e
n
s
io
n
,
g
r
o
u
n
d
p
lan
e
len
g
t
h
is
tr
u
n
ca
t
ed
.
T
h
e
p
a
r
am
etr
ic
v
al
u
es
o
f
th
e
o
p
ti
m
ized
s
tack
ed
T
s
h
ap
e
ar
e
m
en
tio
n
ed
in
T
ab
le
1
.
T
h
e
d
im
e
n
s
io
n
s
o
f
th
e
m
o
n
o
p
o
le
an
ten
n
a,
s
u
c
h
a
s
len
g
t
h
(
L
)
an
d
w
id
th
(
W
)
ar
e
d
eter
m
i
n
ed
u
s
in
g
w
ell
-
e
s
tab
lis
h
ed
eq
u
atio
n
s
b
as
ed
o
n
tr
an
s
m
is
s
io
n
li
n
e
ap
p
r
o
a
ch
[1
8
]
.
=
4
√
∈
−
(
1
)
B
y
co
n
s
id
er
in
g
f
r
in
g
i
n
g
f
ield
s
,
th
e
ef
f
ec
ti
v
e
p
er
m
itt
iv
i
t
y
ca
n
b
e
o
b
tain
ed
u
s
in
g
t
h
e
(
2
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
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0
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9
-
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I
n
t J
R
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o
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f
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&
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m
b
ed
d
ed
Sy
s
t
,
Vo
l.
14
,
No
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3
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b
er
2
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2
5
:
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616
∈
=
∈
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1
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−
1
2
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1
+
12
ℎ
(
2
)
I
n
th
i
s
co
n
te
x
t,
“
c”
d
en
o
tes
t
h
e
s
p
ee
d
o
f
lig
h
t
in
a
v
ac
u
u
m
,
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ig
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ar
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I
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r
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8
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el
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ates
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ir
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a
s
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