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I
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I
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,
Vo
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16
,
No
.
4
,
Au
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t
20
26
:
1
9
1
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-
1926
1914
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late
t
h
e
f
r
eq
u
en
cy
allo
ca
tio
n
a
n
d
co
n
tr
o
l
th
e
r
a
d
io
s
p
ec
tr
u
m
to
av
o
id
in
ter
f
er
e
n
ce
[
3
]
.
C
o
n
s
eq
u
en
tly
,
an
y
an
ten
n
a
d
e
s
ig
n
m
u
s
t
co
n
s
id
er
th
e
f
r
e
q
u
e
n
cy
allo
ca
tio
n
s
d
ictated
b
y
th
e
I
T
U
(
e.
g
.,
f
o
r
th
e
u
p
lin
k
,
t
h
e
f
r
e
q
u
en
c
y
b
an
d
is
2
.
0
2
5
to
2
.
1
1
GHz
an
d
f
o
r
th
e
d
o
wn
lin
k
,
t
h
e
f
r
e
q
u
en
c
y
b
a
n
d
is
2
.
2
to
2
.
2
9
GHz
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
th
e
d
esi
g
n
an
d
v
alid
atio
n
o
f
a
c
o
m
p
a
ct,
lig
h
tweig
h
t
cir
cu
lar
ly
p
o
lar
ized
(
C
P)
p
atch
an
ten
n
a
o
p
er
atin
g
in
th
e
S
-
b
an
d
o
v
er
th
e
2
.
0
2
5
to
2
.
1
1
GHz
f
r
e
q
u
en
c
y
r
a
n
g
e,
i
n
ten
d
ed
f
o
r
a
r
ec
eiv
er
m
o
d
u
le
o
f
a
3
U
u
n
iv
e
r
s
ity
C
u
b
eSat
.
Mo
r
e
s
p
ec
if
ically
,
th
e
o
b
jectiv
es
ar
e
to
i)
s
im
u
ltan
eo
u
s
ly
r
ed
u
ce
th
e
an
ten
n
a
’
s
s
ize
an
d
weig
h
t
wh
ile
p
r
eser
v
in
g
its
elec
tr
o
m
ag
n
etic
p
er
f
o
r
m
an
ce
,
ii)
e
n
s
u
r
e
s
tab
le
cir
cu
lar
p
o
lar
izatio
n
ac
r
o
s
s
th
e
en
tire
o
p
er
atin
g
b
an
d
,
an
d
iii)
ac
h
iev
e
s
u
f
f
icien
t
g
ain
t
o
p
r
o
v
id
e
a
lin
k
m
ar
g
i
n
ex
ce
ed
in
g
3
d
B
.
T
h
e
m
ain
s
cien
tific
co
n
tr
ib
u
tio
n
o
f
th
is
w
o
r
k
lies
in
th
e
d
esig
n
o
f
a
co
m
p
ac
t,
lig
h
tweig
h
t,
an
d
in
teg
r
ab
le
s
o
lu
tio
n
th
at
m
ee
ts
th
e
s
tr
in
g
en
t
d
esig
n
co
n
s
tr
ain
ts
o
f
n
an
o
s
atellites
wh
ile
m
ain
tain
in
g
p
er
f
o
r
m
an
ce
s
u
itab
le
f
o
r
S
-
b
an
d
ap
p
licatio
n
s
.
T
h
e
a
r
ticle
is
o
r
g
an
ized
in
to
f
o
u
r
s
ec
tio
n
s
.
Sectio
n
2
is
d
ed
icate
d
to
th
e
s
tu
d
y
o
f
d
if
f
er
en
t
an
ten
n
as
p
u
b
lis
h
ed
in
s
cien
tific
liter
atu
r
e.
I
n
s
ec
tio
n
3
,
th
e
g
e
o
m
etr
y
o
f
m
in
iatu
r
ized
p
atch
an
te
n
n
a
a
n
d
its
d
esig
n
p
r
o
ce
s
s
ar
e
p
r
esen
ted
.
A
p
ar
am
etr
ic
s
tu
d
y
o
f
th
e
d
esig
n
ed
an
ten
n
a
is
co
n
d
u
cted
in
s
ec
tio
n
4
.
B
ef
o
r
e
co
n
clu
d
in
g
,
th
e
d
is
cu
s
s
io
n
an
d
an
aly
s
is
o
f
th
e
ex
p
er
im
en
tal
an
d
s
im
u
lated
r
esu
lts
is
elab
o
r
ated
u
p
o
n
in
s
ec
tio
n
5
.
2.
ST
A
T
E
O
F
T
H
E
ART
Acc
o
r
d
in
g
to
Ab
u
l
g
asem
et
a
l
.
[
4
]
,
p
lan
ar
an
te
n
n
as
o
p
er
atin
g
in
th
e
C
-
b
an
d
o
r
S
-
b
an
d
ar
e
th
e
m
o
s
t
wid
ely
u
s
ed
in
th
e
C
u
b
eSat
co
m
m
u
n
icatio
n
s
s
y
s
tem
.
T
h
ey
h
av
e
s
ig
n
if
ican
t
a
d
v
an
tag
es
s
u
ch
as
lo
w
p
r
o
f
ile
,
lo
w
co
s
t
an
d
ab
ilit
y
to
s
teer
t
h
e
b
ea
m
o
f
ar
r
a
y
s
p
atch
an
te
n
n
a.
On
e
m
ajo
r
q
u
ality
o
f
p
la
n
ar
an
ten
n
as
is
th
at
th
e
m
ajo
r
ity
d
o
n
o
t
r
eq
u
ir
e
a
d
ep
lo
y
m
e
n
t
s
y
s
tem
,
wh
ich
s
im
p
lifie
s
th
eir
in
teg
r
atio
n
in
to
th
e
C
u
b
eSat
.
I
n
th
e
f
o
llo
win
g
,
a
ch
r
o
n
o
lo
g
ical
lis
t
o
f
a
n
ten
n
a
d
esig
n
s
f
o
r
C
u
b
e
Sats
p
r
esen
ted
in
d
if
f
er
en
t
r
ec
en
t
r
esear
ch
wo
r
k
s
ar
e
an
aly
ze
d
a
n
d
ev
al
u
ated
in
ter
m
s
o
f
th
eir
s
tr
u
ctu
r
e
s
,
o
p
er
atin
g
f
r
eq
u
e
n
cies,
r
ef
lectio
n
lo
s
s
(
S
11
)
,
b
an
d
wid
th
,
g
ain
a
n
d
if
th
e
y
ar
e
co
n
f
o
r
m
in
g
to
th
e
I
T
U
f
r
eq
u
en
cy
b
a
n
d
s
.
Acc
o
r
d
in
g
to
th
e
r
ep
o
r
ted
w
o
r
k
b
y
Yg
n
ac
io
-
E
s
p
in
o
za
et
a
l
.
[
5
]
,
a
q
u
asi
-
tr
an
s
p
ar
en
t
m
esh
p
atch
an
ten
n
a
d
esig
n
p
r
o
v
id
e
a
g
ai
n
o
f
4
.
8
7
d
B
i
with
r
e
f
lectio
n
lo
s
s
es
o
f
ar
o
u
n
d
-
1
8
.
5
d
B
o
v
er
a
b
an
d
wid
th
o
f
2
5
0
MH
z
2
.
2
0
-
2
.
4
5
GHz
at
2
.
2
5
GHz
.
A
m
etam
ate
r
ial
with
a
r
ea
ctiv
e
im
p
ed
an
ce
s
u
r
f
ac
e
(
R
I
S)
is
em
p
lo
y
e
d
as th
e
g
r
o
u
n
d
p
la
n
e.
Ho
wev
e
r
,
th
e
r
esu
ltin
g
an
te
n
n
a
ex
h
ib
its
a
lim
ited
3
d
B
ax
ial
r
atio
b
an
d
wid
th
.
Fu
r
th
er
m
o
r
e
,
a
s
tack
ed
p
atc
h
an
ten
n
a
with
a
lo
w
-
p
r
o
f
il
e
d
esig
n
is
p
r
o
p
o
s
ed
b
y
Ve
ljo
v
ic
an
d
Sk
r
iv
er
v
ik
[
6
]
.
T
h
is
p
r
o
p
o
s
ed
an
ten
n
a
wo
r
k
s
in
th
e
f
r
e
q
u
en
cy
b
a
n
d
o
f
2
-
2
.
4
5
GHz
an
d
p
r
o
v
id
es
a
m
ea
s
u
r
ed
g
ain
o
f
9
d
B
i
at
2
.
4
5
GHz
.
An
ap
er
tu
r
e
-
c
o
u
p
le
d
in
lin
e
f
ee
d
tech
n
iq
u
e
is
im
p
lem
en
te
d
to
in
cr
ea
s
e
th
e
an
ten
n
a
cr
o
s
s
-
p
o
lar
izatio
n
an
d
g
ain
.
H
o
wev
er
,
th
e
m
ain
lim
itatio
n
o
f
th
e
d
esig
n
ed
an
te
n
n
a
is
th
e
co
n
f
ig
u
r
atio
n
o
f
its
f
ee
d
p
o
i
n
t.
Po
d
ilch
ak
et
a
l
.
[
7
]
d
e
v
elo
p
ed
a
cir
cu
lar
p
o
lar
izatio
n
p
atch
a
n
ten
n
a.
T
h
e
p
ar
ticu
lar
ity
o
f
th
is
an
ten
n
a
is
its
ea
s
e
o
f
in
teg
r
atio
n
in
to
a
s
o
lar
ce
ll.
I
t
is
ch
ar
ac
ter
ize
d
b
y
a
d
im
en
s
io
n
o
f
3
9
.
5
×
2
4
.
8
m
m
an
d
o
f
f
er
s
a
g
ain
o
f
4
.
8
d
B
i
at
th
e
f
r
eq
u
en
cy
2
.
4
5
GHz
.
Ho
wev
er
,
th
e
s
u
g
g
ested
an
ten
n
a
ac
h
ie
v
es
a
b
an
d
wid
th
o
f
2
.
4
5
%
an
d
a
g
ai
n
o
f
4
.
8
d
B
i a
t 2
.
4
5
GHz
,
wh
ich
d
o
es n
o
t c
o
r
r
esp
o
n
d
to
th
e
f
r
eq
u
en
cy
b
an
d
au
th
o
r
ized
b
y
th
e
I
T
U.
As
d
is
cu
s
s
ed
b
y
L
iu
et
a
l
.
[
8
]
,
th
e
p
r
o
p
o
s
ed
a
n
ten
n
a
is
m
a
d
e
u
p
o
f
a
r
ec
tan
g
u
lar
p
atc
h
m
ea
s
u
r
in
g
56
×
6
6
m
m
,
f
ab
r
icate
d
o
n
an
FR
-
4
s
u
b
s
tr
ate
o
f
6
0
×
7
0
m
m
,
an
d
a
m
etallic
g
r
o
u
n
d
p
l
an
e
s
tr
u
ctu
r
e
with
d
im
en
s
io
n
s
o
f
1
0
0
×
1
0
0
×
5
m
m
.
Me
asu
r
em
en
t
r
esu
lts
s
h
o
wed
th
at
th
e
m
an
u
f
ac
tu
r
e
d
an
te
n
n
a
wo
r
k
s
in
a
d
u
al
-
b
an
d
ce
n
ter
ed
o
n
2
.
1
GHz
an
d
2
.
4
5
GHz
,
with
r
e
f
lectio
n
l
o
s
s
es
o
f
-
1
9
.
5
3
d
B
an
d
-
1
6
.
6
1
d
B
r
esp
ec
tiv
ely
,
an
d
b
an
d
wid
th
s
o
f
1
3
0
MH
z
an
d
1
5
0
MH
z
r
esp
ec
tiv
ely
.
T
h
e
s
u
g
g
ested
an
ten
n
a
ex
h
ib
its
a
g
ain
o
f
1
0
.
4
8
d
B
i
at
2
.
4
5
GHz
an
d
1
0
.
1
2
d
B
i
at
2
.
1
GHz
.
Ho
wev
er
,
th
e
m
an
u
f
a
ctu
r
ed
a
n
ten
n
a
d
o
es
n
o
t
co
v
er
th
e
f
r
e
q
u
en
c
y
b
an
d
r
eq
u
ir
ed
b
y
I
T
U,
a
n
d
t
h
e
an
t
en
n
a
d
im
e
n
s
io
n
s
ar
e
q
u
ite
lar
g
e,
wh
ich
m
ay
a
f
f
ec
t
th
e
o
v
e
r
all
s
ize
o
f
th
e
1
U
C
u
b
eSat
.
On
th
e
o
th
er
h
an
d
,
E
l
B
ak
k
a
li
et
a
l
.
[
9
]
in
tr
o
d
u
ce
d
an
eq
u
ilater
al
tr
ian
g
u
lar
s
lo
t
an
ten
n
a
ex
cited
u
s
in
g
a
co
p
lan
ar
wav
e
g
u
id
e
(
C
P
W
)
f
ee
d
.
T
h
e
s
u
g
g
ested
an
t
en
n
a
h
as
a
lig
h
t,
co
m
p
ac
t
s
ize
to
s
u
it
th
e
C
u
b
eSat
s
tr
u
ctu
r
e,
an
d
o
f
f
er
s
a
g
ain
o
f
8
.
2
0
d
B
i
at
2
.
4
5
GHz
b
y
u
s
in
g
a
m
etal
p
ar
t
o
f
th
e
C
u
b
eSat
ch
ass
is
b
en
ea
th
th
e
s
lo
t
an
ten
n
a
as
a
r
e
f
lecto
r
.
T
h
e
o
b
tain
ed
r
esu
lts
in
d
icate
th
a
t
th
e
d
esig
n
ed
an
ten
n
a
ac
h
iev
es
a
r
etu
r
n
l
o
s
s
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J E
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&
C
o
m
p
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n
g
I
SS
N:
2088
-
8
7
0
8
Min
ia
tu
r
iz
ed
p
a
tch
a
n
ten
n
a
fo
r
th
e
S
-
b
a
n
d
co
mmu
n
ica
tio
n
s
u
b
s
ystem
… (
N
a
b
il E
l H
a
s
s
a
in
a
te
)
1915
ap
p
r
o
x
im
ately
−2
3
d
B
an
d
an
u
ltra
-
wid
e
b
an
d
wid
th
o
f
-
1
0
d
B
f
r
o
m
1
2
4
0
MH
z
2
.
2
3
0
-
3
.
4
7
0
GHz
.
Ho
wev
er
,
th
e
an
ten
n
a
’
s
o
p
er
atin
g
b
an
d
o
n
ly
co
v
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r
s
a
p
ar
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f
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I
T
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a
p
p
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i
at
i
n
g
e
le
m
en
t
w
i
t
h
d
i
m
e
n
s
i
o
n
s
W
p
=
L
p
=
4
7
.
5
m
m
a
n
d
a
g
r
o
u
n
d
p
l
a
n
e
m
e
a
s
u
r
i
n
g
7
0
×
7
0
m
m
.
I
t
o
p
e
r
a
t
e
s
at
a
r
e
s
o
n
a
n
t
f
r
e
q
u
e
n
c
y
o
f
2
.
0
8
3
G
H
z
,
e
x
h
i
b
i
t
i
n
g
a
r
e
f
l
e
ct
i
o
n
c
o
e
f
f
i
c
ien
t
o
f
−
2
7
.
2
9
d
B
a
n
d
a
b
a
n
d
w
i
d
t
h
o
f
3
9
.
1
2
M
H
z
(
2
.
0
6
3
t
o
2
.
1
0
2
G
H
z
)
.
(
a)
(
b
)
Fig
u
r
e
3
.
Dev
el
o
p
ed
a
n
ten
n
a
1
(
s
tep
1
)
f
r
o
m
(
a)
to
p
v
iew
an
d
(
b
)
b
ac
k
v
iew
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
-
8
7
0
8
Min
ia
tu
r
iz
ed
p
a
tch
a
n
ten
n
a
fo
r
th
e
S
-
b
a
n
d
co
mmu
n
ica
tio
n
s
u
b
s
ystem
… (
N
a
b
il E
l H
a
s
s
a
in
a
te
)
1917
T
h
e
s
ec
o
n
d
s
tep
is
to
m
in
im
ize
th
e
d
im
en
s
io
n
s
o
f
an
ten
n
a
1
f
o
r
b
etter
in
teg
r
atio
n
in
to
th
e
C
u
b
eSat,
wh
ile
r
etain
in
g
th
e
an
ten
n
a
’
s
r
ad
io
elec
tr
ic
ch
ar
ac
ter
is
tics
,
i.e
.
,
o
p
er
atin
g
f
r
eq
u
en
cy
b
a
n
d
,
r
ad
iatio
n
p
atter
n
an
d
g
ain
.
I
n
o
r
d
er
to
ac
h
iev
e
th
is
,
tr
u
n
ca
ted
b
o
u
n
d
ar
y
o
f
th
e
r
ad
iatin
g
elem
en
t
is
u
s
ed
.
B
y
ad
d
in
g
th
ese
co
n
to
u
r
s
,
th
e
elec
tr
ical
le
n
g
th
in
cr
ea
s
es
in
a
s
m
aller
v
o
lu
m
e.
Kn
o
win
g
th
at
t
h
e
r
a
d
io
-
ele
ctr
ic
ch
ar
ac
ter
is
tics
o
f
th
e
an
te
n
n
a
ch
a
n
g
e
with
th
e
m
o
d
if
icatio
n
o
f
th
e
c
h
o
s
en
el
ec
tr
ical
len
g
th
,
it is
esp
ec
ially
ass
o
ciate
d
with
th
e
r
eso
n
an
t
f
r
eq
u
en
cy
.
As
th
e
elec
tr
ical
len
g
th
in
cr
ea
s
es,
th
e
r
eso
n
an
t
f
r
e
q
u
en
c
y
d
ec
r
e
ases
,
lead
in
g
to
a
s
ig
n
if
ican
t r
ed
u
ctio
n
in
an
te
n
n
a
s
ize.
R
ed
d
y
et
a
l
.
[
1
4
]
–
[
1
7
]
,
em
p
lo
y
s
s
y
m
m
etr
ical
o
r
asy
m
m
et
r
ical
f
r
ac
tal
cu
r
v
es
alo
n
g
th
e
r
ib
s
o
f
a
s
q
u
ar
e
p
atch
a
n
ten
n
a.
T
h
ese
f
r
ac
tal
cu
r
v
es
ca
n
b
e
U
-
s
h
ap
ed
,
p
o
l
y
g
o
n
al,
tr
ian
g
u
lar
o
r
s
em
icir
cu
lar
.
I
n
o
u
r
ca
s
e,
we
o
p
te
d
f
o
r
asy
m
m
etr
i
ca
l
h
alf
-
cir
cle
ar
o
u
n
d
th
e
e
d
g
es
o
f
th
e
s
q
u
ar
e
p
atc
h
an
te
n
n
a,
as
illu
s
tr
ated
in
Fig
u
r
e
4
.
Fig
u
r
e
4
(
a
)
s
h
o
ws th
e
to
p
v
iew
o
f
An
ten
n
a
2
,
wh
il
e
Fig
u
r
e
4
(
b
)
p
r
esen
ts
th
e
b
ac
k
v
iew.
(
a)
(
b
)
Fig
u
r
e
4
.
Seco
n
d
s
tep
o
f
d
esig
n
p
r
o
ce
s
s
(
an
ten
n
a
2
)
f
r
o
m
(
a)
to
p
v
iew
an
d
(
b
)
b
ac
k
v
iew
Usi
n
g
s
em
icir
cle
tr
u
n
ca
tio
n
s
alo
n
g
b
o
th
ax
es
(
x,
y
)
as
s
h
o
w
n
in
Fig
u
r
e
4
,
we
o
b
tain
an
a
n
ten
n
a
with
r
ed
u
ce
d
d
im
en
s
io
n
s
W
p
=
L
p
=
3
2
m
m
an
d
g
r
o
u
n
d
p
lan
e
W
ground
plane
=
L
ground
plane
=5
5
m
m
.
I
n
d
ee
d
,
th
is
tech
n
i
q
u
e
all
o
we
d
t
h
e
m
in
iat
u
r
iz
ati
o
n
o
f
an
t
e
n
n
a
1
a
n
d
w
e
n
o
t
e
a
g
a
in
o
f
3
2
%
co
m
p
a
r
e
d
t
o
th
e
d
i
m
e
n
s
io
n
s
o
f
an
te
n
n
a
1
.
I
n
ad
d
itio
n
,
a
n
ten
n
a
2
o
p
er
ate
s
in
two
r
eso
n
a
n
t
f
r
e
q
u
en
cies.
T
h
e
f
ir
s
t
f
r
eq
u
e
n
cy
was
2
.
0
2
GHz
with
an
S
11
r
ef
lectio
n
co
ef
f
icien
t
o
f
u
p
t
o
-
4
0
.
9
5
d
B
an
d
a
n
im
p
ed
an
ce
b
an
d
wid
th
o
f
1
6
5
.
5
MH
z
f
r
o
m
1
.
9
7
6
5
GHz
to
2
.
1
4
2
GHz
.
T
h
e
s
ec
o
n
d
im
p
ed
an
ce
b
an
d
wid
th
was 2
.
8
3
3
t
o
2
.
9
1
5
GHz
,
ce
n
te
r
ed
at
2
.
8
7
5
GHz
.
T
h
e
f
in
al
s
tep
in
v
o
lv
es
in
tr
o
d
u
cin
g
m
o
d
if
icatio
n
s
to
th
e
an
ten
n
a
g
r
o
u
n
d
p
la
n
e,
eith
er
as
a
s
in
g
le
alter
atio
n
(
u
n
it
ce
ll)
o
r
as
m
u
lt
ip
le
f
ea
tu
r
es
ar
r
an
g
e
d
in
p
er
io
d
ic
o
r
ap
er
io
d
ic
g
eo
m
etr
ies.
T
h
ese
m
o
d
if
icatio
n
s
ar
e
r
ef
er
r
ed
to
as
a
d
ef
ec
ted
g
r
o
u
n
d
s
tr
u
ctu
r
e
(
DGS)
.
T
h
is
tech
n
iq
u
e
h
as
b
ee
n
wid
ely
u
til
ized
in
m
icr
o
wav
e
tech
n
o
lo
g
ies:
f
ilter
s
,
co
p
lan
ar
wav
eg
u
id
e,
am
p
lifie
r
an
d
an
t
en
n
a.
I
n
ad
d
itio
n
,
s
ev
e
r
al
s
tu
d
ies
[
1
8
]
–
[
2
3
]
h
av
e
in
v
esti
g
ated
th
e
d
esig
n
o
f
m
icr
o
s
tr
ip
an
ten
n
as
u
s
in
g
th
is
tec
h
n
iq
u
e.
T
h
ese
wo
r
k
s
h
ig
h
lig
h
t
its
ef
f
ec
tiv
en
ess
in
r
ed
u
cin
g
an
ten
n
a
s
ize,
m
itig
atin
g
cr
o
s
s
-
p
o
lar
izatio
n
an
d
m
u
tu
al
co
u
p
lin
g
in
a
n
ten
n
a
ar
r
ay
s
,
s
u
p
p
r
ess
in
g
h
ar
m
o
n
ic
r
esp
o
n
s
es,
an
d
,
m
o
s
t im
p
o
r
tan
tly
,
ac
h
iev
in
g
cir
cu
l
ar
p
o
lar
izatio
n
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
s
tep
is
to
m
o
d
if
y
th
e
c
u
r
r
e
n
t
d
is
tr
ib
u
tio
n
o
n
th
e
g
r
o
u
n
d
p
la
n
e
in
o
r
d
e
r
to
o
b
tain
cir
cu
lar
p
o
lar
izatio
n
.
Var
io
u
s
tech
n
iq
u
es
an
d
m
eth
o
d
s
h
a
v
e
b
ee
n
r
ep
o
r
ted
in
th
e
liter
atu
r
e
f
o
r
ac
h
iev
in
g
cir
cu
lar
p
o
lar
izatio
n
in
p
lan
a
r
an
ten
n
as
[
2
4
]
.
As
r
ep
o
r
ted
b
y
Kh
an
d
elwa
l
et
a
l
.
[
2
0
]
,
o
n
e
co
m
m
o
n
ly
u
s
e
d
tech
n
iq
u
e
co
n
s
is
ts
o
f
in
tr
o
d
u
c
in
g
s
lo
ts
in
th
e
g
r
o
u
n
d
p
lan
e
,
wh
ich
m
o
d
if
y
th
e
tr
an
s
m
is
s
io
n
ch
ar
ac
ter
is
tics
o
f
th
e
s
tr
u
ctu
r
e
b
y
ad
d
in
g
s
lo
t
ca
p
ac
itan
ce
,
s
lo
t
in
d
u
ctan
ce
,
an
d
s
lo
t
r
esis
tan
ce
.
Fig
u
r
e
5
illu
s
tr
ates
th
e
th
ir
d
s
tep
o
f
th
e
d
esig
n
p
r
o
ce
s
s
f
o
r
a
n
t
en
n
a
3
.
Fig
u
r
e
5
(
a)
p
r
esen
ts
t
h
e
to
p
v
iew,
wh
ile
Fig
u
r
e
5
(
b
)
p
r
esen
ts
th
e
r
ea
r
v
iew
s
h
o
win
g
th
e
s
lo
ts
in
tr
o
d
u
ce
d
in
th
e
g
r
o
u
n
d
p
lan
e.
(
a)
(
b
)
Fig
u
r
e
5
.
T
h
ir
d
s
tep
o
f
d
esig
n
p
r
o
ce
s
s
(
an
ten
n
a
3
)
f
r
o
m
(
a)
t
o
p
v
iew
an
d
(
b
)
b
ac
k
v
iew
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
9
1
3
-
1926
1918
Fig
u
r
e
6
s
h
o
ws
th
e
p
r
o
ce
s
s
o
f
an
ten
n
a
3
.
T
h
e
r
ef
lectio
n
co
e
f
f
icien
ts
o
f
t
h
e
th
r
ee
s
tep
s
o
f
th
e
an
ten
n
a
d
esig
n
p
r
o
ce
s
s
ar
e
s
h
o
wn
in
Fig
u
r
e
6
(
a)
.
I
t
ca
n
b
e
o
b
s
er
v
e
d
th
at
ad
d
in
g
a
s
lo
t
in
th
e
g
r
o
u
n
d
p
la
n
e
en
h
a
n
ce
s
th
e
b
an
d
wid
th
f
r
o
m
3
9
.
1
2
M
Hz
o
b
tain
ed
in
s
tep
1
,
to
1
6
5
.
5
MH
z
in
s
tep
2
,
to
2
1
6
.
9
MH
z
in
th
e
last
s
tep
th
e
f
r
eq
u
e
n
cy
b
an
d
[
1
.
9
8
4
;
2
.
2
0
1
]
GHz
.
Als
o
,
th
e
in
co
r
p
o
r
atio
n
o
f
s
lo
ts
h
as
in
f
lu
e
n
ce
d
th
e
an
t
en
n
a
’
s
p
o
lar
izatio
n
,
as
illu
s
tr
ated
in
F
ig
u
r
e
6
(
b
)
.
T
h
e
in
tr
o
d
u
ctio
n
o
f
s
lo
ts
in
th
e
g
r
o
u
n
d
p
lan
e
h
av
e
r
esu
lted
in
a
cir
cu
lar
ly
p
o
lar
ized
a
n
ten
n
a
i
n
th
e
2
.
0
3
8
-
2
.
0
8
5
GHz
b
an
d
,
with
an
a
x
ial
r
atio
b
a
n
d
wid
th
e
q
u
al
to
4
7
.
4
7
MH
z
th
at
is
s
y
m
m
etr
ical
r
eg
ar
d
i
n
g
th
e
r
eso
n
an
t
f
r
eq
u
e
n
cy
o
f
2
.
0
6
GHz
.
Fin
ally
,
th
e
in
co
r
p
o
r
atio
n
o
f
s
lo
ts
in
th
e
g
r
o
u
n
d
p
lan
e
o
f
th
e
d
esig
n
ed
a
n
ten
n
a
im
p
r
o
v
es
b
o
th
its
b
an
d
wid
th
an
d
cir
cu
la
r
p
o
la
r
izatio
n
p
e
r
f
o
r
m
an
ce
,
a
n
d
a
b
o
v
e
all
p
lay
ed
an
im
p
o
r
ta
n
t r
o
le
in
r
ed
u
cin
g
th
e
an
te
n
n
a
’
s
weig
h
t
.
(
a)
(
b
)
Fig
u
r
e
6
.
An
te
n
n
a
3
:
(
a)
r
e
f
lectio
n
co
ef
f
icien
t S1
1
s
tep
1
,
s
te
p
2
,
s
tep
3
an
d
(
b
)
a
x
ial
r
atio
:
s
tep
2
an
d
s
tep
3
4.
P
ARAM
E
T
R
I
C
S
T
UDY
T
o
ac
h
iev
e
a
cir
c
u
lar
ly
p
o
la
r
ized
(
C
P)
an
ten
n
a
o
p
er
atin
g
in
th
e
2
.
0
2
5
to
2
.
1
1
GHz
f
r
e
q
u
en
cy
b
an
d
with
ad
eq
u
ate
g
ai
n
,
a
f
ir
s
t
p
a
r
am
etr
ic
s
tu
d
y
o
f
th
e
len
g
th
L
s
o
f
th
e
s
lo
ts
in
tr
o
d
u
ce
d
a
n
d
t
h
eir
p
o
s
itio
n
in
th
e
g
r
o
u
n
d
p
la
n
e
was
ca
r
r
ied
o
u
t.
T
h
e
ef
f
ec
t
o
f
in
tr
o
d
u
cin
g
s
lo
ts
in
to
th
e
g
r
o
u
n
d
p
lan
e
was
ex
am
in
ed
in
th
is
f
ir
s
t
p
ar
am
etr
ic
s
tu
d
y
,
as
s
h
o
wn
in
Fig
u
r
e
7
.
Fig
u
r
e
7
(
a)
p
r
esen
ts
s
tep
1
with
two
s
y
m
m
etr
ical
s
lo
ts
,
Fig
u
r
e
7
(
b
)
s
h
o
ws s
tep
2
with
f
o
u
r
s
lo
ts
,
an
d
Fig
u
r
e
7
(
c)
illu
s
tr
ates step
3
with
eig
h
t slo
ts
.
(
a)
(
b
)
(
c)
Fig
u
r
e
7
.
Dev
el
o
p
m
en
t step
o
f
th
e
m
o
d
if
ie
d
g
r
o
u
n
d
p
lan
e:
(
a
)
s
tep
1
,
(
b
)
s
tep
2
,
an
d
(
c)
s
tep
3
T
h
e
r
esu
lts
ar
e
illu
s
tr
ated
in
Fig
u
r
e
8
.
T
h
e
o
n
e
o
b
tain
ed
i
n
ter
m
s
o
f
r
ef
lectio
n
co
ef
f
icien
t
S
11
is
s
h
o
wn
in
Fig
u
r
e
8
(
a
)
an
d
a
x
ial
r
atio
is
in
Fig
u
r
e
8
(
b
)
.
An
im
p
r
o
v
em
e
n
t
in
th
e
an
ten
n
a
b
an
d
wid
th
ca
n
b
e
o
b
s
er
v
ed
f
r
o
m
s
tep
1
to
s
tep
3
o
f
th
e
d
esig
n
e
d
a
n
ten
n
a,
r
a
n
g
in
g
f
r
o
m
1
8
1
.
3
3
MH
z
th
r
o
u
g
h
1
8
7
.
9
1
MH
z
to
1
9
7
.
4
5
MH
z.
W
e
also
n
o
te
th
at
cir
cu
lar
p
o
lar
izatio
n
is
o
b
tain
ed
f
r
o
m
s
tep
2
a
n
d
a
n
im
p
r
o
v
em
e
n
t
in
ax
ial
r
atio
b
an
d
wid
t
h
b
y
ad
d
in
g
s
lo
ts
in
th
e
g
r
o
u
n
d
p
lan
e.
T
h
e
ci
r
cu
lar
p
o
lar
izatio
n
b
a
n
d
wid
th
(
ax
ial
r
atio
)
v
ar
ies
f
r
o
m
2
4
.
6
MH
z
,
2
.
0
2
4
to
2
.
0
4
8
GHZ
f
o
r
s
tep
2
to
2
2
.
5
9
MH
z
,
2
.
0
2
9
to
2
.
0
5
2
GHz
f
o
r
th
e
t
h
ir
d
s
tep
.
T
o
en
h
an
ce
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
s
im
u
lated
an
ten
n
a
i
n
s
tep
3
,
an
o
th
e
r
p
ar
am
et
r
ic
s
tu
d
y
w
as c
ar
r
ied
o
u
t,
in
v
o
lv
in
g
th
e
in
tr
o
d
u
ctio
n
o
f
m
o
r
e
s
lo
ts
in
th
e
g
r
o
u
n
d
p
lan
e.
T
o
d
o
th
is
,
eig
h
t
s
y
m
m
etr
ical
s
lo
ts
ar
e
in
tr
o
d
u
ce
d
o
n
th
e
m
o
d
el
co
r
r
esp
o
n
d
in
g
to
s
tep
3
with
a
s
lo
t
len
g
th
o
f
L
s
=6
m
m
(
Fig
u
r
e
9
(
a)
s
tep
4
)
,
th
en
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
-
8
7
0
8
Min
ia
tu
r
iz
ed
p
a
tch
a
n
ten
n
a
fo
r
th
e
S
-
b
a
n
d
co
mmu
n
ica
tio
n
s
u
b
s
ystem
… (
N
a
b
il E
l H
a
s
s
a
in
a
te
)
1919
eig
h
t
o
th
er
s
y
m
m
etr
ical
s
lo
ts
o
f
th
e
s
am
e
s
lo
t
len
g
th
(
Fig
u
r
e
9
(
b
)
s
tep
5
)
an
d
f
in
ally
Fig
u
r
e
9
(
c)
s
tep
6
co
r
r
esp
o
n
d
s
to
th
e
u
s
e
o
f
s
lo
ts
o
f
th
e
s
am
e
len
g
th
L
s
=9
m
m
as illu
s
tr
ated
in
Fig
u
r
e
9.
(
a)
(
b
)
Fig
u
r
e
8
.
Dev
el
o
p
ed
a
n
ten
n
a
d
esig
n
: (
a)
r
e
f
lectio
n
co
e
f
f
icie
n
t s1
1
f
o
r
s
tep
1
,
s
tep
2
an
d
s
tep
3
o
f
th
e
m
o
d
if
ied
g
r
o
u
n
d
p
la
n
e
an
d
(
b
)
ax
ial
r
ati
o
f
o
r
e
ac
h
d
e
v
elo
p
m
e
n
t
s
tep
o
f
th
e
m
o
d
if
ied
g
r
o
u
n
d
p
la
n
e
(
a)
(
b
)
(
c)
Fig
u
r
e
9
.
Mo
d
if
icatio
n
s
m
ad
e
to
th
e
g
r
o
u
n
d
p
lan
:
(
a)
s
tep
4
,
(
b
)
s
tep
5
,
an
d
(
c)
s
tep
6
Fig
u
r
e
1
0
p
r
esen
ts
r
esu
lts
o
b
t
ain
ed
o
f
d
ev
elo
p
ed
a
n
ten
n
a
d
esig
n
in
ter
m
s
o
f
r
ef
lectio
n
c
o
ef
f
icien
t
S
11
an
d
ax
ial
r
ati
o
.
Fig
u
r
e
1
0
(
a)
s
h
o
ws
th
e
r
esu
lts
f
o
r
r
ef
le
ctio
n
co
e
f
f
icien
t
S
11
.
A
s
ig
n
if
ican
t
im
p
r
o
v
em
en
t
in
th
e
b
an
d
wid
t
h
o
f
th
e
d
esi
g
n
ed
an
ten
n
a
is
o
b
s
er
v
ed
f
r
o
m
s
tep
s
4
to
6
,
i
n
cr
ea
s
in
g
f
r
o
m
1
9
7
.
1
2
MH
z
,
1
.
9
8
7
-
2
.
1
8
4
GHz
to
2
0
3
.
8
5
MH
z
,
1
.
9
8
5
-
2
.
1
8
9
GHz
,
an
d
r
ea
ch
in
g
2
1
7
.
5
6
MH
z
,
1
.
9
8
4
-
2
.
2
0
1
GHz
.
Fig
u
r
e
1
0
(
b
)
s
h
o
ws
th
e
r
esu
lts
o
b
tain
ed
in
ter
m
s
o
f
th
e
ellip
ticity
r
atio
o
f
t
h
e
d
ev
el
o
p
e
d
an
ten
n
a
.
T
h
e
an
te
n
n
a
ci
r
cu
lar
p
o
lar
iz
atio
n
h
as
b
ee
n
im
p
r
o
v
ed
b
y
th
e
i
n
tr
o
d
u
ctio
n
o
f
th
e
s
lo
t
s
.
T
h
e
a
x
ial
r
atio
b
an
d
wid
th
f
o
r
s
tep
4
is
2
7
.
7
1
MH
z,
ce
n
ter
ed
o
n
th
e
r
eso
n
a
n
t
f
r
eq
u
en
c
y
o
f
2
.
0
6
GHz
.
I
n
s
tep
5
,
it
in
cr
ea
s
es
to
ap
p
r
o
x
im
ately
3
5
.
3
MH
z
ar
o
u
n
d
th
e
s
am
e
f
r
eq
u
e
n
cy
.
Fin
ally
,
in
s
tep
6
,
th
e
ax
ial
r
atio
b
an
d
wid
th
r
ea
ch
es
4
7
.
4
7
MH
z,
s
till
ce
n
ter
ed
o
n
2
.
0
6
GHz
.
T
h
is
r
ep
r
esen
ts
an
in
cr
ea
s
e
o
f
5
8
.
3
7
%
in
th
e
ellip
ticity
o
f
th
e
d
esig
n
ed
an
ten
n
a.
Acc
o
r
d
in
g
t
o
B
an
er
jee
[
2
4
]
,
th
e
d
ef
ec
ted
g
r
o
u
n
d
s
tr
u
ctu
r
e
s
(
DGS)
tech
n
iq
u
e
d
o
es
n
o
t
af
f
ec
t
th
e
an
ten
n
a
g
ain
a
n
d
d
i
r
ec
tiv
ity
.
As illu
s
tr
ated
in
T
ab
le
2
,
f
r
o
m
th
e
p
r
o
p
o
s
ed
wo
r
k
is
o
b
s
er
v
e
d
th
at
th
er
e
is
n
o
b
ig
ch
an
g
e
i
n
ter
m
s
o
f
g
ain
an
d
d
i
r
ec
tiv
ity
o
f
th
e
a
n
ten
n
a.
T
h
e
g
ain
an
d
d
ir
ec
tiv
ity
d
ec
r
ea
s
e
f
r
o
m
4
.
8
8
t
o
4
.
6
8
d
B
an
d
5
.
8
9
to
5
.
4
4
d
B
,
r
esp
ec
tiv
ely
,
f
r
o
m
s
tep
1
to
s
tep
6
,
c
o
r
r
esp
o
n
d
in
g
t
o
th
e
p
r
o
p
o
s
ed
an
ten
n
a.
Ho
wev
er
,
th
er
e
is
an
in
cr
ea
s
e
in
th
e
ax
ial
r
atio
b
an
d
wid
t
h
,
r
ea
ch
i
n
g
4
7
.
8
MH
z,
alo
n
g
with
a
3
d
B
b
ea
m
wid
th
im
p
r
o
v
em
e
n
t
o
f
a
p
p
r
o
x
im
atel
y
9
°,
wh
ich
h
elp
s
r
ed
u
ce
t
h
e
p
o
in
tin
g
lo
s
s
in
th
e
co
m
m
u
n
ica
tio
n
lin
k
b
u
d
g
et,
as
d
escr
ib
ed
b
y
(
5
)
,
p
o
i
n
t
i
n
g
=
12
×
(
er
r
o
r
3
dB
)
2
(
5
)
w
h
er
e
θ
error
is
th
e
p
o
in
tin
g
er
r
o
r
i
n
r
a
d
ian
s
(
an
g
u
lar
d
e
v
iatio
n
f
r
o
m
th
e
o
p
tim
al
d
ir
ec
tio
n
)
an
d
θ
3
dB
is
an
ten
n
a
’
s
3
d
B
b
ea
m
wid
th
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
16
,
No
.
4
,
Au
g
u
s
t
20
26
:
1
9
1
3
-
1926
1920
Fig
u
r
e
1
1
d
ep
icts
a
co
m
p
ar
is
o
n
b
etwe
en
th
e
s
im
u
lated
r
esu
l
ts
o
f
Far
f
ield
Gain
Ab
s
o
f
s
tep
4
to
s
tep
6
at
f
r
eq
u
en
c
y
o
f
2
.
0
5
GHz
.
I
t
ca
n
b
e
s
tated
f
r
o
m
th
e
Fig
u
r
e
th
at
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
p
r
o
p
o
s
ed
an
ten
n
a
in
ter
m
s
o
f
g
ain
a
n
d
d
ir
ec
tiv
ity
is
n
o
t a
f
f
ec
te
d
b
y
th
e
in
tr
o
d
u
cti
o
n
o
f
s
lo
ts
in
th
e
g
r
o
u
n
d
p
lan
e
.
(
a)
(
b
)
Fig
u
r
e
1
0
.
Dev
elo
p
e
d
an
ten
n
a
d
esig
n
: (
a)
r
ef
lectio
n
co
e
f
f
ici
en
t s
11
f
o
r
ea
ch
d
ev
elo
p
m
en
t s
tep
o
f
th
e
m
o
d
if
ie
d
g
r
o
u
n
d
p
la
n
e
(
s
tep
4
t
o
s
u
g
g
es
ted
an
ten
n
a
(
s
tep
6
)
)
an
d
(
b
)
e
v
o
lu
tio
n
o
f
th
e
ellip
ticity
r
ate
o
f
th
e
d
esig
n
ed
an
ten
n
a
f
r
o
m
s
tep
4
to
s
u
g
g
ested
an
ten
n
a
T
ab
le
2
.
Par
am
etr
ic
s
tu
d
y
s
u
m
m
ar
y
A
n
t
e
n
n
a
p
e
r
f
o
r
ma
n
c
e
S
t
e
p
1
S
t
e
p
2
S
t
e
p
3
S
t
e
p
4
S
t
e
p
5
S
t
e
p
6
f
r
(
G
H
z
)
2
.
0
5
2
.
0
5
2
.
0
5
2
.
0
5
2
.
0
5
2
.
0
5
B
a
n
d
w
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Evaluation Warning : The document was created with Spire.PDF for Python.