I
nte
rna
t
io
na
l
J
o
urna
l o
f
E
lect
rica
l a
nd
Co
m
p
ute
r
E
ng
in
ee
ring
(
I
J
E
CE
)
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
201
7
,
p
p
.
3
46
7
~
3
4
7
4
I
SS
N:
2088
-
8708
,
DOI
: 1
0
.
1
1
5
9
1
/i
j
ec
e.
v
7
i
6
.
pp
3
46
7
-
347
4
3467
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ia
e
s
jo
u
r
n
a
l.c
o
m/o
n
lin
e/in
d
ex
.
p
h
p
/I
JE
C
E
A Lea
k
y
Wav
e A
ntenna D
esig
n Ba
sed o
n
H
a
l
f
-
m
o
de
S
ubstra
t
e
I
ntegra
ted
W
a
v
eg
uide
Techno
lo
g
y
f
o
r
X Ba
nd Appl
i
ca
tions
S.
Do
ucha
1
,
M
.
Abri
2
,
H
.
Abri
B
a
da
o
ui
3
,
B
.
F
ella
h
4
T
e
le
c
o
m
m
u
n
ica
ti
o
n
D
e
p
a
rtem
e
n
t,
F
a
c
u
lt
y
o
f
Tec
h
n
o
lo
gy
,
Un
iv
e
rsi
t
y
o
f
T
le
m
c
e
n
–
BP
2
3
0
,
Ch
e
to
u
a
n
e
,
1
3
0
0
0
T
le
m
c
e
n
,
A
l
g
e
ria
Art
icle
I
nfo
AB
ST
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Dec
3
1
,
2
0
1
6
R
ev
i
s
ed
A
pr
2
4
,
2
0
1
7
A
cc
ep
ted
Ma
y
18
,
2
0
1
7
A
n
e
w
t
y
p
e
o
f
le
a
k
y
-
w
a
v
e
a
n
ten
n
a
(L
WA
)
u
sin
g
h
a
l
f
-
m
o
d
e
su
b
stra
te
in
teg
ra
ted
w
a
v
e
g
u
id
e
(HMS
IW
)
a
s
th
e
b
a
se
stru
c
t
u
re
is
p
r
o
p
o
s
e
d
in
th
is
p
a
p
e
r.
T
h
e
stru
c
tu
re
c
o
n
sists
o
f
a
n
a
rra
y
o
f
slo
t,
a
n
ten
n
a
d
e
sig
n
e
d
to
o
p
e
ra
te
in
X
b
a
n
d
a
p
p
l
ica
ti
o
n
s
f
ro
m
8
to
1
2
G
Hz
.
HMS
IW
p
re
se
r
v
e
s
n
e
a
rly
a
ll
th
e
a
d
v
a
n
tag
e
s
o
f
S
IW
w
h
e
re
a
s
it
s
siz
e
is
n
e
a
rly
re
d
u
c
e
d
b
y
h
a
lf
.
T
h
e
a
n
ten
n
a
ra
d
iate
s
o
n
e
m
a
in
b
e
a
m
th
a
t
c
a
n
b
e
ste
e
re
d
f
ro
m
th
e
b
a
c
k
w
a
rd
to
th
e
f
o
r
w
a
rd
d
irec
ti
o
n
b
y
c
h
a
n
g
in
g
f
re
q
u
e
n
c
y
.
K
ey
w
o
r
d
:
L
ea
k
y
w
a
v
e
a
n
ten
n
a
H
alf
M
o
d
e
s
u
b
s
tr
ate
i
n
te
g
r
at
ed
W
av
eg
u
id
e
X
-
B
an
d
C
ST
Co
p
y
rig
h
t
©
2
0
1
7
In
stit
u
te o
f
A
d
v
a
n
c
e
d
E
n
g
i
n
e
e
rin
g
a
n
d
S
c
ien
c
e
.
Al
l
rig
h
ts
re
se
rv
e
d
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
1.
I
NT
RO
D
UCT
I
O
N
Su
b
s
tr
ate
I
n
teg
r
ated
W
av
e
g
u
i
d
es
(
SIW
)
is
u
s
ed
f
o
r
tr
an
s
m
is
s
io
n
o
f
E
lectr
o
m
a
g
n
etic
w
a
v
es.
T
h
e
y
ar
e
p
lan
ar
s
tr
u
ctu
r
es
b
elo
n
g
i
n
g
to
th
e
f
a
m
il
y
o
f
S
u
b
s
tr
ate
I
n
teg
r
ated
C
ir
cu
i
ts
.
B
ec
au
s
e
o
f
t
h
eir
p
lan
ar
n
at
u
r
e,
th
e
y
ca
n
b
e
f
ab
r
icate
d
o
n
p
la
n
ar
cir
cu
it
s
li
k
e
P
r
in
ted
C
ir
cu
it
B
o
ar
d
s
(
P
C
B
)
an
d
ca
n
b
e
in
teg
r
ated
w
it
h
o
t
h
er
p
lan
ar
tr
an
s
m
i
s
s
io
n
lin
e
s
li
k
e
m
icr
o
s
tr
ip
s
.
T
h
e
y
r
etai
n
th
e
lo
w
lo
s
s
p
r
o
p
er
ty
o
f
t
h
eir
co
n
v
e
n
tio
n
al
m
etallic
w
a
v
e
g
u
id
es
an
d
ar
e
w
id
el
y
u
s
ed
as
in
ter
co
n
n
ec
t
io
n
i
n
h
ig
h
s
p
ee
d
cir
cu
it
s
,
f
ilter
s
,
d
i
r
ec
tio
n
al
co
u
p
ler
s
,
an
ten
n
a
s
.
T
h
e
SIW
co
n
s
is
t
s
o
f
t
w
o
l
in
ea
r
m
etall
ic
co
n
n
ec
te
d
v
ia
d
ielec
tr
ic
s
u
b
s
tr
ate
w
i
th
a
h
ei
g
h
t
o
f
h
.
T
h
e
elec
tr
o
m
ag
n
etic
f
ield
s
w
it
h
i
n
t
h
e
SIW
ar
e
co
n
f
i
n
ed
b
y
t
h
ese
m
etallic
v
ia
ar
r
a
y
s
[
1
]
.
A
m
o
r
e
co
m
p
ac
t
g
u
id
ed
w
a
v
e
s
tr
u
c
tu
r
e
ca
lled
h
a
lf
-
m
o
d
e
s
u
b
s
tr
ate
in
teg
r
ated
w
a
v
e
g
u
id
e
(
HM
SIW
)
h
as
r
ec
en
tl
y
b
ee
n
p
r
o
p
o
s
ed
[
2
]
,
[
3
]
,
w
h
ic
h
p
r
eser
v
es
n
ea
r
l
y
all
t
h
e
ad
v
a
n
tag
e
s
o
f
SIW
w
h
er
ea
s
it
s
s
ize
i
s
n
ea
r
l
y
r
ed
u
ce
d
b
y
h
al
f
.
T
h
e
t
r
an
s
v
er
s
e
s
lo
tted
r
ec
tan
g
u
lar
w
a
v
e
g
u
id
e
is
a
s
i
m
p
le
s
tr
u
ct
u
r
e
th
at
w
o
r
k
s
as
a
leak
y
-
w
a
v
e
an
te
n
n
a
h
av
i
n
g
f
r
eq
u
en
c
y
b
ea
m
-
s
ca
n
n
i
n
g
ca
p
a
b
ilit
y
,
w
it
h
an
o
r
th
o
g
o
n
al
p
o
l
ar
izatio
n
f
r
o
m
t
h
e
co
n
v
e
n
tio
n
al
tr
av
el
lin
g
-
w
a
v
e
s
lo
tted
an
te
n
n
a.
B
ec
au
s
e
o
f
t
h
e
p
o
lar
izatio
n
,
t
h
e
tr
an
s
v
er
s
e
s
lo
tted
r
ec
tan
g
u
lar
w
a
v
e
g
u
id
e
ca
n
s
ca
n
f
r
o
m
n
ea
r
b
r
o
ad
s
id
e
t
o
en
d
f
ir
e
if
t
h
e
w
a
v
eg
u
id
e
is
f
illed
w
it
h
a
d
ielec
t
r
ic
m
ater
ial
[
4
]
.
Du
e
to
th
eir
s
u
p
er
io
r
f
r
eq
u
en
c
y
-
s
ca
n
n
i
n
g
ca
p
ab
ilit
y
a
n
d
ea
s
e
o
f
f
ee
d
in
g
,
lea
k
y
-
w
a
v
e
an
ten
n
a
s
(
L
W
A
s
)
p
o
s
s
ess
ce
r
tai
n
ad
v
a
n
tag
e
s
o
v
er
co
n
v
e
n
tio
n
al
an
te
n
n
a
ar
r
a
y
s
.
A
h
i
g
h
-
g
ain
L
W
A
ca
n
b
e
ac
h
iev
ed
b
y
s
i
m
p
l
y
e
x
te
n
d
in
g
its
p
h
y
s
ica
l
len
g
t
h
,
w
h
ic
h
ca
n
r
es
u
l
t
in
a
co
m
p
ac
t
s
ize
esp
ec
iall
y
i
n
m
il
li
m
e
ter
-
w
a
v
e
ap
p
licatio
n
s
.
F
u
r
th
er
m
o
r
e,
L
W
A
s
ca
n
b
e
d
esi
g
n
ed
to
ex
h
i
b
it
b
o
th
f
o
r
w
ar
d
an
d
b
ac
k
w
ar
d
b
ea
m
s
teer
i
n
g
b
y
in
co
r
p
o
r
atin
g
m
e
ta
m
ater
ia
ls
i
n
to
th
eir
u
n
it
ce
lls
[
5
],
[
6
]
.
N
ev
er
th
ele
s
s
,
th
e
f
r
eq
u
e
n
c
y
-
s
ca
n
n
i
n
g
ca
p
ab
ili
t
y
o
f
m
eta
m
ater
ial
-
b
ased
L
W
As
is
n
o
t
s
u
itab
le
f
o
r
m
o
r
e
co
m
m
o
n
f
i
x
ed
-
f
r
eq
u
e
n
c
y
ap
p
licatio
n
s
.
T
h
u
s
,
th
er
e
h
a
s
b
ee
n
co
n
s
id
er
ab
le
in
ter
est i
n
t
u
n
ab
le
s
ca
n
a
n
g
le
L
W
A
s
[
7
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
201
7
:
3
4
6
7
–
3
4
7
4
3468
I
n
th
i
s
p
ap
er
,
a
n
o
v
el
leak
y
-
w
a
v
e
an
te
n
n
a
b
ased
o
n
th
e
HM
SIW
tech
n
iq
u
e
i
n
th
e
b
an
d
X
is
p
r
esen
ted
,
f
ir
s
t
w
e
d
esi
g
n
a
H
MSI
W
co
m
p
o
n
e
n
t
o
p
er
atin
g
i
n
X
-
b
a
n
d
f
o
r
T
E
1
0
m
o
d
e
w
it
h
C
ST
Mic
r
o
w
av
e
Stu
d
io
®
co
m
m
er
cial
s
o
f
t
w
ar
e'
s
.
T
h
e
d
esig
n
p
r
o
ce
d
u
r
es
b
e
g
in
b
y
e
x
tr
ac
ti
n
g
t
h
e
eq
u
i
v
ale
n
t
w
id
th
g
u
id
e
an
d
th
en
ca
lcu
late
t
h
e
w
id
t
h
o
f
H
MSI
W
,
b
y
t
h
e
f
o
llo
w
i
n
g
f
o
r
m
u
las
d
es
ig
n
.
Af
ter
t
h
at,
an
d
f
o
r
tr
an
s
it
HM
SIW
to
m
icr
o
s
tr
ip
w
e
u
s
e
th
e
A
D
S (
ad
v
a
n
ce
d
d
esig
n
s
y
s
te
m
)
So
f
t
w
ar
e.
Fin
all
y
,
w
e
d
esi
g
n
a
lea
k
y
-
w
a
v
e
a
n
te
n
n
a
b
ased
o
n
h
al
f
m
o
d
e
s
u
b
s
tr
ate
i
n
te
g
r
ated
w
a
v
e
g
u
id
e
(
HM
SIW
)
w
it
h
tr
a
n
s
v
er
s
e
s
lo
t
s
; t
h
e
a
n
ten
n
a
r
ad
iate
s
o
n
e
m
a
in
b
ea
m
t
h
at
ca
n
b
e
s
teer
ed
f
r
o
m
t
h
e
b
ac
k
w
ar
d
to
th
e
f
o
r
w
ar
d
d
ir
ec
tio
n
b
y
ch
a
n
g
i
n
g
f
r
eq
u
e
n
c
y
.
T
o
co
n
f
ir
m
o
u
r
r
esu
lts
an
o
th
er
s
i
m
u
lato
r
HFSS
is
u
s
ed
f
o
r
co
m
p
ar
is
o
n
.
a)
SIW
b
)
HM
SIW
Fig
u
r
e
1
.
s
h
o
w
s
t
h
e
co
n
s
tr
u
cti
o
n
o
f
SIW
an
d
HM
SIW
2.
H
M
SI
W
E
Q
UA
T
I
O
N
S
W
h
en
th
e
d
o
m
i
n
a
n
t
m
o
d
e
p
r
o
p
ag
ates
in
a
SIW
,
th
e
m
a
x
i
m
u
m
v
alu
e
o
f
E
-
f
ie
ld
is
p
lace
d
at
th
e
v
er
tical
ce
n
ter
p
lan
e
alo
n
g
t
h
e
tr
an
s
m
is
s
io
n
d
ir
ec
tio
n
.
I
n
ad
d
itio
n
,
b
ec
au
s
e
o
f
lar
g
e
w
id
t
h
to
h
ei
g
h
t
r
atio
(
W
HR
)
,
th
e
n
o
r
m
al
m
a
g
n
e
tic
f
ield
i
s
eq
u
al
to
ze
r
o
at
th
i
s
p
lan
e.
A
s
a
r
es
u
lt,
t
h
e
s
y
m
m
et
r
ical
p
lan
e
o
f
SIW
co
u
ld
b
e
co
n
s
id
er
ed
as
a
m
ag
n
etic
w
al
l
w
h
e
n
i
t
w
o
r
k
s
a
t
it
s
d
o
m
i
n
an
t
m
o
d
e.
B
ased
o
n
t
h
is
th
eo
r
y
,
t
h
e
SIW
s
tr
u
ct
u
r
e
co
u
ld
b
e
b
is
ec
ted
i
n
to
h
al
v
es
at
th
e
m
a
g
n
etic
w
all.
E
ac
h
h
al
f
is
ca
lled
HM
SIW
an
d
is
ab
le
to
s
u
p
p
o
r
t n
ea
r
l
y
h
al
f
o
f
t
h
e
o
r
ig
i
n
al
f
ield
d
is
tr
ib
u
tio
n
.
I
n
t
h
is
s
ec
tio
n
w
e
ca
lc
u
late
t
h
e
p
ar
a
m
eter
s
o
f
HM
SIW
b
y
th
e
f
o
llo
w
in
g
eq
u
atio
n
s.
Si
n
ce
SIW
d
esig
n
g
e
n
er
all
y
w
o
r
k
s
i
n
T
E
1
,
0
m
o
d
e,
s
o
h
er
e
m
=1
,
n
=0
.
T
h
er
ef
o
r
e
th
e
eq
u
atio
n
f
o
r
cu
to
f
f
f
r
eq
u
e
n
c
y
r
ed
u
ce
s
to
:
a
c
f
c
2
Fo
r
DFW
w
it
h
s
a
m
e
cu
t o
f
f
f
r
eq
u
en
c
y
,
d
i
m
e
n
s
io
n
"
ad
"
is
f
o
u
n
d
b
y
:
r
d
a
a
Hav
i
n
g
d
eter
m
in
ed
t
h
e
d
i
m
e
n
s
io
n
ad
f
o
r
th
e
DFW
,
w
e
ca
n
n
o
w
p
ass
to
t
h
e
d
esig
n
eq
u
atio
n
s
f
o
r
SIW
[
8
].
)
95
.
0
(
2
s
d
a
a
d
s
w
h
er
e,
a
i
s
t
h
e
to
tal
b
r
o
ad
s
id
e
d
i
m
e
n
s
io
n
o
f
t
h
e
r
ec
ta
n
g
u
lar
w
a
v
e
g
u
id
e,
a
s
i
s
t
h
e
s
ep
ar
atio
n
b
et
w
ee
n
v
ia
r
o
ws
(
ce
n
tr
e
to
ce
n
tr
e)
,
a
is
th
e
w
i
d
th
o
f
DFW
,
d
is
th
e
d
ia
m
ete
r
(
as
s
h
o
w
n
i
n
Fi
g
u
r
e
2
)
an
d
c
is
th
e
v
e
lo
cit
y
o
f
lig
h
t in
f
r
ee
s
p
a
ce
.
Fo
r
SIW
d
esig
n
,
th
e
f
o
llo
w
i
n
g
t
w
o
co
n
d
i
tio
n
s
ar
e
r
eq
u
ir
ed
[9
]:
5
g
d
M
e
t
a
l
v
i
a
S
u
bs
tr
a
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
A
Lea
ky
W
a
ve
A
n
ten
n
a
Desig
n
B
a
s
ed
o
n
Ha
lf
-
mo
d
e
S
u
b
s
tr
a
te
I
n
teg
r
a
ted
W
a
ve
g
u
id
e
.
.
.
.
(
S
.
Do
u
ch
a
)
3469
d
s
2
w
h
er
e
: λg
(
g
u
id
ed
w
a
v
elen
g
t
h
)
is
[
10
]
2
2
2
2
2
a
c
f
r
g
3.
H
M
SI
W
DE
SI
G
N
T
h
e
F
ig
u
r
e
2
s
h
o
w
s
th
e
tr
an
s
m
i
s
s
io
n
co
ef
f
icien
t
an
d
th
e
r
ef
lectio
n
co
ef
f
icie
n
t
o
f
HM
SIW
w
it
h
d
if
f
er
e
n
t
v
alu
e
s
o
f
g
u
id
e
w
id
t
h
(
a
s2
)
,
f
r
o
m
t
h
e
f
ig
u
r
e
it
ca
n
b
e
s
ee
n
t
h
at
t
h
er
e
is
a
tr
a
n
s
m
i
s
s
io
n
f
r
o
m
th
e
c
u
t
-
o
f
f
f
r
eq
u
e
n
c
y
(
8
.
5
GHZ
)
f
o
r
a
w
id
t
h
eq
u
al
to
h
al
f
o
f
g
u
id
e
SIW
(
a
s2
=
a
s
/ 2
)
.
Fig
u
r
e
2
.
T
h
e
tr
an
s
m
i
s
s
io
n
co
ef
f
icien
t a
n
d
th
e
r
e
f
lecte
d
p
o
w
er
o
f
th
e
HM
SIW
w
av
e
g
u
id
e
f
o
r
d
if
f
er
en
t
v
alu
e
s
a
s2
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
HM
SIW
is
s
k
etc
h
ed
in
Fi
g
u
r
e
3
.
T
h
e
s
u
b
s
tr
ate
is
co
v
er
ed
w
it
h
co
p
p
er
o
n
b
o
th
s
id
es
f
o
r
m
i
n
g
a
w
a
v
e
g
u
id
e,
to
g
eth
er
w
it
h
on
e
r
o
w
o
f
m
eta
lli
c
v
ia
s
alo
n
g
th
e
w
av
e
p
r
o
p
ag
atio
n
d
ir
ec
tio
n
,
T
h
e
th
ic
k
n
e
s
s
an
d
th
e
w
id
t
h
o
f
th
e
HM
SIW
ar
e
h
an
d
a
s2
,
r
esp
ec
tiv
el
y
.
T
h
e
d
iam
eter
o
f
th
e
m
e
talli
c
v
ias
is
d
,
an
d
th
e
p
er
io
d
o
f
th
e
v
ias
i
s
s
.
W
e
u
s
e
T
h
e
p
r
ev
io
u
s
eq
u
atio
n
s
to
b
u
ild
a
HM
SIW
w
i
th
C
S
T
b
y
th
e
f
o
llo
w
in
g
s
p
ec
if
icatio
n
s
;
cu
to
f
f
f
r
eq
u
en
c
y
o
f
T
E
10
m
o
d
e
in
SIW
is
s
elec
ted
ab
o
u
t
8
.
5
GHz
w
it
h
th
e
f
o
llo
w
i
n
g
p
ar
am
et
er
s
:
s
u
b
s
t
r
at
t
y
p
e
A
r
l
o
n
C
u
2
3
3
lx
(
lo
s
s
y
)
,
d
ielec
tr
ic
co
n
s
ta
n
t
o
f
εr
=
2
.
3
3
an
d
tan
g
δ=0
.
0
0
1
3
.
T
h
e
f
i
g
u
r
e
4
s
h
o
w
s
th
e
d
o
m
in
a
n
t
m
o
d
e
elec
tr
ic
f
ield
s
o
f
H
MSI
W
g
u
id
e
s
i
m
u
lated
in
f
r
eq
u
e
n
c
y
1
0
GHz
.
7
8
9
10
11
12
13
14
15
-
7
0
-
6
0
-
5
0
-
4
0
-
3
0
-
2
0
-
1
0
0
a
s
2
=
a
s
/
2
a
s
2
=
3
a
s
/
4
a
s
2
=
a
s
7
8
9
10
11
12
13
14
15
-5
-4
-3
-2
-1
0
a
s
2
=
a
s
a
s
2
=
3
a
s
/
4
a
s
2
=
a
s
/
2
S
11
S
12
Fre
q
u
e
n
c
y
[G
H
z
]
Fre
q
u
e
n
c
y
[G
H
z
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
201
7
:
3
4
6
7
–
3
4
7
4
3470
.
Fig
u
r
e
3
.
HM
SIW
p
ar
am
eter
s
Fig
u
r
e
4
.
T
h
e
d
o
m
in
a
n
t
m
o
d
e
elec
tr
ic
f
ield
s
o
f
H
MSI
W
g
u
id
e
s
i
m
u
lated
i
n
f
r
eq
u
e
n
c
y
1
0
G
HZ
T
h
e
s
i
m
u
latio
n
r
e
s
u
lt
s
b
et
w
ee
n
th
e
f
r
eq
u
e
n
cies
r
a
n
g
e
s
[
8
-
1
5
GHz
]
ar
e
illu
s
tr
ated
i
n
t
h
e
f
i
g
u
r
e
5,
it
is
clea
r
th
at
th
e
tr
a
n
s
m
i
s
s
io
n
b
etw
ee
n
[
7
-
8
.
5
GHz
]
is
i
m
p
o
s
s
ib
le
b
ec
au
s
e
it is
b
e
f
o
r
e
th
e
cu
to
f
f
f
r
eq
u
e
n
c
y
,
w
h
ic
h
is
8
.
5
GHz
as
ca
lcu
la
ted
th
eo
r
etica
ll
y
.
I
n
th
i
s
ca
s
e,
t
h
e
tr
a
n
s
m
is
s
io
n
b
et
w
ee
n
[
8
.
5
-
15
GHz
]
is
lo
w
an
d
th
is
is
d
u
e
to
th
e
in
co
r
r
ec
t a
d
ap
ta
tio
n
o
f
th
e
g
u
id
e
.
(
a)
(
b
)
Fig
u
r
e
5
.
(
a
)
:
T
h
e
r
ef
lecte
d
p
o
w
er
an
d
(
b
)
:
th
e
tr
an
s
m
is
s
io
n
co
ef
f
icie
n
t o
f
th
e
HM
SIW
w
a
v
eg
u
id
e.
T
h
e
HM
SIW
w
a
v
eg
u
id
e
p
ar
a
m
eter
s
ar
e
s
et
to
:
a
s2
=
7
.
4
m
m
,
d
=2
.5
m
m
,
s
=
3.
25
m
m
,
h
=0
.
5
0
8
m
m
On
ce
t
h
e
SIW
is
d
esig
n
ed
,
it
is
n
ec
es
s
ar
y
to
h
a
v
e
a
tr
an
s
i
tio
n
to
a
tr
an
s
m
is
s
io
n
l
in
e
to
en
s
u
r
e
a
p
er
f
ec
t
ad
ap
tatio
n
.
T
h
is
tr
an
s
it
io
n
co
n
ta
in
s
t
w
o
m
a
in
p
ar
a
m
e
ter
s
,
th
e
o
r
ig
i
n
al
w
id
th
W
0
,
th
e
f
i
n
al
w
id
th
W
o
f
th
e
p
r
o
f
ile
li
n
e
.
I
t
is
n
ec
e
s
s
ar
y
to
ca
lcu
late
t
h
e
i
m
p
ed
an
ce
o
f
SIW
g
u
id
e,
w
h
ic
h
is
g
iv
e
n
b
y
t
h
e
f
o
llo
w
i
n
g
f
o
r
m
u
la
[
8
]
:
s
a
b
8
Z
=
Z
2
TE
pi
S
d
as
2
S
u
b
s
t
r
a
t
(
ε
r
,
tan
g
δ
)
h
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
A
Lea
ky
W
a
ve
A
n
ten
n
a
Desig
n
B
a
s
ed
o
n
Ha
lf
-
mo
d
e
S
u
b
s
tr
a
te
I
n
teg
r
a
ted
W
a
ve
g
u
id
e
.
.
.
.
(
S
.
Do
u
ch
a
)
3471
Fo
r
th
e
ca
lcu
la
tio
n
o
f
t
h
e
g
u
id
e
i
m
p
ed
an
ce
,
it
is
a
ls
o
n
ec
es
s
a
r
y
to
ca
lc
u
late
th
e
w
a
v
e
i
m
p
e
d
an
ce
o
f
T
E
m
o
d
e,
w
h
ic
h
is
g
iv
e
n
b
y
[
8
]
:
Z
TE
=
j
=
=
√
×
g
T
h
e
ca
lcu
lated
p
ar
a
m
eter
s
ar
e
u
s
ed
to
co
n
s
tr
u
ct
a
tap
er
b
y
u
s
i
n
g
A
DS
(
ad
v
an
ce
d
d
esi
g
n
s
y
s
te
m
)
s
o
f
t
w
ar
e,
th
e
p
h
y
s
ical
tr
an
s
itio
n
s
tr
u
ctu
r
e
o
f
m
icr
o
s
tr
ip
li
n
e
w
it
h
t
h
e
g
u
id
e
HM
SIW
is
s
h
o
w
n
i
n
Fi
g
u
r
e
6
.
Fig
u
r
e
6
.
T
o
p
o
lo
g
y
o
f
tr
a
n
s
iti
o
n
w
ith
HM
SIW
g
u
id
e.
w
i
th
w=
5
.
5
9
m
m
,
w
0
=1
.
5
9
m
m
,
L
=1
6
.
6
3
an
d
L
0
=1
6
.
9
9
mm
T
h
e
R
ef
lecte
d
p
o
w
er
a
n
d
th
e
t
r
an
s
m
is
s
io
n
co
e
f
f
icie
n
t
o
f
th
e
tr
an
s
itio
n
to
p
o
lo
g
y
w
it
h
HM
S
I
W
g
u
id
e
is
o
b
tain
ed
b
y
s
i
m
u
latio
n
u
s
i
n
g
C
ST
s
o
f
t
w
ar
e
ar
e
s
h
o
w
n
i
n
th
e
Fi
g
u
r
e
7
.
On
e
ca
n
o
b
s
er
v
e
th
at
i
n
th
e
to
tal
p
ass
b
an
d
(
8
.
5
-
1
5
GHz
)
t
h
e
r
ef
lectio
n
co
ef
f
icien
t
S
1
1
is
le
s
s
th
a
n
-
1
0
d
B
an
d
th
e
S1
2
in
cr
ea
s
es
r
ap
id
ly
f
r
o
m
th
e
c
u
t
-
o
f
f
f
r
eq
u
e
n
c
y
to
a
to
ta
l
tr
an
s
m
i
s
s
io
n
o
f
t
h
e
p
o
w
er
,
o
b
tain
ed
r
es
u
lt
s
ar
e
co
n
f
ir
m
ed
with
H
FS
S
w
h
ic
h
i
s
u
s
ed
f
o
r
co
m
p
ar
is
o
n
.
(
a)
(
b
)
Fig
u
r
e
7
.
(
a)
:
R
ef
lecte
d
p
o
w
er
an
d
(
b
)
:
th
e
tr
an
s
m
is
s
io
n
co
ef
f
icie
n
t o
f
t
h
e
tr
an
s
itio
n
to
p
o
lo
g
y
w
i
th
HM
SIW
g
u
id
e
4.
L
WA
B
AS
E
D
O
N
H
M
SI
W
DE
S
I
G
N
T
h
e
leak
y
-
w
av
e
a
n
te
n
n
a
s
ar
e
ess
en
t
ial
to
p
r
o
v
id
e
th
e
b
en
ef
it
o
f
h
i
g
h
d
ir
ec
ti
v
it
y
wi
t
h
o
u
t
co
m
p
le
x
f
ee
d
in
g
n
et
w
o
r
k
.
T
h
e
g
eo
m
e
tr
y
o
f
t
h
e
H
MSI
W
w
it
h
tr
an
s
v
er
s
e
s
lo
t
i
s
s
h
o
w
n
i
n
Fi
g
u
r
e
8.
T
h
e
leak
a
g
e
i
s
o
b
tain
ed
b
y
t
h
e
i
n
tr
o
d
u
ctio
n
o
f
a
p
er
io
d
ic
ar
r
ay
o
f
tr
a
n
s
v
er
s
e
s
lo
ts
o
n
t
h
e
to
p
o
f
HM
SIW
w
h
ic
h
in
ter
r
u
p
t
th
e
cu
r
r
en
t
f
lo
w
o
n
t
h
e
to
p
w
all.
T
h
e
ar
r
an
g
e
m
e
n
t
o
f
th
e
s
lo
ts
d
eter
m
in
e
s
t
h
e
p
o
lar
izatio
n
a
n
d
th
e
d
ir
ec
tio
n
o
f
r
ad
iatio
n
o
f
th
e
L
W
A
a
n
ten
n
a.
T
h
e
L
W
A
an
te
n
n
a
i
n
HM
S
I
W
tech
n
o
lo
g
y
i
s
d
esig
n
ed
o
n
a
s
u
b
s
tr
ate
w
ith
a
co
n
s
ta
n
t d
ielec
tr
ic
o
f
2
.
3
3
,
tan
g
δ =
0
.
0
0
1
3
an
d
th
ick
n
e
s
s
0
.
5
0
8
m
m
f
o
r
X
-
b
an
d
ap
p
licatio
n
s
.
W0
W
L
L
0
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
201
7
:
3
4
6
7
–
3
4
7
4
3472
(
a)
(
b
)
Fig
u
r
e
8
.
(
a)
Stru
ctu
r
e
o
f
leak
y
-
w
av
e
a
n
te
n
n
a
b
ased
o
n
HM
SIW
,
(
b
)
L
W
A
HM
SIW
alig
n
m
en
t in
t
h
e
co
o
r
d
in
ates
T
h
e
s
i
m
u
la
ted
r
esu
lts
o
f
S
-
p
ar
a
m
eter
s
f
o
r
leak
y
w
av
e
an
ten
n
a
b
ased
o
n
HM
SIW
is
s
h
o
w
n
in
Fi
g
u
r
e
9
.
I
t
ca
n
b
e
o
b
s
er
v
ed
th
at
s
i
m
u
lated
S
11
is
b
elo
w
–
1
0
d
B
f
r
o
m
8
.
5
to
15
GHz
an
d
S
21
is
b
ig
g
er
th
a
n
–
5
d
B
f
r
o
m
9
to
15
G
Hz
.
T
h
e
F
i
g
u
r
e
10
s
h
o
w
s
th
e
d
o
m
in
a
n
t
m
o
d
e
elec
tr
ic
f
ield
s
o
f
L
W
A
H
MSI
W
s
i
m
u
lated
i
n
f
r
eq
u
en
c
y
1
0
GHz
.
T
h
e
s
a
m
e
r
esu
lt
s
ar
e
also
o
b
tain
ed
w
it
h
HFSS
s
i
m
u
lato
r
.
(
a)
(
b)
Fig
u
r
e
9
.
(
a
)
:
R
ef
lecte
d
p
o
w
er
an
d
(
b
)
:
th
e
tr
an
s
m
is
s
io
n
co
e
f
f
icien
t o
f
L
W
A
b
ased
o
n
HM
S
I
W
S
l
o
t
s
S
u
b
s
t
r
a
t
(
ε
r
,
tan
g
δ
)
f
=
8
G
H
z
f
=
8
.5 G
H
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
E
C
E
I
SS
N:
2088
-
8708
A
Lea
ky
W
a
ve
A
n
ten
n
a
Desig
n
B
a
s
ed
o
n
Ha
lf
-
mo
d
e
S
u
b
s
tr
a
te
I
n
teg
r
a
ted
W
a
ve
g
u
id
e
.
.
.
.
(
S
.
Do
u
ch
a
)
3473
Fig
u
r
e
10
.
T
h
e
s
i
m
u
lated
r
ad
iatio
n
p
atter
n
s
i
n
p
o
lar
co
o
r
d
in
ates
Fig
u
r
e
11
.
T
h
e
s
i
m
u
lated
r
ad
iatio
n
p
atter
n
s
i
n
3
-
D
Fig
u
r
e
10
an
d
11
s
h
o
w
s
r
esp
ec
tiv
el
y
t
h
e
s
i
m
u
lated
r
ad
iati
o
n
p
atter
n
s
in
p
o
lar
a
n
d
3
-
D.
As
s
h
o
w
n
,
th
e
m
a
in
lo
b
e
d
ir
ec
tio
n
o
f
th
is
L
W
A
H
MSI
W
s
ca
n
s
f
r
o
m
0
◦
at
8
GHz
t
o
4
6
◦
at
9
.
5
.5
G
Hz
,
w
it
h
a
m
a
x
i
m
al
r
ea
lized
g
ain
o
f
1
0
.
8
d
B
at
32
◦
(
f
=
9
GHz
)
.
S
o
w
h
e
n
t
h
e
f
r
eq
u
e
n
c
y
i
s
i
n
cr
ea
s
ed
,
th
e
n
ar
r
o
w
b
ea
m
s
ca
n
s
s
m
o
o
th
l
y
f
r
o
m
t
h
e
b
r
o
ad
s
id
e
to
en
d
f
ir
e
d
ir
ec
tio
n
.
B
o
th
o
f
HFSS
a
n
d
C
ST
g
iv
e
t
h
e
s
a
m
e
r
e
s
u
lt.
f
=
9
.5 G
H
z
f
=
9
G
H
z
f
=
8
G
H
z
f
=
8
.5
G
H
z
f
=
9
G
H
z
f
=
9
.5 G
H
z
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8708
I
J
E
C
E
Vo
l.
7
,
No
.
6
,
Dec
em
b
er
201
7
:
3
4
6
7
–
3
4
7
4
3474
5.
CO
NCLU
SI
O
N
A
lea
k
y
-
w
a
v
e
an
ten
n
a
b
ased
o
n
th
e
HM
SIW
tech
n
iq
u
e
is
p
r
o
p
o
s
ed
.
T
h
e
an
ten
n
a
is
c
h
ar
a
cter
ized
b
y
m
an
y
attr
ac
ti
v
e
ad
v
a
n
ta
g
es,
i
n
clu
d
i
n
g
co
m
p
ac
t
s
ize,
ea
s
y
f
ab
r
icatio
n
,
lo
w
co
s
t,
lo
w
lo
s
s
,
w
id
e
b
an
d
w
i
d
t
h
,
an
d
d
ir
ec
t
in
teg
r
atio
n
w
it
h
p
lan
ar
cir
cu
its
.
T
h
e
d
esig
n
i
s
f
ir
s
t
p
ass
ed
b
y
ca
lcu
la
tin
g
th
e
p
ar
am
eter
s
o
f
HM
SIW
,
th
an
w
e
o
p
ti
m
ize
t
h
e
tap
er
to
m
a
k
e
th
e
tr
an
s
iti
o
n
b
et
w
ee
n
s
u
p
p
l
y
a
n
d
i
n
p
u
t
g
u
id
e
to
en
s
u
r
e
a
p
er
f
ec
t
ad
ap
tatio
n
,
af
ter
th
a
t
w
e
d
es
ig
n
a
lea
k
y
w
a
v
e
a
n
te
n
n
a
b
ased
o
n
a
h
al
f
m
o
d
e
s
u
b
s
tr
ate
i
n
te
g
r
ated
w
a
v
e
g
u
id
e
(
HM
SIW
)
,
s
i
m
u
lat
io
n
s
ar
e
r
ea
lis
ed
w
i
th
b
o
th
o
f
C
ST
an
d
HFS
S
(
f
o
r
co
m
p
ar
is
o
n
)
,
th
e
d
ir
ec
tio
n
o
f
r
ad
iatio
n
in
t
h
is
a
n
te
n
n
a
c
h
an
g
e
ac
co
r
d
in
g
to
th
e
v
ar
iatio
n
o
f
f
r
eq
u
en
c
y
.
RE
F
E
R
E
NC
E
S
[1
]
A
.
Na
sri,
e
t
a
l.
,
“
A
Co
m
p
a
c
t
S
I
W
M
ix
e
r
f
o
r
M
il
li
m
e
ter
-
Wav
e
Ap
p
li
c
a
ti
o
n
s,”
I
n
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
trica
l
a
n
d
Co
m
p
u
ter
E
n
g
i
n
e
e
rin
g
(
IJ
ECE
)
,
v
ol
/i
ss
u
e
:
4
(
6
)
,
p
p
.
9
0
2
~
9
0
8
,
2
0
1
4
.
[2
]
Y.
Q.
W
a
n
g
,
e
t
a
l.
,
“
Ha
l
f
m
o
d
e
s
u
b
stra
te
in
teg
ra
ted
w
a
v
e
g
u
id
e
(H
M
S
IW
)
f
il
ter,”
IEE
E
M
icr
o
w.
W
i
re
les
s
Co
mp
u
t
.
L
e
tt
.
,
v
o
l
/
issu
e
:
17
(
4
)
,
p
p
.
2
6
5
–
2
6
7
,
2
0
0
7
.
[3
]
B.
L
iu
,
e
t
a
l
.
,
“
Ha
lf
m
o
d
e
su
b
stra
te.i
n
teg
ra
ted
w
a
v
e
g
u
id
e
(HMS
IW
)
3
-
d
B
c
o
u
p
ler,”
IEE
E
M
icr
o
w.
W
ire
les
s
Co
mp
u
t
.
L
e
tt
.
,
v
o
l
/i
ss
u
e
:
17
(
1
)
,
p
p
.
2
2
–
2
4
,
2
0
0
7
.
[4
]
T
.
V
.
R
.
Krish
n
a
,
e
t
a
l.
,
“
M
i
c
r
o
strip
L
in
e
F
e
d
L
e
a
k
y
W
a
v
e
A
n
te
n
n
a
w
it
h
S
h
o
rt
in
g
V
ias
f
o
r
W
id
e
b
a
n
d
S
y
ste
m
s
,
”
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
E
lec
trica
l
a
n
d
C
o
mp
u
ter
En
g
in
e
e
rin
g
,
v
ol
/
issu
e
:
6
(
4
)
,
p
p
.
1
7
2
5
~
1
7
3
1
,
2
0
1
6
.
[5
]
Y.
W
e
it
sc
h
a
n
d
T
.
Ei
b
e
rt,
“
A
le
f
t
-
h
a
n
d
e
d
/ri
g
h
t
-
h
a
n
d
e
d
lea
k
y
-
wa
v
e
a
n
ten
n
a
d
e
ri
v
e
d
f
ro
m
slo
tt
e
d
re
c
tan
g
u
lar
h
o
ll
o
w
w
a
v
e
g
u
id
e
,
”
in
E
u
ro
p
e
a
n
M
icr
o
wa
v
e
Co
n
f
.
,
M
u
n
ic
h
,
G
e
r
m
a
n
y
,
p
p
.
9
1
7
–
9
2
0
,
2
0
0
7
.
[6
]
K.
Ok
u
b
o
,
e
t
a
l.
,
“
Ne
w
c
o
m
p
o
site
rig
h
t/
lef
t
-
h
a
n
d
e
d
tran
sm
issio
n
li
n
e
u
sin
g
s
u
b
stra
te
i
n
teg
ra
ted
w
a
v
e
g
u
id
e
a
n
d
m
e
tal
-
p
a
tch
e
s,” in
IEE
E
M
T
T
-
S
I
n
t.
M
icr
o
wa
v
e
S
y
m
p
.
Di
g
.
,
B
o
sto
n
,
M
A
,
p
p
.
4
1
–
44
,
2
0
0
9
.
[7
]
S
.
L
i
m
,
e
t
a
l.
,
“
El
e
c
tro
n
ica
ll
y
-
c
o
n
tro
ll
e
d
m
e
ta
m
a
t
e
rial
b
a
se
d
tran
s
m
issio
n
li
n
e
a
s a c
o
n
ti
n
u
o
u
s
-
sc
a
n
n
i
n
g
lea
k
y
-
w
a
v
e
a
n
ten
n
a
,
”
i
n
IEE
E
M
T
T
-
S
In
t.
M
icr
o
wa
v
e
S
y
mp
.
Di
g
.
,
F
o
rt
W
o
rth
,
T
X
,
p
p
.
3
1
3
–
3
1
6
,
2
0
0
4
.
[8
]
X
.
Ch
e
n
,
e
t
a
l.
,
“
S
u
b
stra
te
I
n
teg
ra
ted
W
a
v
e
g
u
id
e
(S
IW
)
L
in
e
a
r
P
h
a
se
F
i
lt
e
r,
”
IEE
E
M
icr
o
wa
v
e
a
n
d
W
ire
les
s
Co
mp
o
n
e
n
ts
L
e
tt
e
rs
,
v
ol
/i
ss
u
e
:
15
(
11
)
,
2
0
0
5
.
[9
]
J.
E.
R
.
S
a
n
c
h
e
z
a
n
d
V
.
G
.
Ay
a
l
a
,
“
A
G
e
n
e
ra
l
EM
-
Ba
se
d
De
sig
n
P
ro
c
e
d
u
re
f
o
r
S
i
n
g
le
-
L
a
y
e
r
S
u
b
s
trate
In
teg
ra
ted
W
a
v
e
g
u
id
e
In
terc
o
n
n
e
c
ts
w
it
h
M
icro
strip
T
ra
n
siti
o
n
s
,
”
IEE
E
M
T
T
-
S
In
t
.
M
icr
o
wa
v
e
S
y
mp
.
Dig
.
,
A
tl
a
n
ta,
GA
,
p
p
.
983
-
9
8
6
,
2
0
0
8
.
[1
0
]
Y
.
J
.
B
an
,
“
T
u
n
a
b
le F
e
rrit
e
P
h
a
se
S
h
if
ters
Us
in
g
S
u
b
stra
te I
n
teg
ra
ted
W
a
v
e
g
u
id
e
T
e
c
h
n
iq
u
e
,
”
t
h
e
se
s
,
2
0
1
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.