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De
p
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sta
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sir
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Un
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e
rsity
,
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a
q
Art
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nfo
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ev
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K
ey
w
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r
d
s
:
C
ST
PIFA
PIN
d
io
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e
R
ec
o
n
f
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a
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ten
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a
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s
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rticle
u
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th
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CC B
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SA
li
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C
o
r
r
e
s
p
o
nd
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A
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o
r
:
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d
u
llah
Ali Jab
b
er
,
E
lectr
ical
E
n
g
in
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r
in
g
Dep
ar
t
m
en
t,
Al
Mu
s
tan
s
ir
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h
Un
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s
ity
,
B
ag
h
d
ad
,
I
r
a
q
.
E
m
ail:
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lh
u
s
s
ein
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g
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co
m
1.
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NT
RO
D
UCT
I
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T
h
e
co
n
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u
o
u
s
d
ev
elo
p
m
en
t
in
co
m
m
u
n
icatio
n
s
esp
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in
th
e
wir
eless
co
m
m
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n
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n
s
n
ee
d
ed
m
o
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e
co
m
p
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an
d
m
u
ltifu
n
ctio
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ev
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to
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esig
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ap
p
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.
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e
co
m
m
u
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n
s
tan
d
ar
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s
lik
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(
PC
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0
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0
0
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-
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etc.
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r
eq
u
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o
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y
u
s
in
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s
m
all
r
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with
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m
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d
lo
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n
as.
T
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s
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if
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tan
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s
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s
m
all
s
tr
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d
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a
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q
u
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f
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u
c
h
ap
p
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ca
tio
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s
.
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h
e
d
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in
g
in
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an
ten
n
a
d
im
en
s
io
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s
ca
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s
till
wh
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th
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s
p
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if
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allo
w
s
witch
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b
etwe
en
d
if
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s
[
1
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]
.
Mic
r
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p
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m
m
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t
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lo
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t,
lo
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p
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ltifu
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ctio
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m
o
r
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d
etails
in
[
1
1
,
1
2
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.
Slo
t
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ty
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(
PIFAs)
ar
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th
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m
o
s
t
cu
r
r
en
t
m
u
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b
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a
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A
m
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wn
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n
d
m
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s
t
lik
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u
s
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f
o
r
m
o
b
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ap
p
licatio
n
d
e
v
ices
[
5
]
.
B
ec
au
s
e
o
f
s
u
itab
le
Sp
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if
ic
Ab
s
o
r
p
tio
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R
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(
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,
lo
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lo
w
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[
2
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6
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1
3
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1
4
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.
T
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ar
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f
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class
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f
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tech
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f
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[
3
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5,
1
5
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1
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,
r
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p
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r
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f
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u
r
ab
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[
1
7
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,
p
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lar
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n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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:
1
6
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T
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KOM
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m
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p
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tr
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2
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r
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an
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b
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witch
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a
n
d
v
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to
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io
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es
[
2
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to
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f
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,
a
n
d
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an
elec
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witch
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ME
MS)
[
1
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2
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n
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eq
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f
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g
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is
d
es
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th
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o
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an
d
s
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f
m
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ile
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n
tr
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u
tio
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s
b
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h
in
d
th
is
r
esear
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ar
e:
−
A
New
co
m
p
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f
r
eq
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co
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f
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u
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f
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0
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to
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GHz
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wh
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is
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to
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ly
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2.
P
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F
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H
E
O
RY
A
r
ec
tan
g
u
lar
elem
en
t
with
a
s
h
o
r
t
m
etallic
p
late
to
th
e
g
r
o
u
n
d
p
la
n
e
m
ad
e
u
p
a
PIFA.
T
h
e
f
ir
s
t
r
eso
n
an
t f
r
e
q
u
en
c
y
o
f
th
e
n
o
n
-
s
lo
tted
PIFA
is
g
iv
en
b
y
(
1
)
:
=
4
(
+
)
(
1
)
wh
er
e
C
is
th
e
s
p
ee
d
o
f
lig
h
t,
L
p
is
th
e
len
g
th
an
d
Hr
es
is
th
e
h
eig
h
t
o
f
th
e
r
ad
iatin
g
elem
e
n
t
[
1
]
.
T
h
e
an
te
n
n
a
tak
es
th
e
in
v
er
te
d
-
F
s
h
ap
e
as
s
h
o
wn
in
Fig
u
r
e
1
(
a
)
,
an
d
it
r
eso
n
ates
at
a
q
u
a
r
ter
-
wav
elen
g
th
b
ec
a
u
s
e
o
f
th
e
s
h
o
r
t
-
p
in
at
th
e
e
n
d
.
T
h
e
f
ee
d
in
g
o
f
t
h
e
an
te
n
n
a
f
o
u
n
d
b
etwe
en
th
e
s
h
o
r
ted
a
n
d
o
p
e
n
e
n
d
,
a
n
d
th
e
d
is
tan
ce
f
r
o
m
th
e
f
ee
d
in
g
to
th
e
s
h
o
r
t
-
p
in
co
n
tr
o
ls
th
e
in
p
u
t
i
m
p
ed
an
ce
,
wh
e
n
ev
er
it
clo
s
ed
to
th
e
s
h
o
r
t
-
p
in
th
e
im
p
ed
an
ce
d
ec
r
ea
s
ed
as
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
[
2
4
]
.
Fro
m
Fig
u
r
e
1
(
b
)
th
e
PIFA
an
ten
n
a
h
as
a
len
g
th
(
L
1
)
,
wid
th
(
L
2
)
,
s
h
o
r
t
-
p
in
wid
th
(
W
)
,
an
d
d
is
tan
ce
(
D)
f
r
o
m
th
e
s
h
o
r
t
-
p
in
.
T
h
e
s
h
o
r
t
-
p
in
at
h
ig
h
f
r
eq
u
e
n
cies
(
≥
1
GHz
)
in
t
r
o
d
u
ce
s
p
ar
allel
in
d
u
ctan
ce
(
jXL
)
with
th
e
a
n
t
en
n
a
im
p
e
d
an
ce
(
Z
A)
an
d
it
s
h
if
ts
th
e
r
eso
n
an
t
f
r
eq
u
e
n
cy
as sh
o
wn
in
Fig
u
r
e
2.
(
a)
(
b
)
Fig
u
r
e
1
.
Plan
ar
i
n
v
er
ted
-
F a
n
ten
n
a
(
PIFA)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
C
o
mp
a
ct
r
ec
o
n
fig
u
r
a
b
le
P
I
F
A
a
n
ten
n
a
fo
r
w
ir
eless
a
p
p
lica
ti
o
n
s
(
A
b
d
u
lla
h
A
li J
a
b
b
er
)
597
Fig
u
r
e
2
.
E
q
u
iv
alen
t c
ir
c
u
it o
f
PIFA
an
ten
n
a
T
h
e
r
eso
n
an
t
f
r
eq
u
en
cy
ca
n
b
e
f
o
u
n
d
b
y
(
2
)
,
wh
ich
r
e
p
r
ese
n
ts
th
e
g
en
er
al
f
o
r
m
o
f
a
PIF
A
an
ten
n
a
ac
co
r
d
in
g
to
t
h
e
f
ar
-
f
ield
c
r
iter
ia
f
r
o
m
th
e
f
ar
t
h
est
p
o
in
t
o
n
th
e
an
ten
n
a
cl
o
ck
wis
e
an
d
co
u
n
ter
clo
c
k
wis
e
th
e
r
eso
n
an
t f
r
eq
u
e
n
cy
is
g
iv
e
n
b
y
:
1
+
2
−
=
4
(
2
)
if
(
W
<<
L
2
)
,
W
is
ju
s
t a
p
in
,
s
o
(
1
)
c
an
b
e
ap
p
r
o
x
im
ated
t
o
:
1
+
2
=
4
(
3
)
if
(
W
=
L
2
)
th
e
a
n
ten
n
a
o
p
er
at
es in
m
ax
im
u
m
e
f
f
icien
cy
a
n
d
(
1
)
b
e
co
m
es:
1
=
/
4
(
4
)
af
ter
th
at
to
f
in
d
th
e
r
eso
n
an
t f
r
eq
u
en
c
y
s
u
b
s
titu
te
(
5
)
:
=
0
√
(
5
)
3.
P
RO
P
O
SE
D
P
I
F
A
AN
T
E
N
NA
DE
S
I
G
N
AND
P
I
N
DIO
DE
M
O
D
E
L
I
NG
3
.
1
.
P
r
o
po
s
ed
P
I
F
A
a
nte
nn
a
des
ig
n
T
h
e
p
r
o
p
o
s
ed
d
esig
n
o
f
m
u
ltib
an
d
r
ec
o
n
f
ig
u
r
ab
le
PIFA
ca
n
b
e
s
h
o
wn
in
Fig
u
r
e
3
.
Af
ter
t
h
e
s
tu
d
y
o
f
th
e
latest
r
esear
ch
es
an
d
d
eter
m
in
e
wh
ich
ap
p
licatio
n
s
to
co
v
er
b
y
th
e
an
ten
n
a
th
e
p
r
o
p
o
s
ed
an
ten
n
a
s
h
ap
e
is
ch
o
s
en
af
ter
s
o
m
e
p
ar
am
etr
ic
s
tu
d
y
o
f
t
h
e
p
atch
d
im
en
s
io
n
s
to
b
e
co
m
p
letely
d
if
f
e
r
en
t
f
r
o
m
th
e
liter
atu
r
e.
T
h
e
an
te
n
n
a
is
co
n
s
is
ts
o
f
a
p
a
tch
p
r
i
n
ted
o
n
an
FR
-
4
s
u
b
s
tr
a
te
with
εr
=
4
.
3
,
tan
(
δ)
=0
.
0
0
2
r
elativ
e
d
ielec
tr
ic
co
n
s
tan
t
an
d
lo
s
s
tan
g
en
t
r
esp
ec
tiv
ely
,
th
e
th
ick
n
ess
o
f
(
1
.
6
m
m
)
a
n
d
5
0
Ω
co
ax
ial
f
ee
d
lin
e.
T
h
e
p
atch
h
eig
h
t
ab
o
v
e
th
e
g
r
o
u
n
d
b
y
a
d
is
tan
ce
o
f
(
1
.
6
7
m
m
)
.
a
s
h
o
r
t
p
late
f
r
o
m
th
e
p
atch
t
o
th
e
g
r
o
u
n
d
with
(
4
m
m
)
wid
th
is
p
r
o
d
u
ce
d
.
T
h
e
o
v
e
r
all
an
te
n
n
a
s
ize
is
4
5
.
6
x
3
9
.
6
x
1
.
6
m
m
3
,
wh
ich
is
ap
p
licab
le
in
th
e
m
o
b
ile
ap
p
licatio
n
d
ev
ices
an
d
m
ee
t
th
e
co
m
p
ac
t
an
ten
n
a
p
r
o
p
er
ties
an
d
class
if
icatio
n
s
.
All
o
p
tim
u
m
p
ar
am
e
ter
s
o
f
th
e
an
ten
n
a
ar
e
s
u
m
m
ar
ized
in
T
ab
le
1
.
(
4
m
m
)
th
e
wid
th
o
f
th
e
s
h
o
r
t
-
p
i
n
,
an
d
o
n
ly
s
in
g
le
(
D
SM8
1
0
0
-
0
0
0
Me
s
a
B
ea
m
-
L
ea
d
)
f
r
o
m
Sk
y
wo
r
k
s
PIN
d
io
d
e
u
s
ed
to
m
o
d
i
f
y
th
e
len
g
th
o
f
th
e
PIFA
to
r
ec
o
n
f
ig
u
r
e
th
e
r
eso
n
a
n
t
f
r
eq
u
e
n
cy
to
m
ee
t
o
th
er
b
a
n
d
s
o
f
f
r
eq
u
e
n
cies.
T
h
e
PIN
d
io
d
e
is
p
lace
d
in
an
o
p
tim
ized
p
o
s
itio
n
to
ac
h
iev
e
th
e
d
esire
d
o
p
er
atio
n
.
3
.
2
.
P
in dio
de
m
o
dellin
g
T
h
e
s
tates
o
f
th
e
elec
tr
o
n
ic
s
witch
ar
e
ON
an
d
OFF.
T
h
ey
ca
n
b
e
r
ea
lized
b
y
b
iasi
n
g
th
e
PIN
d
io
d
e
in
th
e
f
o
r
war
d
o
r
r
e
v
er
s
e
b
ias.
At
th
e
ON
s
tate,
th
e
s
witch
is
f
o
r
war
d
b
ias
an
d
it
h
as
lo
w
im
p
ed
an
ce
ac
ts
as
a
s
h
o
r
t
cir
c
u
it
an
d
th
e
c
u
r
r
en
t
ca
n
p
ass
th
r
o
u
g
h
th
e
d
io
d
e,
wh
ile
in
th
e
OFF
s
tate
th
e
s
w
itch
is
r
ev
er
s
ed
b
ias
an
d
it
p
r
esen
ts
a
h
ig
h
im
p
ed
an
ce
an
d
ac
ts
as
an
o
p
en
cir
cu
it
wh
ich
in
d
icate
s
n
o
cu
r
r
en
t
f
lo
wn
th
r
o
u
g
h
th
e
d
io
d
e.
An
elec
tr
ical
cir
cu
it
is
s
h
o
wn
in
Fig
u
r
e
4
,
wh
ich
ex
p
lain
th
e
f
o
r
war
d
an
d
r
ev
er
s
e
b
iased
,
wh
er
e
th
e
o
n
ly
r
esis
to
r
o
f
(
3
.
5
o
h
m
s
)
in
s
er
ies
with
an
in
d
u
cto
r
o
f
(
0
.
1
5
n
H)
in
t
h
e
ON
s
tate
a
n
d
a
co
m
b
in
atio
n
o
f
(
1
Ko
h
m
)
r
esis
to
r
in
p
ar
allel
with
th
e
ca
p
ac
itan
ce
o
f
(
0
.
0
2
5
p
F)
all
in
s
er
ies
with
an
in
d
u
cto
r
o
f
(
0
.
1
5
n
H)
[
2
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
1
8
,
No
.
2
,
Ap
r
il
2
0
2
0
:
5
9
5
-
602
598
(
a)
(
b
)
(
c)
Fig
u
r
e
3
.
T
h
e
p
r
o
p
o
s
ed
m
u
ltib
an
d
r
ec
o
n
f
ig
u
r
ab
le
PIFA
an
te
n
n
a
T
ab
le
1
.
T
h
e
Op
tim
u
m
p
ar
am
eter
s
o
f
r
ec
o
n
f
ig
u
r
ab
le
P
I
FA
an
ten
n
a
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
i
n
mm
P
a
r
a
me
t
e
r
s
V
a
l
u
e
s
i
n
mm
Wg
3
9
.
6
L4
5
Lg
4
5
.
6
W4
4
L1
33
L5
5
.
9
W1
10
Rs
11
L2
33
t
0
.
0
3
5
W2
19
h
1
.
6
L3
5
.
2
L6
1
7
.
9
W3
9
L7
8
.
2
Ld
1
W7
10
Ws
4
Ls
1
.
6
7
(
a)
(
b
)
Fig
u
r
e
4
.
PIN
d
i
o
d
e
m
o
d
elin
g
u
n
d
er
(
a)
f
o
r
war
d
(
b
)
r
ev
er
s
ed
b
iased
co
n
d
itio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
C
o
mp
a
ct
r
ec
o
n
fig
u
r
a
b
le
P
I
F
A
a
n
ten
n
a
fo
r
w
ir
eless
a
p
p
lica
ti
o
n
s
(
A
b
d
u
lla
h
A
li J
a
b
b
er
)
599
4.
RE
SU
L
T
S AN
D
AN
AL
Y
SI
S
T
h
e
C
ST
s
o
f
twar
e
is
u
s
ed
to
s
im
u
late
th
e
p
r
o
p
o
s
ed
r
ec
o
n
f
i
g
u
r
ab
le
PIFA.
T
h
e
f
ab
r
icate
d
an
ten
n
a
is
s
h
o
wn
in
Fig
u
r
e
5
.
T
h
e
o
b
tai
n
ed
s
im
u
lated
an
d
m
ea
s
u
r
ed
m
u
lti
-
b
an
d
s
with
th
e
(
S1
1
)
th
r
o
u
g
h
th
e
two
s
tates
o
f
th
e
PIN
d
io
d
e
is
p
r
ag
m
atica
lly
s
h
o
wn
in
Fig
u
r
e
6
,
wh
er
e
o
b
tain
ed
l
o
west
S1
1
o
f
(
-
3
9
.
0
5
4
)
in
th
e
(
5
.
7
5
GHz
)
.
T
h
e
r
e
ar
e
f
iv
e
f
r
eq
u
e
n
cy
b
a
n
d
s
u
n
d
er
th
e
(
S1
1
≤
-
1
0
d
B
)
co
n
d
itio
n
h
a
v
e
r
esu
lted
in
th
e
ON
s
tate
o
f
th
e
PIN
d
io
d
e,
th
ey
ar
e
0
.
9
8
0
GHz
,
3
.
3
9
2
GHz
,
3
.
9
2
4
GHz
,
4
.
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Un
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[1
]
P
a
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P
a
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t
a
l.
,
“
M
EM
S
-
Ba
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fig
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ra
b
le
A
n
ten
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s,”
2
0
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IEE
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In
ter
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.
[2
]
J.
H.
Lee
,
Y.
S
u
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g
.
,
“
A
Re
c
o
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u
ra
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le
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IF
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Dio
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/P
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S
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IEE
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In
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a
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n
An
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d
Pr
o
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g
a
ti
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,
p
p
.
1
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,
2
0
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.
[3
]
F
.
A.
As
sa
d
a
ll
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,
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A
M
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Re
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ra
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De
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S
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A
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Pro
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(AP
S
UR
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I)
,
p
p
.
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.
[4
]
P
.
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M
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,
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.
T.
Th
a
o
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N.
T.
Du
c
,
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V.
Ye
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,
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A
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M
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re
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ra
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s (
AT
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,
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Vin
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Ra
k
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V.,
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In
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Res
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.
[6
]
F
.
A.
As
a
d
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ll
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h
,
J.
Co
sta
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,
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n
d
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k
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ro
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[9
]
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.
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1
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A.
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Ja
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2
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A.
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[1
3
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H.
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4
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.
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T
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,
20
1
5
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[1
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.
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[1
7
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.
[1
8
]
H.
Wo
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g
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p
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1
-
9
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2
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1
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.
[1
9
]
A.
G
h
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ffa
r,
X.
J.
Li
,
a
n
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B
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0
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Tro
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p
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4
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[2
1
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M.
-
J.
Lee
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-
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.
Kim
,
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n
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g
,
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p
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.
[2
2
]
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.
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.
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h
n
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3
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[2
4
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p
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sa
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0
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B
I
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RAP
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AUTH
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RS
Mr.
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h
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a
b
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