Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
1
3
,
No.
2
,
Febr
uar
y
201
9
, pp.
7
79
~
7
8
6
IS
S
N: 25
02
-
4752, DO
I: 10
.11
591/ijeecs
.v1
3
.i
2
.pp
7
79
-
7
8
6
779
Journ
al h
om
e
page
:
http:
//
ia
es
core.c
om/j
ourn
als/i
ndex.
ph
p/ij
eecs
Frequen
cy tuni
ng var
act
or
-
loade
d rec
onfigurable
antenna
fo
r
m
-
WiM
AX and
WLAN
a
pp
lications
S. M. Sh
ah
1
, K. H
am
dan
2
, Z
.
Z
. A
bidi
n
3
, F
. C. Se
ma
n
4
,
S. A. Ha
mz
ah
5
,
N. K
at
ir
an
6
,
F. Z
ubir
7
1,2,3,4,5,6
Resea
rch
Cent
re
for
Appl
i
ed
E
le
c
tromagne
ti
cs,
Univer
sit
i T
un
Hus
sein
Onn
Ma
lay
s
ia
,
Johor,
Malay
si
a.
7
School
of El
ec
t
ric
a
l
Eng
ineeri
n
g,
Univer
si
ti T
ek
nolog
i
Ma
lay
sia
,
Johor,
Ma
lay
sia
.
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
1
1
, 201
8
Re
vised
Dec
12
, 2
018
Accepte
d
Dec
26
, 201
8
A
design
appr
oac
h
for
a
m
ic
rostrip
p
atch
antenna
to
a
chi
ev
e
th
e
rec
onfigur
able
d
ual
-
band
op
erati
on
with
a
tuna
bl
e
device
is
pre
se
nte
d
in
thi
s
work.
The
appr
o
ac
h
uses
a
BB83
3
var
actor
diod
e
in
the
m
iddl
e
of
a
slott
e
d
pat
ch
an
te
nn
a
which
which
is
abl
e
to
p
roduc
e
dua
l
-
ba
nd
resona
nt
fre
quencie
s.
Th
e
rec
onf
igura
b
le
ant
enn
a
is
desig
ned
and
sim
ula
t
ed
in
CS
T
Microwa
ve
Stud
io®
software
an
d
is late
r
,
f
abr
i
cate
d
on
a
FR
-
4
subs
tra
te wit
h
a
di
el
e
ct
r
ic
const
ant
,
ε
r
of
4
.
5,
loss
t
ange
nt
,
t
an
δ
of
0.
019
and
th
ic
kn
ess,
h
of
1.
6
m
m
.
B
y
ch
angi
ng
th
e
DC
volt
ag
es
of
th
e
var
a
ct
or
diod
e,
diff
ere
n
t
ca
pa
ci
t
ance
va
l
ues
of
the
v
aract
or
diod
e
ar
e
obta
in
ed
which
dic
t
at
e
the
spec
ific
resona
n
t
fre
quencie
s.
F
rom
the
sim
ula
ti
on
result
s,
the
ca
pa
ci
t
ance
val
ue
of
0.
5
pF
with
a
bia
s
volt
age
of
2.
0
V
is
chose
n
as
it
produc
es
th
e
req
uire
d
dua
l
-
b
and
resona
nt
fr
eque
nc
ie
s
at
3.
38
GH
z
and
5.
37
GH
z
for
desire
d
appl
i
cati
ons i
n
th
e
m
-
W
iMAX
and
W
LAN ba
nds.
Ke
yw
or
ds:
Mi
cro
strip
an
te
nn
a
m
-
W
iM
AX
Re
config
ur
a
bl
e anten
na
Var
act
or
diode
WL
AN
Copyright
©
201
9
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed.
Corres
pond
in
g
Aut
h
or
:
Sh
a
har
il
Mo
hd
Sh
a
h,
Re
search
Centr
e f
or
A
pp
li
ed
Ele
ct
ro
m
agn
et
ic
s,
Un
i
ver
sit
i T
un
Hu
s
sei
n O
nn
Ma
la
ysi
a,
86400 B
at
u Pa
hat, J
ohor, Mal
ay
sia
.
Em
a
il
: shah
aril
@u
t
hm
.ed
u.
m
y
1.
INTROD
U
CTION
W
i
reless
c
omm
un
ic
at
ion
ha
s
pro
gr
es
sed
ve
ry
rap
i
dly
in
recent
ye
ars
.
The
ra
pi
d
de
ve
lop
m
ent
is
br
i
ng
i
ng
a
bout
a w
ave
of n
e
w wirel
ess
dev
ic
e
s an
d sy
ste
m
s
t
o
m
eet
s the d
em
and
s
of
m
ultim
edia app
li
cat
ion
s
.
Mult
i
-
fr
e
qu
e
nc
y
and
m
ulti
-
mo
de
de
vices
s
uc
h
as
cel
lula
r
phones,
Wirele
ss
Local
A
rea
Netw
orks
(
WL
AN
s
)
and
Wireless
Pers
on
al
A
rea
Networ
ks
(
W
PANs)
place
sever
al
dem
ands
on
the
a
nten
nas.
T
her
e
f
or
e
,
rad
i
o
fr
e
qu
e
ncy
(RF
)
eng
i
neer
s
a
r
e
facing
co
ntinuo
us
chall
en
ges
to
desig
n
anten
na
with
s
m
al
l
-
vo
lum
e
bu
t
sti
l
l
op
e
rati
ng
in
m
ulti
band
f
re
quencies.
T
o
s
olv
e
these
pro
bl
e
m
s,
reconfi
gurab
le
a
nten
nas
offer
a
good
s
olu
ti
on
because
they
can
ex
pand
th
e
capab
il
it
y
of
the
com
m
un
ic
at
ion
syst
e
m
s.
In
ad
diti
on,
the
reco
nfi
gu
rab
le
anten
nas
are m
or
e d
e
sired
in
wireless com
m
un
ic
at
io
n
ap
p
li
cat
ion
s b
eca
use
o
f
their f
le
xi
bili
ty
an
d
their abili
ty
to
sat
isfy
the
changin
g
syst
e
m
s
req
uirem
ents.
Re
co
nf
i
gurab
le
ante
nnas
that
hav
e
the
abili
ty
to
radi
at
e
at
m
ul
ti
ple
fr
eq
ue
ncies
are
re
quire
d
in
the
m
od
ern
com
m
un
ic
at
io
n
syst
e
m
s.
By
reco
nf
i
gurin
g
it
s
o
per
at
in
g
fr
e
qu
e
ncies,
th
e
rec
onfig
ur
a
bl
e
anten
na
is
a
ble
to
accom
m
od
at
e
t
he
num
erous
fr
e
quenc
y
bands
of
wir
el
ess
com
m
un
ic
at
ion
syst
em
s
[1]
.
Var
i
ou
s
te
c
hniqu
e
s
ha
ve
bee
n
ad
opte
d
t
o
a
chieve
t
he
rec
onfig
ur
at
io
n
a
bili
ty
in
anten
nas
s
uc
h
as
the
us
ed
of
switc
hing
a
nd
tun
in
g
de
vices
on
the
a
nten
na
s.
Fiel
d
Ef
fec
ts
Transi
stor
(
FET)
and
P
os
it
ive
-
I
nt
rinsic
-
Neg
at
iv
e
(PIN
)
diodes
are
the
exam
ples
of
act
i
ve
s
witc
hes
a
nd
va
ractor
di
od
e
ac
ts
as
a
tun
in
g
de
vice
[2
]
.
A
par
t
from
that,
by
us
ing
ph
oto
c
on
du
ct
ive
s
witc
hi
ng
el
e
m
ents
wh
ic
h
are
bas
ed
on
op
ti
cal
ly
tun
i
ng c
on
ce
pt ca
n al
so
r
ec
onfi
gur
e an
a
nten
na
[3]
.
Planar
a
nten
na
s,
su
c
h
as
m
ic
r
os
trip
a
nd
pri
nt
ed
anten
na,
ha
ve
the
at
tract
i
ve
featu
res
of
low
prof
il
e,
sm
a
ll
siz
e,
and
co
nfor
m
ability
to
m
ou
nting
host
and
ve
ry
prom
is
ing
cand
i
dates
for
sat
isfyi
ng
the
desi
gn
consi
der
at
io
n.
Mi
cro
strip
a
nt
enn
a
s
ha
ve
bec
om
e
po
pula
r
in
the
1970s
pr
i
m
aril
y
fo
r
sp
ac
e
born
e
a
ppli
cat
ion
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
1
3
, N
o.
2
,
Fe
bru
ary
201
9
:
77
9
–
7
8
6
780
To
day
the
antenn
a
s
are
us
e
d
for
gove
r
nm
ent
and
com
m
erc
ia
l
app
li
cat
ions.
Mi
cro
stri
p
anten
nas
co
ns
is
t
of
a
m
et
al
l
ic
patch
on
t
he
gro
unded
s
ub
st
rate.
The
m
et
allic
patc
h
ca
n
ta
ke
m
any
co
nfi
gurati
on
s
.
H
oweve
r,
because
of
the
ease
of
a
naly
sis,
fabrica
ti
on
and
at
tract
ive
rad
ia
ti
on
cha
r
act
erist
ic
s,
rectangula
r
a
nd
ci
rcu
l
a
r
patches
are
t
he
m
os
t
po
pula
r
[
4]
.
T
hese
a
nte
nn
a
s
ca
n
be
m
ounted
on
t
he
s
urface
of
hi
gh
perform
ance
ai
rcr
a
ft,
sp
acec
ra
ft, sate
ll
it
es,
m
issiles, cars
a
nd e
ven
hand
held
m
ob
i
le
tel
ephon
es
[
5]
.
This
w
ork
is
f
oc
us
in
g
on
the desi
gn,
sim
ulati
on
a
nd
fa
br
ic
at
ion
o
f
a
re
co
nfi
gurab
le
a
nten
na
that
us
e
s
a
BB
83
3
va
ra
ct
or
diode
f
rom
In
fine
on
Te
chnolo
gies
to
tun
e
the
f
requ
encies
t
o
op
e
r
at
e
in
the
wirer
el
ess
fr
e
qu
e
ncy
bands.
Var
act
or
di
od
e
is
a
s
olid
-
sta
te
sem
ic
ondu
ct
or
de
vice
that
is
us
e
d
to
tun
e
t
he
f
requen
c
y
range
of
the
a
nten
na
[6
]
.
By
cha
ng
i
ng
the
bias
vo
lt
ages
on
the
di
od
e
,
it
will
var
y
t
he
c
apacit
ances
a
nd
tu
ne
the
res
on
a
nt
frequ
e
ncies.
T
he
desig
n
an
d
si
m
ula
ti
on
proce
sses
are
do
ne
by
us
in
g
CST
Mi
cro
wa
ve
St
ud
i
o®
(M
W
S
)
s
oft
wa
re.
T
he
sim
ula
ti
on
resu
lt
is
optim
iz
ed
to
ac
hieve
the
best
perform
ance
of
the
ante
nna.
The
n,
the
ante
nn
a
is
fabrica
te
d
on
a
FR
-
4
s
ubstrat
e
with
a
relat
iv
e
diele
ct
ric
co
ns
ta
nt,
ε
r
of
4.5,
thick
ness,
h
of
1.
6
m
m
and
loss
ta
ng
e
nt,
ta
n
δ
of
0.019.
T
he
m
easur
em
ents
of
the
a
nten
na
is
per
f
or
m
ed
by
us
in
g
the
Z
VB14
R
ohde
&
Sc
hwarz
Vecto
r
N
et
work
A
naly
ser
(
V
NA).
Ba
s
ed
on
t
he
sim
ulati
on
res
ults,
t
he
ca
pacit
ance
of
0.5
pF
with
a
bias
vo
lt
age
of
2.0
V
is
ch
os
e
n
a
s
it
pr
od
uces
t
he
de
sired
dua
l
-
ba
nd
res
on
a
nt
fr
eq
ue
ncies.
As
a
resu
lt
,
th
e
va
ra
ct
or
diode
ha
s
su
ccess
fu
ll
y
tu
ne
d
t
he
re
sona
nt
fr
e
quen
ci
es
of
t
he
ante
nn
a
to
operate
in
the
m
-
W
iM
AX a
nd
WL
AN b
a
nds
at
3
.
50 GHz a
nd
5.20 G
Hz.
2.
RESEA
R
CH MET
HO
D
OL
OGY
In
orde
r
to
pro
du
ce
a
w
orki
ng
rec
onfi
gurabl
e
anten
na
with
a
var
act
or
di
od
e
,
a
few
a
nt
enn
a
s
ha
ve
been
desi
gn
e
d
and
sim
ulate
d
in
an
orde
rly
m
ann
er
.
T
his
s
ta
ge
is
co
nduc
te
d
to
in
vestig
at
e
the
directi
on
an
d
m
ov
e
m
ent
of
the
res
onant
fr
e
qu
e
ncies
f
or
e
ach
ante
nn
a
a
nd
ho
w
the
place
m
ent
of
the
va
ractor
diode
i
n
the
structu
re
of
th
e
anten
na
ca
n
tun
e
t
he
re
son
ant
f
reque
ncies
to
op
e
rate
in
the
desire
d
f
r
equ
e
ncy
bands
.
I
n
thi
s
work, t
he
a
ntenn
a
is
op
ti
m
iz
e
d
to
wo
rk in t
he
m
-
W
iM
A
X
a
nd
WLAN a
pp
li
cat
ion
b
a
nds.
2.1.
Micros
tr
ip Pa
tch An
te
nna
The
first
de
sign
of
the
ant
enn
a
is
a
m
icr
os
t
rip
patc
h
anten
na
that
operates
at
3.5
0
G
Hz.
Th
e
dim
ension
s
of
the
ante
nn
a
ha
ve
been
cal
c
ul
at
ed
f
ro
m
the
f
or
m
ulas
in
[
7].
Fig
ur
e 1
s
how
s
the
m
ic
ro
strip p
at
ch
anten
na
at
3.
50
GH
z
an
d
Ta
ble
1
li
sts
the
di
m
ension
s
of
th
e
antenn
a
.
The
di
m
ension
s
of
the
m
ic
ro
strip
patc
h
anten
na
a
re s
i
m
il
ar f
or all
ant
enn
as
in
t
his
work.
Figure
1. Mi
cr
os
trip
an
te
nna
at
3
.
50 GHz
Table
1.
Dim
e
ns
io
ns
of the
Mi
cro
strip
Pat
ch An
te
nn
a
at
3.5
0 G
Hz
Para
m
eter
Valu
e (
m
m
)
Para
m
eter
Valu
e (
m
m
)
L
g
33
W
f
3
.04
W
g
3
5
.9
G
pf
0
.14
L
1
9
.9
F
i
7
.5
W
2
5
.9
2.2
.
Micros
tr
ip Pa
tch An
te
nna w
ith
a
Sl
ot
an
d
Micr
os
t
ri
p S
lo
t Ant
e
n
na
wi
th a
n I
de
al Swi
tch
Nex
t,
a
12
× 1
m
m
2
slot
is
introd
uced
i
n
the
m
idd
le
of
the pat
ch
in
t
he
sec
ond
desig
n
of
the
a
nten
na.
A
par
am
et
ric
stud
y
is
per
f
or
m
ed
to
ob
ta
in
the
best
locat
ion
of
the
slot
with
res
pect
to
the
upper
ed
ge
of
the
patch.
F
ro
m
the
par
am
et
ric
st
ud
y,
the b
est
l
ocati
on
o
f
the slot
is
at
4
m
m
fr
om
the
up
pe
r
edg
e o
f
the pat
ch
for
L
g
W
g
L
W
G
pf
F
i
W
f
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Freq
uen
cy
tu
ni
ng
va
ra
ct
or
-
l
oade
d rec
onfi
gu
ra
ble
anten
na f
or
m
-
Wi
M
AX
and WLAN
…
(
S. M.
Shah
)
781
m
-
W
iM
AX
an
d
WL
AN
ap
pl
ic
at
ion
s.
I
n
the
thir
d
desig
n,
an
ide
al
switc
h
is
i
ntr
oduce
d
in
t
he
m
idd
le
of
the
slot
to
obser
ve
the
cha
ng
es
in
resona
nt
f
reque
ncy
an
d
ref
le
ct
io
n
coe
f
fici
ent.
A
para
m
et
ric
stud
y
is
al
so
cond
ucted
t
o
determ
ine
the
best
locat
io
n
of
t
he
ideal
s
witc
h.
The
i
de
al
switc
h
is
a
coppe
r
bri
dge
with
a
dim
ension
of
1
×
1
m
m
2.
Figure
2
s
hows
the
m
ic
ro
strip
patch
a
nten
na
with
a
slot
an
d
the
m
ic
ro
strip
slot
anten
na wit
h
a
n
ideal
switc
h (
coppe
r br
id
ge
).
(a)
(b)
Figure
2. Mi
cr
os
trip
p
at
c
h
a
nt
enn
a:
(a)
With
a slot; (
b)
W
it
h
a c
oppe
r br
i
dge
(ideal s
witc
h) acr
os
s t
he
sl
ot
2.3
.
Reconfi
gurable
Anten
na
wi
th a
BB
833 V
ar
actor
D
iode
The
c
oppe
r
br
i
dg
e
is
re
place
d
by
a
var
act
or
diode
in
the
four
t
h
desig
n
of
the
a
nten
na
.
I
niti
al
ly
,
a
SMV14
05
va
r
act
or
di
ode
is
chosen
.
H
ow
e
ver,
the
pr
oduc
ti
on
has
bee
n
disco
ntin
ued
by
Sk
yw
orks
S
ol
ution
s
,
In
c
.
T
her
e
f
or
e,
it
is
re
placed
with
a
BB
833
var
act
or
di
od
e
from
In
fi
neon
Tech
no
l
og
ie
s
.
The
va
ractor
di
od
e
is
represe
nted
by
a
disc
rete
po
r
t
in
CST
M
W
S®
s
of
t
war
e
wh
ic
h
ca
n
be
viewe
d
in
Fig
ur
e
3(a)
.
T
he
act
ual
var
act
or
di
od
e
m
od
el
is
repre
sented
by
t
he
*.s2
p
file
that
is
sup
plied
by
th
e
m
anu
factu
rer.
T
he
*.
s
2p
is
t
he
2
-
port
S
-
pa
ram
eter
s
file
w
hich
i
s
un
i
que
f
or
ea
ch
capaci
ta
nce
and
bias
vo
lt
a
ge
of
the
var
ac
tor
diode.
How
ever,
du
e
to
t
he
un
a
vaila
bili
ty
of
t
he
BB
83
3
varac
tor
diode
*.
s
2p
file
s
f
r
om
t
he
m
anu
fact
urer,
t
he
*.
s
2p
fi
le
s
of
SMV14
05
varac
tor
di
od
e
f
r
om
S
kywo
r
ks
S
olu
ti
ons,
I
nc.
are
us
e
d
instea
d.
I
n
the
sche
m
at
ic
diagr
am
of
the
CST
M
WS®
s
of
t
war
e,
the
*.
s2
p
file
is
tra
nsfer
red
to
the
To
uch
st
on
e
fil
e.
Fi
gure
3(b
)
sh
ows
the
sch
e
m
at
i
c
diag
ram
o
f
the
reconfi
gura
ble
anten
na wit
h
t
he *.s
2p f
il
e
of the
var
act
or d
i
o
de
.
(a)
(b)
Figure
3. The
re
config
ur
a
ble
anten
na wit
h
a
BB
833 varact
or
diode: (a
)
T
he
d
isc
rete
port
to
represe
nt the v
aractor
d
i
ode;
(b) The
*.s
2p f
i
le
to
re
pr
e
sent
the v
a
racto
r di
od
e
in
t
he
sc
he
m
at
ic
diag
ram
o
f
CS
T M
W
S
® s
of
t
war
e
2.4
.
An
te
nn
a
Fa
bric
at
i
on
The
a
nten
nas
are
fa
br
ic
at
ed
on
t
he
FR
-
4
s
ub
st
rate
with
a
relat
ive
diel
ect
ric
const
ant
,
ε
r
of
4.5
,
thickne
ss,
h
of
1.6
m
m
and
loss
ta
ngent,
ta
n
δ
of
0.0
19.
T
he
m
easur
e
m
ents
are
c
on
du
ct
e
d
by
us
i
ng
the
ZVB14
R
ohde
&
Schwa
rz
V
ect
or
Netw
ork
An
al
yz
e
r
(VN
A)
.
Fig
ur
e
4
s
hows
th
e
fa
br
i
cat
ed
ante
nn
as
in
this
work.
C
o
p
p
e
r
B
r
i
d
g
e
D
i
s
c
r
e
t
e
P
o
r
t
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
1
3
, N
o.
2
,
Fe
bru
ary
201
9
:
77
9
–
7
8
6
782
(a)
(b)
(c)
Figure
4. The
fa
br
ic
at
ed
an
te
nnas:
(
a
)
Mi
cr
ost
rip patc
h
a
nte
nn
a
w
it
h a sl
ot; (
b)
Mi
cr
os
tri
p
patch
a
nte
nn
a
with
a co
pp
e
r br
i
dge (id
eal
s
witc
h);
(
c
)
Re
co
nfi
gura
ble a
nten
na wit
h
a BB
833 varact
or
diode
3.
RESU
LT
S
A
ND AN
ALYSIS
Du
e
t
he
la
ck
of
facil
it
ie
s,
on
l
y
the
ref
le
ct
io
n
coe
ff
ic
ie
nt
of
the
ante
nnas
is
m
easur
ed
in
this
wor
k.
Fu
rt
her
m
or
e,
t
he
m
easur
em
e
nts
of
th
e
rec
onfi
gurab
le
a
nt
enn
a
with
a
va
ractor
di
od
e
are
not
al
lo
we
d
to
be
perform
ed
to
avo
i
d
any
dam
a
ges
to
t
he
RF
port
of
the
Z
V
B14
R
ohde
&
Schwarz
V
NA.
The
refor
e
,
on
ly
the
si
m
ulati
on
r
es
ul
ts of
t
he reco
nfi
gura
ble an
te
nna
with a
va
rac
tor dio
d
e is
sho
wn in t
his
wor
k.
3.1
.
Micros
tr
ip Pa
tch An
te
nna and
Micr
os
trip
P
at
ch
An
te
nn
a
w
ith
a
Sl
ot
Figure
5
s
hows
the
sim
ula
te
d
re
flect
ion
coeffic
ie
nt
of
the
m
ic
ro
strip
patch
ante
nna.
Since
th
e
anten
na
is
not
fabrica
te
d
a
nd
m
easur
ed
,
on
l
y
the
sim
ulati
o
n
re
s
ult
is
s
ho
wn.
T
he
ref
le
c
ti
on
c
oeffici
ent
of
the
anten
na
is
-
20.
87 at 3
.50 G
Hz
.
Figure
5. Sim
ulate
d
ref
le
ct
io
n coe
ff
ic
ie
nt
of the m
ic
ro
strip
pa
tc
h
ante
nna at
3
.
50
GH
z
Figure
6
s
ho
ws
the
c
om
par
iso
n
of
t
he
s
i
m
ulate
d
an
d
m
easur
ed
re
flect
ion
c
oeffici
ents
of
t
he
m
ic
ro
strip
patc
h
ante
nn
a
with
a
slot.
Fr
om
t
he
fig
ure,
the
pr
e
viously
si
m
ulate
d
res
onan
t
fr
eq
ue
ncy
at
3.5
0
GH
z
ref
e
r
Fi
gure
4
has
been
sh
ifte
d
to
3.3
15
G
Hz
du
e
t
o
prese
nce
of
the
slot.
At
th
e
sam
e
t
i
m
e,
a
no
t
he
r
resona
nt
fr
e
qu
ency
is
gen
e
ra
te
d
at
5.
34
GHz.
The
ref
le
ct
ion
c
oeffici
ents
at
tho
se
res
on
ant
fr
e
quencie
s
are
-
15.94
dB
an
d
-
22.
11
dB.
T
he
refor
e
,
it
is
sh
ow
n
that
the
pr
ese
nce
of
a
slot
in
the
str
uc
ture
of
the
a
nt
enn
a
pro
du
ces
dual
-
ba
nd
res
ona
nt
fr
e
qu
e
ncies.
The
re
is
a
good
a
gr
e
e
m
ent
betwee
n
the
sim
ulatio
n
an
d
m
easur
em
ent r
esults.
The
disp
la
y
of
the
m
easur
ed
r
eflect
ion
c
oeffi
ci
ent
on
the
V
NA
can
be
vie
wed
in
Fig
ur
e
7.
From
the
fig
ur
e,
the
a
nt
enn
a
res
onat
es
at
3.37
G
Hz
a
nd
5.5
5
GH
z
wh
ic
h
var
y
sli
gh
tl
y
f
ro
m
the
si
m
ulate
d
res
ult.
This
m
igh
t
be
at
tr
ib
uted
to
t
he
fa
bri
cat
ion
i
nc
on
s
ist
encies.
T
he
ref
le
ct
io
n
c
oeffici
ents
ar
e
-
19
.12
dB
at
3.3
7
G
Hz
and
-
17.
92 d
B
at
5
.
55 GHz
w
hich
a
re
reas
onable.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Freq
uen
cy
tu
ni
ng
va
ra
ct
or
-
l
oade
d rec
onfi
gu
ra
ble
anten
na f
or
m
-
Wi
M
AX
and WLAN
…
(
S. M.
Shah
)
783
Figure
6. Re
fle
ct
ion
c
oeffici
ents
of
t
he
m
ic
ro
strip
p
at
c
h
a
nt
enn
a
with a
sl
ot
Figure
7. Me
as
ur
e
d reflect
io
n coef
fici
ent
of
t
he
m
ic
ro
strip
pa
tc
h
ante
nna
w
it
h
a slot
3.2
.
Micros
tr
ip Slo
t Ant
e
n
na
wi
th a
n I
de
al Swi
tch
Figure
8
s
how
s
the
com
par
ison
of
th
e
sim
ul
at
ed
an
d
m
eas
ur
e
d
re
flect
ion
coeffic
ie
nts
of
the
anten
na
with
an
ide
al
switc
h.
F
ro
m
the
figure,
th
e
pr
evio
us
ly
si
m
ulate
d
res
on
a
nt
f
reque
ncies
at
3.3
15
GHz
an
d
5.34
GH
z
ref
e
r
Fig
ur
e
5
ha
ve
be
en
sh
i
fted
sli
ghtl
y
to
3
.4
G
H
z
and
5.3
G
Hz
du
e
to
t
he
pr
esence
of
the
coppe
r
br
i
dg
e
as
a
n
i
de
al
switc
h.
T
he
co
pp
e
r
bri
dge
has
res
ulted
in
the
cu
rrent
tra
vels
s
horter
sin
ce
it
passes
th
r
ough
the
co
pper
bri
dg
e
instea
d
of
goin
g
rou
nd
the
sl
ot
[
8].
T
her
e
fore,
the
r
eso
nan
t
fr
e
que
ncy
i
nc
reases
wh
ic
h
exp
la
in
s
the
s
hi
ft
in
the
fi
rst
r
eso
nan
t
f
re
qu
e
ncy
of
the
a
nte
nn
a
.
T
he
re
flec
ti
on
co
ef
fici
ent
at
3.40
G
Hz
is
-
11
dB
an
d
at
5.3
0
GH
z
is
-
16.
16
dB.
Fig
ure
9
s
hows
t
he
m
easur
e
d
ref
le
ct
ion
c
oeffici
ent
of
the
a
nten
na
.
The
ref
le
ct
io
n
c
oeff
ic
ie
nts
are
-
26.
88 d
B
at 3
.42
6 GH
z
and
-
12.30 dB at
5.51 G
Hz.
Figure
8. Re
fle
ct
ion
c
oeffici
ent of t
he
m
ic
ro
strip sl
ot an
te
nna
with a
n
id
ea
l swit
ch (co
ppe
r br
id
ge
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
1
3
, N
o.
2
,
Fe
bru
ary
201
9
:
77
9
–
7
8
6
784
Figure
9. Me
as
ur
e
d reflect
io
n coef
fici
ent
of
t
he
m
ic
ro
strip s
lot wit
h
a
n
i
de
al
sw
it
ch (co
pp
e
r br
id
ge
)
3.3
.
Reconfi
gurable
Anten
na
wi
th a
BB
833 V
ar
actor
D
iode
Diff
e
re
nt
capa
ci
ta
nce
val
ues
of
t
he
var
act
or
diode
ca
n
be
va
ried
by
c
hang
ing
t
he
DC
vol
ta
ges
wh
ic
h
dicta
te
the
pr
es
ence
of
sp
eci
fi
c
resonan
t
f
requen
ci
es
.
The
c
apacit
ance
val
ue
an
d
DC
volt
age
of
eac
h
va
ractor
diode
is
uniq
ue
for
each
*.s2
p
file
.
F
ro
m
the
si
m
ulati
on
re
su
lt
s,
the
var
ac
tor
diode
with
the
capaci
ta
nc
e
valu
e
of
0.5
pF
with
a
bias
vo
lt
age
of
2.0
V
pro
duces
the
desired
resonan
t
f
requ
encies
for
m
-
W
iM
AX
a
nd
WL
A
N
app
li
cat
io
ns
.
F
igure
10
sho
w
s
the
si
m
ulate
d
re
flect
ion
c
oeffici
ents
of
the
anten
na.
F
ro
m
the
figur
e,
the
resona
nt
freq
ue
ncies
at
3.4
0
GH
z
a
nd
5.30
GH
z
ref
e
r
Fi
gure
8
hav
e
bee
n
sli
ghtl
y
sh
ifte
d
to
3.3
8
G
H
z
an
d
5.375
GH
z
due
to
pr
e
sence
of
the
va
ractor
diode.
T
he
re
f
le
ct
ion
coe
f
fici
ents
at
tho
se
pa
rtic
ular
f
requ
encies
are
-
21.
86
dB an
d
-
21.17 d
B wh
ic
h
s
how
a
r
easo
nab
le
im
pr
ov
em
ent
as
co
m
par
ed
to
the
an
te
nna w
it
h
a
n
idea
l
switc
h.
Figure
10. Si
m
ulate
d reflect
io
n
c
oeffici
ent
of the
reconfi
gur
able ante
nna
w
it
h
a v
a
racto
r d
iod
e
4.
CONCL
US
I
O
N
A
rec
onfi
gurabl
e
anten
na
wit
h
a
BB
83
3
varac
tor
diode
is
desig
ne
d,
sim
ulate
d
an
d
fa
bri
cat
ed
in
t
his
work.
The
rec
onfig
ur
a
ble
an
te
nn
a
is
tun
e
d
by
the
var
act
or
diode
to
op
erate
at
3.
38
GH
z
a
nd
5.3
7
GH
z
fr
e
qu
e
ncy
ba
nds
f
or
m
-
W
iM
AX
a
nd
W
L
A
N
ap
plica
ti
on
s
.
The
ca
pacit
an
ce
values
of
t
he
var
act
or
diode
are
var
ie
d
by
va
ryi
ng
the
bias
vo
lt
ages.
It
is
found
that
the
va
ractor
diode
w
it
h
the
capaci
ta
nce
val
ue
of
0.5
pF
and
a
bias
volt
age
of
2.0
V
is
the
m
os
t
prefe
rr
e
d
si
nce
it
ge
ner
at
es
the
des
ired
du
al
-
band
resona
nt
f
re
quencies
require
d
in
t
his
wor
k.
Du
e
to
t
he
un
a
vaila
ble
dev
ic
e
i
n
the
l
aborato
ry,
the
m
easur
em
ent
of
the
recon
fig
urable
anten
na
with
a
va
racto
r
diod
e
co
uld
not
be
pe
rfor
m
ed
to
avo
i
d
a
ny
dam
ages
t
o
t
he
RF
port
of
the
Z
VB14
Rohde
&
Schwarz
V
N
A.
T
he
refor
e
,
only
t
he
si
m
ulati
on
r
esults
of
the
re
config
ur
a
ble
anten
na
with
a
var
act
or
diode
is
sho
w
n
in
this
w
ork.
Howe
ver,
tw
o
anten
nas
a
re
f
abr
ic
at
ed
a
nd
m
easur
ed
nam
el
y,
m
ic
ro
strip
patch
anten
na
with
a
slot
and
m
ic
ro
strip
sl
ot
ante
nn
a
with
a
n
id
eal
switc
h
(c
oppe
r
bri
dge
)
but
due
to
the
l
ack
of
facil
it
ie
s,
on
ly
the
ref
le
ct
ion
coeffic
ie
nts
ar
e
m
easur
ed
.
From
the
si
m
ula
ti
on
an
d
m
eas
ur
em
ent
resu
lt
s,
it
is
ob
s
er
ved that t
hey ag
ree
well
with eac
h othe
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Freq
uen
cy
tu
ni
ng
va
ra
ct
or
-
l
oade
d rec
onfi
gu
ra
ble
anten
na f
or
m
-
Wi
M
AX
and WLAN
…
(
S. M.
Shah
)
785
ACKN
OWLE
DGE
MENTS
The
aut
hor
w
ould
li
ke
to
ack
nowled
g
e
U
ni
ver
sit
i
Tu
n
Hussei
n
O
nn
Ma
la
ysi
a
fo
r
the
fund
i
ng
of
this
work un
der the
Internal
G
ran
t
of Tier
1 (H2
47)
.
REFERE
NCE
S
[1]
Rouissi,
Ine
s,
J
e
an
Mari
e
Floc
'
h
,
Hate
m
Rm
il
i,
a
nd
Hiche
m
Tr
ab
el
si.
"D
esign
of
a
fre
qu
ency
r
ec
o
nfigura
bl
e
pa
tc
h
ant
enn
a
using
capac
i
ti
ve
lo
adi
ng
and
var
actor
dio
de.
"
In
Antennas
and
Propagati
on
(
EuCA
P)
,
201
5
9th
European
Confe
renc
e
on
,
pp.
1
-
4
.
IE
EE,
2
015.
[2]
Haupt,
R
and
y
L
.
,
and
Michael
Lanaga
n.
"Rec
onf
i
gura
ble a
nt
enna
s
.
"
IE
EE
Ant
enna
s and
Propagation Magazine
55
,
no.
1
(2013):
49
-
61.
[3]
D
ixi
t,
L
.
,
and
P.
K.
S.
Pourus
h
.
"Radi
a
ti
on
ch
a
rac
t
eri
sti
cs
of
sw
it
cha
b
le
fer
r
it
e
m
ic
rostrip
arr
a
y
an
te
nna
.
"
I
EE
Proce
ed
ings
-
Mi
crowave
s, Ant
en
nas and
Propag
ati
on
147
,
no
.
2
(2000):
151
-
155
.
[4]
Bal
ani
s
,
Constan
ti
ne
A.
"A
nte
nn
a
The
or
y
:
Ana
l
y
s
i
s &
Design
,
Joh
n
W
i
ll
e
y
&
Sons
.
"
Inc
.
Publ
i
cat
i
on
(1997).
[5]
W
ong,
Kin
-
Lu.
"A
dvanc
ed
Pl
ana
r
Ant
enna
Designs
for
W
ire
le
ss
Devi
ce
s
[Z]
.
"
Taiwan:
Dept.
o
f
E
lectrical
Engi
ne
ering
Nat
ional
Sun
Y
a
t
-
Se
n
Unive
rs
ity
Ka
ohsiung
80424.
[6]
Frenz
el, Louis.
Princ
iples of
e
lectronic c
omm
uni
cat
ion
systems
.
McGraw
-
Hill
,
In
c.
,
2007.
[7]
Chit
ra
,
R.
Jothi
,
K.
Ja
y
ant
hi
,
a
nd
V.
Naga
raja
n.
"D
esign
of
m
ic
rostrip
slot
ant
enn
a
for
W
iMAX
appl
ic
atio
n.
"
In
Aut
omat
ion,
Computing,
Comm
unic
ati
on,
C
ontrol
and
Com
press
ed
Sensing
(
iMac
4s)
,
2013
Inte
rnational
Mu
lt
i
-
Confe
renc
e
on
,
pp.
645
-
649
.
I
E
EE
,
2013.
[8]
Yang,
Fan,
and
Yah
y
a
Rahmat
-
Sam
ii
.
"P
at
ch
an
te
nnas
with
sw
it
cha
bl
e
slots
(PASS
)
in
wire
le
ss
comm
unic
at
ions
:
Conce
pts,
desig
ns,
and
applic
at
i
ons."
IEEE
An
tennas
and
propagation
Magazin
e
47,
no
.
2
(2005):
13
-
29.
BIOGR
AP
HI
ES OF
A
UTH
ORS
Sh
aharil
Mohd
Sh
ah
obta
ine
d
h
is
B.
Eng
in
Mic
rowave
and
Co
m
m
unic
at
ion
fro
m
Multi
m
edi
a
Univer
sit
y
(MM
U)
in
2002.
H
e
recei
ved
his
M
.
Sc
in
Mi
cro
wa
ve
Engi
n
ee
r
ing
and
W
ire
l
ess
Subs
y
st
ems
Des
ign
from
the
U
nive
rsit
y
of
Surre
y
,
UK
in
2
004
and
pursuing
his
Ph.D
i
n
Com
m
unic
at
ion
Engi
ne
eri
ng
fr
om
the
Univer
sit
y
of
Birmingh
am,
UK
bef
ore
gra
duating
in
2016.
He
is
cu
rre
ntly
a
senior
le
ct
ur
er
in
the
Depa
rtment
of
Com
m
unic
at
ion
Engi
ne
eri
ng,
Facul
t
y
of
El
e
ct
ri
ca
l
and
Ele
ct
roni
c
Engi
n
eering,
Univ
ersi
ti
Tun
Hus
sein
Onn
Malay
si
a
(UTHM
).
His
ar
ea
of
rese
ar
ch
in
cl
udes,
but
no
t
lim
it
ed
to
,
design
of
m
ic
rowave
d
e
vic
es,
activ
e
ant
enn
as
m
ea
sur
ement
and
nonl
i
nea
r char
ac
t
eri
sa
ti
on
of
a
ct
iv
e
d
e
vic
es.
Z
u
hairi
ah
Z
ain
al
Ab
idin
was
born
in
Kuala
Lumpur,
Malays
ia
,
in
1978
.
She
recei
ved
the
B.
Eng.
from
th
e
Univer
siti
Te
kn
ologi
Mal
a
y
si
a,
in
2001,
th
e
M.
Eng
from
the
Kolej
Univ
ersit
i
Tun
Hus
sein
Onn
Malay
sia
,
J
ohor,
Mal
a
y
s
ia
,
in
2003,
and
Ph.D.
degr
e
e
fr
om
Bradf
ord
Univer
sit
y
,
U.K
in
2011.
Curre
nt
l
y
,
she
was
a
Princi
pa
l
Resea
r
ch
er
at
Appli
ed
Elec
tromagne
ti
c
Cent
er
,
Univer
si
ti
Tun
Hus
sein
Onn
Malay
si
a.
She
has
aut
hore
d
and
co
-
au
thor
ed
num
ber
s
of
journa
ls
and
p
roc
ee
d
ings,
in
cluding
the
IE
E
E
TRANS
ACTION
ON
AN
T
ENNA
AND
PR
OPAGA
TIO
N,
MICROWA
V
E
AND
OPTICA
L
TECHN
OLOG
Y
LET
TERS
and
IEEE
AW
PL.
Her
rese
arc
h
in
t
ere
sts
inc
lud
e
MIM
O
ant
enna
,
print
ed
m
ic
rost
rip
ant
enn
a,
we
ara
bl
e
antenna
s,
el
e
ct
rom
agne
t
ic
bandga
p
(EBG)
for
wire
le
ss
and
m
obil
e
and
high
spee
d
digi
tal
ci
r
cui
t’s
appl
i
ca
t
ions.
Fau
z
ia
han
im
Ch
e
Seman
re
ce
iv
ed
the
B.
E
ng
.
degr
ee
in
el
e
ct
ri
ca
l
communic
a
ti
on
from
Univer
siti
Te
kn
ologi
Malay
sia
.
In
2002,
she
was
awa
rde
d
M
.
Eng
.
degr
ee
in
comm
unic
at
ion
engi
ne
eri
ng
fro
m
Kolej
Univer
siti
Tun
Hus
sein
Onn,
now
kn
own
as
Univer
siti
Tun
Hus
sein
Onn
(UTHM
).
She
recei
ved
he
r
Ph
.
D
.
in
elec
t
ric
a
l
eng
ineeri
n
g
Quee
ns
Univ
ersity
,
Bel
f
ast,
Northe
rn
Ire
la
n
d
in
2011.
Sh
e
serve
s
as
ac
ade
m
ic
i
an
in
Depa
rtment
of
Com
m
unic
at
io
n
Engi
ne
eri
ng,
Fa
cul
t
y
of
El
e
ct
ri
ca
l
Elec
troni
c
Engi
ne
eri
ng
at
Univer
siti
Tun
Hus
sein
On
n
Malay
s
ia
(UTH
M)
since
2002.
She
is
al
so
a
r
e
sea
rch
f
el
low
in
Resea
rch
Cente
r
for
Applie
d
El
e
ct
rom
agne
t
(
EM
-
Cent
er)
.
She
has
aut
hor
ed
and
co
-
au
thore
d
over
40
ref
err
e
d
journa
l
and
conf
ere
n
ce
tech
nic
a
l
pap
ers.
Du
e
to
h
er
signif
icant
con
tri
but
ion
s
she
has
bee
n
a
warde
d
as
Top
Scopus
Inde
x
Author
b
y
Publish
er’
s
Offic
e
,
UT
HM
in
2014.
Si
nce
2011
,
she
active
l
y
s
erv
ed
as
an
associ
at
e
rev
i
ewe
r
for
m
ore
t
han
20
in
te
rn
at
i
onal
con
fer
en
ce
s
.
Sinc
e
2014,
she
serve
s
on
the
IEE
E
Malay
si
a
AP
/MTT
/E
MC
Joint
Chapter
as
execut
iv
e
com
m
it
te
e
.
She
is
a
ct
iv
ely
invo
lve
s
with
industrial
–
a
ca
demia
a
ct
iv
it
i
es
and
cur
ren
tly
has
joi
n
t
r
ese
ar
ch
co
ll
abor
at
ion
with
T
elekom
Malay
s
ia
RnD.
Her
rese
arc
h
intere
sts
inc
lud
e
fr
eque
nc
y
se
le
c
ti
v
e
surfac
es,
ant
en
na
design
and
appl
i
ed
e
lectr
om
agne
t
ic
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vo
l.
1
3
, N
o.
2
,
Fe
bru
ary
201
9
:
77
9
–
7
8
6
786
Sh
ipu
n
Anuar
Hamz
a
h
was
born
in
Per
ak,
M
al
a
y
si
a
in
1975.
He
re
ce
iv
ed
th
e
B.
Eng
.
and
Ph.D
.
in
elec
tri
c
al
eng
ine
er
ing
f
rom
Univer
siti
Te
knologi
M
al
a
y
sia
(U
TM),
Ma
lay
s
ia
in
1998
and
2013,
respe
ct
iv
ely
and
M.
E
ng.
of
Engi
n
ee
r
i
ng
in
Com
m
uni
ca
t
ion
and
Com
pute
r
S
y
st
em
from
Nati
onal
Univer
sit
y
of
Mal
a
y
si
a
(UK
M),
Sela
ngor
,
Malay
si
a,
in
2000
.
From
1998
to
2004,
he
worked
as
a
le
ct
ur
er
at
Kolej
UN
ITI
Sdn.
Bhd,
Malay
s
ia.
Since
April
2004,
he
has
bee
n
working
as
a
Lectu
rer
at
the
Fa
cul
t
y
of
Elec
tri
c
al
and
E
le
c
tronic
Engi
ne
eri
ng
,
Univer
siti
Tun
Hus
sein
Onn
Malay
si
a
(UTHM
).
He
is
now
a
S
eni
or
Lectu
rer
with
th
e
sam
e
i
nstit
uti
on
.
His
rese
arc
h
in
te
r
ests
inc
lude
ac
t
ive
ant
enn
a,
har
m
onic
suppress
ion
ant
enna,
rec
t
if
y
in
g
-
ant
enn
a
and
RF
propa
gation.
Norsh
idah
Kati
ran
re
ce
iv
ed
h
er
Ph.D
in
Elec
tri
c
al
Engi
ne
ering
from
Univer
siti
T
eknol
ogi
Malay
s
ia,
in
20
15,
her
M.E
ng
.
degr
e
e
in
Co
m
m
unic
at
ion
an
d
Com
pute
r
En
gine
er
ing
from
Univer
siti
Keb
a
ngsaa
n
Malay
si
a,
in
2004
,
and
her
B.
Eng
.
de
gre
e
i
n
El
e
ct
ri
c
al
Engi
n
ee
r
ing
(Te
l
ec
om
m
unic
a
ti
ons)
from
Univer
siti
Te
knolog
i
Malay
si
a,
in
2
001.
Curre
nt
l
y
,
she
is
a
Senior
Le
c
ture
r
in
th
e
Depa
rtment
of
Com
m
unic
at
ion
Engi
nee
r
ing
at
Univer
siti
Tun
Hus
sein
Onn
Malay
s
ia.
Her
m
aj
or
r
ese
ar
ch
in
t
ere
sts in
cl
ude
op
ti
m
iz
ation
of
res
ourc
e al
lo
cation in
coop
era
t
ive
net
works
and
m
ult
iple
input
m
ul
ti
ple out
pu
t
(MI
MO
)
tra
nsm
issions
.
Far
id
Z
u
bir
rec
e
ive
d
the
B.
Eng
.
deg
re
e
in
Elec
tr
ica
l
Engi
n
ee
r
ing
m
aj
oring
in
Te
l
ec
om
m
unic
ation
as
we
ll
as
M
.
Eng
.
d
egr
e
e
(C
om
m
unic
at
ion)
f
rom
the
Univ
ersit
i
Te
kno
logi
Malay
s
ia
in
200
8
and
2010
resp
ec
t
ive
l
y
.
In
201
6,
he
the
n
obt
ained
his
Ph.D
de
gre
e
from
the
Univer
si
t
y
of
Bi
rm
ingha
m
,
UK
,
for
rese
arc
h
in
t
o
dire
ct
int
egr
ation
of
power
amplifi
ers
with
ant
enn
as
in
m
i
cro
wave
tra
nsm
it
te
rs
.
He
is
cur
ren
tly
serve
s
as
a
Senior
Le
c
ture
r
at
th
e
Depa
rtment
of
Com
m
unic
at
ion
Engi
ne
eri
ng
,
Facul
t
y
of
Elec
tri
c
al
Engi
ne
ering,
Univer
si
t
i
Te
knologi
Mal
a
y
sia
.
His
cur
ren
t
rese
ar
ch
in
te
res
t
and
spe
ci
a
lization
are
in
the
ar
ea
of
RF
and
Microwa
ve
t
ec
h
nologi
es
includi
ng
Plana
r
Arra
y
Antenn
as,
Di
el
e
ct
ri
c
Resonator
Antenna
s
(DRA
s),
Acti
ve
Inte
gra
te
d
Anten
na
(AIA
),
Microstri
p
Refl
e
ct
a
rra
y
Antenn
a
(MRA
),
Mill
imeter
wave
Antenn
as,
El
e
ct
rom
agne
t
ic
Band
Gap
(EBG
),
Artifici
al
Mag
net
i
c
Conduct
or
(AM
C),
Full
-
int
egr
at
ed
Tra
ns
m
it
ti
ng
Am
pli
fiers
,
Li
ne
ar
PA
s,
Dohert
y
PA
s
an
d
Bia
s
Dec
oupling
Circ
uit
s.
H
e
has
publi
shed
ov
er
40
articles i
n
j
ourna
ls,
book
ch
apt
er
s,
conf
ere
n
ce
p
ape
rs
and
pr
oce
ed
ings.
Evaluation Warning : The document was created with Spire.PDF for Python.