In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
2, June
2
01
9, pp.
611~
6
1
6
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
6
11-
61
6
611
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
D
e
sign and analysis of 2-coil
wireless power transfer (WPT)
using magnetic coupli
n
g technique
A. Ali
1
,
M
.
N
.
M
Y
a
s
i
n
2
,
M
.F.
C
.
Hu
s
i
n
3
,
N
.
A.
M
Ah
mad
Ham
b
ali
4
1
School o
f
Electrical
Sy
s
te
ms
E
n
g
ineering,
U
ni
ve
rsiti Malays
i
a
Perlis,
Mal
a
ysia
2,
4
Bio
e
lect
rom
a
gn
eti
c
s Research
Gro
up
(BioEM
)
, U
n
i
versi
t
i
M
a
la
y
s
i
a
P
erlis (
UniM
AP)
, Ma
l
aysi
a
3
F
acu
lt
y
of
En
g
ineerin
g
Techn
o
lo
gy, Un
i
versit
i
Malaysi
a
P
erl
i
s
(U
n
i
M
A
P
)
,
M
al
a
y
s
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
No
v
2
3
,
2
018
Re
vise
d Jan
2
8
, 2019
A
c
c
e
pte
d
F
eb 13,
2
0
1
9
2-co
il
n
on-rad
i
ativ
e
wi
reless
power
t
rans
f
e
r
(WPT
)
is
s
t
udi
ed
t
o
fi
nd
t
he
c
o
i
l
di
am
eter
r
at
io to
ef
f
ecti
v
e
d
i
s
t
an
ce of
p
ow
er
t
ran
s
f
e
r
effici
en
cy
(
P
T
E
)
.
Si
ngl
e
circu
l
ar co
i
l
and
sp
iral
co
i
l are d
e
si
gn
ed an
d
s
im
ulat
e
d
u
sin
g
C
S
T
softw
a
re
t
o
com
p
are
th
e
res
u
lt
o
f
coil
di
a
m
et
er
v
ersus
eff
ective
di
st
a
n
ce
o
f
PTE
b
y
u
si
ng
S2
1
va
lue
.
A
c
c
o
rding
l
y
,
t
h
e
q
ua
lity
fa
c
t
or
(
Q)
o
f
b
o
th
c
oi
ls
a
r
e
presen
ted
as
Q
f
acto
r
i
s
on
e
o
f
t
he
p
aram
eter
t
h
a
t
aff
e
c
t
t
he
p
e
r
f
o
rm
ance
of
W
P
T
s
y
s
t
e
m
.
Th
e
re
s
u
lt
i
s
p
ro
m
i
s
i
ng
as
t
he
e
ff
ectiv
e
d
i
stance
is
m
o
r
e
th
an
th
e
co
il
di
am
eter
w
it
h
(P
TE)
m
o
re
t
h
a
n
5
0
%
usin
g
s
p
i
r
al
c
o
i
l
as
c
om
p
a
re
to
s
i
n
g
l
e
coi
l
d
es
i
gn.
K
eyw
ord
s
:
2-co
il n
o
n
-r
adi
a
ti
ve
Powe
r tr
ansfer
efficie
n
c
y
(P
T
E)
Q-factor
W
i
re
l
e
ss
p
ower
t
ransf
e
r (
W
PT)
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Azu
w
a Al
i
,
S
c
hoo
l
o
f
Ele
c
t
rica
l
S
y
stem
s En
gi
neer
ing,
Uni
v
ersi
ti
M
al
ays
i
a P
e
rlis,
P
a
uh P
u
tra
Cam
pus,
0260
0
A
r
au,
P
e
rlis,
M
a
lay
s
ia.
Em
ail:
azuw
a
@u
n
i
ma
p
.
edu.
my
1.
I
N
TR
OD
U
C
TI
O
N
Wi
r
e
less
pow
e
r
s
ystem
s
s
ta
rt
ed
by
N
i
ko
la
T
e
s
l
a
b
as
ica
l
l
y
can
b
e
d
iv
ide
d
i
n
t
o
tw
o
c
a
t
e
gor
ies
w
h
ic
h
are
radiati
v
e
a
nd
no
nrad
iat
i
v
e.
T
he
nonra
d
ia
t
i
ve
a
re
k
n
o
w
n
a
s
i
n
d
u
ct
i
v
e
cou
p
l
i
ng
a
nd
m
a
gnet
i
c
reso
nanc
e
cou
p
l
i
ng
w
h
e
n
c
ou
pl
e
d
w
i
t
h
reso
nat
o
r
c
o
il.
B
ot
h
tec
h
niq
u
e
s
b
a
s
i
c
a
l
l
y
f
or
l
ow
-
pow
er
a
pp
lica
t
i
on
ha
v
i
ng
n
e
a
r
to
m
ed
ium
fi
e
l
d
ra
nge
o
f
d
i
s
t
ance
.
Man
i
pu
la
t
i
o
n
o
f
w
i
re
le
ss
pow
er
s
ys
t
e
m
to
a
pp
lica
t
io
n
are
grow
in
g
ra
pi
d
l
y
suc
h
a
s
in
p
o
w
e
r
up
se
nsor
,
c
h
arg
i
ng
c
ons
um
er
e
lec
t
r
oni
c
de
vice
,
b
i
o
m
ed
i
c
al
i
mpl
a
n
t
s,
e
l
e
ct
ri
c
ve
hicl
e
an
d
eve
n
n
ow
un
d
e
r
w
a
ter
appli
c
a
tio
ns.
The
o
reti
ca
l
as
pec
t
s
of
W
P
T
a
re
r
igoro
u
s
l
y
st
ud
ie
d
a
s
t
he
s
ys
tem
h
a
s
f
e
w
l
i
m
i
t
at
ion
s
e
spec
ia
ll
y
o
n
t
h
e
eff
e
c
t
i
v
e
d
i
st
an
ce
o
f
p
o
wer
b
e
i
n
g
t
r
ansf
er
a
n
d
th
e
si
zi
ng
o
f
th
e
co
il
.
B
i
g
g
e
r
c
oi
l
s
i
z
e
c
an
t
ra
nsfer
p
o
w
e
r
wi
re
l
e
s
s
l
y
t
h
r
ou
gh
l
ong
e
r
d
i
s
ta
n
c
e
,
b
ut
i
t
will
b
e
b
u
lk
y
a
nd
s
u
i
t
a
b
le
o
nl
y
for
bi
g
a
p
p
l
i
c
at
io
n.
S
a
m
e
aspec
t
t
o
the
c
o
il
de
sig
n
as
p
r
e
vi
ous
r
e
s
e
a
rc
her
desi
g
n
t
he
c
o
i
l
ran
g
e
s
f
rom
sim
p
le
c
i
r
cular
co
i
l
t
o
he
lica
l
s
ha
p
e
a
nd
the
n
p
la
nar
i
z
e
d
f
or
W
P
T
.
B
o
th
a
spec
ts
a
r
e
i
nfl
u
enc
e
by
p
ar
am
ete
rs
s
u
c
h
as
m
ut
ua
l
i
n
d
u
c
t
anc
e
,
c
o
up
l
i
n
g
fa
ct
or (
k) a
nd qua
l
ity
(
Q
)
fa
c
tor t
h
a
t
c
o
n
t
ri
b
u
t
e
d i
n
P
TE per
f
o
rm
ance [1].
I
n
o
r
d
er
t
o
fi
n
d
t
h
e
b
es
t
par
a
m
e
ter,
t
he
c
o
i
l
de
si
g
n
i
s
va
ry
w
h
er
e
some
r
e
s
ear
cher
s
us
in
g
he
l
i
c
a
l
,
w
i
re
w
ou
nd,
s
pira
l
re
cta
n
g
u
l
ar
a
nd
a
l
s
o
p
ri
n
t
e
d
s
p
i
r
a
l
c
o
i
l
(
PS
C)
[
1-
2].
G
e
ner
a
ll
y,
t
he
d
i
ffe
re
nt
c
o
il
d
e
sig
n
gi
ves di
ffere
n
t val
u
e of
e
ffe
c
t
i
v
e
d
i
s
t
ance
a
n
d
P
TE
bu
t
s
t
i
ll t
he va
l
ue
of k, Q
and
im
pe
da
n
c
e ma
t
c
hi
ng ar
e not
di
sc
usse
d
in
d
e
p
th
w
it
h
re
la
tio
n
t
o
c
oi
l
de
si
gn.
T
he
c
o
i
l
i
s
a
l
s
o
b
i
g
i
n
s
i
z
e
w
h
ic
h
l
i
m
its
t
he
a
p
p
l
ic
a
t
ion
t
o
b
e
use
d
l
a
t
er.
A
p
art
from
t
he
c
oi
l
des
i
g
n
,
t
h
e
s
i
z
e
o
f
tran
sm
itte
r
a
nd
r
ece
i
v
er
c
oi
l
are
a
l
so
v
a
r
i
e
d
to
f
in
d
the
be
st
parameter
with
h
igher
P
TE
a
t
h
ig
h
e
r
d
i
st
a
n
ce
o
f
t
r
a
n
sf
er.
Th
e
s
i
z
e
o
f
t
ran
s
mi
t
t
er
c
an
b
e
bi
gg
e
r
a
s
co
mp
are
t
o
rec
e
iver
o
r
v
i
c
e
versa
part
ic
u
l
arl
y
t
o
incr
eas
e
or
m
ax
imiz
e
t
h
e
d
i
s
t
a
n
c
e
of
P
TE
and
re
du
c
i
ng
t
h
e
s
ki
n
e
f
fe
ct
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
6
1
1
–
6
16
61
2
wh
en
t
h
e
c
oils
a
re
c
l
o
se
t
o
e
a
c
h
o
t
h
er.
Th
e
ma
in
c
ons
id
era
t
ion
if
b
igge
r
t
r
an
sm
i
t
t
e
r
or
v
ice
ver
s
a
,
t
he
ef
f
ect
iv
e
di
st
an
ce
i
s
stil
l
l
e
ss
a
s
co
mp
are
t
o
c
o
i
l
d
i
a
m
e
t
er
w
h
ic
h
co
ncl
u
d
e
t
o
ine
f
fe
c
tive
WPT
system
i
n
term
o
f
PTE.
Ther
ef
or
e
,
i
n
t
h
i
s
p
a
p
e
r
,
t
h
e
des
i
g
n
a
nd
a
n
a
l
y
s
i
s
o
f
2
c
o
i
l
s
am
e
siz
e
s
y
s
t
e
m
is
i
nv
e
s
ti
g
a
te
d.
T
he
2
-
c
o
il
s
am
e
siz
e
WP
T
sin
g
l
e
c
i
rcular
c
oi
l
a
n
d
sp
i
r
al
c
o
i
l
are
inv
e
s
ti
gate
d
b
a
sed
o
n
t
he
e
f
f
ec
t
i
ve
d
i
s
tan
c
e
,
P
TE
a
nd
r
a
t
i
o
o
f
di
sta
n
c
e
(
D
)
t
o
diam
et
er
o
f
t
h
e
c
o
ils
(
D
/
d
m
).
T
he
a
im
i
s
to
t
a
r
ge
t
t
h
e
effe
cti
v
e
d
i
s
t
a
n
ce
i
s
mor
e
tha
n
t
he
d
iam
e
ter
of
t
he
c
oi
l
a
nd
e
f
f
i
c
i
e
n
cy
i
s
m
o
r
e
t
ha
n
50%
.
The
m
o
t
i
v
a
t
i
o
n
f
or
t
he
d
e
s
i
gn
is
t
o
f
i
nd
s
ma
ll
an
d
ef
fi
c
i
e
n
t
co
il
d
esi
g
n
t
h
at
g
iv
e
hi
gh
e
r
e
f
f
e
c
t
iv
e
di
st
an
c
e
(
m
o
r
e
t
han
t
h
e
dia
m
e
t
e
r
c
o
i
l
)
a
nd
P
TE.
Q
-
f
a
c
to
r
of
t
he
c
o
i
l
i
s
a
l
s
o
i
nves
t
iga
t
e
d
t
o
f
i
nd
the
e
f
f
e
ct
t
o
t
h
e
d
i
st
a
n
ce
and
PTE.
B
a
s
i
c
w
i
r
e
less tr
a
n
sf
er
oper
a
t
i
on
in
vo
lves
t
h
e
t
r
a
nsmiss
ion
o
f
ener
g
y
f
r
o
m a transm
itter
t
o
a
r
ece
i
v
e
r
via
osc
i
l
l
a
t
i
n
g
ma
gnet
i
c
fie
l
d.
T
he
o
per
a
t
i
on
s
tar
t
s
by
c
o
n
v
e
r
t
i
n
g
d
i
r
e
c
t
c
ur
r
e
nt
(
D
C
)
su
p
p
lie
d
by
a
p
o
w
e
r
sour
c
e
t
o
hi
gh
f
r
e
que
nc
y
a
l
t
e
r
n
at
ing
c
u
r
r
e
nt
(
A
C
)
usi
n
g
s
p
ec
i
f
i
c
des
i
g
n
e
d
o
f
e
l
e
c
tro
n
i
c
c
i
r
c
u
it
bu
il
t
to
ge
the
r
wit
h
t
ra
n
s
m
i
t
t
e
r
.
The
AC
c
urr
e
nt
e
xc
ite
a
w
ire
coi
l
i
n
the
tra
n
smi
t
t
e
r
t
h
a
t
i
nduc
e
a
m
a
g
n
e
tic
f
ie
l
d
.
When
a
r
ece
i
v
e
r
co
il is
p
lac
e
d
w
it
hi
n vic
i
ni
ty o
f t
h
e
m
a
gne
tic
fie
l
d
,
t
h
e
f
i
eld
ca
n
en
e
r
gi
ze
a
n
alt
e
rn
a
t
i
n
g
c
u
rren
t
i
n
th
e
r
ece
i
v
e
r
c
oil.
E
lec
t
r
onic
circ
uit
in
t
he
r
e
cei
ver
con
v
e
r
ts
b
ac
k
t
he
A
C
c
u
r
r
e
nt
i
n
t
o
D
C
c
ur
r
e
nt
w
h
i
c
h
t
ur
n
to
usa
b
le
p
ow
e
r
.
WP
T
m
a
in
pur
pose
i
s
t
r
a
ns
fe
r
r
i
n
g
t
he
e
ner
g
y
i
t
se
l
f
n
o
t
t
he
i
nf
or
m
a
ti
on
e
nc
ode
d
i
n
t
he
e
n
e
r
gy.
F
o
r
max
i
mu
m PTE,
th
e
t
rans
m
i
t
t
e
r
a
n
d
the
r
ec
eiver
co
il m
u
st
r
es
ona
te
a
t
t
h
e
sam
e
f
r
e
qu
ency.
N
o
w
a
da
ys,
WP
T
techn
o
l
o
g
i
es
a
r
e
going
t
h
r
o
ug
h
a
c
t
i
ve
r
e
s
ear
ch
w
h
i
c
h
f
o
c
u
se
d
on
m
a
ximiz
i
n
g
powe
r
t
ran
s
fe
r
efficie
n
c
y
(
PTE)
.
Many
fa
ct
o
r
s
affec
t
t
he
P
TE
as
s
ta
te
d
e
a
r
lier
b
u
t
t
he
m
a
i
n
f
o
c
u
sed
her
e
a
r
e
the
d
e
sig
n
o
f
the
transm
i
tter
and
re
ce
ive
r
c
oi
l
a
n
d
t
h
e
Q-fac
t
o
r
.
T
he
b
i
gge
r
t
h
e
c
o
il,
t
he
h
ig
her
the
e
f
fe
ct
i
v
e
di
sta
n
ce
a
nd
P
TE
due
t
o
m
o
r
e
m
a
gnet
i
c f
i
e
l
ds
i
nduc
e
i
n
b
e
t
w
e
e
n
t
h
e
t
r
ans
m
i
tter
an
d rec
e
iver
co
i
l. B
i
g
g
e
r
coil
w
i
l
l
b
e
bu
l
ky,
heav
y i
n
ter
m
of w
ei
g
h
t
a
nd
cer
tai
n
ly n
o
t
s
uita
b
l
e
for
s
m
a
ll
a
p
p
lica
tio
n.
B
y
t
u
n
i
ng the Q-fa
ctor
o
f
t
h
e
c
oi
l
,
t
he
d
i
s
t
a
n
c
e
a
nd
PTE
i
s
b
e
l
i
e
ve
t
o
i
m
p
r
ov
e
as
h
igh
er
Q
-
f
ac
to
r
ma
de
t
he
c
oi
ls
a
c
h
ieve
d
to
i
t
s
m
a
xim
u
m
a
m
p
l
i
t
u
d
e
a
nd
s
t
aye
d
l
on
ge
r
at
r
eso
n
an
t
fr
e
que
nc
y
t
h
us
a
l
l
o
w
i
n
g
m
a
x
im
um
pow
er
t
r
a
nsfer
.
The
r
ef
ore,
s
a
m
e
resona
nt
f
r
e
q
u
enc
y
e
x
h
ib
it
a
t
t
r
ansm
itter
-rec
e
i
ver
c
o
il
pr
od
uc
e
l
o
w
r
a
te
o
f
e
n
er
g
y
l
oss
a
p
ar
t
f
r
o
m
other
d
i
m
e
ns
io
na
l
f
act
or
s
such
a
s
num
be
r
of
t
ur
n
of
c
o
ils
and c
o
ils d
i
a
m
e
te
r.
F
u
r
t
he
r
s
upp
or
t
a
nd
r
e
la
te
t
he
Q
-
f
actor
e
ffe
c
t
t
o
WP
T
per
f
or
ma
n
ce
is
t
he
F
igur
e
of
M
er
it
(
F
oM)
for
c
o
il.
T
he
F
o
M
s
ug
ges
t
t
ha
t
t
h
e
Q
-
f
act
or
f
o
r
a
c
oil
s
h
ou
ld
b
e
m
o
re
t
ha
n
10
0
to
b
e
effec
tive
l
y
o
p
er
at
e
and
tr
a
n
sf
er
pow
er
e
ffic
i
e
n
tl
y
[
9
-
10]
.
Most
o
f
the
r
e
sear
ch
una
bl
e
to
r
e
l
ate
th
e
FoM,
Q
-fa
c
tor
and
P
T
E
pe
r
f
or
m
a
nc
e
in
d
etai
l
e
i
t
h
er
by
the
o
r
y
o
r
exp
e
r
i
me
nt
a
l
.
2.
COMPL
ETE
S
Y
STEM DESIGN
F
i
gur
e
1
sh
ow
t
he
b
as
ic
c
on
c
e
pt
ua
l
o
f
2
c
oi
l
WP
T
w
h
ic
h
co
ns
ist
o
f
a
t
ra
nsmi
tte
r
an
d
a
r
ece
ive
r
c
o
ils.
T
h
e
de
sign
o
f
the
co
i
l
i
s
si
n
g
le
c
ircu
la
r
lo
op
t
o
be
a
s
a
referen
ce
design
.
Both
c
oils
a
re
c
o
n
n
e
c
t
e
d
w
i
t
h
sour
c
e
a
nd
the
place
me
nt
s
e
p
a
r
ati
on
of
t
he
c
oil
is
t
he
d
is
ta
nce
o
f
t
r
ansf
e
r
o
r
ef
f
ect
iv
e
d
i
st
a
n
ce
.
T
a
bl
e
1
sh
ow
the
s
i
n
g
l
e
coi
l
pa
r
am
eter
. T
h
e
wir
e m
a
te
rial sele
c
tio
n
in t
he
C
ST simu
l
ation
is cop
p
e
r
p
u
r
e
.
Tab
l
e
1.
S
ingl
e
coil
pa
r
a
m
e
te
r
Co
i
l
P
ar
ame
t
e
r
(
cm
)
Wire
t
hic
kne
s
s
0
.
1
Inne
r
r
a
dius
4
.
9
O
u
te
r
ra
di
us
4
.
8
F
i
gur
e
1.
B
a
s
ic
c
onc
ep
t
u
a
l
o
f
WP
T
system
The
di
s
t
a
n
c
e
i
s
var
y
s
ta
r
t
i
n
g
f
r
o
m
4
cm
to
ma
xi
m
u
m
7
cm
a
nd
t
h
e
va
l
ue
o
f
S
11
a
nd S
21
of
the c
o
il ar
e
m
e
a
s
ur
ed
t
o
f
i
nd
t
h
e
P
TE
acc
or
d
i
n
g
t
o
the
e
qua
t
i
o
n
:
2
0
(1
)
=
x
100%
(
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
sign
a
nd a
n
a
ly
sis o
f
2-c
o
il w
i
rele
ss po
wer
tra
n
sfe
r
(W
PT)
usi
n
g
m
a
g
n
et
ic c
o
u
p
l
i
n
g te
c
h
n
i
que
(A.
Ali)
61
3
The
va
lue o
f
m
ea
sur
e
S
21
s
i
m
ula
t
e
d
i
s
the
n
c
om
par
e
w
i
t
h
c
a
lcu
l
a
t
io
n us
in
g equa
tio
n be
lo
w:
|
|
(
3
)
The
Q-fact
or
o
f
t
h
e
co
i
l
i
s
ta
ken
for
ea
ch
d
ista
nc
e
varia
t
io
n
t
o
an
aly
ze
t
h
e
e
f
f
e
c
t
o
f
th
e
Q
f
act
o
r
tow
a
rds
dis
t
a
n
ce
.
The Q
fa
ctor
e
qua
ti
o
n
usi
ng for
ca
l
c
u
l
a
tion
i
s
as bel
ow
:
(
4
)
The
c
o
il
is
d
es
i
g
n
w
i
t
h
s
p
i
r
a
l
sha
p
e
c
o
il
w
i
t
h
t
he
s
a
m
e
d
i
a
m
ete
r
a
s
s
i
n
g
l
e
2-c
o
i
l
.
F
i
gure
2
s
how
t
he
2-co
il
s
pira
l de
si
gn
w
i
t
h
the
p
a
ra
me
t
e
r as
i
n Tab
l
e 2
.
T
h
e
v
a
l
u
e
o
f
S
11
,
S
21
and Q
-factor are
tak
en
f
or
d
ifferent
di
sta
n
c
e
f
or
f
ur
ther
a
na
l
y
s
i
s o
n
the
ef
f
ec
t
an
d
com
p
a
r
is
on
w
i
t
h
the
s
in
g
l
e
circu
l
ar
2-c
oil
des
i
gn.
Tab
l
e 2.
2-c
oi
l
sp
i
r
al par
am
eter
Coil
paramet
e
r (
c
m
)
Wire
r
a
d
i
u
s
0.
05
C
o
il
progre
ss
(ga
p
)
0.
4
Inn
e
r Ra
dius
0
.5
Nu
m
b
er
o
f
tu
r
n
s
5
F
i
gure
2.
2
-coi
l sp
iral
d
es
i
g
n
3.
RESULT
S
A
N
D
ANALY
S
IS
Bot
h
c
oi
l
desi
gns
a
re
s
i
m
ul
ated
a
t
di
ffere
n
t
d
i
stanc
e
s
t
a
rting
from
4
c
m
t
o
7
cm
.
The
effect
i
v
e
di
sta
n
c
e
a
n
d
P
TE
for
bo
t
h
d
e
s
igns
a
re
c
om
p
a
r
e
d
and
t
h
e
re
su
lt
s
how
e
d
t
h
a
t
the
sp
ira
l
c
o
i
l
gi
ves
be
t
t
er
r
e
s
ult
w
ith
i
ncre
ase
P
TE
over
di
s
t
a
n
ce
a
roun
d 10%
.
G
r
aph in F
ig
u
r
e
3 s
how
the
o
vera
ll
resul
t
s.
F
i
gure
3.
P
ow
er tra
nsfer
effic
i
en
c
y
f
o
r
s
i
ngl
e a
n
d
s
p
i
r
al
c
oi
l
w
ith d
iam
e
ter
4.9c
m
Ta
ble
3.
C
omp
a
r
i
so
n
w
i
t
h
p
revi
o
u
s w
o
rk
R
e
f
e
re
n
c
e
D
i
m
e
nsion
(d
tx
,d
rx
)(
c
m
)
Fre
que
n
c
y
Ef
f
i
ci
e
n
cy
D
i
s
t
a
n
c
e
(D(c
m
)
,D
/d
m
)
C
o
il t
y
p
e
Jise
ong
K
i
m
,
J
o
ngho
o
n
K
im
,
Sunky
u
K
ong,
H
o
ngse
ok
K
i
m
,
I
n-Soo
Suh,
N
a
m
P
y
o
S
uh,
D
ong-
H
o
C
ho,
J
ou
ng
h
o
K
i
m
,
S
e
n
ior
a
nd
S
e
ungy
oung
Ah
n
(
2
01
3)
(30,
3
0
)
30kHz
91%
(
20,
0
.
6
7
)
W
ir
e
w
ound
c
o
i
l
Pa
ulo
J. Aba
tti,
Sé
r
g
i
o
F
.
P
ic
h
o
r
im
,C
aio
M
. d
e
M
i
ra
nd
a
(2015
)
(15,
1
5
)
589kH
z
50%
(
5,
0.
33
)
He
li
c
a
l
Z
h
iga
ng
Da
ng,
J
a
b
e
r
A
.
A
bu
Qa
houq
(2
0
1
4
)
(
11.
5,
1
1
.
5
)
3M
Hz
40%
(
10,
0.
8
7
)
He
li
c
a
l
Y
i
m
i
ng
Z
h
a
n
g
,
a
n
d
Z
h
e
n
gm
ing
Zh
a
o
(
2
0
1
4
)
(28,
2
8
)
289kH
z
90%
(
10,
0.
3
5
7
)
H
e
l
i
c
a
l
T
h
is
w
ork
(5,
5
)
212M
H
z
44.
53
%
(5,
1
.
0
2
)
S
pira
l
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 2
,
Ju
n
e
2
019
:
6
1
1
–
6
16
61
4
In
c
o
m
p
a
ri
s
o
n
w
i
t
h
p
r
e
v
i
o
u
s
wo
r
k
a
s
i
n
T
a
b
l
e
3
,
m
o
s
t
o
f
t
h
e
p
r
e
v
i
ou
s
p
a
pe
r
h
a
vi
ng
l
arg
e
c
o
i
l
d
e
si
gn
w
h
ic
h
a
r
e
mor
e
t
ha
n
10
cm
.
The
pr
evi
o
us
r
ese
a
r
c
h
i
s
b
a
s
e
d
o
n
sa
m
e
s
ize
2
c
o
il
co
n
v
e
n
tio
na
l
WP
T
as
m
an
y
ot
her
r
e
sea
r
ch
m
or
e
foc
u
si
ng
on
3,
4
o
r
m
o
re
c
o
i
ls
t
o
i
n
cr
e
a
se
the
PTE
ve
r
s
us
d
i
s
t
a
nce
[
1
4
]
.
The
com
p
ar
i
s
o
n
is
m
ade
base
d
on
t
he
r
at
i
o
o
f
d
i
sta
n
ce
t
o
t
h
e
co
il
d
i
am
eter
(
D/
d
m
).
T
he
(
D
/
d
m
)
valu
e
a
r
e
low
com
p
ari
n
g
t
h
e
e
f
f
i
cie
n
c
y
t
o
t
h
is
w
or
k.
A
par
t
f
r
o
m
the
r
a
t
i
o,
t
he
d
es
ign
o
f
t
h
e
c
o
i
l
i
s
a
l
so
i
m
p
or
t
a
n
t
a
s
pr
evi
o
us
r
esea
rch
ar
e
f
o
c
u
s
i
n
g
t
o
s
i
n
g
le,
he
l
i
ca
l
or
w
ir
e
w
ound
c
o
i
l
d
es
i
gn.
D
ue
t
o
d
if
fic
u
lt
o
f
d
es
ig
n
i
n
g
a
nd
de
ve
l
o
p
i
ng
t
h
e
spir
a
l
c
o
il,
o
t
h
er
d
esi
gn
i
s
m
uch
pr
efe
r
r
e
d.
The
a
d
va
nta
g
e
o
f
t
h
i
s
des
i
gn
a
pa
r
t
f
r
o
m
sm
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t
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i
g
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e
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o
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a
c
t
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t
h
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h
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Q
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fa
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a
s
co
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to
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ing
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e
ci
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c
oil
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n
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ti
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f
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t
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h
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per
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ffe
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en
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ur
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on
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spec
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as
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sim
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11
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21
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k
A
n
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V
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F
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5 cm as
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t
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t s
p
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g
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nc
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[
4
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.
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and
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[
6]
c
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par
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m
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la
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on
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su
l
t
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F
i
gur
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show
e
d
t
he
s
pi
r
a
l
coi
l
d
es
ig
n
us
in
g
Li
tz
w
ir
e.
F
i
gur
e
4.
Q
-
f
act
or
f
or
s
i
n
g
l
e
a
n
d
sp
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r
al
c
o
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l
F
i
gur
e
5.
C
om
par
i
s
on
o
f
e
x
p
e
r
i
me
nt
a
l
a
nd
simu
la
ti
on r
e
su
lt
F
i
gur
e
6.
T
he
s
pir
a
l
c
o
i
l
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
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e
c
&
D
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IS
S
N
:
2088-
86
94
D
e
sign
a
nd a
n
a
ly
sis o
f
2-c
o
il w
i
rele
ss po
wer
tra
n
sfe
r
(W
PT)
usi
n
g
m
a
g
n
et
ic c
o
u
p
l
i
n
g te
c
h
n
i
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(A.
Ali)
61
5
4.
CONCL
U
S
ION
The
ma
i
n
o
b
j
e
c
ti
ve
o
f
t
h
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p
a
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r
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he
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renc
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o
f
effec
t
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v
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sta
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e
,
PTE
and
als
o
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-factor.
The
sp
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d
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s
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t
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n
a
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a
n
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o
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une t
he freque
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the
Q
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F
u
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e
ff
ect
o
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e
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gap)
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w
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e
ter
can
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w
het
h
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s
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Q-factor
a
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t
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P
TE.
ACKNOW
LEDG
E
MEN
T
S
Thi
s
s
t
u
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y
was
s
u
ppo
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e
d
b
y
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al
ay
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a
Pe
rl
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i
M
AP)
a
n
d
t
h
e
M
i
n
i
s
t
r
y
o
f
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i
g
h
e
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i
o
n
(
M
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)
un
de
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ant
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u
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b
er
U
niMA
P
/
R
M
I
C
/F
RG
S
/
90
0
3
-0
0-
0
0
562
(F
R
G
S
/
1
/
201
4/
TK03/
U
N
IM
AP/
0
2/
4
)
.
REFE
RENCES
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B
.
H
.
W
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t
e
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s
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M
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h
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e
y
,
G
.
L
e
e
,
a
n
d
J
.
R
.
S
m
i
t
h
,
“
O
p
t
i
m
a
l
coil
s
i
ze
rati
os
f
or
w
i
r
ele
s
s
power
t
ran
s
fer
app
l
i
cati
o
n
s
,” i
n
P
r
o
ceedin
gs
- IEEE
Inter
nati
o
n
a
l
Symp
os
ium o
n
Ci
rcu
i
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m
,
a
n
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n
d
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“
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a
x
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ansfer
v
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Eff
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c
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Mid-Ran
g
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,”
Jou
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n
a
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f
Micr
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e
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p
toel
ectr
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n
d El
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ma
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t
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ons,
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4
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Z.
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an
d
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ahou
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“
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e
an
d
M
i
s
a
lig
n
m
en
t
Tolerance
Co
mpa
r
ison
s
be
twe
e
n
Two-
c
o
il
a
n
d
Fo
ur-c
o
i
l
Wi
reless
P
o
wer
Transf
er
S
ystems,”
i
n
Appl
i
e
d
P
o
we
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ronic
s
Conferen
ce
and E
x
position (
A
PE
C
)
, 2015
I
E
E
E
,
20
15
,
p
p.
1
23
4–12
40.
[4]
Y.
Z
hang
a
nd
Z
.
Z
h
ao,
“Frequen
cy
s
plitting
analysi
s
o
f
two-c
o
il
r
es
onan
t
w
i
r
e
l
ess
p
o
wer
tran
sf
er,”
I
E
EE
Antennas
Wi
rel.
P
r
op
ag.
Let
t
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,
vol.
1
3
,
pp.
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40
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N.
A
.
Z
a
karia,
M
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J
usoh
,
N.H
.
G
h
azal
i,
M
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in
,
T.S
a
b
a
pat
hy,
M
.N.
O
s
m
a
n
,
N
.A
h
m
ad,
M
.
Z.Z
a
kari
a,”A
Com
p
ut
a
tio
na
l
S
t
u
dy
o
n
t
he
M
ag
neti
c
Reso
nan
ce
Co
up
lin
g
T
echni
qu
e
f
o
r
W
i
r
e
les
s
P
ow
er
T
ransf
e
r,”
ICE
E
S
I
20
17
.
[6]
N.
A.
R
ashid
,
M
.
N
.M
.
Y
a
si
n,
M
.
N
.
No
rizan,
S.
K
hat
un,
S
.
A.
Z
.
M
u
rad
,
I
.S
.
Mo
hamad
an
d
M
.
I
.
Sulaiman
,
”
Des
i
g
n
a
nd
O
ptim
izatio
n
o
f
M
agnet
i
c
Reso
nance
Cou
p
ling
by
u
s
in
g
R
elay
E
ffect
”,
10th Euro
pea
n
Conf
eren
ce
o
n
Ante
nn
as
an
d Pro
p
a
g
a
tio
n
(EuC
AP
),
2
0
16.
[7]
M.
N
.
M
.
Y
asin
,
S.
A
.
Ibrah
i
m,
S
.
A.
Z
.
Mu
ra
d,
M
.
I.
S
u
l
ai
man,
M
.
J
u
s
o
h
,
A
.
A
l
i
,
I
.
A
d
a
m
a
n
d
S
.
A
.
T
a
j
u
l
Arus
,“
W
i
rel
e
ss
p
ow
er
t
rans
f
e
r
vi
a
mag
n
etic
r
eso
n
ance
co
upl
in
g”,
Jou
r
n
a
l
of
En
gi
neer
ing and Ap
p
l
i
e
d Sci
e
n
c
e
11(
5
)
:3
341
-33
4
4
, March
20
1
6
[8]
N.
A
.
Ras
h
id,
M.N
.
M.Yasin,
K
.Kam
ar
di
n,
N
.
R
a
m
li,
M
.
Ju
so
h
,
S
.
A
.Z
.
M
urad
,
M
.
I
.S
ul
a
i
m
a
n
,
”
A
s
tu
dy
o
n
R
elay
Eff
ect
v
i
a
M
agneti
c
Reson
a
nt
C
ou
pl
in
g
f
o
r Wi
re
less
P
ow
er Tran
s
f
er”,
ICo
n
G
D
M 201
6
,
Jan
u
ary
201
6.
[9]
M
e
hd
i
K
i
ani,
M
aysam
Gh
ov
a
n
l
o
o
,
”A
F
ig
ure-o
f-M
erit
f
o
r
Desig
n
i
ng
Hig
h
-P
erf
o
rm
an
ce
I
n
duct
i
v
e
P
ower
Transmi
s
si
on Links”,
I
EEE Tran
s
Ind Electron
. No
v
em
b
e
r
20
12.
[10]
Aaro
n
L.
F
.
S
t
e
i
n
,
P
hyo
A
un
g
Kyaw,
Ch
arles
R.
S
ulli
v
an,
”
Figu
re
o
f
m
e
rit
f
o
r
re
s
o
n
a
n
t
w
ire
l
es
s
po
wer
tran
sf
er”,
IEEE 1
8
t
h
W
o
r
k
sh
op
on
Control and
M
o
d
e
l
in
g
f
o
r
Power Elect
roni
cs
(
C
O
M
PE
L)
,
20
17
.
[11]
C
.
M
.
D
e
M
i
r
a
n
d
a
a
n
d
S
.
F
.
P
i
c
h
o
r
i
m
,
“
A
S
e
l
f
-
R
e
s
o
n
a
n
t
T
w
o
-
C
o
i
l
W
i
r
e
l
e
s
s
P
o
w
e
r
T
r
a
n
s
f
e
r
S
y
s
t
e
m
U
s
i
n
g
O
p
e
n
Bi
f
ilar Coils,”
I
E
E
E
Tr
an
s.
C
i
rc
u
i
t
s
S
y
s
t
.
I
I
E
x
pr
e
s
s Br
ie
fs
,
vol.
6
4
,
no
.
6
,
p
p
.
6
15–6
19,
2
0
1
7
.
[12]
Z.
D
an
g
an
d
J
.
A
.
Ab
u
Qaho
u
q
,
“Exten
ded
-ran
g
e
t
w
o
-
coil
ad
apti
ve
l
y
r
eco
nfig
urab
le
w
ireles
s
pow
er
t
ran
s
f
e
r
syst
e
m
,”
Co
nf.
Pr
oc.
- IEEE
Ap
pl.
Po
wer Elect
ron.
Conf
.
E
x
po
.
-
APE
C
,
v
o
l
.
2
01
5
–
M
a
y
,
n
o.
M
ay,
pp.
1
6
3
0
–
1
636
,
20
15
.
[13]
Y.
Z
hang
a
nd
Z
.
Z
h
ao,
“Frequen
cy
s
plitting
analysi
s
o
f
two-c
o
il
r
es
onan
t
w
i
r
e
l
ess
p
o
wer
tran
sf
er,”
I
E
EE
Antennas
Wi
rel.
P
r
op
ag.
Let
t
.
,
vol.
1
3
,
no.
2
,
p
p
.
4
00
–40
2,
20
1
4
.
[14]
W.
M
.
Ng
,
C.
Z
h
a
ng
,
D
.
Lin
,
and
S.
Y
.
R
.
H
u
i
,
“Two-
and
t
h
ree-d
im
en
si
ona
l
o
m
n
i
d
i
rec
t
io
na
l
wireles
s
power
tran
s
f
er,”
IEEE Trans. Power El
ect
ron.
,
v
o
l
.
2
9
,
no
.
9
,
pp
.
4
4
7
0–447
4,
2
0
14.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
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l
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c
&
D
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yst
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V
ol.
10,
N
o.
2
, June
20
1
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:
611
–
6
16
61
6
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ro
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al
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a
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elangor
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.
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s
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ra
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ly
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alaysi
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Institute
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nstitut
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n
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o
a
rd o
f
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g
i
neers
M
a
l
a
ys
ia (B
E
M
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.