Intern
ati
o
n
a
l
Jo
u
r
n
a
l
of
P
o
we
r El
ec
tr
on
i
c
s
an
d D
r
i
v
e
S
y
stem
(I
JPE
D
S)
V
o
l.
11
, N
o
. 2, Jun
e
20
20
, pp
. 71
1
~
72
5
I
SSN
:
208
8-8
6
9
4
, D
O
I:
10.
115
91
/i
jp
e
d
s.v
1
1
.i2
.
p
p71
1-7
25
7
11
Jo
urn
a
l
h
o
me
pa
ge
: h
t
t
p
:/
/ijpe
d
s.
i
a
e
s
c
o
re.
c
o
m
Design and implementati
on
of an effi
ci
ent WPT system
A
b
d
u
l
k
ar
ee
m
Mo
k
i
f Ob
ai
s
1
,
Al
i
F
a
eq
Ruzi
j
2
1
De
pa
rt
me
n
t
of
Bi
om
e
d
ic
al E
ngin
e
e
r
i
ng, Uni
v
e
r
si
ty
Ba
by
lo
n, Ira
q.
2
De
p
a
rtme
n
t
o
f
El
ec
tric
a
l
E
ngi
n
e
e
r
i
ng,
Un
ive
r
si
ty
of
Ba
b
y
lo
n,
Ira
q
.
A
r
ticle In
fo
A
B
S
T
RAC
T
A
r
tic
le
h
i
st
o
r
y:
Rec
e
i
v
ed
O
c
t
1
0
,
2
019
Re
vise
d N
o
v
9
,
20
19
A
c
ce
p
t
ed
Jan
22
, 20
20
Wire
les
s
p
o
wer
trans
f
er (
W
P
T
)
is
a te
chniqu
e in
tro
d
u
ced
to tr
a
n
sfer
pow
er
wireles
s
ly. Gen
e
rally
, WP
T
s
y
s
t
e
m
s ar
e
ch
arac
terized
by
lo
w
ef
ficien
cy
and
l
o
w ou
tp
ut po
w
e
r. Si
nc
e
W
P
T
p
r
oc
e
ss
d
e
pe
nd
s m
a
i
n
l
y
o
n
m
u
tu
a
l
c
o
up
li
n
g
between tr
ansmit
ti
ng and recei
v
i
ng coi
l
s
i
n
addition to
load
requi
r
eme
n
t
s
,
i
t
i
s
focuse
d
in this work
tow
a
rd
en
han
c
ing
th
e
m
u
tu
al co
up
ling
and
con
d
ition
i
ng
the
re
ce
iv
ing
circui
t
so
as
to
op
timally
s
a
tisfy
th
e
lo
ad
d
e
m
a
nd
.
Th
e
mutua
l
cou
p
l
ing
b
e
tween
tr
ans
m
ittin
g
an
d r
ece
iving
nod
es i
s
en
han
ced
via ins
e
r
t
ing
thr
ee r
e
son
a
ting
ci
rcuits
a
l
on
g with en
erg
y
tran
sm
iss
i
on
path
and
co
nd
itio
n
in
g the r
eceiving
circu
i
t su
ch
th
a
t
it acco
m
p
lish
es deliv
e
ring
maximu
m p
o
w
e
r to
th
e
load
no
de. In
th
is
wo
rk
,
an
ad
a
p
tive
ef
f
i
cient
WP
T
sy
stem is
in
trod
uced.
Th
is
s
y
s
t
e
m
is
carried
ou
t on
P
S
pic
e
an
d v
a
lidated
e
x
pe
rim
e
n
t
a
l
ly.
Bo
t
h
sim
u
lat
i
v
e
a
nd e
xpe
rim
e
nta
l
W
P
T syste
m
s ha
ve
acco
mp
lished
sig
n
ific
ant
enh
a
n
cem
ent in
e
ffic
i
ency
.
The
pro
p
o
s
ed WPT
sy
stem
has
th
re
e reson
a
to
rs an
d three
p
a
rallel co
n
n
ect
e
d
id
entica
l
re
ceiv
i
ng
coils
lo
c
a
ted
at 6
.
61
m f
r
om
th
e
p
o
w
e
r
tr
ans
m
itter.
The
eff
i
c
i
en
cy
enh
a
nc
emen
t
ap
pro
a
c
h
es
th
ou
sa
nd
s of t
i
m
e
s th
e effic
i
en
c
y
of
a
c
o
n
v
en
tion
al
W
P
T syste
m
havi
ng
si
m
i
l
a
r
powe
r
t
r
a
n
sm
i
tter located at the
sam
e
dist
a
n
ce
from
t
h
e recei
vi
ng
circuit,
w
h
ich has
a
s
i
ngle
coi
l
iden
t
i
cal
to those i
n
the
p
roposed
efficient
WPT s
y
s
t
em
.
Ke
yw
ords:
Ef
fi
ci
en
cy
e
nha
n
c
em
e
n
t
I
ndu
c
tiv
e
l
i
nk
M
u
tu
al
co
up
li
ng
M
u
tu
al
in
du
ct
an
c
e
Wi
re
le
s
s
p
o
we
r
t
r
a
n
s
f
e
r
Th
is
is a
n
o
p
en
acces
s a
r
ticle
un
d
e
r the
C
C
B
Y
-SA
licens
e
.
Corres
p
o
n
din
g
A
u
t
h
or:
A
bdu
lk
a
r
e
e
m M
o
k
i
f
Ob
ai
s,
Depa
rt
me
nt o
f
Bi
ome
d
i
cal
E
ngi
nee
r
i
n
g,
Uni
v
ersi
t
y
o
f
Ba
byl
on
,
Hi
ll
a
,
Bab
y
l
o
n, Ira
q.
Emai
l:
kari
m
o
b
a
i
s
@
y
a
h
o
o
.c
om
1.
IN
TR
O
DUCTION
In
th
e
l
a
st years, t
h
e
enhanci
n
g t
echnology
o
f
p
o
w
e
r
tran
sf
er (
W
PT) d
e
v
e
lop
s
qui
ck
l
y
. The mo
biles
or
other
el
ectronic
de
vic
e
s s
u
c
h
as l
a
p
t
o
p
s
or
el
e
c
tri
c
al
ve
hi
cles
co
u
l
d
be char
g
e
d
by
WPT tech
n
o
l
o
g
y
.
These t
e
chniques coul
d
be
use
d
i
n
pl
aces whe
n
w
i
ring
is di
ffic
u
lt to
b
e
a
c
c
o
mpli
she
d
[1-5]. Lo
ng-ra
nge
c
once
p
t of
W
P
T
ha
d
b
e
e
n
fo
rmul
a
t
e
d
aft
e
r mi
cr
o
w
ave
amp
l
i
f
ier
inv
e
nt
i
o
n
for
high
p
o
w
e
r
p
u
r
p
oses.
Th
e possib
ilit
y o
f
po
w
e
r
t
r
ansmi
s
si
o
n
via
el
ectro
magnet
i
c waves
gai
n
ed
mo
r
e
and mo
r
e
intention
fo
r
ap
p
l
i
c
a
t
i
on pu
r
p
o
s
es
[
6
,
7]
.
T
h
e wo
r
k
s cur
r
i
e
d ou
t
by
[7
,
8
]
p
r
esent analytical
mod
e
l
s
for cal
culat
i
ng
the mu
t
u
al
inductance
b
e
tw
een
plan
ar
spiral
co
il
s.
Th
ese models ar
e
ver
y
u
s
eful
i
n
th
e desi
g
n
and opti
m
ization of wi
r
e
l
e
ss p
o
wer tr
ansf
er s
y
st
ems.
T
h
e pr
op
ose
d
models
of
mutual
in
d
u
ct
ances bet
w
een
coil
s
w
e
r
e
d
e
ri
v
e
d u
s
i
n
g
th
e sol
u
t
i
on
o
f
Neu
m
ann’s int
e
gr
a
l
.
A
n
approx
imate fo
r
m
u
l
a for
deter
m
i
n
i
n
g
t
h
e self-r
esist
a
nce
o
f
a
cir
c
ula
r
mu
l
t
i
-
l
o
op induc
t
o
r
hav
i
n
g
u
n
eq
u
a
l
p
itches w
a
s i
n
tro
d
u
c
ed b
y
[
9
]. B
o
t
h
prox
imi
t
y an
d
ski
n
eff
e
ct
s
w
e
re included i
n
t
h
e suggest
ed
for
m
u
l
a.
P
r
o
x
imi
t
y
eff
e
ct was d
e
t
e
r
m
i
n
ed
u
s
i
n
g
the
ma
gnet
ic f
i
e
l
ds
exer
te
d
o
n
a
wir
e
d
u
e to
o
t
h
e
r
wir
e
s
.
Th
e s
t
u
d
y
co
nd
u
c
ted
b
y
[1
0] an
a
l
y
z
ed
w
ith a
c
o
n
t
e
x
t
o
f
no
n-
f
e
r
r
o
m
agn
e
tic
me
ta
llic
p
l
a
t
e
,
th
e
WP
T
perfo
rma
n
ce
s.
The
mode
l
of
t
h
e
WP
T
i
m
pe
dance
i
n
t
h
e
me
t
a
l
en
vi
ron
m
e
n
t
was
bui
l
t
.
T
h
e
p
r
o
p
o
se
d
sy
st
em
i
n
[11
]
c
o
m
p
ri
sed se
veral
l
o
op i
n
d
u
ct
ors
h
a
vi
n
g
di
ffe
re
n
t
siz
e
s. De
pe
nd
ing
on
t
h
e c
h
a
nge
s
o
f
t
h
e
di
st
anc
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
71
1 –
72
5
71
2
b
e
t
w
e
e
n
th
e tra
n
smit
tin
g
and r
e
ce
iv
in
g sid
e
s,
th
e
po
w
e
r wa
s sw
i
t
ch
e
d
to
o
n
e
loo
p
o
f
t
h
e
i
n
du
c
t
or
s
f
o
r p
o
w
e
r
tr
an
sm
issio
n
an
d
pow
er r
e
cep
ti
o
n
.
A
W
P
T
sy
ste
m
of
13
.5
6 M
H
z w
a
s
i
n
t
r
o
d
u
ced
by
[
1
2
]
and
i
n
ve
stig
a
t
e
d
bo
t
h
th
eo
r
e
t
i
c
a
ll
y
and
ex
p
e
r
i
men
t
a
lly
i
n
add
i
tio
n to si
mu
la
tio
n
.
A re
la
tiv
e
h
i
gh
i
m
p
r
ov
em
e
n
t
i
n
eff
i
c
i
e
n
c
y
of
ab
ou
t
41
.7
%
w
a
s
ac
h
i
e
v
ed
.
T
h
ree
ph
a
s
e
a
n
g
l
es h
a
d b
e
e
n
d
e
sign
e
d
a
n
d
an
al
y
z
e
d
i
n
[13
]
. S
i
ng
l
e
pow
er a
m
pl
if
ier
on
th
e pr
i
m
ary
si
de an
d t
w
o
po
we
r ampli
f
i
e
rs
w
e
re
l
o
ca
t
e
d
a
t
t
h
e sec
onda
r
y
side
. T
h
e pr
op
ose
d
mu
l
t
i
-
d
egre
es me
t
h
o
d
of
pha
se
co
nt
r
o
l
w
a
s c
a
p
a
bl
e
of
ac
hi
e
v
i
n
g
simul
t
a
n
e
o
u
s
l
y
addi
t
i
o
n
a
l
co
mpe
n
sat
i
o
n o
f
t
h
e
rea
c
t
a
nc
e
,
out
put
re
gu
la
ti
o
n
, a
n
d
lo
a
d
tran
sfo
r
ma
tio
n
.
A co
nsi
s
t
e
nt
o
p
ti
mi
zat
i
on
t
e
c
hni
que
w
a
s
c
o
nd
uct
e
d
b
y
[
1
4
]
f
o
r WPT s
y
st
e
m
s eq
ui
p
p
e
d
wi
th pas
s
i
v
e
el
em
en
t’
s
e
n
ha
n
c
em
e
n
t
b
e
g
i
n
n
i
n
g
fro
m
si
m
p
le ref
l
e
c
t
o
rs
, in
te
rm
e
d
i
a
te
r
e
lay
s
,
a
n
d gen
e
r
a
l e
l
ec
tr
oma
g
n
e
tic
fo
cu
si
ng and gu
id
ing stru
c
t
ures,
lik
e me
ta
ma
ter
i
a
l
s a
n
d
me
ta
su
rfa
c
e
s. The pro
p
o
s
ed
wor
k
e
ffi
ci
en
t
l
y so
lv
ed
t
h
e
p
r
obl
em
o
f
opt
imi
zat
i
o
n
u
s
i
n
g
ar
bit
r
a
r
y
num
ber
s
o
f
pass
ive
e
l
e
m
e
n
ts.
The
w
o
r
k
c
o
n
duct
e
d
b
y
[
1
5
]
pre
s
e
n
t
e
d
an
d e
xpl
a
i
ne
d t
h
e
pu
bl
i
s
he
d t
e
chni
que
s a
n
d
p
r
i
n
ci
pl
es
c
once
r
nin
g
al
l
aspec
t
s
of
i
n
d
u
ct
i
v
e l
i
nk
des
i
gn
p
r
oc
esses
suc
h
t
h
a
t
no
s
p
eci
f
i
c
p
r
e
cedi
n
g
i
n
f
o
rma
t
i
o
n
a
b
o
u
t
in
du
c
tiv
e li
n
k
d
e
sign
s ar
e
r
e
q
u
i
re
d.
Th
e
wo
rk
in [1
6] in
tro
d
u
c
e
d
a
ccu
rat
e
fo
rmu
l
as
fo
r c
a
l
c
u
lat
i
ng
m
u
tu
a
l
i
n
d
u
ct
anc
e
bet
w
e
e
n s
p
ir
al
c
o
i
l
s usi
ng G
a
us
sia
n
int
e
g
r
at
io
n met
h
o
d
. T
h
e
r
e
sea
r
c
h
e
s
int
r
o
d
u
ce
d
by [
1
7-
2
2
]
c
once
r
n
e
n
ha
nc
in
g c
o
u
p
li
n
g
c
o
e
ffi
c
i
e
n
ts
i
n
di
ff
e
r
e
n
t
e
nvi
r
o
nme
n
ts
of
in
d
u
c
t
i
v
e l
i
nks
i
n
a
ddi
t
i
on
t
o
a
ppli
c
a
t
io
ns of
WP
T te
ch
n
o
l
ogi
e
s
i
n
co
nt
ac
tl
e
s
s el
ec
tr
ic
al
v
e
hic
l
es
a
n
d
e
n
e
r
gi
zi
n
g
medi
ca
l sens
ors
.
In t
h
is
wo
r
k
,
po
or e
f
fi
ci
e
n
cy
of
c
o
nve
nt
iona
l
w
i
r
e
l
e
ss po
we
ri
n
g
pr
oce
s
s
i
s
en
ha
nce
d
by
str
e
n
g
t
h
e
n
i
ng
t
h
e
mu
tu
a
l
coup
lin
g
al
on
g w
i
t
h
p
o
w
e
r tr
an
smis
sio
n
p
a
t
h
an
d c
ond
it
io
n
i
ng
th
e re
c
e
i
v
i
n
g c
i
r
c
u
i
t
su
ch
th
a
t
it
ac
co
mp
li
sh
e
s
m
a
xi
mu
m po
w
e
r
rec
e
p
t
i
o
n t
o
lo
a
d
no
d
e
.
2.
De
sign
o
f
th
e
prop
os
ed
ef
fi
c
i
en
t WPT
s
y
s
t
e
m
Th
e
in
du
ct
iv
e
mu
t
u
al
cou
p
ling
M
ab
bet
w
ee
n t
w
o
1
-
t
u
r
n
pl
a
n
ar
spi
r
al
coi
l
s
is sh
ow
n
i
n
F
i
g
u
r
e
1a
. T
h
e
mut
u
al
i
n
d
u
ct
a
n
c
e
be
tw
ee
n t
h
e
s
e
t
w
o c
o
i
l
s
i
s
gi
ve
n b
y
[7
]
⁄
1
(1)
(2)
Wh
er
e,
a
an
d
b
are
th
e ou
t
e
r r
a
d
ii
of
t
h
e
f
i
r
s
t
and
se
cond
c
o
ils,
re
sp
e
c
t
i
v
e
ly
.
µ
0
is t
h
e
p
e
r
m
e
a
b
i
lity
o
f
fr
ee
spac
e a
n
d
z
i
s
t
h
e
di
st
ance
bet
w
e
e
n
t
h
e
ce
nte
r
s of
t
h
e t
w
o c
o
i
l
s
, w
h
ic
h
ar
e
al
igne
d
c
o
a
x
i
a
l
l
y.
(a)
(b
)
F
i
gu
re
1.
I
n
d
u
c
t
ive
l
i
nk,
(a
)
c
o
upl
i
n
g bet
w
e
e
n
t
w
o
1
-
t
u
rn
c
o
i
l
s
, (
b
)
mode
l
i
n
g
of
t
w
o c
o
i
l
i
nduc
t
i
ve
l
i
n
k
.
F
o
r
mul
t
i
-
t
ur
ns pl
ana
r
s
p
ir
al
c
o
il
s, (
1
) ca
n be
modi
fi
e
d
t
o
∑∑
⁄
1
(3)
(4)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
D
e
si
gn
a
n
d
i
m
pl
eme
n
t
a
t
i
on
o
f
an
e
f
f
i
c
i
e
nt
WPT syst
e
m
(Ab
dulk
a
ree
m
M
o
ki
f
Ob
ai
s)
7
13
Whe
r
e,
N
1
an
d
N
2
are t
h
e
n
u
m
be
rs
of t
u
r
n
s of
the
first a
nd se
co
n
d
c
o
i
l
s, res
p
ec
t
i
ve
l
y
.
If t
w
o
in
duc
ti
vel
y
cou
p
l
e
d c
o
i
l
s
a
r
e formi
n
g
a
re
son
a
nt
i
n
d
u
ct
i
v
e li
nk sh
ow
n
i
n
F
i
g
u
re
1b
, t
h
e
n
t
h
e
l
i
nk
c
u
rre
n
t
s
an
d vol
t
a
ge
s at
re
so
na
nce fre
q
u
enc
y
ca
n be gi
ve
n
b
y
,
≫
(5
)
,
≫
(6
)
Whe
r
e,
L
1
an
d
L
2
a
r
e
self-
i
nd
u
c
ta
n
c
es
o
f
th
e f
i
rst
an
d se
cond
co
ils, r
e
sp
e
c
tiv
el
y
.
M
12
i
s
th
e mu
tu
a
l
ind
u
c
ta
n
ce
bet
w
ee
n the
t
w
o c
o
i
l
s.
R
1
an
d
R
2
a
r
e t
h
e AC
resi
sta
n
ces
o
f
t
h
e fi
rst
a
n
d se
con
d
c
o
i
l
s
,
res
p
e
c
t
i
ve
ly
.
C
1
an
d
C
2
are t
h
e
t
u
ni
ng
capa
c
i
t
a
nce
s
o
f
the
sen
d
i
n
g
(tr
a
nsmit
t
i
n
g
)
a
nd
re
cei
vi
ng
c
i
r
c
ui
ts,
re
sp
ect
i
v
el
y,
w
h
ere
a
s
ω
0
=2
π
f
0
is
th
e
indu
c
tiv
e l
i
n
k
op
er
a
ting
a
n
gu
la
r
fre
qu
en
cy.
R
re
f
l
i
s
de
fi
ne
d
b
y
(7
)
The o
u
tp
ut
v
o
l
t
age
V
2
i
s
d
e
te
rmin
e
d
by
,
≫
,
(8
)
Th
e
l
i
nk
in
pu
t p
o
w
e
r
P
i
, ou
tpu
t
pow
e
r
P
0
, an
d
e
ffi
cie
n
cy
η
ca
n be
gi
ve
n b
y
|
|
,
≫
(9)
|
|
,
≫
(1
0)
,
≫
(1
1)
Whe
r
e,
Q
1
,
Q
2
, an
d
Q
L
are
t
h
e
qual
i
t
y fa
ct
ors
of the
first
coi
l
, secon
d
c
o
i
l
, and l
o
a
d
, res
p
e
c
t
ive
l
y at
reso
na
nce
fre
que
nc
y
f
0
.
Q
1
,
Q
2
, and
Q
L
a
r
e de
fi
n
e
d b
y
ω
0
L
1
/
R
1
,
ω
0
L
2
/
R
2
, and
R
L
/
ω
0
L
2
, re
s
p
ect
i
v
el
y.
k
12
is t
h
e coe
f
fi
ci
ent
of co
u
p
li
ng
bet
w
een
t
h
e
t
w
o
c
o
i
l
s an
d
i
s
de
fi
ned
b
y
(1
2)
For
l
o
osel
y
co
upl
e
d
in
d
u
c
t
i
v
e l
i
nk
(11
)
ca
n
cl
osel
y be a
p
proxi
mat
e
d t
o
,
≫
an
d
≪
1
(1
3)
A
cco
rdi
n
g to
(1
1),
t
h
e ef
fi
c
i
ency
of
WPT
proc
ess
i
s
di
re
ct
ly p
r
o
p
o
rt
i
onal
t
o
t
h
e
sq
uare of
t
h
e
cou
p
l
i
ng
c
o
e
f
fi
ci
ent
.
T
h
e pro
p
o
se
d
e
f
fi
ci
e
n
t
WPT
syste
m
c
a
n
be depi
ct
e
d
by
bl
oc
k
di
a
g
ra
m
o
f
Fi
g
u
re 2
.
F
i
gu
re 2.
The
bl
oc
k di
ag
ram of t
h
e pr
o
pose
d
s
y
ste
m
.
Cl
a
s
s
E
P
o
w
e
r
A
m
p
l
i
f
i
e
r
F
i
rs
t R
e
s
o
n
a
to
r
C
i
r
c
u
i
t
WP
T
1
S
e
c
o
nd
R
e
s
o
na
t
o
r
C
i
r
c
ui
t
WP
T
2
T
h
i
r
d
R
e
s
o
n
a
to
r C
i
rc
u
i
t
WP
T
3
R
ecei
v
i
n
g
C
i
r
c
u
i
t
WP
T
4
T
r
a
n
s
m
ittin
g
C
o
il
S
e
cond
r
e
s
onat
o
r
C
o
i
l
F
i
r
s
t r
e
s
o
n
a
to
r
C
o
il
P
a
r
a
l
l
el
-
c
on
n
ect
ed
R
ecei
v
i
n
g
C
o
i
l
s
T
h
ir
d
r
e
s
o
n
a
to
r
C
o
il
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
71
1
– 72
5
71
4
It i
s
o
bvi
ous t
h
at
t
h
e
pro
p
o
s
ed
syst
em sh
ow
n
i
n
F
i
g
u
re
2 c
o
mp
ri
ses
fo
ur se
ri
es
WPT
s
y
ste
m
s. In t
h
i
s
wo
rk
,
t
h
ree
re
sona
t
i
ng c
o
i
l
s are
i
n
se
rt
ed
on t
h
e pa
th
joi
n
i
n
g
t
h
e
t
r
a
n
smi
t
t
i
n
g
a
nd re
cei
vi
ng
coi
l
s.
Th
e
l
o
c
a
t
i
on
s
o
f
r
e
son
a
tin
g
c
o
il
s a
r
e se
le
c
t
ed
su
ch t
h
at
ma
x
i
mu
m pow
e
r
i
s
tr
a
n
sferre
d b
e
t
w
e
e
n
e
a
ch
t
w
o
a
d
ja
ce
n
t
co
ils.
Fi
g
u
re
3
shows
th
e
a
l
i
gnme
n
t
o
f
c
o
il
s in
t
h
e
pr
opo
se
d
indu
c
t
i
v
e
li
nk
.
The
f
i
r
s
t
co
il
from
th
e
le
f
t
is
L
1
, whi
c
h
re
prese
n
ts
t
h
e t
r
ansmit
t
i
ng coi
l
and it
s
di
s
t
a
n
ce
z
12
fro
m
t
h
e se
con
d
co
i
l
L
2
(f
ir
st
r
e
s
o
nat
o
r
c
o
il)
i
s
156
c
m
. A
t
22
7
c
m
to
th
e
rig
h
t
o
f
th
e fi
rs
t r
e
son
a
t
o
r is l
o
ca
te
d
th
e
th
ird
c
o
il
L
3
(second
r
e
sonator coil),
w
h
ere
a
s
t
h
e fou
r
t
h
co
i
l
L
4
(t
h
i
rd
re
so
nat
o
r
c
o
i
l
) i
s
l
o
cat
ed
at
14
0cm t
o
ri
ght
of
t
h
e
sec
ond
res
onat
o
r.
Thre
e
simi
l
a
r rec
e
i
v
ing
c
o
il
s
L
5
,
L
6
, a
nd
L
7
are
or
ien
t
ed
50
c
m
t
o
t
h
e r
i
gh
t
o
f
th
e th
ird
r
e
so
n
a
tor an
d ea
ch
a
d
jac
e
n
t
coi
l
s
are 2
0
c
m
apa
r
t
.
Fi
gu
re
3. Al
ig
n
m
ent
of
coi
l
s
i
n
t
h
e
p
r
op
ose
d
syst
em.
The
t
r
a
n
smi
t
t
i
ng c
o
i
l
i
s
show
n i
n
Fi
g
u
re
4
a
.
It
i
s
wo
u
nd
wi
t
h
1
2
.6
67 t
u
rn
’s c
o
p
p
er
pi
pe
ha
vi
n
g
a
n
out
e
r
di
a
m
et
er of 1
9
.0
5 m
m
a
nd wa
ll
t
h
ic
kne
ss of 0.
9
1
m
m.
T
h
e
c
o
il
out
e
r
di
a
m
et
er i
s
62c
m,
w
h
e
r
e
a
s it
s
in
n
e
r
d
i
a
m
e
t
e
r
is
12
cm. Th
e fi
rst
re
so
n
a
t
o
r sh
own
in
F
i
gur
e 4b
i
s
a
p
l
ana
r
sp
ir
al
c
o
i
l
w
oun
d w
ith
5.5
t
u
rn’
s
cop
p
e
r
pipe
h
a
vin
g
out
e
r
di
amet
e
r
of
1
9
.0
5 m
m
a
n
d
wa
l
l
t
h
ic
kne
ss
of
0.91
mm.
T
h
e
coi
l
out
e
r
a
n
d
i
n
n
e
r
di
amet
ers a
r
e
15
0cm
a
n
d 30
c
m
, res
p
ec
t
i
ve
l
y
.
T
h
e
se
c
o
nd
reso
na
to
r s
h
o
w
n in F
i
g
u
re
4c
is a pl
ana
r
spi
r
a
l
c
o
il
wo
u
n
d
wi
t
h
7.25
t
u
rn
’s c
o
pp
er pipe
ha
vi
n
g
o
u
t
e
r
dia
m
e
t
e
r
of 6.3
5
mm a
nd wal
l
t
h
ic
k
n
ess o
f
0.
71
mm.
T
h
e
coi
l
o
u
t
e
r di
a
m
et
e
r
is
11
0c
m
a
n
d
i
t
s
i
nne
r di
amet
e
r
is
2
0
cm. T
h
e t
h
i
r
d reso
nat
o
r sh
ow
n i
n
F
i
gu
re
4
d
is a
coni
ca
l
c
o
i
l
w
o
u
n
d
wi
t
h
9.2
5
t
u
rn’s
c
o
p
p
e
r
pi
pe
, whi
c
h has
an
out
e
r
di
amet
er
o
f
19
.0
5
mm
a
nd wa
ll
th
i
c
k
n
e
ss o
f
0
.
9
1
mm. Th
e c
o
i
l
o
u
ter a
n
d
inne
r
d
i
am
et
e
r
s are
72
c
m
an
d 20c
m,
r
e
s
p
ec
tiv
e
l
y
.
Th
e
co
il
le
ng
th
i
s
68c
m.
(a
)
(b
)
(
c
)
(d
)
F
i
gu
re
4.
P
hot
os
of
(a
)
the
t
r
a
n
smi
t
t
i
n
g
c
o
il
(
L
1
)
,
(b
) t
h
e
fi
rs
t
r
e
s
o
nat
o
r c
o
i
l
(
L
2
), (c
) the
se
c
ond
re
sona
t
o
r
coi
l
(
L
3
)
,
(
d
)
the
thi
r
d res
o
nator coil
(
L
4
)
.
The
rece
i
v
i
n
g
ci
rcui
t
is
sh
ow
n i
n
F
i
g
u
re
5.
It
is c
o
m
p
ose
d
of
t
h
re
e
si
mi
la
r pla
n
ar spi
r
al
coi
l
s
con
n
ec
t
e
d i
n
p
a
ral
l
e
l
.
E
ach
c
o
i
l
is w
o
und
wi
th
6 t
u
r
n
’s c
o
p
p
e
r
pi
pe
ha
v
i
ng
oute
r
di
am
et
er of
6.35
m
m
an
d
wal
l
thi
c
kne
ss
of
0.71
mm.
Th
e coi
l
out
er
a
n
d
i
n
ner di
amet
ers
a
r
e
33
.5c
m
and
6cm
,
res
p
ect
i
v
el
y. T
h
e c
o
i
l
s
i
n
t
h
e prop
ose
d
WPT
s
y
st
em are
wo
u
n
d
wi
t
h
pi
pe
co
n
duc
t
o
rs
i
n
o
r
de
r
t
o
de
cre
a
s
e the
i
r
AC
resi
sta
n
ces
b
y
d
e
cr
e
a
s
i
n
g
th
e sk
i
n
e
f
f
e
c
t
,
w
h
ich
h
a
s
g
r
e
a
t i
m
p
a
ct
on
th
e
qu
a
lity
fac
t
o
r
s
o
f
co
i
l
s. D
e
c
r
e
a
sing
t
h
e A
C
re
si
st
ance
s
of
coi
l
s i
n
c
r
ease
s
t
h
e c
o
il
s
qual
i
t
y
fa
ct
or, whic
h in
t
u
rn
i
n
c
r
e
a
ses t
h
e
l
i
nk
e
f
fi
ci
enc
y
g
ove
rned
b
y
(1
1)
o
r
(1
3
)
,
w
h
i
c
h i
s
a
p
pli
c
a
b
l
e
f
o
r l
o
osel
y
c
o
u
p
l
e
d
i
n
du
ct
ive
l
i
nks.
227c
m
15
6c
m
50c
m
68c
m
140c
m
62c
m
20c
m
20c
m
150c
m
110c
m
72c
m
T
r
a
n
s
m
it
t
i
n
g
C
o
il
F
i
rs
t R
s
on
a
t
or
C
o
i
l
T
h
re
e
P
a
ra
l
l
el
C
o
n
n
e
ct
e
d
R
e
ce
i
v
i
n
g
C
o
i
l
s
T
h
i
r
d R
s
on
at
or
C
o
i
l
Secon
d
R
s
on
at
or
C
o
i
l
12
c
m
30c
m
20c
m
20c
m
6c
m
30c
m
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
D
e
sign
an
d i
m
p
l
em
en
ta
t
i
on
o
f
a
n
e
ffic
ie
n
t
W
P
T
s
y
st
e
m
(Abd
u
l
k
a
r
eem
Mok
if
O
b
a
i
s)
7
15
The
p
r
op
ose
d
WPT
s
y
st
em
depi
ct
ed
i
n
F
i
gu
re
2
ca
n
be
sch
e
ma
ti
ca
ll
y r
e
pre
s
e
n
te
d
b
y
t
h
e
ci
rc
uit
sh
own
F
i
gu
r
e
6
.
I
n
t
h
is F
i
gure
,
R
1
,
R
2
,
R
3
,
R
4
,
R
5
,
R
6
, a
n
d
R
7
a
r
e t
h
e
AC
re
si
st
a
n
ces
of t
h
e coi
l
s
L
1
,
L
2
,
L
3
,
L
4
,
L
5
,
L
6
, and
L
7
, r
e
sp
e
c
t
i
v
e
ly
.
C
1
,
C
2
,
C
3
,
C
4
, an
d
C
5
ar
e
tu
n
i
n
g
cap
a
c
i
t
o
r
s of
t
r
an
sm
itti
n
g
,
fi
rst
r
e
son
a
t
o
r,
sec
o
n
d
r
e
son
a
to
r
,
th
ird r
e
son
a
t
o
r, a
nd r
ece
iv
in
g
ci
rcu
its, re
sp
e
c
ti
v
e
ly
. Ea
ch
M
r
e
pr
e
s
en
ts th
e mu
tu
a
l
in
du
c
t
a
n
ce
b
e
t
w
ee
n two
c
e
r
tai
n
co
i
l
s. For
ex
amp
l
e
M
12
r
e
p
r
e
s
e
n
t
s
th
e mu
t
u
al
indu
c
t
a
n
ce
b
e
tw
een
L
1
and
L
2
.
M
12
is equ
a
l to
M
21
(
M
12
=
M
21
) and
th
is
is a
pplic
a
b
le f
o
r e
ach
t
w
o
co
ils
.
Fi
gu
re
5.
A
ph
ot
o
of
t
h
e
rec
e
i
v
i
ng ci
rc
uit
,
w
h
i
c
h is
co
mp
ose
d
of
t
h
ree
pl
a
n
ar
spi
r
al
coi
l
s
(
L
5
,
L
6
, a
n
d
L
7
).
F
i
gu
r
e
6.
S
c
he
ma
ti
c re
pr
ese
n
t
a
t
i
on of
t
h
e
pr
o
pose
d
syst
e
m
.
The
i
n
d
u
ct
anc
e
s
o
f
pl
ana
r
s
p
i
r
al
c
o
il
s
can
be
c
a
l
c
ul
at
e
d
by
[
15]
.
0.2
(14
)
Wh
er
e, th
e a
v
e
r
ag
e
d
i
a
m
e
t
e
r
i
s
d
e
n
o
t
e
d
by
d
a
vg =
0
.
5(
d
o
+
d
i
).
d
i
and
d
0
a
r
e t
h
e i
n
n
e
r
an
d
o
u
t
e
r di
a
m
et
e
r
s
o
f
th
e
c
o
il,
r
e
sp
e
c
t
i
v
e
l
y
, w
h
ile
β
is
th
e
f
i
l
l
-
f
a
c
t
or
, w
h
ich
is
g
i
ve
n
b
y
(15
)
The
i
n
d
u
ct
anc
e
o
f
t
h
e
co
ni
cal
coi
l
sh
own
i
n
Figu
re 7 ca
n b
e
ca
lc
ula
t
e
d
a
s
fol
l
o
ws [23
]
:
.
,
(16
)
Wh
er
e,
n
,
d
i
,
s
, and
Y
ar
e co
il
nu
mb
e
r
o
f
turn
s, inn
e
r d
i
ame
t
e
r
,
d
i
st
an
c
e
be
tw
ee
n two
ad
jac
e
n
t
turn
s, an
d
c
o
i
l
an
g
l
e, r
e
sp
e
c
tiv
el
y
.
Y
a
nd
s
a
r
e
de
fi
ne
d
by
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
71
1
– 72
5
71
6
.
(1
7)
(1
8)
Whe
r
e,
d
0
i
s
t
h
e c
o
i
l
o
u
t
e
r
di
amet
e
r
.
W
an
d
l
a
r
e co
il
ax
i
a
l
a
n
d
l
o
ng
itu
d
i
n
a
l
len
g
t
hs,
r
e
sp
ec
ti
v
e
ly. A
l
l
di
me
n
s
i
o
ns a
r
e
i
n
i
n
c
h
e
s
.
Su
bsti
t
u
t
i
ng
for
n=
9.
25
,
d
i
=2
0
c
m=7
.
874 in
c
h
e
s
,
d
0
=7
2c
m=
28
.3
4
6
i
n
c
h
e
s
,
l
=
6
8
c
m=
26
.7
72
in
ch
es, a
n
d
W
=
7
2.8cm=
28
.6
61
i
n
c
h
e
s
i
n
to (1
6)
to (18
)
g
i
ve
s
L
co
n
=2
2 µ
H
.
Fi
gu
re
7.
The
i
nve
rse c
o
ni
ca
l
coi
l
.
The
DC
resi
st
ance
s of al
l
coi
l
s
i
n
t
h
e
prop
os
ed WPT
sy
st
em can
be
c
a
l
c
u
l
at
ed b
y
(1
9)
Whe
r
e,
l
C
,
σ
Cu
,
w
, a
nd
w
th
, a
r
e t
h
e
c
o
i
l
l
e
n
g
t
h
, co
n
duc
ti
vi
ty
o
f
c
o
p
p
er,
o
u
te
r
di
amet
er
of
coi
l
pi
pe
c
o
n
duc
t
o
r,
and
wa
ll
t
h
ic
k
n
ess
o
f
t
h
e
pipe
.
The
c
a
l
c
ul
at
ed i
n
d
u
ct
anc
e
s an
d
DC
res
i
sta
n
ces a
r
e
l
i
ste
d
in
Ta
b
l
e
1. T
h
e
mutua
l
i
n
duct
a
nce
s
be
t
w
een
c
o
i
l
s
ca
n
be
ca
l
c
ul
at
ed
usi
n
g
(3)
.
T
h
e
coe
ffi
c
i
ent
s
of co
u
p
l
i
ng
bet
w
e
e
n
c
o
i
l
s a
r
e
ca
lc
ula
t
e
d
acc
ordi
ng t
o
(1
2)
. T
h
e ca
lc
ula
t
e
d
mut
u
al
i
n
d
u
ct
anc
e
s
an
d
the
i
r
c
o
rre
sp
on
di
n
g
c
o
effic
i
e
n
ts
of
c
o
up
lin
g
are
list
e
d
in Tab
l
e
2.
Ta
ble
1.
C
o
il
’s
cal
cul
a
te
d DC
re
sist
anc
e
an
d i
n
d
u
ct
anc
e
s
Coi
l
Na
m
e
D
C
Re
sista
n
ce
(
Ω
) I
nducta
nce
(
µ
H)
L
1
0.
0041
827
46.
334
L
2
0.
0044
8
23.
864
L
3
0.
0184
74
29.
3
L
4
0.
0039
22
L
5
,
L
6
,
L
7
0.
0045
8
6.
0745
Th
e A
C
re
sis
t
an
ce
R
AC
of
a c
o
i
l
wo
un
d w
i
t
h
c
o
p
p
e
r
c
o
n
d
u
ct
ors
can
be
c
a
l
c
ul
at
ed
by
[2
4]
(2
0)
(2
1)
Whe
r
e,
R
DC
,
σ
Cu
,
w
, a
nd
δ
Cu
a
r
e t
h
e
DC
re
si
st
ance
of
t
h
e
coi
l
,
c
o
nd
uc
ti
v
i
ty o
f
co
p
p
e
r
,
o
u
t
e
r di
amet
er
o
f
t
h
e
coi
l
co
nd
uc
t
o
r, a
n
d c
oppe
r
ski
n
de
pt
h
at
f
0
. R
e
spec
ti
ve
ly
.
A
ppl
yi
ng (
2
0
)
usin
g t
h
e c
o
nd
uct
o
r o
u
t
e
r
di
amet
ers
a
n
d cal
cul
a
t
e
d DC
res
i
st
ance
in Tabl
e 1, the
A
C
re
si
st
ance
s o
f
a
l
l
coi
l
s
a
r
e cal
c
u
l
a
te
d
a
n
d
l
i
st
ed in
Ta
bl
e 3
.
W
Y
o
d
d
i
l
Evaluation Warning : The document was created with Spire.PDF for Python.
In
t
J
P
o
w
Elec
& Dri
Sy
st
I
SSN
: 208
8-8
6
9
4
D
e
sign
an
d i
m
p
l
em
en
ta
t
i
on
o
f
a
n
e
ffic
ie
n
t
W
P
T
s
y
st
e
m
(Abd
u
l
k
a
r
eem
Mok
if
O
b
a
i
s)
7
17
Tabl
e
2.
Mut
u
a
l
ind
u
c
t
a
n
ces
a
n
d
t
h
ei
r co
rres
po
n
d
i
ng c
o
u
p
l
i
ng
coef
fi
ci
ent
s
Mutual
I
nducta
nce
Va
lu
e (µH
)
Coe
f
f
i
ci
ent of
Coupl
in
g
Va
lu
e
M
12
0.
2621
k
12
0.
0078
82
M
13
0.
0161
k
13
0.
0004
37
M
14
0.
003
k
14
0.
0000
94
M
15
0.
0002
81
k
15
0.
0000
167
5
M
16
0.
0002
564
k
16
0.
0000
154
M
17
0.
0002
345
k
17
0.
0000
129
5
M
23
0.
1592
k
23
0.
006
M
24
0.
0179
k
24
0.
0007
81
M
25
0.
0015
k
25
0.
0001
246
M
26
0.
0013
k
26
0.
0001
08
M
27
0.
0012
k
27
0.
0001
M
34
0.
1358
k
34
0.
0053
5
M
35
0.
007
k
35
0.
0005
28
M
36
0.
0057
k
36
0.
0004
27
M
37
0.
0046
k
37
0.
0003
448
M
45
0.
1931
k
45
0.
0167
M
46
0.
0985
k
46
0.
0085
2
M
47
0.
0558
k
47
0.
0048
27
M
56
0.
5018
k
56
0.
0836
33
M
57
0.
1161
k
57
0.
0193
5
M
67
0.
5018
k
67
0.
0836
33
Ta
ble
3.
C
o
il
’s ca
lc
ula
t
ed AC
resi
sta
n
ces
Coi
l
Na
m
e
AC
Re
sista
n
ce
AC Re
sista
n
ce
Valu
e
(
Ω
)
L
1
R
1
0.
185
L
2
R
2
0.
2
L
3
R
3
0.
27246
L
4
R
4
0.
172
L
5
R
5
0.
0676
L
6
R
6
0.
0676
L
7
R
7
0.
0676
S
i
n
c
e
th
e t
r
an
sm
itti
n
g
co
il (
L
1
) a
n
d
t
h
e t
h
re
e re
so
na
ti
n
g
c
o
il
s
(
L
2
,
L
3
, and
L
4
) are
o
p
er
at
i
ng wi
thi
n
l
oosel
y c
o
u
p
le
d c
o
n
d
it
i
o
n
s
,
t
h
e
n
t
h
e
t
uni
ng
ca
paci
t
o
rs
C
2
,
C
3
, and
C
4
sho
w
n
i
n
F
i
g
u
re 6
c
a
n be det
e
r
m
i
n
ed
as
9.
25
nF
,
7.
53
4
5nF
,
a
n
d 1
0
.
0
34
463
nF
,
re
s
p
ect
i
v
el
y.T
h
e
ci
rcu
i
t
el
ement
s
C
1
a
nd
L
1
i
n
Figur
e
6
are
p
a
rt
s of
th
e
out
put
c
i
r
c
ui
t o
f
the
c
l
a
s
s-
E
p
o
we
r am
pli
f
i
e
r
,
w
h
i
c
h r
e
p
r
e
s
e
n
t
s
t
h
e
pow
er t
r
ans
m
it
t
e
r
of t
h
e pr
op
ose
d
e
f
fi
ci
ent
WP
T sy
ste
m
.
T
h
e
se
r
i
es
c
o
mb
in
at
ion formed
by
C
1
an
d
L
1
A
r
e
desi
gn
ed
t
o
re
s
o
na
t
e
at
a
fre
qu
enc
y
sl
i
ghtl
y
less than
f
0
a
n
d
t
h
ei
r
e
q
ui
val
e
nt
i
m
pe
da
nc
e
a
t
t
h
e
res
o
nanc
e
fre
que
nc
y
f
0
is
R
1
+
jX
,
wh
er
e
X
is de
fi
ne
d
b
y
[
2
5
]
1.1
5
2
(22
)
Wh
er
e,
R
r
e
pr
esen
ts t
h
e
r
e
si
sti
v
e
lo
ad
of
c
l
a
s
s-
E
p
o
w
er
a
m
pl
if
ier
and
c
a
n
be
d
e
te
rm
in
ed
by
(23
)
The tu
ni
n
g
c
a
p
ac
i
t
or
C
5
o
f
t
h
e
rec
e
i
v
in
g c
o
i
l
s
sh
ow
n
i
n
F
i
gu
r
e
6
ca
n be
a
p
p
r
oxi
mat
e
l
y
de
t
e
rmi
n
e
d
i
n
a
di
f
f
e
r
e
n
t
pr
o
cedu
r
e.
Fi
g
u
r
e
8
mo
del
s
t
h
e
rec
e
i
v
i
n
g c
o
i
l
s
wi
t
hout
C
5
an
d
R
L
. S
i
n
c
e
the
r
e
ce
iv
i
n
g
c
i
rcu
i
t
is
sym
m
e
t
ri
cal
ar
o
u
n
d
t
h
e
bra
n
c
h
inc
l
udi
ng
L
6
, th
en
I
5
=
I
7
an
d
I
6
=-2
I
5
. C
o
nse
que
ntl
y
,
t
h
e i
m
p
e
da
nc
e
Z
RCV
of
th
e
pa
ral
l
e
l
-
c
onne
ct
ed
rec
e
i
v
i
ng
coi
l
s
ca
n
be
de
t
e
r
m
i
n
e
d
by
0.5
0.5
0.
5
//
2
(24
)
Su
bst
i
t
ut
i
n
g
t
h
e cal
cul
a
te
d
ci
r
c
ui
t pa
ra
me
t
e
rs
in
(2
4)
gi
ve
s
0.02
3
4.04
,
(25
)
F
i
gu
r
e
8.
M
o
d
e
l
i
ng of
the
r
e
c
e
i
vi
ng
c
o
i
l
s
wi
t
h
o
u
t
C
5
and
R
L
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-86
94
I
n
t J
P
o
w
El
ec
&
D
r
i S
y
st
,
V
o
l
.
11,
N
o
.
2,
J
u
ne
20
2
0
:
71
1 –
72
5
71
8
A
c
cord
ing
to
(2
5
)
,
t
h
e r
e
qu
ire
d
v
a
lu
e
fo
r
C
5
to ac
com
p
l
i
s
h
r
e
s
o
nance
i
s
11
6.
3
n
F.
A
t
resonance
fre
qu
ency
f
0
and
aft
e
r tuning all
ca
pa
ci
tors s
u
c
h
tha
t
all li
nk
ci
rc
ui
ts
r
e
s
o
nat
e
a
t
t
h
e
s
a
m
e
time,
th
e l
i
nk
curr
ents
c
a
n
be
relat
e
d
to each o
t
her
by
⎣
⎢
⎢
⎢
⎢
⎢
⎡
0
0
0
0
0
0
⎦
⎥
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎢
⎢
⎡
⎦
⎥
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎢
⎢
⎡
⎦
⎥
⎥
⎥
⎥
⎥
⎤
(26
)
Wher
e,
I
1
,
I
2
,
I
3
,
I
4
,
I
5
,
I
6
, a
n
d
I
7
ar
e the cu
r
r
ent
s
f
l
owing
th
ro
u
g
h
coils
L
1
,
L
2
,
L
3
,
L
4
,
L
5
,
L
6
, a
n
d
L
7
, res
p
e
c
ti
ve
l
y
.
Sin
c
e,
L
1
an
d
C
1
are
par
t
s
of the
clas
s-E dri
v
i
n
g power
am
plifier
and
res
o
nat
e
a
t
a fre
quen
c
y
slig
htl
y
les
s
th
an
th
e
link
resonan
c
e f
r
eq
uency
f
0
,
the
indu
cti
v
e
re
ac
ta
nc
e
X
repr
es
ents
the
i
r e
q
uivale
nt r
e
a
c
tan
ce
at
f
0
.
Z
55
,
Z
56
,
Z
57
,
Z
65
, Z
66
,
Z
67
,
Z
75
,
Z
76
, a
n
d
Z
77
are
de
f
i
ned by
⎣
⎢
⎢
⎢
⎡
⎦
⎥
⎥
⎥
⎤
(27
)
A
c
cord
ing
to th
e
b
l
o
c
k
d
i
ag
ram o
f
th
e ov
era
ll
pro
p
o
s
ed
WP
T sy
s
t
em
, th
er
e
are fo
ur
se
ri
es
WP
T
s
y
s
t
em
s
n
a
me
l
y
WP
T
1
, WP
T2,
WP
T
3
,
an
d WP
T
4
.
T
h
e
fi
rs
t
t
h
re
e
s
y
st
em
s
WP
T
1
,
WP
T2,
a
n
d
W
P
T3
ar
e
l
oosel
y
co
u
p
l
e
d sy
st
ems due t
o
t
h
e rel
a
t
i
v
el
y
l
a
r
g
e
di
sta
n
c
e
s
be
tw
ee
n
t
h
e
i
r tr
ans
m
it
t
i
ng
and re
ce
ivi
ng coi
l
s
,
t
hus t
h
e
fi
r
s
t
WP
T s
y
st
em
(
W
PT
1)
c
a
n
be
anal
yze
d
se
par
a
te
ly
fr
om
ot
h
e
r
syste
m
s.
F
i
gur
e
9 s
h
o
w
s
t
h
e
mo
del
of
t
h
e
res
ona
nt
i
nduc
t
i
ve
l
i
n
k c
o
r
r
es
po
n
d
i
n
g
t
o
WPT1
syste
m
.
A
t
re
sona
nce
f
r
e
q
ue
ncy
f
0
,
th
e r
e
flec
te
d
re
sis
t
an
ce
R
ref
l
f
r
o
m
the
sec
o
n
d
a
r
y
si
de
(
f
i
r
s
t
,
sec
o
n
d
,
a
n
d
t
h
ir
d
reso
na
t
o
r
s
)
i
n
the
pri
m
a
r
y si
de
(t
ra
nsmi
t
t
i
ng
c
o
il
) is de
te
r
m
ine
d
acc
o
r
di
ng
t
o
E
q
uat
i
on
(
7
)
as 1.
5
6
Ω
.
V´
in F
i
g
u
r
e
9 r
e
p
r
e
s
en
ts t
h
e vo
lt
ag
e
acro
s
s th
e
re
sis
tiv
e
l
o
a
d
o
f
c
l
a
s
s-
E
p
o
we
r
a
m
p
l
ifi
e
r
.
Ac
co
rd
ing
to
[
2
5
]
,
V´
ha
s a
n
a
m
pli
t
ude
o
f
V
om
a
nd ph
ase
o
f
φ
=-
32
.
4
0
.
T
h
e ma
xi
mu
m
po
ssi
bl
e
val
u
e
o
f
V
om
i
s
1.07
4
V
DD
=1.
0
7
4
×
1
2
V
=
12.
8
8
8
V
,
t
h
us t
h
e
vol
t
a
ge
V
i
c
a
n be
d
e
t
e
r
m
in
ed by
1
.
74
63
2
(28
)
S
u
b
s
tit
u
tin
g
a
ll ca
lc
u
l
a
t
e
d
mutu
al
in
du
c
t
an
c
e
s, c
o
il
’s
sel
f
-
i
nd
u
c
tan
c
es,
co
il’
s A
C
resis
t
an
ce
s,
X
, an
d
C
5
int
o
(
2
6)
a
n
d (2
7)
gi
ves
⎣
⎢
⎢
⎢
⎢
⎢
⎡
0
0
0
0
0
0
⎦
⎥
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎢
⎢
⎡
0.1
8
5
2
0.5
5
8
0.0
3
4
0.00
64
0.00
06
0
.
00
05
5
0.00
05
0.5
5
8
0.
2
0
.
338
8
0
.
038
1
0
.
003
2
0
.
002
8
0
.
002
6
0.
0
3
4
0
.
33
88
0
.
27
246
0.
2
8
9
0
.
01
49
0
.
01
21
0
.
00
98
0.00
64
0.03
81
0.2
8
9
0.17
2
0.4
1
1
0.2
1
0.11
88
0
.
00
06
0
.
00
32
0
.
01
49
0.4
1
1
0.0
7
8.9
2.9
7
2
3.7
9
3
0.
000
55
0
.
00
28
0
.
01
21
0.
2
1
2.9
7
2
0.0
7
8.9
2.9
7
2
0
.
00
05
0
.
00
26
0
.
00
98
0
.
11
88
3.7
9
3
2.9
7
2
0.0
7
8.9
⎦
⎥
⎥
⎥
⎥
⎥
⎤
⎣
⎢
⎢
⎢
⎢
⎢
⎡
⎦
⎥
⎥
⎥
⎥
⎥
⎤
(29
)
Fi
gu
re
9.
M
o
d
e
l
i
ng
of
the
fi
rs
t
WPT
s
y
st
e
m
(WP
T
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J Po
w El
ec
&
Dr
i
S
y
st
IS
SN:
208
8-8
6
9
4
D
e
si
gn
a
n
d
i
m
pl
eme
n
t
a
t
i
on
o
f
an
e
f
f
i
c
i
e
nt
WPT syst
e
m
(Ab
dulk
a
ree
m
M
o
ki
f
Ob
ai
s)
7
19
S
u
bsti
t
u
ti
ng
(28
)
i
n
t
o
(29
)
and
det
e
r
m
i
n
i
n
g
t
h
e i
n
ve
rse o
f
t
h
e
res
u
l
t
e
d ma
tri
x
pro
duce
0
.
136
1.
61
,
0.
8
0.
341
,
0.
306
1.
1
8
4
,
0.
0
3
9
0.
13
,
0.
031
0.
101
,
an
d
0.
0
3
3
0
.
101
.
The
out
put
vo
l
t
a
g
e
V
0
, i
nput
po
wer
P
i
, ou
tput
po
w
e
r
P
0
,
a
n
d
ov
er
al
l l
i
n
k
ef
fi
ci
en
cy
η
ov
e
r
a
l
l
are
d
e
te
rm
i
n
e
d
by
1.462
0.40
4
(3
0)
1.74
63
(3
1)
|
.
.
|
.
(3
2)
%
10
0%
.
1
00%
(3
3)
Th
e ab
ov
e ove
ra
ll
li
n
k
e
ffi
cie
n
c
y
co
rre
sp
on
d
s
to
w
i
r
e
le
ssly
en
er
g
i
z
i
ng a lo
a
d
c
i
r
c
u
it lo
c
a
t
e
d
at
6.61
m fr
om t
h
e p
o
we
r so
urc
e
ta
kin
g
i
n
t
o
ac
cou
n
t
st
ren
g
t
heni
n
g
t
h
e
i
n
duct
i
ve
c
o
u
p
l
i
ng
en
vi
ro
nme
n
t
an
d
con
d
i
t
i
oni
n
g
t
h
e
p
o
w
er re
cei
v
i
ng
c
i
rc
ui
t
fo
r
maxi
mum
po
w
e
r re
ce
pt
i
o
n
.
If
o
n
ly
o
n
e rec
e
i
v
in
g coi
l
i
s
use
d
a
n
d
l
o
cat
ed a
t
the
sa
me di
st
a
n
ce
from
t
h
e
po
w
e
r
s
o
urc
e
wi
t
hout
usi
n
g res
o
n
a
t
o
rs
for
stre
n
g
t
h
e
n
in
g
t
h
e
i
n
duct
i
v
e
cou
p
l
i
ng, t
h
en
ac
co
rdi
n
g
t
o
(
1
3
)
,
t
h
e
e
ffi
ci
e
n
c
y
for
si
ngl
e
coi
l
rece
ivi
n
g
c
i
rcui
t
wi
t
h
o
u
t
usi
n
g
res
onat
o
rs
is
c
a
l
c
u
l
at
ed
at
R
L
=1
30
Ω
as
fol
l
ows:
%
10
0%
0
.
00
42
1%
(3
4)
Th
e ov
e
r
a
ll
li
nk
ef
fic
i
e
n
cy
o
f
th
e
pro
p
o
s
ed
sy
ste
m
at
a lo
a
d
of
1
3
0
Ω
i
s
c
a
lcu
l
at
ed
as
.
10
0%
.
10
0%
1
.
01
54%
(3
5)
To s
how
t
h
e
si
gni
fic
a
nc
e o
f
t
h
e
e
ffi
ci
enc
y
e
nha
nceme
n
t
pr
ocesse
d in
thi
s
w
o
r
k
, w
h
a
t
i
s
k
n
o
w
n
as
th
e
eff
i
c
i
en
cy
g
a
i
n
G
eff
a
d
o
p
t
e
d he
re
re
fl
ect
s
t
h
i
s
as
fol
l
ow
s:
.
.
24
1.1
8
4
(3
6)
Ma
ny
te
ch
ni
q
u
es
a
r
e
e
x
pl
oi
t
e
d i
n
t
h
e
desi
gn
of t
h
e
WP
T
tra
n
smi
t
t
e
r
to
ta
rget
rel
a
t
i
vel
y
re
mot
e
el
ec
tric
al
no
de
s re
qui
re
d
t
o
b
e
wi
rel
e
ssl
y
en
ergiz
e
d
.
T
h
e
most
effi
c
i
e
n
t t
e
c
hni
que
i
s
cl
as
s-E
po
we
r
a
m
p
l
i
f
i
e
r,
whi
c
h is a
s
w
i
t
c
h
m
o
de
po
w
e
r a
m
pl
i
f
i
e
r ch
a
r
ac
te
ri
ze
d b
y
hig
h
e
f
fic
i
enc
y
a
n
d
hig
h
po
wer
.
T
h
ere
f
ore
su
c
h
ki
nd
of
po
wer
ampl
ifie
rs
are
re
comme
n
d
e
d
t
o
be a
d
opt
e
d
i
n
t
h
e
de
sig
n
o
f
WP
T s
y
st
e
m
s
.
F
i
g
u
re
10
sh
o
w
s
t
h
e
P
S
p
i
c
e
d
e
si
g
n
o
f
t
h
e p
r
op
osed
ef
fi
ci
en
t W
P
T
sy
stem.
The
cl
ass
-
E
p
o
w
er am
pl
i
f
i
e
r i
n
t
h
e
pro
pose
d
syste
m
i
s
l
o
a
d
ed
by a
n
R
L
C
c
o
mbi
n
at
i
o
n
c
o
mpo
s
ed
o
f
a
s
e
r
i
e
s
RLC
c
i
r
c
u
i
t repr
esen
te
d by
C
1
,
L
1
,
a
nd
R
1
s
h
u
n
t
e
d by
a
ca
pa
ci
t
o
r
C
SH
.
L
1
and
R
1
re
pres
ent
t
h
e
inductance
a
n
d AC resistance of t
h
e
transmitting coil, respectively.
C
1
is a t
unin
g
ca
paci
t
o
r re
so
na
te
s wi
t
h
L
1
a
t
a f
r
e
qu
e
n
cy slig
h
t
ly le
ss t
h
a
n
f
0
, whe
r
ea
s
C
SH
resonates
with t
h
e se
r
i
es RLC
(
C
1
,
L
1
, and
R
1
) cir
c
uit at
f
0
.
Usi
ng
(2
2) at
a
n
ope
rat
i
ng fre
que
nc
y
of
3
3
8
.
6
kHz
,
C
1
i
s
c
a
lcu
l
at
ed
as
4
.
86
31n
F
.
C
SH
is d
e
ter
m
in
ed
by
[25
]
.
52
.1
(3
7)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN
: 2
088
-8
6
94
Int
J
P
o
w
Ele
c
& D
r
i
S
y
st, V
o
l
.
1
1
,
N
o
.
2, Ju
ne
20
2
0
:
71
1
– 72
5
72
0
F
i
gu
re 1
0
.
T
h
e
P
S
p
i
ce de
si
g
n
of t
h
e
pr
opo
se
d s
y
ste
m
.
3.
R
E
S
U
LTS
AND D
I
SCU
S
S
I
O
N
Th
e
prop
o
s
e
d
eff
i
c
i
e
n
t
W
P
T
sy
ste
m
was
fi
rs
t
d
e
sign
ed on
PSp
ic
e, test
ed
, a
nd th
en
pra
c
tic
al
ly
i
m
pl
eme
n
t
e
d,
t
hus
i
n
t
h
i
s
wo
rk, t
h
ere
a
r
e
simul
a
t
i
v
e
res
u
l
t
s, w
h
i
c
h
are
va
li
dat
e
d
b
y
e
xpe
ri
me
nt
al
re
sult
s.
3.1. Si
mu
l
a
tio
n
r
e
sul
t
s
Th
e M
O
S
F
ET tr
ig
g
e
r
i
ng
vo
lt
ag
e
sign
a
l
V
S
i
s
a
sq
ua
re wa
v
e
vol
t
a
ge ha
ving a 3
3
8
.
6 k
H
z
fre
que
nc
y
and
±10V
vol
t
a
ge le
vel
s
.
The
DC
cu
rre
n
t
I
DC
o
f
t
h
e s
y
st
e
m
pow
er a
m
pl
i
f
i
e
r a
n
d
the
out
p
u
t
rec
e
i
v
e
d
vol
ta
ge
v
o
d
u
ri
ng
50
Ω
resi
st
ance
are
show
n
in F
i
g
u
re
11
(a
). T
h
e
DC i
n
p
u
t
cu
rre
n
t
is a
b
o
u
t
2.5A
a
n
d t
h
e
out
p
u
t
re
cei
ve
d AC
vol
t
a
ge
i
s
ab
o
u
t
5
.
3
6
V
p
e
a
k
val
u
e.
The
s
y
ste
m
i
n
p
u
t p
o
we
r
i
s
I
DC
V
DC
, whic
h
i
s
e
q
ual
t
o
L1
46.
334
uH
C1
4
.
8631n
F
L2
23
.
8
64uH
R1
0.
1
8
5
R2
0.
2
CS
H
52.
1
n
F
C2
9.
25
nF
0
0
L3
29.
3uH
R3
0.
2724
6
C3
7.
53
45nF
0
L4
22uH
R4
0.
172
C4
10
.
0
3446
3nF
0
L5
6.
0745
uH
R5
0.
0676
C5
116.
3n
F
L6
6.
0745
uH
R6
0.
0676
L7
6.
0745
uH
R7
0.
0676
R8
50
0
LR
F
C
1m
H
0
VD
C
12
V
V1
TD
=
0
T
F
=
1ns
P
W
=
1
.
47666
86us
P
E
R
=
2.
95
33372
7us
V
1
=
-10V
TR
=
1
n
s
V
2
= +1
0
V
0
Rs
5
K
K1
C
O
U
P
LI
N
G
=
0.
007
882
K
_Li
near
K
K2
C
O
U
P
LI
N
G
=
0.
000
437
K
_Li
near
K
K3
C
O
U
P
LI
N
G
=
0.
000
094
K
_Li
near
K
K4
C
O
U
P
LI
N
G
=
0
.
0
0001
675
K
_
Line
ar
K
K5
C
O
U
P
LI
N
G
=
0.
000
0154
K
_Li
near
K
K6
C
O
U
P
LI
N
G
=
0.
000
0129
5
K
_Li
near
K
K7
C
O
U
P
L
I
N
G
=
0.
006
K
_Li
near
K
K8
C
O
U
P
L
I
N
G
=
0.
000
781
K
_Li
near
Trans
mitting Cir
cuit
K
K9
C
O
U
P
L
I
N
G
=
0.
000
1246
K
_Li
near
Second Re
sonator Circ
uit
Firs
t Resonator
Circuit
K
K1
0
C
O
U
P
LI
N
G
=
0.
000
108
K
_Li
near
Re
ce
ivi
ng Ci
rcu
it
T
hir
d Res
ona
to
r
C
irc
ui
t
K
K1
1
C
O
U
P
LI
N
G
=
0.
000
1
K
_Li
near
K
K1
2
C
O
U
P
L
I
N
G
=
0.
005
35
K
_Li
near
K
K1
3
C
O
U
P
L
I
N
G
=
0.
000
528
K
_Li
near
K
K1
4
C
O
U
P
LI
N
G
=
0.
000
427
K
_Li
near
K
K1
5
C
O
U
P
LI
N
G
=
0.
000
3448
K
_Li
near
K
K1
6
C
O
U
P
L
I
N
G
=
0.
016
7
K
_Li
near
K
K1
7
C
O
U
P
L
I
N
G
=
0.
008
52
K
_Li
near
K
K1
8
C
O
U
P
LI
N
G
=
0
.
00482
7
K
_
Line
ar
K
K1
9
C
O
U
P
L
I
N
G
=
0.
083
633
K
_Li
near
K
K2
0
C
O
U
P
L
I
N
G
=
0.
083
633
K
_Li
near
K
K2
1
C
O
U
P
L
I
N
G
=
0.
019
35
K
_Li
near
I
I
I
I
I
M1
IR
FP
2
5
0
M2
I
R
F
P
250
M3
I
R
F
P
250
M4
IR
FP
2
5
0
M5
I
R
F
P
250
M6
IR
F
P
2
5
0
Evaluation Warning : The document was created with Spire.PDF for Python.