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.
4, D
e
c
e
m
ber
201
9,
pp.
2157~
21
64
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp2157-2164
2157
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
Efficiency investi
gation of SS
a
nd SP compensation topologies
for wireless power transfer
M
a
sood
R
ehm
a
n
1
,
Perum
a
l
N
a
lla
g
o
wn
den
2
,
Zu
ha
i
r
i
B
a
ha
r
u
d
i
n
3
1,
2,
3
E
l
ect
rical
a
n
d
E
l
e
ct
ron
i
cs Engi
neerin
g D
e
partmen
t
,
Univers
i
ti T
ekn
o
l
o
g
i
PET
RON
A
S
32
61
0 Ban
d
ar Seri
Isk
a
ndar,
P
erak, M
al
aysia
3
S
IRIM
B
erh
a
d,
N
o. 1 Pers
i
aran
D
at
o
’
Men
t
e
ri, S
ection
2
P.
O.
Bo
x
7
0
3
5
,
4
07
00
Shah
A
l
a
m
,
M
alay
sia
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
11,
2
0
1
9
Re
vise
d Ma
y
2
8
, 201
9
A
c
c
e
pte
d
J
u
l
3
,
2019
Wi
reles
s
pow
er
t
ransf
e
r
(W
PT
)
usi
n
g
i
n
duct
ive
and
re
s
o
nant
c
o
u
p
lin
g
has
been
w
i
d
el
y
ex
p
l
ored
i
n
rece
n
t
y
ears
f
o
r
ease
an
d
saf
e
ty
o
v
e
r
c
on
ven
tio
nal
cabl
e
c
h
a
rg
ing
sy
st
e
m
s.
T
he
e
f
f
i
c
iency
of
W
PT
s
ystem
s
i
s
redu
c
i
ng
dras
ti
ca
lly
d
u
e
t
o
an
i
n
c
reas
e
in
a
ir-g
aps
and
m
i
s
a
lig
n
m
e
n
t
b
et
we
e
n
transmitter
(Tx)
a
nd
r
eceiver
(Rx)
.
M
a
ny
c
ircui
t
t
opo
l
ogies
hav
e
be
en
anal
yzed
t
o
im
prov
e
t
h
e
ef
fici
e
n
cy
o
f
W
P
T
syst
em
b
ased
o
n
sy
mm
e
tr
ical
coi
l
s.
H
ow
ever,
th
e
ci
rcui
t
to
p
o
log
i
es
h
ave
no
t
been
s
tu
died
w
i
de
ly
f
or
un
sy
mmet
r
ical
c
o
i
l
s
.
T
h
is
p
a
p
er
p
resent
s
the
investigat
i
o
n
of
t
wo
f
u
n
d
am
ent
a
l
t
o
p
o
lo
gi
es
i
.
e
.
S
e
ries-S
eri
e
s
(SS
)
a
nd
S
e
ries
-P
aral
lel
(SP)
f
or
un
sy
mmet
r
ical
c
oi
ls
a
s
w
e
ll
as
s
ym
m
e
tri
c
al
c
oi
ls
.
T
h
eoret
i
cal
a
nalysi
s
o
f
b
o
th
t
h
e
c
omp
e
nsa
t
io
n
to
po
log
i
e
s
h
a
v
e
b
e
e
n
a
c
c
o
m
pl
ishe
d,
t
he
n
m
od
e
lin
g
of
bo
th
t
he
t
o
pologies
h
ave
been
d
on
e
u
s
i
ng
t
w
o
d
i
f
f
e
rent
c
o
m
bin
a
t
io
n
of
circu
l
ar
c
oi
ls
.
In
f
irs
t
case,
t
wo
s
i
m
ilar
s
ize
coi
l
s
have
b
een
d
es
ig
ned
an
d
in
seco
nd
c
ase
tra
n
smi
t
ter
co
il
o
f
h
i
g
h
er
d
im
ensio
n
s
than
r
eceiv
e
r
c
o
i
l
i
s
des
i
g
n
ed.
Th
e
ef
fici
ency
o
f
the
s
y
st
em
h
as
b
een
a
n
a
ly
zed
a
t
m
u
l
ti
pl
e
di
s
t
ances
i
n
b
o
th
cas
es
b
y
i
n
te
g
r
ati
n
g
coil
stru
ct
ure
w
i
t
h
t
h
e
circuit.
T
he
o
v
e
r
a
l
l
r
e
s
u
l
t
s
h
o
w
t
h
a
t
w
h
e
n
T
x
i
s
b
i
g
g
e
r
t
h
a
n
R
x
,
t
h
e
S
P
t
o
p
o
logy
g
i
v
es
bet
t
er effi
ciency
th
a
n SS
c
oun
terp
art.
K
eyw
ord
s
:
Circ
ular
C
oil
Effic
i
e
n
c
y
I
nv
estiga
tio
n
Series-P
a
r
all
e
l
(SP)
T
opology
Series-S
e
r
ies
(
S
S
)
T
opology
Un
sy
mme
t
ri
cal
Co
i
l
s
Wire
l
e
ss
P
ow
e
r
Tr
a
nsfe
r
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:
Mas
o
od Rehm
a
n,
Elec
tric
a
l
and
Elec
tron
ics
E
n
g
i
ne
eri
n
g D
e
partm
e
nt,
Un
iv
ersit
i
T
ekn
o
lo
gi
P
ETRO
NAS,
32
6
10
Ban
d
ar
S
e
r
i Iska
n
d
ar,
P
e
ra
k, Ma
l
a
y
sia
Em
ail:
ma
soo
d
.
rehm
an_g
03
2
2
9
@
ut
p.ed
u.
my
1.
I
N
TR
OD
U
C
TI
O
N
Wi
r
e
less
power
tran
sfer
(
WPT)
u
si
ng
in
d
u
ct
i
v
e
an
d
re
so
na
n
t
c
o
u
p
l
i
n
g
h
as
b
ec
om
e
one
o
f
t
h
e
dem
a
nde
d
tec
h
n
o
lo
g
i
es
i
n
r
ece
nt
y
e
a
rs.
WP
T
c
a
n
be
v
ery
use
f
u
l
f
or
c
harg
in
g
e
l
ec
t
r
i
c
v
e
h
ic
les,
e
le
ctro
nic
a
p
pli
a
n
ces
a
n
d
i
mpl
a
nt
ab
l
e
m
ed
i
c
al
d
ev
i
c
e
s
.
Th
e
id
e
a
of
W
PT
w
a
s
i
nit
i
a
ll
y
pr
esen
te
d
by
N
i
kola
Te
s
l
a
in
t
he
late
19t
h
Ce
nt
ury
[1].
W
P
T
c
an
b
e
w
i
de
l
y
s
e
p
ara
t
e
d
i
n
t
o
tw
o
ty
p
es
;
ra
d
i
a
tive
or
n
o
n
-radia
tive
[2,
3].
N
o
te
t
h
at
b
e
cau
se
o
f
u
n
id
i
r
e
c
t
i
on
al
n
at
u
r
e
of
ra
d
i
a
t
i
v
e
ap
p
r
o
a
c
h
o
f
W
P
T
,
it
doe
s
no
t
o
ffe
r
a
ny
go
o
d
a
d
j
u
s
t
m
en
t
betw
ee
n
the
e
f
fic
i
e
n
c
y
o
f
WP
T
a
n
d
i
t
s
d
i
re
ct
iona
lit
y
[4].
T
h
e
n
o
n
-r
adi
a
t
i
ve
W
P
T
w
orks
o
n
ba
sis
of
i
n
d
u
c
ti
ve
c
o
upl
in
g
an
d
ma
g
n
e
ti
c
re
son
a
nt
c
ou
pli
n
g
t
o
t
ran
s
f
e
r
t
h
e
en
e
r
gy
fr
om
t
he
t
ra
n
s
m
i
tt
in
g
coi
l
t
o
re
cei
v
i
ng
c
o
i
l.
U
s
ual
l
y
,
t
h
e
se
lf-re
sona
nce
fr
e
que
nc
y
of
c
o
i
ls
i
s
ac
h
i
eve
d
f
rom
p
ara
s
it
i
c
c
ap
a
c
i
t
a
n
c
e
and
s
e
l
f
-i
ndu
c
t
anc
e
o
f
coi
l
s,
h
ow
eve
r
,
the
par
a
si
tic
c
apa
c
i
t
a
n
ces
a
re
i
na
de
qua
t
e
f
or
r
e
s
ona
tin
g
b
o
t
h
t
h
e
c
o
ils
a
c
c
o
rd
in
g
to
e
s
t
i
m
ated
fre
que
nc
y,
the
n
a lum
p
ed
c
a
p
a
c
itor
ca
n be
in
c
lu
de
d to
m
a
k
e
it o
pe
ra
te
on d
e
sire
d fr
eq
uenc
y [5,
6].
I
n
y
ear
2
0
07,
a
t
e
c
h
n
i
q
u
e
o
f
W
P
T
u
si
ng
ma
gnet
i
c
re
so
na
nce
c
o
u
p
l
in
g
(M
RC)
w
a
s
prop
ose
d
b
y
rese
arc
h
ers
a
t
M
assa
c
h
uset
t
s
I
nsti
tu
te
o
f
Techn
o
l
o
g
y
(
MIT).
The
y
use
d
f
o
u
r
se
lf-re
so
nan
t
c
oi
l
s
o
f
30
c
m
radi
us
t
o
l
i
gh
t
up
a
bu
l
b
o
f
6
0
W
a
t
t
s
a
t
2
m
d
i
sta
n
c
e
w
i
t
h
effi
c
i
e
n
c
y
o
f
4
0
%
[
8
,
9
]
.
T
h
e
r
e
a
f
t
e
r
,
t
h
e
W
P
T
tech
n
o
l
o
gy
w
a
s
a
l
so
c
omm
e
rcial
i
ze
d
for
th
e
c
h
argi
n
g
o
f
por
t
a
b
l
e
e
l
e
c
t
ro
ni
c
c
o
m
p
on
en
ts,
su
c
h
a
s
mo
bil
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
1
5
7
– 2
164
2
158
ph
o
n
es, too
t
h brus
hes
e
t
c. [7
]
.
WP
T t
e
chno
lo
g
y
u
s
i
ng i
n
d
u
ct
ive
and
reson
a
nt
c
o
upl
ing
c
a
n
b
e
a
g
ood
s
ol
uti
on
f
o
r
ch
a
r
gi
ng
o
f
mo
bil
e
p
h
one
s
in
a
r
o
o
m
,
c
h
argin
g
of
r
o
bot
i
n
f
ut
ure
,
c
harg
i
ng
o
f
i
mplan
t
a
b
le
m
edica
l
dev
i
ce
s
e
t
c.
N
e
v
erthe
l
ess,
W
P
T
u
sin
g
i
n
duc
tive
a
nd
r
e
so
nan
t
c
o
u
pl
i
ng
pos
se
ss
ad
va
nta
g
e
s
o
ver
ot
her
tech
n
i
q
u
es
a
t
shor
t
an
d
me
dium
d
is
t
a
nces,
but
s
t
ill
t
h
i
s
t
ec
hno
l
ogy
i
s
in
e
f
f
e
ct
iv
e
b
eca
u
s
e
t
h
e
v
a
ri
ati
o
n
i
n
di
sta
n
c
e
b
e
t
w
e
en
t
he
t
ra
nsm
i
t
t
e
r
(
Tx)
an
d
rec
e
iver
(
Rx)
ca
uses
t
h
e
c
h
a
nge
i
n
res
ona
nc
e
freq
ue
ncy,
t
h
u
s
affec
t
s
the
e
ffi
cienc
y
.
F
u
rt
he
rm
ore,
t
he
m
i
s
ali
g
nme
n
t
bet
w
ee
n
t
he
T
x
a
n
d
Rx
can
a
ff
ect
t
he
pow
er
t
rans
fe
r
efficie
n
c
y
[
1
0
,
11].
Man
y
r
e
s
ear
ch
s
t
u
d
i
e
s
h
ave
be
en
c
ond
uc
t
e
d
t
o
i
m
p
ro
ve
t
he
e
f
f
i
c
ienc
y.
S
tu
dy
on
t
h
e
circ
u
i
t mo
de
l and fre
que
nc
y a
n
al
ys
is ar
e
p
r
e
sen
t
ed in [1
2,
13].
T
he
s
p
l
i
t
t
i
ng frequ
enc
y
o
c
c
urs, w
hen sing
le
or
mult
i
p
le
c
o
i
l
s
f
rom
prim
ary
a
nd
sec
o
nda
r
y
s
ide
com
e
i
n
c
l
o
s
e
v
i
ci
nit
y
t
o
e
a
c
h
ot
h
e
r,
t
he
n
th
e
p
r
o
d
u
c
t
i
on
of
st
ron
g
r
el
a
t
i
v
e
ma
g
n
e
ti
c
fi
el
d
i
s
i
n
e
vit
a
bl
e
,
w
h
i
ch
c
an
c
au
se
t
he
s
pl
it of
fre
que
n
c
y i
n
tw
o
differ
e
nt
p
e
a
k
s
[14]
,
w
h
ic
h
u
l
tima
t
e
l
y
re
duc
es
t
he
pow
er
t
ran
s
fe
r
c
a
pab
i
l
ity
o
f
WP
T
s
y
s
t
e
m.
M
an
y
c
i
rc
uit
to
po
l
ogi
e
s
h
av
e
b
e
e
n
stud
ie
d
t
o
i
mp
rove
t
he
e
ffic
ie
ncy
o
f
W
P
T
s
ys
tem
.
A
na
lysis
of
s
e
c
o
n
d
a
r
y
series
a
nd
p
a
r
al
lel
to
po
l
o
gy
f
or
in
duc
t
i
ve
pow
e
r
t
ransfe
r
for
a
c
hie
v
in
g
opt
i
m
al
e
ff
i
c
i
e
nc
y
is
c
a
rri
e
d
ou
t
in
[
15
]
a
n
d
lo
ad
i
nd
ep
e
n
d
e
n
t
v
olt
a
ge
trans
f
e
r
i
s
d
i
sc
usse
d,
how
eve
r
,
unsym
m
e
trica
l
c
o
i
ls
h
a
v
e
no
t
be
e
n
u
ti
liz
ed.
H
ybr
id
t
op
ol
o
g
ie
s
for
WP
T
ar
e
in
ves
tiga
t
e
d
f
o
r
c
ons
ta
n
t
c
urre
nt
a
n
d
co
ns
ta
nt
v
o
ltage
o
utp
u
t
t
o
c
h
arge
t
h
e
b
a
t
ter
i
e
s
i
n
[16].
Mo
de
li
ng
a
nd
η
-
α-pa
r
eto
opt
im
i
z
at
i
o
n
of
W
P
T
c
oi
ls
f
or
e
le
ctric
ve
h
i
cle
s
u
s
i
n
g
d
i
ffere
nt
t
o
p
o
l
og
ies
is
c
on
d
u
cte
d
i
n
[17].
A
gene
ra
l
the
o
r
y
f
oc
us
in
g
o
n
S
P-Com
b
ine
d
t
o
p
o
l
ogy
is
s
t
u
d
i
e
d
i
n
[
18]
a
n
d
e
qua
t
i
o
n
s
of
e
f
f
icie
nc
y
a
r
e
der
i
ve
d.
A
n
al
ys
is
o
f
WP
T
usin
g
S
S
a
nd
S
P
-Com
bin
e
d
To
pol
og
y
is
p
rov
i
de
d
i
n
[
1
9,
20].
A
n
op
tim
iza
t
i
o
n
tech
ni
q
u
e
to
e
n
h
a
n
ce
t
he
e
ff
icie
nc
y
of
W
P
T
s
y
s
tem
u
s
i
n
g
S
S
t
opo
l
o
gy
i
s
pr
o
pose
d
i
n
[2
1].
It
w
as
d
em
on
st
r
a
te
d
tha
t
t
he
ma
ximum
effi
c
i
e
n
c
y
can
b
e
ac
hi
e
v
e
d
w
hen
Tx
a
n
d
R
x
are
no
t
on
sa
m
e
p
lane
a
nd
R
x
h
a
s
s
ome
m
i
sali
g
n
m
e
nt
wi
t
h
t
ilt
a
n
g
l
e
o
f
π
/
4
.
In
g
en
era
l
,
til
t
ang
l
e
a
f
fe
ct
s
t
h
e
co
up
lin
g
c
o
effic
i
e
n
t;
how
e
v
e
r
,
th
is
p
aper
d
o
e
s
not
d
i
s
c
u
ss
t
h
e
ove
ra
l
l
i
mp
a
c
t
o
f
c
ou
plin
g
co
effi
c
i
e
n
t
on
th
e
e
f
fi
c
ie
nc
y
of
s
ys
t
e
m.
F
ini
t
e
El
e
m
e
n
t
A
n
a
l
ys
is
i
s
con
d
u
cte
d
b
y
de
s
i
g
n
i
n
g
t
w
o
E
t
y
p
e
fe
rri
te
c
ore
s
w
it
h
S
S
c
om
pen
s
at
i
on
a
nd
a
m
e
ta
m
ate
r
ia
l
is
p
l
a
c
e
d
n
e
ar
t
he
transm
itt
er
s
i
d
e
E
ty
pe
c
ore
to
i
m
p
r
ove
t
he
t
r
a
ns
fe
r
d
i
s
t
a
n
ce
b
y
en
ha
nc
i
n
g
e
l
ec
t
r
oma
g
net
i
c
i
n
duc
t
i
o
n
[
2
2
]
,
how
e
v
e
r
t
o
de
sign
E
t
y
pe
T
x
a
nd
Rx
c
o
i
ls
m
ay
n
ot
b
e
fe
asi
b
le
i
n
m
a
n
y
si
t
u
a
tio
ns.
Si
m
u
l
a
ti
on
o
f
M
u
l
tip
le
Coi
l
M
ode
l
for
WP
T
S
y
stem
a
re
car
ried
o
ut
i
n
[23].
In
t
h
i
s
m
ode
l,
4
overl
appe
d
c
o
i
l
s
w
e
r
e
u
se
d
a
s
a
T
x
c
o
il
and
sin
g
l
e
c
o
i
l
w
as
u
se
d
as
a
r
ece
i
v
e
r
c
oi
l
to
o
b
t
a
i
n
1
5
%
m
o
re
efficie
n
c
y
t
ha
n
j
u
s
t
s
i
n
gle
T
x
c
oil,
b
u
t
t
h
i
s
ty
pe
o
f
mo
de
l
ha
s
i
n
cre
a
se
d
c
a
pi
ta
l
co
st.
S
i
mula
ti
on
a
n
d
A
n
al
ys
is
o
f
WP
T
syst
e
m
a
re
c
on
d
u
cte
d
i
n
[2
4],
it
w
a
s
conc
l
ude
d
t
h
at
t
he
c
han
g
es
i
n
n
u
m
b
e
r
o
f
tur
n
s
o
f
c
oi
ls
a
n
d
d
i
st
a
n
c
e
aff
e
c
t
s
t
h
e
ov
e
r
al
l
e
ffi
ci
ency
of
s
ys
tem
.
Thi
s
p
ape
r
p
re
sent
s
t
h
e
i
nve
sti
g
ati
o
n
of
t
wo
f
un
d
a
me
nta
l
t
opol
o
gi
es
i
.e.
Series-S
e
r
ies
(SS)
a
nd
S
e
r
i
e
s
-
P
ar
a
l
le
l
(
S
P
)
o
f
in
d
u
c
t
i
v
e
W
P
T
s
y
s
t
e
m
.
S
i
m
u
l
a
t
i
o
n
is
p
e
r
form
ed
b
y
de
si
gni
n
g
t
h
e
c
oi
l
a
n
d
i
n
te
gra
t
i
n
g
it
w
i
th
c
i
r
c
u
i
t
s
truc
ture
t
o
e
x
am
ine
t
h
e
o
v
e
r
all
pe
rform
anc
e
o
f
t
he
m
o
d
e
l.
T
he
or
et
ica
l
a
na
lys
i
s
o
f
b
oth
t
h
e
com
p
en
sat
i
on
top
o
l
o
gie
s
h
a
v
e
been
acc
ompl
is
he
d,
t
he
n
m
odel
i
ng
o
f
b
o
t
h
t
he
t
o
p
o
lo
gie
s
h
a
v
e
be
e
n
d
one
us
i
n
g
t
w
o di
ffe
rent c
ombi
na
ti
on o
f
coils.
I
n
f
i
r
st case, t
wo
s
a
me
s
i
z
e
coi
l
s
h
av
e
b
e
en
t
ake
n
a
nd
i
n
sec
o
n
d
case
transm
itt
er
c
oi
l
of
h
i
g
her
di
me
nsi
ons
t
ha
n
r
ece
i
v
e
r
c
oil
i
s
d
e
s
i
g
ned.
T
he
e
ffic
i
en
cy
o
f
th
e
sys
t
em
h
as
b
ee
n
ana
l
yz
e
d
a
t
m
u
l
tip
le
d
ista
nc
es
i
n
b
o
t
h
ca
s
e
s.
S
e
c
ond
cas
e
c
o
il
c
o
m
b
i
n
a
t
i
o
n
ca
n
be
s
u
i
ta
ble
fo
r
b
i
o
m
edica
l
app
l
ica
t
i
o
ns,
where
r
ece
i
v
e
r
c
oi
l
m
o
s
t
l
y
r
em
ains
s
m
a
l
l
e
r
a
s
com
pare
d
to
t
r
a
nsm
i
t
t
er
c
oi
l.
T
h
i
s
pa
pe
r
is
orga
nize
d
in
s
uc
h
a
m
a
n
n
e
r
t
hat
the
sec
t
i
o
n
1
i
n
c
l
u
d
es
t
he
I
ntr
o
duc
t
i
o
n
.
S
ectio
n
2
com
p
rises
of
t
he
a
nal
y
s
i
s
and
d
e
riva
t
i
o
n
of
e
ffic
ie
n
c
y
e
qua
t
i
on
f
or
W
P
T
s
yste
m.
T
h
e
d
e
s
ig
n
of
c
ir
cula
r
c
o
il
a
n
d
fin
i
t
e
e
lem
e
n
t
a
nal
y
s
i
s
is
p
ro
v
i
de
d
i
n
s
ec
tio
n
3.
T
he
s
im
u
l
a
t
i
on
r
e
s
u
lts
o
f
WP
T
m
o
de
l
a
re
g
ive
n
i
n
se
ct
ion
4
and
the
c
onc
l
u
sion
is
prese
n
t
e
d i
n
se
c
tio
n
5.
2.
RESEARCH
M
ETH
O
D
Th
is
s
ec
ti
on
i
n
cl
u
d
es
t
he
e
ffi
c
i
e
n
cy
a
nal
y
sis
o
f
S
er
ies-Series
(
S
S
)
t
op
olo
gy,
S
e
r
ies-P
a
ra
ll
e
l
(
S
P
)
to
pol
o
gy.
T
he
e
qua
t
i
o
n
s
o
f
e
f
f
ic
ie
ncie
s
for
bo
t
h
t
he
c
ircui
t
t
o
p
o
lo
gi
es
h
a
v
e
be
en
d
e
r
ive
d
i
n
sec
t
i
o
n
2.
1
a
n
d
sect
io
n
2.
2.
T
h
e
c
om
bina
ti
on of
s
ym
m
e
trica
l
a
nd
u
n
sym
m
e
trica
l
c
o
ils
s
tru
c
ture
s
ha
s
bee
n
d
e
s
i
g
n
e
d
i
n
s
e
c
tio
n
2.3.
T
he
m
ag
ne
tic
f
ie
l
d
a
t
thre
e
differ
e
n
t
di
sta
n
ce
s
for
bo
t
h
c
ombi
n
a
ti
o
n
s
is
c
a
l
cu
late
d
us
i
n
g
3
D
f
ini
t
e
elem
en
t
a
n
al
ys
is
b
y
a
p
p
l
y
i
n
g
t
he
c
urre
nt
e
xc
i
t
a
tio
n
of
1
A
.
The
S
S
an
d
S
P
t
op
o
l
og
y
m
o
de
ls
a
r
e
e
xam
i
n
e
d
for
ca
se
s.
I
n
the
fi
rst
case
the
c
o
i
l
s
a
r
e
s
y
mm
etrica
l
i.e
.
t
he
t
ra
n
s
mit
t
er
a
n
d
rece
i
v
e
r
c
oi
l
s
r
emai
n
sa
me
s
i
ze,
w
h
i
l
e
in
t
he
s
ec
o
n
d
c
ase
the
c
o
il
s
a
r
e
uns
ym
me
t
r
i
c
al
i
.
e
.
the
tra
n
sm
i
tt
e
r
c
o
i
l
i
s
b
ig
ge
r
tha
n
t
he
r
ece
ive
r
c
o
il.
I
n
sect
io
n
2.4.
,
th
e
co
ils
a
re
i
n
t
e
g
r
a
te
d
w
i
t
h
c
irc
u
it
sim
u
l
a
t
i
o
n
s
t
o
a
c
h
i
ev
e
the
ac
c
u
ra
t
e
a
n
a
ly
si
s
re
sul
t
s
a
t
th
ree
di
ffe
re
nt d
is
ta
n
c
e
s
f
or
b
o
t
h
ca
se
s usi
n
g
S
S
and S
P
topo
l
o
g
y
.
2.1.
Efficien
cy
i
n
v
estig
a
ti
on
a
nd d
eri
v
a
t
io
ns
o
f series-series (
SS)
to
po
l
o
g
y
m
o
de
l
To
d
e
r
i
v
e
th
e
eq
u
a
ti
on
s
of
e
ffi
c
i
en
c
y
,
a
n
e
q
u
i
v
al
en
t
c
i
rc
ui
t
o
f
S
S
top
o
l
o
gy
m
odel
i
s
s
ho
w
n
i
n
F
i
g
u
re
1(a)
.
Thi
s
r
ese
a
rc
h cons
iders
t
h
e
f
unda
me
n
t
a
l
com
po
ne
n
t
of v
o
l
t
a
g
e a
n
d cur
r
ent
for sim
p
lic
it
y.
Usi
n
g
Ki
r
c
h
hof
f
’
s
Vo
lt
ag
e
Law (KVL
), fo
l
l
o
wi
ng
eq
u
a
t
i
o
n
s
can
b
e
derived using F
i
gur
e
1
(
a
)
.
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
Ef
f
i
c
i
e
n
cy in
v
e
st
i
g
a
t
i
o
n
of
S
S
and SP
c
o
m
p
e
n
sa
ti
on to
po
l
o
gi
e
s
for wi
re
l
e
ss …
(M
a
s
o
od
Rehm
a
n
)
2
159
U
Z
I
j
ω
M
I
(
1
)
0
j
ω
M
I
Z
I
(
2
)
wher
e
Z
R
R
j
ω
L
and
Z
j
ω
L
R
R
(a)
(
b
)
F
i
gur
e 1.
(a
)
E
qu
iva
l
e
n
t
circ
uit o
f
S
S
t
o
p
o
l
o
gy m
ode
l (b)
S
P
t
o
po
l
o
g
y
m
odel
F
i
gure
1
de
p
i
c
t
s
t
h
e
S
S
t
op
o
l
og
y
mode
l
,
w
h
e
re
U
S
i
s
t
h
e
s
ourc
e
v
ol
ta
ge
a
pp
l
i
e
d
on
t
h
e
tra
n
smit
ter
resona
t
o
r
a
t
r
eson
a
n
ce
freq
u
e
nc
y
(
ω
)
,
a
n
d
Z
1
a
nd
Z
2
a
re
t
h
e
i
mp
ed
a
n
c
e
s
o
f
t
ran
s
mitt
er
a
n
d
re
ce
iv
er
s
i
d
e
re
sp
ec
ti
v
e
ly
.
Th
e
mut
u
al
i
n
d
u
ct
a
n
c
e
(M)
b
e
t
w
een
t
he
t
r
a
ns
mitter
a
n
d
t
h
e
rec
e
iver
c
a
n
b
e
ex
pre
s
se
d
in
t
er
ms
of
c
o
u
p
li
ng
co
efficie
n
t
k
and
coi
l
i
nd
uc
ta
nce
s
,
w
h
ic
h is gi
v
en by,
Mk
L
L
(
3
)
N
o
te
t
ha
t
the
hi
g
h
er
c
ou
p
lin
g
c
o
e
f
f
i
c
i
en
t
repr
esen
ts
t
he
s
m
a
ll
d
i
s
t
a
n
ce
betw
ee
n
the
transm
i
t
ter
a
n
d
rec
e
iver
c
o
i
l
a
nd
vi
ce
v
e
r
sa.
The
curr
en
ts
f
low
i
n
g
t
hro
u
g
h
t
he
so
urc
e
s
ide
a
n
d
t
h
e
l
o
a
d
a
re
c
alcu
la
t
e
d
b
y
si
m
p
li
fy
ing
(1)
and (
2
).
I
a
nd
I
O
u
t
p
u
t
p
ow
e
r
a
t
gi
ve
n
R
L
l
oa
d
and
the
effic
i
enc
y
ɳ
c
a
n be
e
x
p
r
e
sse
d
by
(4),
ƞ
1
0
0
(
4
)
A
d
d
i
t
i
o
n
a
l
l
y,
i
n
S
S
a
nd
S
P
t
opo
lo
g
y
m
o
d
e
l
s,
t
he
r
e
s
ona
nc
e
occ
u
r
s
whe
n
t
he
r
e
act
iv
e
i
m
p
e
danc
e
o
f
t
h
e
co
il
b
e
c
o
m
es
z
e
r
o
and
the
re
ac
t
a
nc
e
o
f
t
h
e
c
oi
l
ap
p
r
oac
h
e
s
to
z
ero,
t
he
n
re
so
na
nce
fr
eq
ue
nc
i
e
s
o
f
t
h
e
transm
itt
er
1
a
nd re
ce
ive
r
2
b
ec
o
m
e,
ω
,
,
,
(5
)
F
r
om
t
he
e
qu
ati
ons
(
3)-(
5),
i
t
i
s
c
o
nc
lu
d
e
d
t
h
a
t
t
he
c
urr
e
nts,
vo
lt
age
s
a
n
d
effi
ci
en
cy
c
a
n
b
e
ca
l
c
u
l
a
t
e
d
by
us
ing
e
q
u
i
va
le
nt
c
irc
u
i
t
m
e
t
h
od.
A
c
c
ord
i
n
g
to
A
la
n
s
o
n
e
t
al
.
[9
],
t
h
e
re
i
s
a
c
r
i
t
i
c
al
c
ou
pli
ng
parameter
for
dis
t
a
n
ce
k
now
n
a
s
the
p
o
in
t
of
c
ri
tic
a
l
c
o
u
p
l
i
n
g
(K
cri
tical
)
,
a
part
f
r
o
m
t
h
at
p
oi
n
t
t
he
s
y
s
tem
ca
nno
t
o
p
e
r
ate
a
presc
r
ibe
d
l
oad
a
t
t
he
m
a
x
i
m
um
e
ff
i
c
i
e
ncy.
I
n
SS
t
op
ol
o
gy
mo
d
e
l
,
w
h
e
n
t
h
e
sy
st
em
i
s
s
y
m
m
e
t
r
i
c
a
l
,
i
.e
.
R
1
=R
2
=R
X
a
nd
R
S
=R
L
=
R
;
the
n
K
critic
al
is
g
i
v
e
n
b
y
(
6
)
.
K
(
6
)
A
s
p
rese
nt
e
d
i
n
(6)
,
K
cr
i
tical
i
s
lar
g
el
y
co
nf
ine
d
by
ω
L
a
nd
t
h
e
l
o
ad
r
esi
s
ta
nce
.
F
or
t
hi
s
r
eason,
t
he
series-
s
e
r
ies
m
odel
is
n
o
t
c
apa
b
le
o
f
t
r
ansfer
ri
ng
p
o
wer
at
l
a
r
ge
d
ista
nc
e.
F
rom
the
a
b
ove
a
na
l
y
t
i
ca
l
equa
t
i
o
n
s,
i
t
c
a
n
be
c
o
n
c
l
u
d
e
d
t
ha
t
se
ries
r
e
s
on
a
n
t
m
ode
l
has
t
h
e
ir
o
w
n
p
ros
an
d
co
ns.
The
S
S
c
i
r
cuit
m
odel
prese
n
t
s
l
ar
g
e
v
al
ue
o
f
m
a
xi
m
u
m
tra
n
sfer
e
fficie
nc
y
ow
ing
t
o
t
h
e
le
ss
se
ns
i
t
i
v
it
y
for
the
para
si
tic
r
e
s
is
tance
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
1
5
7
– 2
164
2
160
But
w
h
en
t
he
i
n
duc
ta
nce
is
i
nc
rea
s
ed
f
or
r
e
a
liz
i
ng
gre
a
t
e
r
t
ra
n
sf
e
r
d
i
s
t
a
n
c
e;
t
h
a
t
wi
ll
l
ea
d
to
d
ec
rea
s
e
th
e
e
ffi
c
i
en
cy
b
ecau
s
e
o
f
l
a
rg
e
r
p
ara
s
it
i
c
r
esi
s
ta
n
c
e
lo
ss
of
l
arg
e
-size
d
c
oi
ls.
Moreo
v
e
r
,
t
h
e
parasi
tic
r
e
sis
t
ances
R1
a
n
d
R2
o
f
the
c
o
il
ha
ve
t
he
h
u
g
e
im
pac
t
o
n
the
e
f
fic
i
e
n
c
y
o
f
the
sy
st
em.
Smal
l
t
h
e
p
a
ra
sit
i
c
resi
sta
n
c
e
,
hi
ghe
r the
over
a
ll ef
fic
i
e
n
cy
o
f system
a
nd
v
i
ce ver
s
a
. A
dd
it
io
na
ll
y, t
he
der
i
v
a
tio
n o
f
cir
c
u
it para
me
t
e
rs o
f SP
c
o
mp
e
n
sa
tio
n
to
pol
ogy
i
s p
r
e
s
e
n
t
e
d
in
t
he
s
ec
t
i
on
2
.2
.
2.2.
Efficien
cy
i
n
v
estig
a
ti
on
a
nd d
erivati
o
ns
o
f se
ries-p
aral
le
l (S
P
)
to
po
l
ogy
mo
d
e
l
The
S
e
ries-
P
aralle
l
(S
P
)
t
op
o
l
o
g
y
c
a
n
b
e
de
fi
ne
d
a
s
t
he
s
e
r
ies
c
o
mpe
n
sa
tio
n
from
tra
n
s
m
it
te
r
s
i
de
and
pa
ralle
l
c
o
mpe
n
sa
tio
n
fro
m
re
ceiver
s
i
d
e
a
s
i
l
l
u
s
t
rate
d
in
Figu
re
1
(
b).
Th
e
fol
l
o
w
i
n
g
eq
u
a
ti
on
s
can
b
e
deri
ve
d
fr
om
F
ig
ure
1
(
b
),
w
here
U
S
i
s
source
v
olta
ge
a
nd
Z
1
a
nd
Z
C2
a
re
t
he
c
orr
e
sp
on
d
i
n
g
i
mpe
d
a
n
ce
s
fr
om
p
r
i
m
ary
a
n
d
sec
o
nd
a
r
y
sid
e
.
In
t
hi
s
to
pol
og
y
C
1
i
s
c
o
nnec
t
e
d
i
n
serie
s
f
r
o
m
prim
ary
side
a
n
d
C
2
i
s
c
o
nn
ec
t
e
d
in par
a
lle
l fr
o
m
s
e
c
ondar
y
si
d
e.
U
Z
I
j
ω
M
I
(7
)
0
j
ω
M
I
Z
I
I
(
8
)
0
(9
)
wher
e
Z
R
R
j
ω
L
a
nd
Z
j
ω
L
R
Th
e cu
rre
n
t
s I
S
,
I
C2
a
nd I
L
can
b
e
calc
u
l
a
t
e
d by
Cra
m
e
r
’s rule.
A
⎣
⎢
⎢
⎡
Z
jωM
0
j
ωM
Z
0
R
⎦
⎥
⎥
⎤
(
1
0
)
I
Z
R
(
1
1
)
I
jωM
R
(
1
2
)
I
(
1
3
)
ƞ
_
_
100
(
1
4
)
The
reso
na
nc
e
fr
eque
nc
y
form
ul
a
w
i
l
l
r
em
ain
the
sam
e
f
or
b
o
t
h
S
S
a
n
d
S
P
t
o
pol
og
y
mo
d
e
ls
a
s
p
r
ov
id
ed
i
n
(5
).
W
e
ca
n
ca
l
c
u
l
at
e
t
h
e
requ
i
r
e
d
c
ap
a
c
i
t
a
n
c
e
v
a
l
u
e
at
o
ur
d
es
ired
f
re
que
ncy
usi
n
g
(5)
i
n
b
o
t
h
ca
se
s.
T
his
re
sona
nce
fre
que
n
c
y
form
u
l
a
is
i
nde
pen
d
e
n
c
e
o
f
c
o
u
p
l
i
n
g
,
b
e
cause
w
e
m
u
st
calc
u
la
t
e
r
es
o
n
anc
e
fre
que
nc
y
for
prima
r
y
a
n
d
sec
onda
ry
s
id
e
separ
a
te
ly.
Th
ere
is
a
n
impa
ct
o
f
co
up
l
i
ng
coe
f
fic
i
e
n
t
(k
)
on
th
e
resona
nce
fr
e
q
uenc
y.
D
ue
t
o
varia
t
i
o
n
in
k
v
a
lue
,
t
he
r
es
on
ati
n
g
poi
nt
o
f
fre
que
ncy
m
a
y
sh
i
f
t
s
lig
ht
l
y
,
w
h
ic
h
is
f
ur
the
r
di
s
cu
ssed i
n
s
e
c
t
i
o
n
3.
The
effi
c
i
e
n
cy
o
f S
P
c
om
pens
a
t
i
on
to
pol
o
gy c
a
n
be c
a
l
c
u
la
te
d
usin
g
(14).
2.3.
D
e
sign
of
circ
u
l
ar
s
t
r
u
c
tu
re
s
of symm
e
tr
i
c
al an
d
u
n
s
ymme
tric
a
l
co
il
s
The
spira
l
i
s
a
very
p
opul
a
r
s
t
r
u
ct
ure
i
n
r
e
s
o
n
a
n
t
w
i
r
e
less
pow
er
t
ra
nsfer
s
y
s
t
em
due
t
o
i
t
s
com
p
ac
t
si
ze
a
n
d
g
r
ea
tly
c
onf
in
ed
e
l
ect
ro
mag
n
e
ti
c
fi
e
l
d
c
h
a
r
ac
t
e
ri
sti
c
s
.
A
n
i
nc
lu
sive
s
t
u
dy
o
f
circu
l
ar
h
e
lix
c
oi
ls,
p
l
an
a
r
s
p
i
ral
c
o
i
l
s
,
an
d
s
q
u
a
re
h
el
ix
c
oi
ls
w
as
c
on
du
ct
ed
i
n
[2
5].
I
t
w
as
s
how
n
tha
t
t
he
c
ircu
la
r
he
lix
c
oils
offe
r
the
bes
t
p
erform
ance
(
e.
g.
t
h
e
h
i
g
h
e
s
t
e
f
f
i
c
i
e
n
c
y
,
t
h
e
w
i
de
s
t
b
andw
id
t
h
,
a
n
d
the
lon
g
es
t
t
r
ansfe
r
di
sta
n
c
e
)
un
de
r
op
tim
al
l
oa
d
w
h
ere
a
s
the
pl
a
n
ar
s
p
i
ral
c
o
i
l
s
e
x
hi
bit
the
w
o
rst
perform
ance
a
m
o
ng
t
he
m.
T
he
op
tim
al
l
oa
d
c
a
n
be
d
ef
ine
d
a
s
the
loa
d
v
a
l
ue,
w
h
er
e
the
ma
xi
m
u
m
e
ffi
ci
e
n
cy
i
s
ach
i
e
v
a
bl
e.
A
n
o
th
e
r
s
t
udy
rega
rdi
n
g
t
h
e
sha
p
e
o
f
t
he
c
oi
l
w
a
s
pre
s
en
ted
i
n
[
26]
.
I
t
w
as
f
oun
d
th
a
t
c
ircu
lar
ge
o
m
etries
o
ffer
b
et
te
r
cou
p
l
i
ng
in p
er
fec
t
a
l
i
gnme
n
t
w
h
i
l
e
sq
uare
ty
p
es
a
re
better
u
n
d
e
r
mi
s
al
ig
nmen
t
b
e
t
w
een
th
e
c
o
i
l
s
.
B
e
cau
se
o
f
abo
v
e
m
e
n
ti
o
n
e
d
a
d
v
a
nt
ag
es
,
c
i
rcul
ar
c
oi
l
s
a
re
s
e
l
e
c
ted
for
this
w
or
k.
T
wo
d
if
ferent
ca
se
s a
r
e consi
d
ere
d
. I
n
the fi
r
st ca
s
e,
simila
r size coi
l
s ar
e
d
e
s
i
g
ne
d as ill
us
trated
i
n F
i
g
u
re
2 (a),
w
h
ile
in t
h
e
seco
nd
c
ase
t
h
e
transm
i
t
ter
c
o
i
l
h
a
s
b
e
e
n
k
e
p
t
bi
g
g
er
t
ha
n
the
re
c
e
i
v
er
c
oi
l
a
s
s
h
o
w
n
in
F
i
g
u
r
e
2
(
b
).
S
e
c
ond
com
b
i
n
a
t
i
o
n
o
f
c
o
ils
c
a
n
b
e
suita
b
l
e
for
b
i
ome
d
i
c
a
l
a
p
p
li
ca
tio
n
s.
T
he
d
i
m
e
n
si
ons
o
f
t
h
e
big
s
i
z
e
c
oi
ls
a
n
d
s
m
a
l
l
s
i
z
e
a
r
e
g
i
v
e
n
i
n
T
a
b
l
e
1
.
B
i
g
s
i
z
e
c
o
i
l
i
n
b
o
t
h
c
a
s
e
s
h
a
s
bee
n
k
e
p
t
si
m
i
lar.
T
he
s
e
l
f-i
n
duc
ta
nce
,
m
utua
l
in
duc
ta
nce
a
n
d
t
h
e
c
o
up
l
i
n
g
c
oe
ff
i
c
i
e
nts
at
t
hree
d
i
f
fer
e
nt
d
is
t
a
nce
s
a
re
calc
u
la
te
d
us
in
g
f
i
n
ite
e
le
me
nt
me
tho
d
(
F
E
M
)
s
imulat
i
o
n
s
.
The
sel
f
-
i
nd
uc
ta
nce
s
o
f
the
c
o
ils,
mu
t
u
al
i
nd
uc
ta
nce
s
b
e
t
w
e
en
t
he
c
oi
ls
a
nd
cou
p
l
i
ng
coe
ffi
cien
t a
r
e
ana
l
y
z
ed a
t m
u
lti
p
l
e
dis
t
ance
s an
d
the
ir re
s
ults a
re pro
vi
de
d in
T
a
b
le
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
Ef
f
i
c
i
e
n
cy in
v
e
st
i
g
a
t
i
o
n
of
S
S
and SP
c
o
m
p
e
n
sa
ti
on to
po
l
o
gi
e
s
for wi
re
l
e
ss …
(M
a
s
o
od
Rehm
a
n
)
2
161
Ta
b
l
e
1.
P
ara
m
e
t
e
r
s of b
ig
ger
and sm
al
l size
coi
ls
B
i
g Si
z
e
C
oi
ls
P
a
r
a
m
ete
r
V
a
l
u
e
(
mm)
S
ma
ll Si
z
e
C
o
il
Pa
r
a
mete
r V
a
l
u
e
(
mm)
Pol
ygon
R
a
dius
2
.
5
m
m
P
oly
gon
Ra
dius
2
.
5
m
m
Sta
r
t
H
e
lix Ra
d
ius
100
m
m
S
ta
r
t
H
e
lix Ra
d
ius
20
m
m
Ra
dius C
ha
ng
e
7m
m
Ra
dius C
ha
ng
e
7m
m
P
i
tch
0
mm
P
i
tch
0
mm
N
o
. o
f Tu
r
n
s
1
7
N
o
. o
f Tu
r
n
s
1
0
D
i
a
m
e
t
e
r
433
m
m
D
i
a
m
e
t
e
r
176
m
m
Tab
l
e 2
.
C
al
cu
la
t
e
d
v
a
lu
e
s
o
f
d
i
s
t
an
ce
v
s
c
oup
li
n
g
c
o
e
f
fi
ci
en
t
of sym
met
r
ical coils and
u
nsymm
e
tr
i
c
a
l
c
oils
S.
No.
Dis
t
a
n
c
e
(m
m
)
Se
l
f
-
I
n
du
c
t
an
ce
of
B
oth
S
y
mm
e
t
r
i
cal
Co
i
l
s
(
µ
H)
Mu
tu
al
Ind
u
c
t
a
n
ce
(µ
H
)
be
twee
n
symme
tr
ica
l
co
i
l
s
C
oupl
ing
C
o
ef
f
i
ci
en
t
(k
)
be
twee
n
sy
mme
tr
i
cal
c
o
ils
Se
lf-
I
n
du
ct
an
ce
of B
ig C
oil
(µH
)
Se
lf-
I
n
du
ct
an
ce
of
S
m
a
l
l
Co
il
(
µH)
Mu
tu
al
I
n
d
u
ct
an
c
e
(µH
)
o
f
unsym
m
e
t
r
i
c
a
l
co
i
l
s
C
oupling
C
o
ef
f
i
ci
en
t
(
k
)
be
twee
n
unsym
m
e
trica
l
co
il
s
1
50
98.
37
52.
36
0
.
519
98.
37
10.
10
3
.
4
0
0.
108
2
100
98.
37
28.
95
0
.
286
98.
37
10.
10
1
.
9
5
0.
062
3
150
98.
37
16.
46
0
.
163
98.
37
10.
10
1
.
1
1
0.
035
(a)
(
b)
F
i
gure
2.
(
a)
D
esi
gn o
f
symm
e
tr
i
c
a
l
c
oils a
n
d
the
ir
m
a
g
n
e
t
i
c
fi
e
l
d
pa
tter
n
(
b) D
esign o
f
U
nsymm
e
trica
l
c
oi
ls
and t
h
e
i
r
ma
gnetic
f
ie
ld pa
t
tern
2.4.
An
al
ys
is of
S
S
an
d
SP
T
o
p
o
logy
M
odel
s
A
schem
a
t
i
c
d
i
a
g
ram
o
f
S
S
to
p
o
l
o
gy
usin
g
s
y
mm
etrica
l
co
i
l
s
is
s
h
o
w
n
i
n
F
i
gur
e
3.
I
ns
tea
d
o
f
in
duc
ta
nce
s
L
1
and L
2
, coi
l
s
truct
u
re
s
w
e
re inte
g
ra
ted i
n
circ
u
it.
S
S and
S
P
t
o
p
o
lo
g
y
ci
rc
uit
s
a
re
s
i
m
ul
at
ed
f
o
r
bo
th
s
ym
me
trical
a
nd
u
ns
ym
me
t
r
i
c
al
c
o
i
l
s
.
The
e
ffic
i
enc
y
i
n
ter
ms
o
f
P
out
/P
in
i
s
cal
c
u
l
a
t
e
d
at
t
h
r
ee
d
i
s
t
a
n
ces
50
m
m
,
100
m
m
,
a
nd
15
0
m
m
.
T
he
c
irc
u
it and
co
i
l
para
m
e
t
ers
u
s
e
d
f
or
s
im
ul
a
t
i
ons
a
re
g
i
v
e
n
in
Ta
b
l
e 3.
T
he
in
duc
ta
nce
of
c
oils
i
s
c
a
lc
u
l
a
t
ed
u
sin
g
F
EM
a
na
lys
i
s
an
d
o
t
he
r
par
a
m
e
te
r
values
a
re
e
x
t
rac
t
e
d
a
ccor
d
i
ng
to
the
gi
ve
n
va
l
u
e
o
f
freq
u
e
n
c
y
a
n
d
i
n
d
uc
t
a
nce.
T
he
r
e
s
o
n
ance
f
r
e
q
u
e
ncy
i
s
k
e
p
t
at
3
00
k
Hz.
An
a
l
ysi
s
i
s
perform
ed
f
or
m
ea
surin
g
p
o
w
er
i
npu
t
an
d
pow
er
o
u
t
pu
t
to
f
i
n
d
o
u
t
the
efficie
n
c
y
o
f
WPT
syste
m
a
t
t
h
re
e
di
ffe
re
nt d
is
ta
n
c
e
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
1
5
7
– 2
164
2
162
F
i
gure
3.
S
imula
t
i
on c
i
rcui
t o
f
S
S
top
o
lo
gy
mode
l
u
s
in
g
sy
m
m
e
tr
ica
l
c
oi
l
s
Ta
b
l
e 3.
Circu
i
t
S
im
ulat
io
n
pa
ra
me
ters use
d for
symm
etric
a
l
a
n
d
u
nsy
m
me
tri
c
al
c
oi
ls
P
a
ra
m
e
te
r
N
a
m
e
o
f
Symme
tr
ica
l
C
oils
Pa
r
a
m
e
t
e
r
Va
lu
e
o
f
S
y
mmetri
c
a
l
C
oils
P
a
r
a
met
e
r
N
a
me o
f
Unsymmet
r
ica
l
C
o
ils
P
a
ra
m
e
te
r
V
a
l
u
e
of
Unsymme
tr
ica
l
C
o
ils
U
S
A
m
p
lit
ude
10
V
U
S
A
m
p
litude
10
V
F
r
e
que
n
c
y
300
kH
z
C
1
2
.
84
nF
C
1
&
C
2
2.
84
n
F
C
2
28.
4
nF
R
S
a
nd R
L
50
Ω
R
S
a
nd
R
L
50
Ω
L
1
&
L
2
98.
37
µH
L
1
a
nd L2
98.
37
µH
a
nd
1
0
.
10
µH
R
1
&
R
2
0
.3
Ω
R
1
&
R
2
0
.3
Ω
3.
RESULT
S
A
N
D
ANALY
S
IS
The
si
m
u
la
t
i
on
r
esult
s
f
o
r
S
S
and
S
P
t
op
o
l
o
gy
m
o
del
s
f
or
t
hre
e
d
i
ffe
r
en
t
di
st
a
n
ces
u
si
n
g
sa
me
s
i
z
e
coi
l
s
are
g
i
ven
in
F
i
gure
5
(a)
.
W
hen
w
e
h
a
v
e
simu
la
te
d
v
a
lue
s
o
f
i
npu
t
pow
e
r
a
n
d
o
u
t
pu
t
pow
e
r
,
the
n
t
he
efficie
n
c
i
es
c
a
n
b
e
c
a
l
cu
la
te
d
by
(
8
)
an
d
(
20)
f
or
S
S
and
S
P
t
o
po
l
ogy
m
od
el
s.
T
h
e
e
f
f
i
c
i
e
n
c
i
e
s
of
S
S
com
p
en
sat
i
on
m
odel
a
t
5
0
mm,
100
mm,
a
nd
1
50
m
m
a
re
98%,
97%
a
n
d
9
3
%
,
r
espe
ct
i
v
e
l
y.
F
or
S
P
com
p
en
sat
i
o
n
m
odel,
t
he
e
ffi
c
ie
nc
ies
at
5
0
m
m
,
100
m
m
a
nd
1
5
0
m
m
a
r
e
72%,
38%
a
nd
5
3%,
re
spe
c
ti
ve
ly.
There
f
ore
,
f
or
t
he
s
am
e
si
z
e
c
oils,
i
t
i
s
ob
v
i
o
u
s
t
h
at
S
S
com
p
e
nsa
tio
n
to
pol
o
gy
pro
v
i
d
es
m
u
c
h
be
t
t
er
e
ffi
c
i
en
cy
t
h
a
n
S
P
t
o
pol
ogy
.
Th
e
si
mu
l
a
ti
on
re
su
lt
s
fo
r
b
o
th
t
o
p
o
l
og
ies
us
in
g
d
i
ffer
en
t
s
i
ze
c
oi
l
s
a
r
e
g
i
v
e
n
i
n
F
i
gure
4.
A
t
t
h
e
d
i
s
t
anc
e
of
5
0
mm
,
the
effic
i
enc
y
i
s
73%.
Wh
il
e
at
1
0
0
m
m,
a
nd
1
50
mm,
t
he
e
ff
i
c
i
e
ncie
s
a
r
e
3
6
%
a
nd
1
3
%
,
res
p
ec
ti
v
e
l
y
.
To
a
na
ly
z
e
t
h
e
ef
fi
ci
e
n
cy
o
f
SP
to
p
o
l
o
gy
m
odel usi
n
g tw
o di
ffe
re
nt c
o
ils,
the
corr
espo
n
d
in
g
efficie
n
c
i
e
s
a
t
50
m
m
,
100
m
m
a
nd
15
0
m
m
a
re
92%,
8
9%
a
n
d
71%
,
re
sp
e
c
ti
ve
l
y
.
There
f
ore
,
from
t
he
d
e
t
a
i
l
e
d
inve
s
tiga
t
i
on,
i
t
is
c
o
n
c
l
ude
d
t
h
a
t
w
he
n
d
i
ff
e
r
e
n
t
s
i
z
e
c
o
i
l
s
a
r
e
u
s
e
d
,
S
P
c
o
m
p
e
n
s
a
t
i
o
n
to
pol
o
gy
i
s
p
r
o
m
i
s
i
n
g
c
h
o
i
c
e
,
be
cause
it
g
i
ve
s
be
tter
effi
cienc
y
t
h
a
n
S
S
c
oun
t
e
rpar
t
.
T
ab
le
6
p
r
o
v
i
d
e
s
the
efficie
n
c
y
c
a
l
c
u
l
a
tio
ns
f
or
b
o
t
h
sym
m
e
t
rica
l
(sam
e
siz
e
)
and
u
n
s
y
m
m
e
t
r
i
c
a
l
(d
i
f
fer
e
n
t
s
ize
)
c
o
il
sim
u
la
tio
n
resul
t
s.
B
e
caus
e
only
re
sis
tive
load
i
s
used,
the
r
efore
o
n
ly
r
e
a
l
com
po
ne
n
t
of
p
o
w
e
r
is inc
lu
de
d.
F
r
om
T
able
4
,
i
t
i
s
ob
v
i
ous
t
ha
t
w
h
e
n
s
y
m
m
e
trica
l
c
o
i
l
s
i
.e
.
sa
m
e
s
ize
coils
for
tra
n
s
m
itt
e
r
and
rec
e
iver
a
re
u
t
i
l
i
ze
d
t
h
e
n
S
S
to
p
o
lo
gy
g
i
ves
m
u
ch
h
i
g
he
r
effici
en
c
y
a
t
all
th
re
e
di
s
t
a
n
ce
s
t
h
an
SP
t
o
po
log
y
.
Wh
i
l
e
b
y
u
sin
g
u
ns
ym
me
t
r
i
c
al
c
o
ils
i
.
e
.
when
t
r
a
nsmit
t
er
c
oi
l
i
s
big
g
e
r
t
han
rec
e
i
ver
c
o
i
l
,
t
h
e
S
P
t
op
olo
g
y
g
i
v
e
s
mu
c
h
b
e
t
t
e
r
e
f
fi
ci
e
n
c
y
t
h
a
n
SS
t
op
ol
og
y
at
a
l
l
t
h
r
e
e
d
i
st
an
ce
s.
T
h
e
ref
o
re,
t
h
e
s
e
r
e
sul
t
s
a
r
e
use
f
u
l
f
o
r
dec
i
d
i
n
g
t
he
d
e
s
ired
t
op
o
l
o
g
y
a
ccor
d
i
n
g
to
s
pe
cific
des
i
gn o
f
c
oi
ls,
i.e
.
s
ymm
e
trica
l
or
unsym
m
e
trica
l
Ta
b
l
e
4.
Effi
c
ie
ncy
com
p
ar
is
on o
f
b
oth
top
o
l
o
g
i
es
Dista
n
c
e
=5
0
mm
Dista
n
c
e
=1
0
0
mm
D
istan
c
e=1
5
0
mm
Ef
f
i
ci
e
n
cy
(
%
)
S
S
S
P
S
S
SP
SS
SP
S
y
mmet
r
i
c
a
l
C
oils
9
8
72
S
ymmetri
c
a
l
C
oils
9
7
38
S
ym
m
e
t
r
i
c
a
l
C
oils
9
3
53
Unsymme
tr
ica
l
C
o
ils
7
3
92
U
nsymmet
r
ica
l
C
o
ils
3
6
89
U
nsymme
tr
ic
a
l
C
o
ils
1
3
71
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
Ef
f
i
c
i
e
n
cy in
v
e
st
i
g
a
t
i
o
n
of
S
S
and SP
c
o
m
p
e
n
sa
ti
on to
po
l
o
gi
e
s
for wi
re
l
e
ss …
(M
a
s
o
od
Rehm
a
n
)
2
163
(a)
(b)
F
i
gure
4. Effic
i
e
nc
y re
sult u
s
i
ng S
S
a
nd S
P
c
om
pen
s
at
i
on (a
) S
y
m
m
e
t
r
i
c
a
l C
o
i
l
s
(b) U
n
sy
m
m
e
trica
l
C
o
i
l
s
4.
CONCL
U
S
ION
The
m
o
d
e
l
i
n
g
a
nd
in
ves
tiga
t
i
on
of
t
w
o
d
iff
e
re
nt
c
ircu
i
t
t
o
p
o
l
og
ies
f
o
r
W
P
T
syst
em
a
re
c
ar
ried
o
ut
by
c
i
rc
u
i
t
the
o
r
y
a
nd
s
i
m
u
l
a
tio
ns.
The
e
q
ua
tio
ns
o
f
p
o
w
e
r
t
r
ans
fe
r
e
f
fic
i
enc
y
i
n
term
s
of
c
ircui
t
p
ar
a
m
eters
and
der
i
va
ti
on
of
c
ur
ren
t
s
are
pr
esente
d.
T
he
e
ffects
of
v
ar
io
u
s
co
u
p
l
i
ng
c
o
effic
i
e
n
t
s
o
n
t
h
e
eff
i
c
i
e
n
cy
o
f
t
h
e
W
P
T
sy
st
e
m
a
re
a
l
s
o
an
al
y
z
e
d
.
It
i
s
con
f
i
r
me
d
t
h
at
w
ith
i
ncre
as
i
n
g
d
i
st
ance
b
et
we
en
t
ran
s
mit
t
er
a
n
d
rec
e
i
v
e
r
coi
l
,
the
c
o
up
li
ng
c
o
e
f
fic
i
e
n
t
is
d
ec
rea
s
in
g
ra
pid
l
y.
T
he
f
r
e
qu
e
n
c
y
s
p
l
it
tin
g
p
h
en
om
en
on
i
s
n
o
t
vis
i
ble
us
in
g
bo
th
t
he
t
o
pol
og
ies
a
t
a
ll
ca
l
c
ula
t
e
d
d
ist
a
nc
es.
There
f
ore
,
i
t
ca
n
be
e
x
t
r
acte
d
t
ha
t
sp
lit
ti
ng
fre
que
nc
y
c
a
n
b
e
miti
ga
te
d
us
in
g
S
S
a
nd
S
P
c
om
pen
s
at
i
on
t
o
p
o
l
o
g
y
w
i
t
h
i
n
cre
a
si
ng
c
oupl
ing
co
eff
i
ci
e
n
t
.
T
h
e
o
v
e
ral
l
resu
l
t
show
s
tha
t
t
ha
t
S
P
t
opo
l
o
g
y
m
odel
is
s
u
i
t
a
bl
e
w
h
e
n
T
x
size
b
ig
g
er
t
ha
n
Rx
s
i
z
e.
B
eca
use
t
h
e
SP
t
op
olo
g
y
gi
ves
m
u
c
h
b
e
tter
effi
c
i
e
n
c
y
t
ha
n
S
S
t
o
p
o
l
o
gy
w
h
e
n
t
w
o
d
iffer
e
n
t
s
i
ze
c
oi
ls
a
re
u
til
iz
e
d
.
SS
top
o
l
o
g
y
i
s
a
go
o
d
cho
ice
w
h
e
n
tw
o
sa
m
e
size
coi
l
s for
transm
itter
an
d
re
c
e
iv
er
ar
e
empl
o
ye
d
.
ACKNOW
LEDG
E
MEN
T
S
Th
e au
t
h
o
r
s wo
ul
d
l
i
k
e to
th
a
n
k
Uni
v
ersi
ti
Tek
nol
ogi
PETR
ONAS
f
o
r
p
ro
vid
i
ng
re
s
e
a
rc
h
f
und
t
o
carry
o
ut
t
his research.
REFE
RENCES
[1]
N.
Tesla, "A
pparat
u
s
f
o
r t
r
ansm
itt
in
g
el
ectri
cal en
e
rgy,
"
e
d
:
G
oo
gle
P
a
tent
s,
1
9
14.
[
2
]
S
.
Y.
R
.
Hu
i
,
W
. Z
ho
ng,
and
C
.
K
.
L
ee,
"A cr
i
t
i
c
al
r
ev
i
e
w
o
f
recent
p
r
ogres
s in mid-ran
g
e
w
i
rel
e
ss po
wer t
r
ansf
er,"
IEEE T
r
an
sa
c
tions
on
P
o
wer
Elect
ro
nics,
v
o
l
.
2
9,
n
o.
9
,
pp
.
45
00
-451
1,
2
0
14.
[3
]
D.
V
a
n
W
a
g
e
n
in
g
e
n
a
n
d
T.
S
ta
ring
,
"
T
he
Q
i
w
i
r
e
le
ss
p
owe
r
s
t
andard
,
"
i
n
Po
wer El
ectro
n
i
cs
an
d M
o
ti
on Co
ntrol
Co
nfe
r
e
n
c
e
(
E
P
E
/P
EM
C),
20
10
14
th
In
te
rn
a
tion
a
l
,
201
0,
p
p
.
S
15-25
-S
15
-3
2:
I
EE
E.
[4]
S
.
D
.
Barm
an
,
A.
W
.
Reza,
N
.
Ku
mar,
M
.
E
.
K
ari
m
,
and
A.
B
.
M
u
n
i
r,
"
Wi
rel
e
ss
pow
erin
g
by
m
agnet
i
c
reso
nan
t
cou
p
l
i
n
g
:
Recent tren
ds in
w
i
reles
s
p
ow
er tran
s
f
e
r
s
y
s
t
em
a
nd
i
ts
a
ppli
cation
s
,"
Re
ne
wa
ble
an
d S
u
sta
i
na
b
l
e
En
e
r
g
y
Revi
ews,
vo
l. 51
,
p
p. 1
52
5-1
5
5
2
,
2
01
5.
[5]
B.
L
.
Cann
on
,
J.
F
.
Ho
bu
rg
,
D.
D
.
St
ancil,
a
nd
S
.
C.
G
ol
d
s
t
e
i
n
,
"
M
a
g
n
eti
c
r
es
on
ant
co
uplin
g
as
a
p
o
t
ential
m
ean
s
f
o
r
wireles
s
p
ow
er
t
rans
fer
t
o
m
ul
t
i
p
l
e
sm
al
l
re
cei
vers
,"
IE
EE
Transaction
s
on
Power Elect
ron
i
c
s
,
vo
l.
2
4,
n
o.
7
,
pp
.
1
81
9-18
25
, 2
00
9.
[6]
D.
V
il
a
t
h
g
am
u
w
a
an
d
J.
S
am
pa
t
h
,
"Wi
r
eless
Power
Tran
sf
er
(
W
PT
)
f
o
r
Elect
ri
c
Vehi
cles
(
EVs
)
—P
res
e
nt
a
nd
Fut
u
re
T
rends,"
i
n
P
l
u
g
In
El
ectric V
e
h
i
cl
es
i
n
S
m
a
r
t G
r
ids
:
S
p
ring
er,
20
15
,
pp
.
33-6
0
.
[7]
C.
E
.
Greene,
D
.
W
.
H
arri
s
t
,
and
M.
T
.
Mc
Elhi
nny,
"
Poweri
ng
cell
p
h
o
n
es
a
nd
s
i
m
ilar
d
e
vices
u
s
i
n
g
R
F
energ
y
harv
est
i
n
g
,
"
e
d: G
oog
le
P
a
t
ent
s
,
200
7.
[8]
A.
K
urs
,
A
.
Karal
i
s,
R
.
M
o
ff
att,
J
.
D.
J
oan
nopou
lo
s,
P
.
Fis
her,
a
nd
M
.
S
o
lj
ačić,
"
Wirel
e
ss
p
o
w
e
r
t
r
ansf
er
v
ia
st
ron
g
l
y
co
u
p
l
ed
m
ag
netic res
on
ances,
"
s
c
ien
ce,
vo
l.
3
1
7
,
n
o
.
5
8
34,
p
p
.
8
3-8
6
,
2
007.
[9
]
A.
P
.
Samp
l
e
,
D.
T
.
Me
yer,
a
n
d
J.
R
.
S
m
it
h
,
"
An
al
y
s
i
s
,
exp
e
rimen
t
al
r
esults,
and
ran
g
e
ad
ap
tati
on
o
f
m
agn
e
ti
cally
cou
p
l
e
d
res
onat
o
rs
f
or
w
ireles
s
p
o
w
e
r
transf
er,"
IEEE
T
r
a
n
s
a
ct
ion
s
o
n
In
du
s
t
rial Elect
ro
n
i
cs,
v
o
l
.
58,
no.
2
,
pp
.
5
4
4
-
55
4, 2
01
1.
[10
]
J
.
W
a
ng
,
S
.
H
o
,
W
.
F
u
,
an
d
M.
S
u
n
,
"An
a
ly
t
i
cal
d
esi
gn
stud
y
o
f
a
nov
el
w
i
t
ri
city
c
harger
w
i
t
h
l
a
teral
and
an
gu
lar
m
i
s
a
l
i
gnments
for
ef
fi
cient
wireles
s
e
nergy
trans
m
is
s
i
on
,
"
IEE
E
Tran
sac
t
io
ns o
n
M
a
gn
e
t
ic
s,
vo
l
.
4
7
,
no.
10,
pp.
2
6
1
6
-2
61
9, 2
01
1.
[11
]
K
.
F
o
t
o
p
o
u
l
ou
a
n
d
B
.
W
.
F
l
ynn,
"
W
i
reles
s
power
t
ransf
e
r
in
l
oos
ely
cou
p
l
e
d
links
:
Coil
mi
sa
l
i
g
n
m
e
nt
m
od
el,
"
IEEE T
r
an
sa
c
tions
on
M
a
g
n
e
ti
cs,
v
o
l
. 47
,
n
o
. 2
,
p
p
. 41
6
-
43
0,
20
1
1.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
I
nt
J
P
ow
Elec
& Dr
i
S
y
st V
ol.
10,
N
o.
4
, Dec
201
9 :
2
1
5
7
– 2
164
2
164
[1
2]
S
.
Cheo
n,
Y
.-
H.
K
im,
S
.
-Y
.
Kang
,
M.
L
.
Lee,
J
.-
M.
L
ee,
a
n
d
T.
Zy
ung
,
"Circu
it
-m
odel
-
bas
e
d
an
a
l
ysis
o
f
a
w
i
reless
energ
y
-t
ransf
e
r
sys
t
e
m
v
ia
c
o
u
p
l
ed
m
agn
e
tic
reson
a
nces
,"
IEE
E
T
r
ans
actio
ns on Ind
u
s
t
r
i
al
Electr
o
n
i
cs
,
vo
l
.
5
8
,
no
.
7
,
p
p
.
2
9
0
6
-2
91
4,
2
01
1.
[13
]
Y
.
Zh
ang
,
Z
.
Zhao
,
an
d
K
.
C
hen,
"
F
r
eq
uen
c
y
d
ecre
a
se
a
n
a
ly
s
is
o
f
resonant
w
irel
ess
power
tr
ans
f
er,"
IE
E
E
Tr
an
sa
c
tio
ns
o
n
P
o
w
e
r
E
l
e
c
t
ro
ni
c
s
,
vol.
29
,
no
.
3,
p
p.
1
05
8-1
063
,
2
0
1
4
.
[
1
4
]
R
.
H
u
a
n
g
,
B
.
Z
h
a
n
g
,
D
.
Q
i
u
,
a
n
d
Y
.
Z
h
a
n
g
,
"
F
r
e
q
u
e
n
c
y
s
p
l
i
t
ti
ng
p
h
e
nom
en
a
of
m
ag
neti
c
reso
nant
c
ou
pl
in
g
wi
reless pow
e
r
transf
er,"
IEE
E
Tr
an
sactio
ns on
M
a
g
n
e
ti
cs,
vo
l.
5
0
, no
. 1
1,
p
p.
1
-4
,
2
0
1
4
.
[
1
5
]
W
.
Z
h
a
n
g
,
S
.
-
C
.
W
o
n
g
,
K
.
T
.
C
h
i
,
a
n
d
Q
.
J
.
I
.
T
.
o
.
P
.
E
.
Ch
en,
"A
naly
s
i
s
and
co
m
p
ariso
n
o
f
seco
ndary
s
eries-an
d
paral
l
el
-com
pen
s
at
e
d
i
nd
ucti
ve
p
o
w
er
t
ransfer
sy
st
e
m
s
o
p
erating
f
or
opti
m
a
l
e
f
f
i
c
iency
an
d
load
-in
d
epen
den
t
vo
lt
age-t
r
an
sf
er rat
io
,
"
vol.
2
9
,
n
o
.
6
,
pp
.
2
9
7
9
-2990
,
2
01
3.
[1
6]
X
.
Qu
,
H.
H
an,
S
.
-C.
W
o
ng
,
K.
T
.
Ch
i
,
a
n
d
W.
J
.
I.
T
.
o.
p
.
e
.
C
h
e
n
,
"
Hy
brid
I
PT
t
op
olog
ie
s
w
i
th
c
o
n
sta
n
t
c
u
rre
nt
o
r
c
o
n
s
ta
nt
vo
lta
ge
o
utpu
t
fo
r ba
t
t
e
r
y c
h
a
r
ging
a
p
p
l
ic
a
tio
ns
,"
v
o
l.
3
0,
n
o.
1
1
,
p
p
.
632
9-6
337
,
2
01
5.
[17]
R
.
B
o
s
s
hard
et al
.
,
"M
od
eli
ng
and
$
\
eta
$-$\al
p
h
a
$-P
a
reto
O
ptimizatio
n
of
I
n
d
uct
iv
e
P
o
w
e
r
T
r
ansf
er
C
o
i
l
s
f
or
El
ectr
i
c Vehic
l
es," v
ol
.
3
,
n
o
.
1
,
p
p
. 5
0-6
4
,
20
1
4
.
[1
8]
S
.
Liu,
L
.
C
hen
,
Y
.
Z
h
ou
,
an
d
T.
J
.
J
.
I
.
j.
o
.
e.
C
u
i
,
"A
g
eneral th
e
o
r
y to anal
y
se a
nd
d
es
ig
n
w
i
rele
s
s
pow
er
t
ra
n
s
f
e
r
bas
e
d
o
n
i
m
p
ed
ance
m
a
tch
i
n
g
,
"
vol
.
10
1,
n
o
.
1
0,
pp.
1
3
75-1
4
0
4
,
2
0
14.
[19
]
M
.
Rehm
an,
Z.
B
ah
aru
d
i
n
,
P
.
N
al
lago
wn
den,
B
.
J.
I
.
J
.
o
.
E
.
E.
I
sl
am
,
an
d
C.
S
cience,
"
M
o
del
ling
and
Eff
i
c
i
en
cy-
An
aly
s
i
s
of Wi
reless
P
ower Tra
n
s
f
e
r usi
ng M
a
g
n
e
t
ic Res
on
ance Co
upl
in
g
,
"
v
o
l.
6,
no
.
3
,
p
p
.
5
63-57
1,
2
01
7.
[20
]
M
.
Rehm
an,
Z
.
B
ah
arudi
n,
P
.
N
a
l
l
ag
own
d
en
,
B.
I
s
l
am,
and
M
.
U
.
J.
I
.
Rehm
an,
"
M
o
d
eli
n
g
an
d
anal
ysi
s
o
f
seri
es-
seri
es
a
nd
seri
es-paral
lel
com
b
ined
t
op
ol
og
y
f
o
r
w
i
reless
po
wer
t
ransfer
using
M
u
ltiple
c
ou
pli
ng
coef
fi
c
i
ents,"
vol
.
17
,
n
o.
11,
p
.
114,
201
7.
[21]
T
.
Li
n
lin,
Q.
H
ao,
H.
X
uel
i
ang,
C
.
W
e
ijie,
and
S.
J
.
T
.
I
.
J
.
o
.
E
.
E.
W
en
hui,
"
A
n
ov
el
o
pt
im
iza
t
io
n
m
e
an
s
o
f
tran
s
f
er effi
ciency
f
or
r
e
s
on
ance co
up
led
wire
l
e
ss po
wer t
r
ans
f
er,
"
vo
l
. 11
,
n
o
.
5
,
p
p
. 2
74
7-2
7
5
2
,
2
0
1
3
.
[22
]
L
.
J
.
J
.
T.
I
.
J.
o
.
E
.
E
.
Y
u
,
"
F
i
n
i
t
e
elem
ent
an
a
l
ysis
o
f
a
c
o
n
t
actless
po
wer
t
r
ansf
orm
e
r
w
i
th
m
et
amaterial
,
"
vo
l.
1
2
,
no
.
1
,
p
p
.
6
7
8
-
6
8
4,
201
4.
[2
3]
D
.
Z
h
ao
,
E
.
D
i
n
g
,
Y
.
Hu
,
an
d
Z
.
J
.
T
.
I
.
J
.
o
.
E
.
E
.
Su
n
,
"
D
esig
n
and
S
i
m
u
la
tio
n
of
M
ulti
ple
Coi
l
M
od
el
f
or
Wi
reless Power T
r
a
n
smi
s
sion
Sy
s
tem,
"
vo
l. 12
, n
o
.
6
,
p
p
. 4
16
6-4
17
7
,
2
01
4.
[2
4]
C
.
K.
H
.
C
.
K
.
Yah
a
ya,
S.
F
.
S
.
A
d
n
an
,
M.
K
as
si
m,
R
.
A.
R
a
hman
,
M.
F
.
B
.
J
.
I.
J
.
o
.
E
.
E
.
R
u
s
d
i
,
and
C.
S
ci
en
ce,
"An
a
l
y
s
i
s o
f
Wirel
ess
P
o
w
e
r
Tra
n
s
f
er on th
e Ind
u
ct
iv
e Cou
p
l
i
ng
Reso
nan
t
,
"
v
ol.
12
,
n
o.
2
,
p
p
.
592-5
99,
2
0
1
8
.
[25]
X
.
Shi
et a
l
.
,
"Eff
ects
of
c
o
i
l
shap
es
o
n
w
i
reles
s
p
o
w
er
t
ran
s
fer
via
m
a
gn
et
i
c
r
es
on
a
n
ce
c
o
u
p
l
i
n
g
,
"
J
o
urna
l o
f
El
ectr
o
m
agn
eti
c
W
a
ves
and
Applications,
v
o
l
. 2
8,
no
. 11
,
p
p
. 1
31
6
-
1
3
2
4
, 2
01
4.
[26
]
M
.
M
c
Don
o
u
g
h
an
d
B.
F
ahimi,
"
Com
p
ari
s
o
n
b
et
ween
c
ircu
lar
a
nd
sq
uare
c
oils
f
or
u
s
e
i
n
Wi
re
l
e
ss
P
ower
Tran
smi
s
si
on,
"
20
14
.
BIOGRA
P
HI
ES
O
F A
U
THO
R
S
M
a
so
od
R
eh
man
rec
e
iv
ed
t
h
e
B
achel
or
o
f
E
ngi
neeri
n
g
Deg
r
ee
i
n
El
ect
ri
cal
T
e
c
hn
ol
og
y
fro
m
Q
u
aid
-
e-Awam
Un
iv
ersit
y
o
f
En
gin
eerin
g,
S
cien
ce
&
T
echn
o
lo
gy
(
Q
.U
.E.S
.T)
Na
wab
s
h
a
h
,
P
a
k
i
s
t
an
i
n
20
0
6
.
M
.
S
c
.
d
e
gree
i
n
E
lectri
cal
&
E
lect
roni
c
En
gi
n
eeri
n
g
,
f
rom
U
n
i
v
ersitä
t
D
u
is
bu
rg-E
ssen
,
Germ
any
,
i
n
20
13
.
H
e
w
orke
d
as
a
n
E
l
ectrical
E
n
gin
eer
w
it
h
SIEM
EN
S
,
P
a
k
i
s
t
an
a
nd
K
-El
ectri
c
K
a
rachi,
P
ak
is
tan
.
C
u
r
rentl
y
,
h
e
i
s
a
s
tudying
PhD
in
E
lectrical
a
nd
E
l
ectro
n
i
cs E
ng
in
e
e
ri
ng
at U
n
i
v
e
r
s
i
t
i
T
eknolo
g
i PET
R
ONAS
, M
a
lay
si
a.
P
e
rum
a
l
Nallagowan
den
is
w
ork
i
n
g
a
s
an
a
s
s
o
c
i
a
te
p
rof
e
ss
or
i
n
t
he
E
lect
rical
&
E
lect
roni
c
E
ngi
neeri
n
g
Dep
a
rtm
e
nt
i
n
Univ
ersiti
Tek
n
o
l
ogi
P
ET
RONA
S.
H
e
rec
ei
ved
hi
s
P
h
.D
.
from
U
n
iv
ersi
ty
o
f
Wal
e
s,
UK.
H
is
e
xp
erien
ce
in
clu
d
es
P
ol
y
t
ecnic
U
n
g
k
u
O
m
a
r,
C
onso
Lig
ht
S
dn
Bh
d
and
U
n
iv
er
siti
T
ekno
lo
g
i
P
E
T
RON
A
S
.
H
is
s
pecial
a
re
as
o
f
i
n
t
eres
t
are
e
l
ectri
cal
p
o
w
er
syste
m
,
dere
gulated
op
eration
of
p
ower
s
yste
m,
p
ower
quality
a
n
d
ren
e
wabl
e
energ
y
(T
idal
en
ergy).
He
h
as
p
ub
lished
m
a
n
y
r
esearch
p
ap
ers.
H
e
is
a
m
em
b
e
r
of
t
he
I
nstitu
t
io
n
of
E
n
g
i
n
e
e
r
s
Ma
la
ysia
a
n
d
i
s
a
pro
f
e
ssion
a
l
e
ng
in
ee
r
registered
with th
e
Boa
rd
of
E
ngin
eers
M
a
lay
s
i
a
Z
uhai
r
i
Baharu
din
recei
ved
h
i
s
Ph
.D.
deg
r
ee
f
r
o
m
U
niv
e
rsi
t
i
T
e
k
no
lo
gi
P
E
T
RO
N
A
S,
M
alay
si
a,
in
2
01
0.
C
u
rre
n
tly,
h
e
i
s
a
n
Ass
oc
ia
te
P
ro
fe
sso
r
i
n
the
de
p
a
rtm
e
n
t
of
E
lect
rical
a
n
d
E
l
ectronics
E
ngi
neeri
ng.
H
e
i
s
v
ery
comm
it
ted
to
h
is
l
ect
u
r
es
a
n
d
a
l
s
o
ac
ti
v
e
ly
doing
r
ese
a
rch
.
H
e
has
pu
bli
s
h
e
d
ma
n
y
p
a
p
e
r
s
in
t
h
e
a
re
a
of
p
owe
r
s
y
s
te
m
s
a
nd
c
o
mmu
n
i
c
ati
o
n
s
t
echn
o
l
ogy
.
His
res
earch
i
nt
erests
i
n
c
lud
e
f
o
r
ecastin
g,
e
m
p
i
r
ical
m
od
eli
n
g
,
r
en
ewab
le
e
nerg
y,
p
o
w
er
q
u
a
lit
y
and
h
a
rmo
n
i
c
s
t
udies, artif
ic
i
a
l i
n
t
e
ll
igen
ce app
l
i
cations
and
comm
u
n
icatio
n techn
o
l
o
g
i
es.
Evaluation Warning : The document was created with Spire.PDF for Python.