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a
v
e
a
t
te
m
p
t
e
d
t
o
a
d
d
r
e
s
s
t
h
is
d
r
a
w
b
a
c
k
.
Pre
v
i
ous
s
tu
d
y
[
1
6
]
,
an
im
p
r
o
v
ed
C
lass
-
E
co
n
f
ig
u
r
atio
n
i
s
d
esig
n
ed
to
m
ain
tain
a
s
ta
b
le
o
u
tp
u
t
cu
r
r
en
t
an
d
m
ain
tain
Z
VS
u
n
d
er
v
ar
y
in
g
lo
ad
s
.
Ho
wev
e
r
,
th
e
im
p
ac
t
o
f
m
ag
n
etic
co
u
p
lin
g
v
ar
iatio
n
s
was
n
o
t
ad
d
r
ess
ed
.
Pre
v
iew
s
tu
d
y
[
1
7
]
,
a
C
las
s
-
E
co
n
f
ig
u
r
atio
n
to
ler
an
t
to
lo
ad
v
ar
iatio
n
s
an
d
eq
u
ip
p
ed
with
p
ar
allel
r
eso
n
an
ce
en
a
b
les
ze
r
o
-
v
o
ltag
e
s
witch
in
g
b
y
en
s
u
r
i
n
g
s
witch
v
o
ltag
e
f
alls
to
ze
r
o
b
ef
o
r
e
tu
r
n
-
o
n
,
r
e
g
ar
d
less
o
f
lo
ad
v
ar
iatio
n
s
.
Pre
v
iew
s
tu
d
y
[
1
8
]
,
Z
VS
is
ac
h
iev
ed
u
s
in
g
a
C
lass
-
E
²
s
tr
u
ctu
r
e
with
th
r
ee
in
d
u
ct
o
r
s
in
a
p
u
s
h
–
p
u
ll
ar
r
an
g
em
en
t
a
n
d
L
C
C
-
S
tan
k
,
en
ab
lin
g
wid
e
-
r
an
g
e
lo
ad
-
in
d
e
p
en
d
e
n
t
s
witch
in
g
with
o
u
t
ac
tiv
e
f
ee
d
b
ac
k
.
I
n
[
1
9
]
,
[
2
0
]
,
an
i
n
tr
o
d
u
ctio
n
to
a
C
lass
-
E
c
o
n
v
er
ter
is
p
r
o
v
id
ed
,
d
esig
n
ed
to
ad
d
r
ess
th
e
h
i
g
h
v
o
ltag
e
s
tr
ess
is
s
u
e
s
in
th
e
W
PT
s
y
s
tem
s
.
B
y
in
co
r
p
o
r
ati
n
g
a
s
u
p
p
lem
e
n
tar
y
cir
c
u
it
in
to
th
e
co
n
v
e
r
ter
,
th
e
in
tr
o
d
u
ce
d
to
p
o
lo
g
y
s
ig
n
if
ica
n
tly
r
ed
u
ce
s
v
o
ltag
e
s
tr
ess
an
d
s
witch
in
g
lo
s
s
es,
wh
ile
also
ac
h
iev
in
g
z
er
o
-
v
o
ltag
e
s
witch
in
g
(
Z
VS)
co
n
d
itio
n
s
to
en
s
u
r
e
ef
f
icien
t
p
o
wer
tr
an
s
f
er
.
He
an
d
Gu
o
[
2
1
]
p
r
o
p
o
s
ed
u
s
in
g
im
p
ed
an
ce
m
atc
h
in
g
an
d
a
s
e
ar
ch
in
g
alg
o
r
ith
m
to
co
m
b
i
n
e
a
s
er
ies/
p
ar
allel
ca
p
ac
ito
r
ar
r
a
y
to
tu
n
e
th
e
C
lass
-
E
in
v
er
ter
o
p
er
atio
n
,
b
r
in
g
in
g
it
b
ac
k
to
th
e
o
p
tim
al
s
tate
f
o
r
d
if
f
er
en
t
c
o
il
d
is
tan
ce
s
.
As
well
as
[
2
2
]
,
t
h
is
p
ap
er
p
r
o
p
o
s
ed
a
tu
n
in
g
m
eth
o
d
b
y
ad
j
u
s
tin
g
th
e
p
h
ase
an
g
le
o
f
th
e
s
er
ies
r
eso
n
an
t
b
r
an
c
h
with
p
u
ls
e
wid
th
mod
u
latio
n
ca
p
a
cito
r
o
n
th
e
t
r
an
s
m
itter
s
id
e.
Ah
m
ad
i
et
a
l.
[
2
3
]
in
tr
o
d
u
ce
d
a
m
eth
o
d
f
o
r
ac
h
iev
in
g
Z
VS
in
C
las
s
-
E
in
v
er
ter
s
f
o
r
t
h
e
W
PT
s
y
s
tem
s
u
tili
zin
g
s
er
ies
-
s
er
ies
co
m
p
en
s
atio
n
.
T
h
is
is
ac
co
m
p
lis
h
ed
b
y
co
n
n
ec
tin
g
a
co
m
p
en
s
atio
n
s
witch
ac
r
o
s
s
th
e
s
ec
o
n
d
a
r
y
s
i
d
e
ca
p
ac
ito
r
.
B
y
co
n
tr
o
llin
g
th
e
ON/OFF
s
tate
o
f
th
is
s
witch
,
th
e
s
ec
o
n
d
ar
y
cir
cu
it
p
ar
am
eter
s
ca
n
b
e
v
ar
ie
d
to
s
atis
f
y
th
e
Z
VS
c
o
n
d
itio
n
.
As
well
as,
in
[
2
4
]
u
s
ed
r
ec
o
n
f
ig
u
r
atio
n
o
f
th
e
r
ec
eiv
er
cir
cu
it
b
y
a
s
witch
ed
-
ca
p
ac
ito
r
t
o
ac
h
iev
e
th
e
Z
V
S
co
n
d
itio
n
u
n
d
er
v
ar
iatio
n
o
f
lo
a
d
.
T
h
e
r
esu
lt
i
n
[
25
]
,
a
m
o
d
if
ied
PS
O
-
b
as
ed
m
eth
o
d
was
p
r
o
p
o
s
ed
f
o
r
d
esig
n
in
g
C
lass
-
E
s
witch
in
g
cir
cu
its
.
W
h
ile
W
P
T
is
n
o
ted
as
a
p
o
te
n
tial
ap
p
li
ca
tio
n
,
th
e
m
eth
o
d
is
n
o
t
im
p
l
em
en
ted
in
a
W
PT
s
y
s
tem
.
Z
VS
in
a
n
in
v
er
ter
b
ased
o
n
C
lass
-
E
to
p
o
l
o
g
y
a
p
p
lied
to
C
W
PT
ca
n
b
e
r
ea
l
ized
b
y
tu
n
in
g
L
C
r
eso
n
an
t
co
m
p
o
n
en
ts
an
d
co
m
p
en
s
atin
g
lo
ad
r
ea
ctan
ce
with
ex
ter
n
al
in
d
u
cto
r
s
o
r
ca
p
ac
ito
r
s
[
26
]
.
Ho
wev
er
,
th
e
s
tu
d
y
d
o
es
n
o
t
ad
d
r
ess
I
PT
s
y
s
tem
s
.
A
n
o
f
f
-
n
o
m
in
al
C
l
ass
-
E
am
p
lific
atio
n
was
u
til
iz
ed
to
attain
Z
VS
b
y
allo
win
g
a
n
o
n
ze
r
o
v
o
ltag
e
s
l
o
p
e
at
t
u
r
n
-
on
[
27
]
.
Ho
we
v
er
,
th
e
m
et
h
o
d
was
n
o
t
ap
p
lied
to
wir
eless
p
o
wer
tr
an
s
f
er
.
A
C
lass
-
E
-
b
ased
W
PT
co
n
f
ig
u
r
atio
n
in
s
en
s
itiv
e
to
lo
ad
v
ar
iatio
n
s
was
in
tr
o
d
u
ce
d
to
en
ab
le
ze
r
o
-
v
o
ltag
e
s
witch
in
g
with
o
u
t
c
o
n
tr
o
l,
u
s
in
g
d
u
al
-
r
eso
n
an
ce
a
n
d
co
n
s
tan
t
r
ea
cta
n
ce
v
ia
p
r
o
p
er
r
ec
eiv
er
t
u
n
in
g
an
d
C
lass
-
D
r
ec
t
if
icatio
n
[
2
8
]
.
T
h
e
m
eth
o
d
was
v
alid
ated
in
a
m
u
ltih
o
p
r
o
b
o
tic
ar
m
s
y
s
tem
.
A
n
in
v
er
ter
b
ased
o
n
C
lass
-
E
to
p
o
l
o
g
y
,
a
lo
n
g
with
a
C
lass
-
DE
r
ec
tific
atio
n
s
tag
e,
was
u
tili
ze
d
in
d
ev
elo
p
in
g
a
W
PT
s
y
s
tem
f
o
r
b
io
m
e
d
ical
im
p
lan
t
s
,
with
Z
VS a
ch
iev
ed
th
r
o
u
g
h
cir
cu
it d
esig
n
[
2
9
]
.
I
n
[
1
6
]
-
[
2
4
]
,
ac
h
iev
in
g
Z
VS
co
n
d
itio
n
s
r
elies
o
n
cir
c
u
it
r
ec
o
n
f
ig
u
r
atio
n
o
r
th
e
ad
d
itio
n
o
f
ex
t
r
a
co
m
p
o
n
en
ts
.
I
n
co
n
tr
ast,
[
2
5
]
-
[
2
9
]
ac
h
iev
e
Z
VS
th
r
o
u
g
h
in
h
e
r
en
t
d
esig
n
ap
p
r
o
ac
h
es.
Ho
wev
er
,
co
m
p
r
eh
e
n
s
iv
e
d
esig
n
g
u
id
eli
n
es
f
o
r
e
n
s
u
r
in
g
Z
VS
in
wir
el
ess
p
o
wer
tr
an
s
f
er
a
p
p
licatio
n
s
,
esp
ec
ially
u
n
d
er
co
il
m
is
alig
n
m
en
t,
r
em
ain
lim
ited
.
T
h
is
p
ap
er
a
d
d
r
ess
es
th
is
g
ap
b
y
p
r
esen
tin
g
a
d
etailed
an
aly
s
is
an
d
d
esig
n
m
eth
o
d
o
l
o
g
y
f
o
r
C
lass
-
E
in
v
er
ter
s
in
W
PT
s
y
s
tem
s
,
en
s
u
r
in
g
r
eliab
le
Z
VS
o
p
er
atio
n
u
n
d
er
m
is
alig
n
m
en
t
with
o
u
t
ad
d
itio
n
al
t
u
n
in
g
o
r
co
n
tr
o
l.
T
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
e
m
p
lo
y
s
th
e
m
ax
im
u
m
ex
p
ec
te
d
c
o
u
p
lin
g
co
ef
f
icien
t a
s
a
k
ey
d
esig
n
p
ar
am
eter
an
d
is
v
alid
ated
th
r
o
u
g
h
b
o
th
s
im
u
latio
n
an
d
ex
p
e
r
im
en
tal
r
esu
lts
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
is
p
ap
er
b
e
g
in
s
with
an
o
v
er
v
iew
o
f
m
et
h
o
d
s
an
d
d
esig
n
ap
p
r
o
ac
h
es
i
n
s
ec
tio
n
2
,
f
o
llo
wed
b
y
v
alid
atio
n
th
r
o
u
g
h
s
im
u
latio
n
s
an
d
ex
p
er
im
e
n
ts
in
s
ec
tio
n
3
,
f
o
llo
wed
b
y
co
n
clu
d
in
g
in
s
ig
h
ts
d
is
cu
s
s
ed
in
s
ec
tio
n
4
.
2.
M
E
T
H
O
D
T
h
is
s
ec
tio
n
p
r
esen
ts
an
in
-
d
e
p
th
an
aly
s
is
of
a
s
y
s
tem
f
o
r
w
ir
eless
p
o
wer
d
eliv
er
y
i
n
teg
r
at
ed
with
a
C
las
s
-
E
to
p
o
lo
g
y
.
T
h
e
f
o
cu
s
is
o
n
id
en
tify
in
g
th
e
r
eg
i
o
n
s
o
f
ze
r
o
v
o
ltag
e
an
d
n
o
n
-
ze
r
o
v
o
ltag
e
b
ased
o
n
th
e
m
ag
n
etic
co
u
p
lin
g
co
ef
f
icien
t
,
d
er
iv
in
g
co
m
p
o
n
en
t
d
esig
n
eq
u
atio
n
s
,
p
r
o
v
id
in
g
a
d
em
o
n
s
tr
ativ
e
d
esig
n
ca
s
e
s
tu
d
y
,
an
d
elu
cid
atin
g
t
h
e
v
ar
i
o
u
s
o
p
er
atio
n
al
m
o
d
es o
f
th
e
s
y
s
tem
.
2
.
1
.
Circ
uit
a
na
ly
s
is
T
h
is
s
ec
tio
n
an
aly
ze
s
th
e
im
p
ed
an
ce
b
eh
av
io
r
with
in
a
W
PT
ar
r
an
g
em
en
t,
em
p
h
a
s
izin
g
th
e
r
elatio
n
s
h
ip
b
etwe
en
im
p
e
d
an
ce
p
h
ase
an
g
le
an
d
m
ag
n
etic
c
o
u
p
lin
g
c
o
ef
f
icien
t,
e
n
ab
lin
g
th
e
id
en
tific
atio
n
o
f
Z
VS
an
d
n
o
n
-
Z
VS
co
n
d
itio
n
s
.
Z
VS
is
cr
u
cial
f
o
r
r
ed
u
cin
g
s
witch
in
g
lo
s
s
es
an
d
en
h
an
ci
n
g
s
y
s
tem
ef
f
icien
cy
.
T
h
is
an
aly
s
is
p
r
o
v
id
es
v
alu
ab
le
in
s
ig
h
ts
f
o
r
d
eter
m
i
n
in
g
o
p
tim
al
d
esig
n
p
ar
am
eter
s
.
T
h
e
ass
u
m
p
tio
n
s
u
n
d
er
ly
i
n
g
th
e
ci
r
cu
it a
n
aly
s
is
in
th
is
s
ec
tio
n
ar
e
as f
o
llo
ws:
-
A
s
witch
o
p
er
ates a
t a
d
u
ty
c
y
cle
o
f
0
.
5
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
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h
e
s
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h
as a
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o
-
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r
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-
o
n
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esis
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-
T
h
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n
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t
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etwo
r
k
h
as
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f
f
icien
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h
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u
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ac
to
r
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r
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g
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e
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r
r
e
n
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th
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h
e
W
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s
in
u
s
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al.
-
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e
lar
g
e
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n
d
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r
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e
n
t
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p
p
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t
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e
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a
n
d
t
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c
h
o
k
e
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d
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esis
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is
r
eg
ar
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.
-
T
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e
ch
o
k
e
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r
'
s
s
elf
-
ca
p
ac
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an
d
p
ar
asit
ic
ca
p
ac
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ce
ar
e
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clu
d
ed
in
th
e
s
h
u
n
t
ca
p
ac
itan
ce
o
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e
s
witch
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2
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1
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1
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Cla
s
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ed
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po
wer
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ra
ns
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er
s
y
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t
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Fig
u
r
e
1
(
a)
illu
s
tr
ates
a
ty
p
ic
al
C
lass
-
E
r
eso
n
an
t
in
v
er
ter
c
ir
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it.
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ts
co
m
p
o
n
en
ts
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e
DC
in
p
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ltag
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V
1
)
,
a
ch
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e
i
n
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r
(
L
f
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a
n
d
a
n
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tr
o
n
ic
s
witch
(
S).
Par
allel
to
t
h
e
s
witch
is
a
s
h
u
n
t
ca
p
ac
ita
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ce
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1
)
,
wh
ich
in
co
r
p
o
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ates
b
o
th
th
e
s
tr
ay
ca
p
ac
itan
ce
o
f
th
e
s
witch
in
g
d
ev
ice
an
d
th
e
in
tr
in
s
ic
ca
p
ac
itan
ce
f
o
r
th
e
ch
o
k
e
in
d
u
ct
o
r
.
T
h
e
in
d
u
c
tan
ce
L
0
f
o
r
m
s
a
s
er
ies
p
ath
alo
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g
s
id
e
r
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n
a
n
t
ca
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ito
r
C
₀
an
d
lo
ad
r
esis
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ce
R
,
f
o
r
m
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g
a
r
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t
n
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k
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at
s
atis
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ies
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e
r
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n
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ce
co
n
d
itio
n
.
T
o
a
p
p
ly
th
e
in
v
e
r
ter
with
t
h
e
W
PT
s
y
s
tem
,
th
e
r
esis
tiv
e
lo
ad
(
R
)
i
n
Fig
u
r
e
1
(
a
)
is
r
ep
lace
d
b
y
t
h
e
wir
eless
p
o
wer
s
y
s
tem
,
d
ep
icted
in
Fig
u
r
e
1
(
b
)
.
T
h
e
co
m
p
o
n
en
ts
o
f
W
PT
cir
cu
it
in
clu
d
e
p
r
im
ar
y
in
d
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c
e
(
L
P
)
an
d
s
ec
o
n
d
ar
y
in
d
u
cta
n
ce
(
L
S
)
o
f
th
e
co
il,
a
s
ec
o
n
d
ar
y
ca
p
ac
ita
n
ce
(
C
S
)
u
s
ed
to
ca
n
ce
l
th
e
s
ec
o
n
d
ar
y
leak
ag
e
in
d
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ctan
ce
u
n
d
er
r
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n
an
t
co
n
d
itio
n
s
,
d
io
d
es
(
D
1
-
D
4
)
ac
tin
g
as
a
r
ec
tifie
r
cir
cu
it
th
at
tr
an
s
f
o
r
m
s
h
ig
h
-
f
r
e
q
u
en
c
y
AC
in
to
DC
,
a
f
ilter
ca
p
ac
ito
r
(
C
f
)
,
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d
th
e
lo
a
d
r
esis
tan
ce
(
R
L
)
.
I
n
p
r
ac
tice,
th
e
r
eso
n
a
n
t
tan
k
(
L
0
)
ca
n
b
e
in
clu
d
e
d
with
th
e
p
r
im
ar
y
in
d
u
ctan
ce
(L
P
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to
b
ec
o
m
e
a
s
in
g
le
i
n
d
u
ct
an
ce
,
an
d
u
s
in
g
t
h
e
ca
p
ac
ita
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c
e
(
C
0
)
to
ca
n
ce
l
th
e
p
r
im
ar
y
le
ak
ag
e
in
d
u
ctan
ce
,
th
er
eb
y
r
ed
u
cin
g
th
e
r
elia
n
ce
o
n
an
e
x
tr
a
co
il a
n
d
ca
p
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itan
ce
.
T
h
e
eq
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i
v
alen
t
r
esis
tan
ce
s
ee
n
f
r
o
m
th
e
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tifie
r
cir
c
u
it
t
o
R
L
,
as
s
h
o
wn
in
F
ig
u
r
e
1
(
b
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,
ca
n
b
e
ex
p
r
ess
ed
b
y
(
1
)
,
an
d
t
h
e
s
ec
o
n
d
ar
y
-
s
id
e
im
p
ed
an
ce
ca
n
b
e
d
ef
in
ed
b
y
(
2
)
.
=
8
2
(
1
)
2
=
+
(
−
1
)
−
(
2
)
As
d
ep
icted
in
Fig
u
r
e
1
(
b
)
,
th
e
cir
cu
it
is
s
im
p
lifie
d
in
to
an
eq
u
iv
alen
t
f
o
r
m
,
wh
ich
is
m
o
d
eled
in
Fig
u
r
e
1
(
c)
,
with
th
e
r
ef
lecte
d
im
p
e
d
an
ce
Z
r
d
ef
in
ed
in
(
3
)
.
=
(
)
2
+
(
3
)
T
h
u
s
,
th
e
co
r
r
esp
o
n
d
in
g
cir
c
u
it,
illu
s
tr
ated
in
Fig
u
r
e
1
(
b
)
,
is
co
n
v
er
ted
in
to
t
h
e
co
n
f
ig
u
r
atio
n
d
e
p
icted
in
Fig
u
r
e
1
(
c)
.
T
h
e
W
PT
s
y
s
tem
's in
p
u
t im
p
ed
a
n
ce
(
Z
in
)
is
d
ete
r
m
in
ed
b
y
+
,
as e
x
p
r
ess
ed
in
(
4
)
.
=
(
)
2
−
+
+
(
4
)
T
h
e
cir
cu
it
in
Fig
u
r
e
1
(
d
)
is
a
s
im
p
lifie
d
v
er
s
io
n
o
f
th
e
cir
cu
it
in
Fig
u
r
e
1
(
c)
.
T
h
e
im
p
ed
an
ce
Z
Ti
,
as
s
ee
n
in
Fig
u
r
e
1
(
d
)
,
is
d
eter
m
in
ed
b
y
th
e
ex
p
r
ess
io
n
(
+
)
+
(
0
−
1
0
0
)
.
T
h
e
im
p
ed
an
ce
Z
Ti
ca
n
b
e
s
ep
ar
ated
in
to
its
r
ea
l
R
Ti
an
d
im
ag
in
ar
y
p
ar
ts
X
Ti
,
as e
x
p
r
ess
ed
in
(
5
)
-
(
7
)
.
=
+
(
5
)
=
(
)
2
2
+
2
(
6
)
=
[
(
2
+
2
)
(
+
0
)
−
(
)
2
]
2
+
2
(
7
)
T
h
e
eq
u
iv
ale
n
t
im
p
ed
an
ce
Z
eq
,
in
F
ig
u
r
e
1
(
d
)
,
ca
n
b
e
d
ete
r
m
in
ed
u
s
in
g
(
8
)
.
B
y
s
u
b
s
titu
tin
g
th
e
ex
p
r
ess
io
n
s
f
r
o
m
(
6
)
an
d
(
7
)
in
to
(
8
)
,
th
e
r
esu
lt is
g
iv
en
b
y
(
9
)
.
=
1
1
∥
(
+
)
(
8
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Wir
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s
s
ch
a
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g
in
g
C
la
s
s
-
E
in
ve
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ter fo
r
z
e
r
o
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vo
lta
g
e
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w
itch
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co
u
p
lin
g
…
(
A
n
o
n
N
a
min
)
1755
=
+
(
1
+
2
1
−
1
2
)
(
1
−
2
1
)
2
+
(
1
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2
(
9
)
T
h
e
p
h
ase
an
g
le
o
f
Z
eq
is
d
er
iv
ed
f
r
o
m
(
9
)
an
d
p
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esen
ted
i
n
(
1
0
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.
=
−
1
[
(
1
−
2
1
−
1
2
)
]
(
1
0
)
Fig
u
r
e
2
illu
s
tr
ates
th
e
r
elatio
n
s
h
ip
b
etwe
en
th
e
p
h
ase
an
g
l
e
(
eq
)
o
f
Z
eq
an
d
th
e
co
u
p
lin
g
co
ef
f
icien
t
(
k
)
.
An
o
p
tim
al
p
h
ase
an
g
le
f
o
r
ac
h
i
ev
in
g
th
e
Z
VS
co
n
d
itio
n
is
ex
p
lain
ed
in
th
e
liter
atu
r
e
[
2
1
]
,
[
2
9
]
,
[
3
0
]
,
an
d
is
s
h
o
wn
in
(
1
1
)
.
=
−
1
(
2
)
=
0
.
569
r
a
d
=
32
.
48
°
(
1
1
)
T
h
e
o
p
tim
al
p
h
ase
an
g
le
(
ϕ
opt
)
is
ca
lcu
lated
to
b
e
3
2
.
4
8
°.
Fig
u
r
e
2
illu
s
tr
ates
th
e
co
r
r
elati
o
n
b
etwe
en
ϕ
eq
an
d
th
e
m
ag
n
etic
co
u
p
lin
g
co
ef
f
i
cien
t
(
k
)
.
W
h
en
k
e
q
u
als
k
d
esigned
(
0
.
6
6
)
,
ϕ
eq
m
atch
es
ϕ
o
pt
,
ac
h
iev
in
g
Z
VS
o
p
er
atio
n
.
T
h
is
k
designed
v
alu
e
was
d
eter
m
in
ed
th
r
o
u
g
h
p
r
a
ctica
l
m
ea
s
u
r
em
en
ts
.
Fo
r
co
u
p
lin
g
co
ef
f
icien
ts
b
elo
w
k
designed
,
ϕ
eq
ex
ce
ed
s
ϕ
opt
.
C
o
n
v
er
s
ely
,
wh
en
k
ex
ce
e
d
s
k
designed
,
ϕ
eq
f
alls
b
elo
w
ϕ
op
t
.
At
th
is
p
o
in
t,
th
e
in
v
er
ter
tr
an
s
itio
n
s
f
r
o
m
Z
VS
to
n
o
n
-
Z
VS
o
p
er
atio
n
,
m
ak
i
n
g
k
designed
th
e
cr
itical
th
r
esh
o
ld
f
o
r
m
ain
tain
i
n
g
Z
VS
co
n
d
itio
n
s
.
T
h
e
r
ef
o
r
e
,
th
e
m
ax
im
u
m
m
ag
n
etic
co
u
p
lin
g
co
e
f
f
icien
t
s
h
o
u
l
d
b
e
u
s
ed
in
th
e
d
esig
n
p
r
o
ce
d
u
r
es to
en
s
u
r
e
Z
VS m
o
d
e
o
f
o
p
er
atio
n
th
r
o
u
g
h
o
u
t a
n
y
m
is
alig
n
m
en
t c
o
n
d
itio
n
s
.
(a
)
(b
)
(c
)
(d
)
Fig
u
r
e
1
.
T
h
e
W
PT
s
y
s
tem
's c
ir
cu
it: (
a)
s
tan
d
ar
d
s
in
g
le
-
en
d
e
d
r
eso
n
an
t c
o
n
v
e
r
ter
em
p
l
o
y
in
g
a
C
lass
-
E
-
b
ased
s
witch
in
g
s
ch
em
e,
(
b
)
im
p
r
o
v
ed
h
ig
h
-
ef
f
icien
cy
to
p
o
l
o
g
y
d
eliv
er
in
g
p
o
wer
to
a
wir
eless
tr
an
s
m
is
s
io
n
co
n
f
ig
u
r
atio
n
,
(
c)
s
im
p
lifie
d
e
q
u
iv
alen
t c
ir
cu
it
o
f
th
e
W
PT
s
y
s
tem
,
an
d
(
d
)
a
f
u
r
th
e
r
s
im
p
lifie
d
m
o
d
el
f
o
r
im
p
ed
an
ce
a
n
aly
s
is
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
175
2
-
1
7
6
4
1756
Fig
u
r
e
2
.
R
elatio
n
s
h
ip
b
etwe
e
n
p
h
ase
an
g
le
(
eq
)
with
th
e
m
ag
n
etic
co
u
p
lin
g
co
e
f
f
icien
t (
k
)
2
.
1
.
2
.
Vo
lt
a
g
e
a
nd
curr
ent
a
na
ly
s
is
T
h
e
cir
cu
it in
Fig
u
r
e
3
ar
e
u
s
ed
in
th
e
an
aly
s
is
.
W
h
en
th
e
s
witch
in
g
v
o
ltag
e
in
th
e
s
witch
e
d
-
o
f
f
s
tate,
th
at
is
,
f
o
r
0
th
e
s
h
u
n
t c
ap
ac
itan
ce
cu
r
r
en
t c
a
n
b
e
r
ep
r
esen
ted
as (
1
2
)
.
1
(
)
=
1
−
(
+
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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N:
2088
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.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
175
2
-
1
7
6
4
1758
1
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[
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T
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k
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f
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3
.
M
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T
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4
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r
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1
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.
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ts
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r
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e
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iv
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in
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u
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5
p
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atin
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ig
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ativ
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ig
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n
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itter
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u
r
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5
(
b
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3
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t
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3
]
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c
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r
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(
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r
in
g
th
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ase,
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e
tr
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s
m
itter
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r
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en
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r
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d
t
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e
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itter
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v
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)
m
ain
tain
s
its
n
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ativ
e
lev
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Fig
u
r
e
5
(
c)
)
.
-
Mo
d
e
4
[
t₃
–
t₄]
:
T
h
e
p
o
we
r
s
witch
co
n
tin
u
es
co
n
d
u
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g
,
e
n
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lin
g
th
e
cu
r
r
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n
t
iS
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f
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th
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o
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d
d
ir
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n
.
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n
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e
tr
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s
m
itter
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r
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t
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m
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en
t
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ed
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ted
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r
o
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g
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es
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in
a
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o
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h
e
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2
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itiv
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lev
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Fig
u
r
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5
(
d
)
)
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-
Mo
d
e
5
[
t₄
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t₅]
:
At
t
4
,
th
e
g
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te
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ig
n
al
v
GS
d
r
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s
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th
e
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s
witch
.
As
a
r
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th
e
s
h
u
n
t
ca
p
ac
ito
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C
1
b
eg
in
s
c
h
ar
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in
g
f
r
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m
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s
u
p
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.
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ter
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h
e
tr
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s
m
itter
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ir
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ile
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tin
u
es
to
f
lo
w
f
o
r
war
d
v
ia
d
io
d
es
D1
an
d
D4
,
s
u
s
tain
in
g
a
p
o
s
itiv
e
r
ec
eiv
er
-
s
id
e
v
o
ltag
e
v
2
.
Alth
o
u
g
h
iP
f
lo
ws
o
p
p
o
s
itely
,
iS
m
ain
tain
s
its
d
ir
ec
tio
n
,
en
s
u
r
i
n
g
th
at
v
2
r
e
m
ain
s
p
o
s
itiv
e
(
Fig
u
r
e
5
(
e)
)
.
-
Mo
d
e
6
[
t₅
–
t₆]
:
W
h
ile
th
e
s
witch
in
g
elem
en
t
s
tay
s
n
o
n
-
co
n
d
u
ctin
g
,
ca
p
ac
ito
r
C
1
co
n
tin
u
es
ac
cu
m
u
latin
g
ch
ar
g
e
f
r
o
m
th
e
in
p
u
t
s
u
p
p
ly
.
At
t
5
,
th
e
tr
a
n
s
m
itter
cu
r
r
en
t
iP
b
eg
in
s
to
f
lo
w
in
t
h
e
f
o
r
war
d
d
ir
ec
tio
n
.
Simu
ltan
eo
u
s
ly
,
th
e
r
ec
eiv
er
c
u
r
r
en
t
is
s
u
s
tain
s
its
p
o
s
itiv
e
f
lo
w
th
r
o
u
g
h
d
io
d
es
D1
a
n
d
D4
,
m
ain
tain
in
g
a
p
o
s
itiv
e
v
o
ltag
e
ac
r
o
s
s
th
e
r
ec
eiv
er
s
id
e
v
2
(
Fig
u
r
e
5
(
f
)
)
.
-
Mo
d
e
7
[
t
6
–
t
7
]
:
W
ith
th
e
p
o
w
er
s
witch
r
em
ain
in
g
in
ac
tiv
e,
t
h
e
s
h
u
n
t
ca
p
ac
ito
r
C
1
b
e
g
in
s
d
is
ch
ar
g
in
g
.
At
th
is
s
tag
e,
th
e
tr
an
s
m
itter
cu
r
r
en
t
iP
f
lo
ws
in
th
e
f
o
r
war
d
d
ir
ec
tio
n
,
wh
ile
th
e
r
ec
eiv
e
r
cu
r
r
en
t
iS
co
n
tin
u
es
its
p
o
s
itiv
e
p
ath
th
r
o
u
g
h
d
io
d
es
D1
an
d
D4
,
th
er
eb
y
s
u
s
tain
in
g
a
p
o
s
itiv
e
v
o
ltag
e
ac
r
o
s
s
t
h
e
r
ec
eiv
er
s
id
e
v
2
(
Fig
u
r
e
5
(
g
)
)
.
-
Mo
d
e
8
[
t
7
–
t
8
]
:
T
h
e
p
o
we
r
s
witch
s
tay
s
in
th
e
o
f
f
s
tate,
p
e
r
m
itti
n
g
th
e
s
h
u
n
t
ca
p
ac
ito
r
C
1
to
d
is
ch
ar
g
e.
Du
r
in
g
th
is
in
ter
v
al,
th
e
tr
an
s
m
itter
cu
r
r
en
t
iP
m
ain
tain
s
its
f
o
r
war
d
d
ir
ec
tio
n
.
Me
an
w
h
ile,
at
t
7
,
th
e
r
ec
eiv
er
cu
r
r
en
t
iS
s
tar
ts
f
lo
win
g
in
th
e
r
ev
e
r
s
e
d
ir
ec
tio
n
v
ia
d
io
d
es
D2
a
n
d
D3
,
lead
i
n
g
to
a
n
e
g
ativ
e
v
o
ltag
e
ac
r
o
s
s
th
e
r
ec
ei
v
er
s
id
e
v
2
(
Fig
u
r
e
5
(
h
)
)
.
-
Mo
d
e
9
[
t
8
–
t
9
]
:
T
h
e
p
o
wer
s
witch
s
tay
s
in
th
e
o
f
f
s
tate.
At
t
8
,
th
e
s
h
u
n
t
ca
p
ac
ito
r
C
1
co
m
p
letes
its
d
is
ch
ar
g
e,
d
ir
ec
tin
g
cu
r
r
en
t
v
ia
th
e
i
n
tr
in
s
ic
d
io
d
e
p
ath
with
in
th
e
s
witch
in
g
d
ev
ice.
C
o
n
s
eq
u
en
tly
,
a
r
ev
er
s
e
-
d
ir
ec
tio
n
cu
r
r
e
n
t
iS
is
co
n
d
u
cte
d
,
estab
lis
h
in
g
ze
r
o
-
v
o
ltag
e
s
witch
in
g
(
Z
VS)
co
n
d
itio
n
s
.
Du
r
in
g
th
is
tim
e,
th
e
tr
a
n
s
m
itter
cu
r
r
e
n
t
iP
r
em
ain
s
c
o
n
s
tan
t,
a
n
d
t
h
e
r
ec
eiv
er
v
o
ltag
e
v
2
r
etain
s
its
n
eg
ativ
e
v
alu
e
(
Fig
u
r
e
5
(
i)
)
.
T
h
e
s
witch
in
g
c
y
cle
th
en
p
r
o
ce
ed
s
b
ac
k
to
Mo
d
e
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Wir
ele
s
s
ch
a
r
g
in
g
C
la
s
s
-
E
in
ve
r
ter fo
r
z
e
r
o
-
vo
lta
g
e
s
w
itch
in
g
o
ve
r
co
u
p
lin
g
…
(
A
n
o
n
N
a
min
)
1759
Fig
u
r
e
4
.
W
av
ef
o
r
m
s
r
elate
d
t
o
th
e
m
o
d
es o
f
o
p
er
atio
n
f
o
r
a
n
aly
s
is
(
a)
(
b
)
(
c)
(
d
)
(
e)
(f)
(
g
)
(
h
)
(
i)
Fig
u
r
e
5
.
Switch
in
g
s
eq
u
en
ce
r
ep
r
esen
tatio
n
f
o
r
ea
ch
o
p
e
r
atin
g
co
n
d
itio
n
: n
i
n
e
-
s
tag
e
o
p
e
r
a
tin
g
s
eq
u
en
ce
:
(
a)
Mo
d
e
1
,
(
b
)
Mo
d
e
2
,
(
c)
M
o
d
e
3
,
(
d
)
M
o
d
e
4
,
(
e)
Mo
d
e
5
,
(
f
)
Mo
d
e
6
,
(
g
)
Mo
d
e
7
,
(
h
)
Mo
d
e
8
,
a
n
d
(
i
)
Mo
d
e
9
ar
e
th
e
co
r
r
esp
o
n
d
in
g
to
tim
e
in
t
er
v
als
t
0
–
t
9
as d
escr
ib
ed
in
t
h
e
m
ain
tex
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
,
Vo
l.
16
,
No
.
3
,
Sep
tem
b
er
20
25
:
175
2
-
1
7
6
4
1760
3.
ST
UDY
RE
S
UL
T
S
T
h
is
s
ec
tio
n
p
r
o
v
id
es
a
d
etail
ed
o
v
er
v
iew
o
f
t
h
e
s
im
u
latio
n
an
d
ex
p
er
im
en
tal
r
esu
lts
.
A
p
r
o
t
o
ty
p
e
f
o
r
u
n
teth
er
e
d
en
e
r
g
y
tr
an
s
m
is
s
io
n
u
tili
zin
g
a
r
eso
n
an
t
-
m
o
d
e
C
lass
-
E
co
n
v
e
r
ter
to
p
o
lo
g
y
was
d
e
v
elo
p
e
d
f
o
llo
win
g
th
e
p
r
o
p
o
s
ed
d
esig
n
f
r
am
ewo
r
k
.
3
.
1
.
P
a
ra
m
et
er
des
ig
n
A
wir
eless
p
o
wer
p
r
o
to
t
y
p
e
is
d
ev
elo
p
e
d
to
v
er
if
y
th
e
p
r
o
p
o
s
ed
m
eth
o
d
f
o
r
tr
an
s
f
er
r
in
g
p
o
wer
to
a
lo
ad
:
a
3
,
4
0
0
m
Ah
lith
iu
m
-
io
n
b
atter
y
d
eliv
er
i
n
g
4
.
2
V
at
its
ter
m
in
als
an
d
ac
ce
p
tin
g
a
2
A
ch
ar
g
e
in
p
u
t.
T
h
is
b
atter
y
'
s
lo
ad
r
esis
tan
ce
is
co
n
s
id
er
ed
co
n
s
tan
t.
Fro
m
th
e
s
im
u
latio
n
,
wh
ich
ex
a
m
in
es
th
e
b
atter
y
'
s
s
tate
o
f
ch
ar
g
e
(
SOC
)
b
etwe
en
2
0
%
to
8
0
%,
it
was
f
o
u
n
d
th
at
th
e
in
ter
n
al
r
esis
tan
ce
r
em
ain
s
r
elativ
ely
co
n
s
tan
t.
T
h
er
ef
o
r
e,
a
lo
ad
r
esis
tan
ce
o
f
2
.
1
Ω
is
s
elec
ted
f
o
r
th
e
s
tu
d
y
.
T
h
e
tr
an
s
m
itter
an
d
r
ec
ei
v
er
co
ils
co
n
s
is
t
o
f
co
n
d
u
ct
o
r
s
p
lace
d
o
n
s
q
u
ar
e
f
er
r
ite
co
r
es,
ea
ch
m
ea
s
u
r
in
g
5
.
3
cm
b
y
5
.
3
cm
,
with
an
in
d
u
ctan
ce
o
f
6
.
2
5
μ
H
p
er
co
il.
T
h
e
m
a
g
n
etic
co
u
p
li
n
g
co
ef
f
icien
t
at
an
alig
n
ed
d
i
s
tan
ce
o
f
1
cm
b
etwe
en
th
e
co
ils
is
0
.
6
6
,
wh
ich
is
u
s
ed
as
th
e
d
esig
n
v
alu
e.
T
h
e
r
em
ain
in
g
p
ar
am
eter
s
wer
e
ca
lcu
lated
u
s
in
g
t
h
e
eq
u
atio
n
s
f
r
o
m
s
ec
tio
n
2
.
3
.
T
h
e
o
b
tain
ed
cir
cu
it
p
ar
am
et
er
s
ar
e
s
u
m
m
a
r
ized
as
f
o
llo
ws:
an
eq
u
i
v
alen
t
r
esis
tan
ce
R
Leq
=
1
.
7
0
2
Ω
,
a
co
m
p
en
s
atio
n
ca
p
ac
ito
r
C
2
=
6
4
.
8
4
5
n
F,
a
r
ef
lecte
d
r
esis
tan
ce
R
reflected
=
2
1
.
4
1
Ω
,
a
r
eso
n
an
t
in
d
u
ctan
ce
L
0
=
2
6
6
.
3
5
μ
H,
an
d
two
ca
p
ac
itan
ce
s
C
1
=
5
.
9
8
9
3
n
F a
n
d
C
0
=
1
.
5
9
5
7
n
F.
3
.
2
.
Sim
ula
t
i
o
n
re
s
ults
B
y
em
p
lo
y
in
g
th
e
cir
cu
it lay
o
u
t
d
ep
icted
in
Fig
u
r
e
1
(
b
)
,
s
im
u
latio
n
s
wer
e
co
n
d
u
cted
f
o
r
ca
s
es wh
er
e
k
=
k
designed
,
k
<
k
designed
,
an
d
k
>
k
designed
.
I
n
th
is
d
esig
n
,
k
designed
r
ep
r
esen
ts
th
e
o
p
tim
al
v
alu
e
,
em
p
ir
ically
d
eter
m
in
ed
to
b
e
0
.
6
6
.
T
h
e
co
r
r
esp
o
n
d
in
g
r
esu
lts
ar
e
p
r
esen
ted
in
Fig
u
r
e
6
.
T
h
e
f
ir
s
t set o
f
m
ea
s
u
r
em
en
ts
was
co
llected
f
o
r
k
=
k
designed
=
0
.
6
6
.
Af
ter
war
d
,
th
e
m
ea
s
u
r
em
en
ts
wer
e
p
er
f
o
r
m
ed
ag
ain
b
y
m
o
d
if
y
in
g
th
e
h
o
r
izo
n
tal
m
is
alig
n
m
en
t
an
d
a
s
ep
ar
atio
n
b
etwe
en
co
ils
to
ac
h
iev
e
ca
s
es
wh
er
e
k
<
k
designed
an
d
k
>
k
designed
.
T
h
e
m
is
alig
n
m
en
t
h
as
af
f
ec
ted
th
e
W
PT
s
y
s
tem
’
s
ef
f
icien
cy
,
as
d
is
cu
s
s
ed
in
[
3
1
]
-
[
3
5
]
.
I
n
p
ar
allel,
en
h
an
ce
d
s
y
s
tem
ef
f
icien
cy
u
n
d
er
v
ar
y
in
g
co
u
p
lin
g
an
d
alig
n
m
en
t c
o
n
d
itio
n
s
h
as a
ls
o
b
ee
n
ex
p
lo
r
ed
in
[
3
6
]
-
[
3
8
]
.
Fig
u
r
e
6
(
a)
illu
s
tr
ates
th
e
g
ate
-
to
-
s
o
u
r
ce
v
o
ltag
e
(
V
GS
)
wav
ef
o
r
m
an
d
s
witch
in
g
v
o
ltag
e
(
V
DS
)
wav
ef
o
r
m
ac
r
o
s
s
th
e
d
r
ain
an
d
s
o
u
r
ce
ter
m
in
als.
I
n
Fig
u
r
e
6
(
a)
,
th
e
V
GS
wav
ef
o
r
m
is
s
ca
led
b
y
a
f
ac
to
r
o
f
7
5
f
o
r
clar
ity
.
T
h
e
ze
r
o
-
v
o
ltag
e
s
witch
in
g
(
Z
VS)
p
o
i
n
t
is
in
d
icate
d
with
a
s
m
all
n
e
g
ati
v
e
s
witch
v
o
ltag
e,
s
h
o
win
g
th
at
th
e
v
DS
r
ed
u
ce
s
to
ze
r
o
p
r
i
o
r
to
th
e
s
witch
ac
tiv
atio
n
,
ac
h
iev
i
n
g
th
e
Z
VS
co
n
d
itio
n
.
Fig
u
r
e
6
(
b
)
illu
s
tr
ates
th
e
s
im
u
latio
n
r
esu
lts
f
o
r
k
<
k
designed
=
0
.
5
1
.
T
h
e
v
o
ltag
e
wav
ef
o
r
m
V
DS
b
ec
o
m
es
n
ar
r
o
wer
an
d
ex
h
ib
its
a
h
i
g
h
er
v
o
ltag
e
am
p
l
itu
d
e.
T
h
e
in
v
e
r
ter
o
p
er
ates
u
n
d
er
Z
VS
c
o
n
d
itio
n
s
,
co
n
s
is
te
n
t
with
th
e
an
aly
s
is
in
s
ec
tio
n
2
.
1
.
1
,
wh
ich
s
tates
th
at
Z
VS
ca
n
b
e
ac
h
iev
e
d
w
h
en
k
<
k
designed
.
T
h
e
s
im
u
latio
n
s
wer
e
p
er
f
o
r
m
ed
f
o
r
k
>
k
designed
=
0
.
8
4
.
T
h
e
r
es
u
lts
,
p
r
esen
ted
in
Fig
u
r
e
6
(
c)
,
in
d
icate
s
th
at
th
e
in
v
er
ter
o
p
er
ates
in
a
n
o
n
-
ze
r
o
-
v
o
ltag
e
co
n
d
itio
n
.
T
h
is
p
h
en
o
m
en
o
n
o
cc
u
r
r
ed
b
ec
au
s
e
t
h
e
m
ag
n
etic
c
o
u
p
lin
g
co
e
f
f
ici
en
t
ex
ce
ed
e
d
th
e
o
p
tim
al
v
al
u
e,
as
d
is
cu
s
s
ed
i
n
s
u
b
s
ec
tio
n
2
.
1
.
1
.
Fin
ally
,
Fig
u
r
e
6
(
d
)
p
r
esen
ts
th
e
s
im
u
l
atio
n
r
esu
lts
f
o
r
k
>
k
designed
=
0
.
9
.
At
th
is
co
u
p
lin
g
co
ef
f
icien
t,
th
e
o
v
er
lap
b
etwe
en
th
e
V
DS
an
d
V
GS
wav
ef
o
r
m
s
co
n
f
ir
m
s
th
at
th
e
in
v
er
ter
s
till
o
p
er
ated
i
n
a
n
o
n
-
Z
VS c
o
n
d
itio
n
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
6
.
T
h
e
s
witch
in
g
v
o
ltag
e
(
V
DS
)
an
d
g
ate
-
to
-
s
o
u
r
ce
v
o
ltag
e
(
V
GS
)
u
n
d
er
d
if
f
er
en
t c
o
u
p
lin
g
co
n
d
itio
n
s
:
(
a)
k
=
k
designed
=
0
.
6
6
; (
b
)
k
<
k
designed
=
0
.
5
1
;
(
c)
k
>
k
designed
=
0
.
8
4
;
a
n
d
(
d
)
k
>
k
designed
=
0
.
9
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Po
w
E
lec
&
Dr
i Sy
s
t
I
SS
N:
2088
-
8
6
9
4
Wir
ele
s
s
ch
a
r
g
in
g
C
la
s
s
-
E
in
ve
r
ter fo
r
z
e
r
o
-
vo
lta
g
e
s
w
itch
in
g
o
ve
r
co
u
p
lin
g
…
(
A
n
o
n
N
a
min
)
1761
T
h
e
s
im
u
lated
o
u
tco
m
es
alig
n
with
th
e
an
aly
tical
f
in
d
in
g
s
o
u
tlin
ed
u
n
d
er
s
ec
tio
n
2
.
1
.
1
.
T
h
e
o
b
s
er
v
ed
Z
VS
an
d
n
o
n
-
Z
VS
s
witch
in
g
b
eh
av
io
r
s
in
Fig
u
r
e
6
co
r
r
esp
o
n
d
d
ir
ec
tly
to
th
e
ca
lcu
lated
p
h
ase
an
g
le
ϕ
eq
in
ea
ch
ca
s
e.
W
h
en
k
=
k
designed
,
th
e
p
h
ase
an
g
le
ap
p
r
o
ac
h
es
th
e
o
p
tim
al
ϕ
opt
,
r
esu
ltin
g
in
Z
VS
o
p
er
atio
n
.
I
n
co
n
tr
ast,
d
ev
iatio
n
f
r
o
m
k
designed
lead
s
to
a
p
h
ase
an
g
le
m
is
m
atch
,
ex
p
lain
in
g
th
e
d
eter
io
r
atio
n
o
f
Z
VS c
o
n
d
itio
n
s
as p
r
ed
icted
b
y
th
e
an
aly
tical
m
o
d
el.
3
.
3
.
E
x
perim
ent
a
l r
esu
lt
s
Fig
u
r
e
7
illu
s
tr
ates
th
e
ex
p
er
im
en
tal
s
etu
p
,
d
etailin
g
th
e
ar
r
an
g
em
en
t
o
f
e
q
u
ip
m
e
n
t
an
d
th
e
p
r
o
ce
d
u
r
es
u
s
ed
to
co
n
d
u
ct
th
e
test
s
an
d
g
ath
er
d
ata.
I
n
t
h
e
ex
p
er
im
en
tal
s
etu
p
,
t
h
e
co
il
s
ep
ar
atio
n
d
is
tan
ce
an
d
m
is
alig
n
m
en
t
wer
e
t
u
n
ed
to
r
ea
ch
th
e
d
esire
d
lev
el
o
f
c
o
u
p
lin
g
c
o
ef
f
icien
t.
T
h
e
f
ir
s
t
s
et
o
f
m
ea
s
u
r
em
en
ts
was
tak
en
with
k
=
k
designed
=
0
.
6
6
.
T
h
e
ex
p
e
r
im
en
t
was
th
en
r
ep
ea
ted
with
ad
ju
s
tm
en
ts
to
th
e
co
il
m
is
alig
n
m
en
t
an
d
s
ep
ar
atio
n
b
etwe
en
co
ils
to
ac
h
iev
e
k
<
k
designed
=
0
.
5
1
,
k
>
k
designed
=
0
.
8
4
,
an
d
k
>
k
designed
=
0
.
9
.
I
n
th
e
ex
p
e
r
im
en
tal
c
o
n
f
ig
u
r
atio
n
,
a
2
0
V
DC
s
u
p
p
ly
was
u
s
ed
to
d
r
iv
e
th
e
in
v
er
ter
,
o
p
er
atin
g
a
t
2
5
0
k
Hz
with
a
5
0
%
d
u
ty
c
y
c
le.
Po
wer
was
wir
eless
ly
d
eli
v
er
ed
to
a
r
esis
tiv
e
lo
ad
lo
ca
t
ed
o
n
t
h
e
s
ec
o
n
d
a
r
y
s
id
e
o
f
th
e
cir
cu
it.
T
h
e
co
ils
wer
e
ac
cu
r
ately
alig
n
e
d
with
a
1
cm
s
p
ac
i
n
g
,
y
ield
in
g
a
m
ag
n
etic
co
u
p
lin
g
co
ef
f
icien
t
o
f
0
.
6
6
u
n
d
er
th
e
in
itial
test
co
n
d
itio
n
.
W
av
ef
o
r
m
s
o
f
V
DS
an
d
V
GS
wer
e
ca
p
tu
r
ed
u
s
in
g
an
o
s
cillo
s
co
p
e,
as
d
ep
icted
in
Fi
g
u
r
e
8
(
a
)
.
T
h
e
o
b
s
er
v
ed
Z
VS
b
eh
av
io
r
o
f
V
DS
an
d
V
GS
co
r
r
elate
s
well
with
th
e
s
im
u
lated
d
ata
(
s
ee
Fig
u
r
e
6
(
a
)
)
.
An
o
u
tp
u
t
p
o
wer
o
f
1
0
W
was
s
u
cc
ess
f
u
lly
tr
an
s
f
er
r
ed
t
o
th
e
o
u
t
p
u
t
s
tag
e,
in
alig
n
m
en
t
with
th
e
in
ten
d
e
d
d
esig
n
cr
iter
ia.
T
h
e
in
p
u
t
p
o
we
r
ass
o
ciate
d
with
th
is
co
n
d
itio
n
was
r
ec
o
r
d
e
d
at
1
0
.
5
W
,
r
esu
ltin
g
in
a
n
o
v
er
a
ll
ef
f
icien
cy
o
f
9
5
%.
T
h
e
co
i
l
m
is
alig
n
m
en
t
was
ad
ju
s
ted
to
g
ain
a
m
ag
n
etic
co
u
p
lin
g
co
e
f
f
icien
t o
f
0
.
5
1
.
Fig
u
r
e
8
(
b
)
p
r
esen
ts
th
e
ex
p
e
r
im
en
tal
r
esu
lts
f
o
r
t
h
e
s
witch
in
g
v
o
ltag
e
(
V
DS
)
an
d
g
ate
-
to
-
s
o
u
r
ce
v
o
ltag
e
(
V
GS
)
,
wh
ich
clo
s
ely
alig
n
with
s
im
u
latio
n
r
esu
lts
,
as
illu
s
tr
ated
in
Fig
u
r
e
6
(
b
)
.
I
n
v
er
ter
c
o
n
tin
u
e
d
to
o
p
er
ate
u
n
d
er
ze
r
o
-
v
o
ltag
e
s
witch
in
g
(
Z
VS)
,
d
eliv
er
in
g
an
a
v
er
a
g
e
o
f
8
.
8
5
W
at
th
e
o
u
tp
u
t,
wh
ile
d
r
awin
g
ap
p
r
o
x
im
ately
1
0
.
1
7
W
at
th
e
in
p
u
t,
r
esu
ltin
g
in
an
o
v
er
all
e
f
f
icien
cy
o
f
8
4
%.
Fig
u
r
e
8
(
c)
p
r
esen
ts
th
e
ex
p
e
r
im
en
tal
r
esu
lts
f
o
r
k
=
0
.
8
4
.
Un
d
er
th
is
co
n
d
itio
n
,
th
e
in
v
er
ter
d
em
o
n
s
tr
ate
d
non
-
o
p
tim
al
p
e
r
f
o
r
m
an
ce
,
as
t
h
e
Z
VS
co
n
d
itio
n
was
n
o
t
m
e
t
.
Me
asu
r
ed
o
u
tp
u
t
p
o
wer
was
8
W
,
w
h
er
ea
s
th
e
m
ea
s
u
r
ed
in
p
u
t p
o
wer
was 9
.
1
W
,
r
esu
ltin
g
in
an
o
v
er
all
ef
f
i
cien
cy
o
f
8
8
%.
L
ik
ewise,
Fig
u
r
e
8
(
d
)
d
ep
icts
th
e
ex
p
er
im
en
tal
r
esu
lt
o
b
tain
e
d
f
o
r
k
=
0
.
9
.
T
h
e
a
v
er
ag
e
o
u
tp
u
t
p
o
wer
was
m
ea
s
u
r
ed
at
7
.
3
1
W
,
with
th
e
av
er
ag
e
in
p
u
t
p
o
wer
m
e
asu
r
e
d
at
8
.
6
W
,
r
esu
ltin
g
i
n
an
o
v
er
all
ef
f
icien
cy
o
f
8
5
%.
E
f
f
icien
cy
d
ec
r
ea
s
es
d
u
e
to
lo
s
s
es c
au
s
ed
b
y
th
e
o
v
er
la
p
p
in
g
o
f
s
witch
v
o
ltag
e
an
d
c
u
r
r
en
t sig
n
als.
T
h
e
s
tu
d
y
r
ev
ea
ls
th
at
wh
en
d
esig
n
in
g
th
e
W
PT
s
y
s
tem
p
o
wer
ed
b
y
th
e
C
lass
-
E
in
v
er
ter
f
o
r
o
p
er
atin
g
u
n
d
er
Z
VS
co
n
d
itio
n
s
,
th
e
m
ax
im
u
m
v
alu
e
o
f
th
e
m
ag
n
etic
co
u
p
lin
g
co
ef
f
icien
t
s
h
o
u
ld
b
e
u
s
ed
in
th
e
d
esig
n
p
r
o
ce
s
s
.
T
h
is
ap
p
r
o
ac
h
en
s
u
r
es th
at
th
e
s
y
s
tem
o
p
er
ates u
n
d
er
Z
VS a
s
lo
n
g
as
k
r
em
ain
s
with
in
th
e
co
n
d
itio
n
k
<
k
designed
.
Ho
wev
er
,
ev
en
th
o
u
g
h
th
e
in
v
er
ter
ca
n
m
ain
tain
Z
VS
o
p
er
atio
n
wh
en
k
is
less
th
an
k
designed
,
th
e
o
u
tp
u
t
p
o
wer
m
ay
d
ev
iate
f
r
o
m
th
e
d
esig
n
ed
v
alu
e
d
u
e
to
wea
k
co
u
p
lin
g
.
E
x
p
er
im
en
tal
r
esu
lts
in
d
icate
th
at
wh
en
k
d
r
o
p
s
to
0
.
5
1
o
r
b
elo
w,
th
e
o
u
tp
u
t p
o
wer
f
alls
b
elo
w
9
watts.
Fig
u
r
e
7
.
T
h
e
lay
o
u
t o
f
t
h
e
ex
p
er
im
en
tal
s
etu
p
an
d
th
e
a
r
r
an
g
em
en
t o
f
eq
u
ip
m
en
t
T
h
ese
ex
p
er
im
en
tal
r
esu
lts
ar
e
in
lin
e
with
th
e
th
eo
r
etica
l
Z
VS
o
p
er
atio
n
zo
n
es
id
en
tifie
d
in
s
ec
tio
n
2
.
1
.
1
.
Sp
ec
if
ically
,
wh
en
th
e
co
u
p
lin
g
co
ef
f
icien
t
eq
u
als
th
e
d
esig
n
ed
v
alu
e
k
=
0
.
6
6
,
th
e
m
ea
s
u
r
ed
V
DS
wav
ef
o
r
m
co
n
f
ir
m
s
th
at
Z
VS
is
ac
h
iev
ed
,
as
p
r
ed
icted
b
y
th
e
p
h
ase
an
g
le
ϕ
eq
r
ea
ch
in
g
th
e
o
p
tim
al
v
alu
e
ϕ
opt
.
A
r
ed
u
ctio
n
in
th
e
co
u
p
lin
g
f
ac
to
r
to
k
=
0
.
5
1
allo
ws
th
e
in
v
er
ter
to
m
ain
tain
Z
VS
o
p
er
atio
n
,
as
p
r
ed
icted
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.