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.
1815~
18
22
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
4.pp1815-1822
1815
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
Dead ti
me inf
luen
c
e on operati
ng m
od
es of transistor resona
nt i
nvert
er
with pulse frequency modulatio
n
(PFM)
Mihail An
t
che
v
1
, Hri
sto
An
tch
e
v
2
1
S
e
ct
io
n P
o
wer E
l
ectro
n
i
cs,
Facu
lt
y
of
El
ectro
nic En
gin
eerin
g
an
d
T
echno
lo
gy
, Techni
cal
U
ni
versi
t
y,
B
ulgari
a
2
Dep
a
rt
men
t
o
f E
l
ectri
cal E
ng
ineer
i
n
g
and
El
ectro
nics
, U
n
i
v
ersit
y o
f
C
h
e
m
i
c
a
l
T
e
c
h
n
o
lo
gy
a
nd
M
e
t
a
l
lu
rg
y,
B
ul
ga
ria
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
ce
i
v
e
d
Mar
19,
2
0
1
9
Re
vise
d A
p
r
14,
201
9
Ac
ce
p
t
ed
M
a
y
2
8
,
2
019
Th
is
s
t
udy
e
xp
lo
res
th
e
im
p
act
o
f
d
ead-t
im
e
on
t
h
e
t
ran
s
istor
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eso
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ant
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vert
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des
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o
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si
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or
s
witchi
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equ
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ncy
and
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onan
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f
req
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nance
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he
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ago
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r
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ridge.
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asis
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f
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dat
a
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ults,
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mitation
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g
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e
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tching
(
ZVS)
.
K
eyw
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s
:
De
ad
t
i
m
e
P
u
lse
fre
q
uenc
y
modu
la
ti
o
n
R
e
so
n
a
nt
i
nv
e
r
t
e
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:
M
i
ha
il
A
n
t
c
he
v,
Section
Po
wer El
ectro
nics,
F
a
cult
y
o
f
E
l
e
c
t
ro
nic
En
gi
ne
e
r
in
g a
n
d
Tec
h
n
o
l
o
gy,
Tec
h
ni
c
a
l
U
ni
ver
s
i
t
y –S
o
f
ia,
10
0
0
,
S
o
fia
, Bul
garia.
Em
ail:
antc
he
v
@
t
u
-so
f
ia
.b
g
1.
I
N
TR
OD
U
C
TI
O
N
The
ne
ed
t
o
i
n
t
r
o
duce
dea
d
-t
i
m
e
in
t
he
c
o
n
t
ro
ll
ing
of
s
in
gle
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g
tran
sis
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or
s
i
n
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he
s
c
h
e
m
e
s
o
f
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h
e
pow
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lec
t
ron
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c
c
o
nv
e
r
ters
i
s
kn
ow
n.
T
h
i
s
is
t
he
t
i
m
e,
w
hic
h
t
h
e
s
i
g
n
a
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o
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s
w
i
t
c
h
i
n
g
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n
o
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e
a
c
h
o
f
t
h
e
trans
i
s
t
or
s
dela
ys
w
i
t
h
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e
spec
t
to
t
he
s
h
u
to
ff
s
igna
l
of
t
he
o
t
he
r.
I
n
some
a
rtic
les,
t
he
n
ec
e
ssity
o
f
s
u
ch
a
t
im
e
is
o
n
l
y
me
n
tio
ned
[1],
w
hi
l
e
i
n
o
t
hers
a
re
r
ese
a
rc
hed
the
proce
sse
s
r
ela
t
e
d
t
o
i
t
i
n
vo
lt
age
so
urce
i
nv
erte
rs,
resona
nt
in
v
ert
e
r
s
a
nd
D
C
/
D
C
co
nver
t
e
r
s,
a
s
differ
en
t
w
a
y
s
f
or
its
d
e
f
i
n
it
io
n
a
n
d
im
ple
m
e
n
ta
ti
o
n
a
re
o
ffere
d.
In
[
2]
t
he
t
i
m
e
is
r
ec
orde
d
on
t
he
g
r
a
p
h
i
c
a
l
t
i
m
e
d
ia
gra
m
s,
but
t
he
p
r
o
ce
sses
a
r
e
n
o
t
st
ud
ie
d.
I
n
[3]
i
s
con
s
i
d
ere
d
a
D
C
/
D
C
c
o
nver
t
e
r
w
ith
a
ze
r
o
vol
ta
ge
sw
itc
h
i
ng (ZV
S
) a
l
gor
ithm
, as t
h
e
dea
d
-t
i
m
e ca
l
c
ul
a
tio
n
i
s
base
d
o
n
t
h
e
i
np
u
t
capa
c
i
tan
c
e
of
t
he
M
O
S
F
ET
and
the
proc
esses
ass
o
cia
t
e
d
w
i
t
h
t
h
e
ga
te
c
harge
dur
in
g
sw
it
c
h
i
n
g.
W
i
t
h
re
gard
t
o
t
r
ans
i
st
or
r
esona
n
t
i
nve
r
t
ers,
one
o
f
w
hi
c
h
i
s
ex
pl
ored
i
n
this
a
r
t
ic
le
,
the
fol
l
o
w
in
g
syste
m
iza
t
i
o
n
can
b
e
done
.
S
o
m
e
c
om
pani
es
r
ecom
m
e
nd
fixe
d
se
t-
u
p
b
y
e
x
t
e
r
na
l
resi
stor
i
n
t
h
e
inte
grate
d
c
o
nt
rol
ci
rcu
i
t
,
p
ro
vid
i
ng
t
h
e
c
o
r
re
sp
on
ding
g
rap
h
i
c
al
d
ep
en
d
e
n
cie
s
[
4,
5
]
.
I
n
[6]
a
f
i
x
e
d
v
a
l
u
e
eq
ual
t
o
33
0
i
s
se
t.
I
n
most
s
t
u
d
i
e
s
,
dead-
tim
e
is
d
e
t
e
r
m
i
ne
d
b
a
se
d
on
t
h
e
r
echa
r
gi
ng
of
t
he
o
u
t
p
u
t
c
apac
i
t
a
n
ces
o
f
the
s
i
n
g
le
l
e
g
M
O
SFETs,
as
t
he
o
ffere
d
form
ulas
f
or
c
alcu
la
t
i
n
g
its
m
i
n
im
um
v
a
l
ue
a
re
a
lm
ost
i
d
e
n
t
i
ca
l
[
7
-10]
.
A
s
i
m
i
l
a
r
form
ula
i
s
o
ff
ered
i
n
[
1
1],
as
t
he
d
elay
t
i
m
e
i
n
t
h
e
dri
v
er
s
is
a
dde
d.
W
he
n
e
x
am
i
n
i
n
g
a
trans
i
s
t
or
r
eso
n
an
t
i
n
ve
rter
f
or
i
n
d
u
ct
i
on
h
eati
n
g
in
[
1
2
],
P
ul
se
F
reque
nc
y
Mod
u
l
at
i
o
n
(
P
F
M
)
is
u
sed
an
d
dea
d
-
t
i
m
e
is
i
n
t
ro
duce
d
,
but
t
he
p
roce
ss
e
s
i
n
it
are
no
t
resea
r
c
h
ed
.
In
[
1
3
]
t
hi
s
ti
me
i
s
opt
i
m
i
zed
b
a
s
e
d
o
n
t
h
e
rati
o
b
e
tw
ee
n
t
h
e
res
ona
nc
e
capa
c
i
ty
a
n
d
t
he
t
r
a
ns
i
s
t
o
r
dra
i
n-s
ourc
e
capa
c
i
tance
,
t
a
k
i
n
g
i
n
m
i
nd
the
ma
ximum
sw
i
t
c
h
i
n
g
fre
q
ue
nc
y.
M
a
n
ua
l
tu
ni
ng
base
d
o
n
t
h
e
e
xperim
e
n
ta
l
loss
m
ea
sur
e
m
e
nt
i
n
t
h
e
c
o
nve
r
t
e
r
is
s
u
g
g
es
ted
i
n
[
14]
.
The
a
r
t
i
c
l
e
[
1
5
]
i
s
i
n
te
res
t
i
ng,
a
s
bes
i
d
e
s
t
he
m
inim
um
v
a
l
ue
lim
ita
ti
o
n
,
it
o
ffers
ma
ximum
val
u
e
li
m
i
t
a
t
i
o
n
a
s
w
e
ll.
T
he
re
a
r
e
a
da
pti
v
e
dea
d
-ti
m
e
de
fin
i
t
i
o
n
s,
f
or
e
xa
mpl
e
[
16
]
,
p
re
se
n
t
i
ng
a
n
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 :
1
8
1
5
– 1
822
1
816
ada
p
t
i
ve
a
d
j
us
tm
ent
sc
hem
e
i
n
the
ran
g
e
o
f
0
3.5
,
s
uita
bl
e
for
hi
g
h
v
olta
ge
a
pp
li
cat
i
ons.
In
[
17]
i
s
prese
n
t
e
d
a
m
e
th
o
d
f
or
c
om
pe
nsa
t
i
ng
dea
d
t
i
m
e,
b
a
s
e
d
o
n
a
com
p
l
e
x
f
or
m
of
t
he
m
o
d
u
l
a
tio
n
s
i
g
n
a
l
.
A
s
a
summ
ar
y
of
a
ll
t
h
e
de
sc
ri
be
d
ca
n
be
c
o
n
cl
u
d
e
d
t
h
at
t
he
s
t
u
die
s
c
ons
i
d
er
t
he
d
e
v
e
l
o
p
m
e
n
t
o
f
t
h
e
proce
sse
s
i
n
the p
o
w
e
r sc
hem
e
w
hen the
d
e
a
d
-t
i
m
e
is
i
nsuf
fic
i
e
n
t
in va
l
ue
.
Q
u
i
t
e
ofte
n,
h
o
w
e
v
er,
the
des
i
gners
c
h
o
o
s
e
a
h
i
g
h
e
r
v
al
ue
t
ha
n
n
eed
ed
,
to
b
e
se
cu
red
in
c
a
s
e
of
l
o
a
d
and
p
o
w
e
r
t
r
ansistor
p
a
r
am
ete
r
s
c
h
an
ges.
N
o
pu
b
lica
t
io
ns
a
re
k
n
ow
n
o
n
h
ow
t
he
o
pera
t
i
on
m
o
des
c
h
an
ge
i
n
ca
se
t
he
d
e
a
d-
time
ha
s
m
u
c
h
g
re
ater
v
a
l
ue.
The
pro
b
l
e
m
is
:
i
f
t
hi
s
ti
me
i
s
mu
ch
g
rea
t
e
r
,
t
h
e
ze
ro
v
ol
t
a
g
e
sw
it
c
h
i
n
g
m
o
d
e
o
f
t
h
e
re
so
na
nt
i
nv
erter
s
c
ha
nge
s.
T
h
i
s
i
n
c
r
ease
s
t
h
e
lo
s
s
es
o
n
t
h
e
t
r
an
sisto
r
s
and
re
du
ces
t
h
e
efficie
n
c
y
.
Th
e
aim
of
t
h
i
s
s
t
u
d
y
i
s
t
o
p
rese
nt
a
r
esea
rch
of
t
he
i
mpa
c
t
on
de
a
d
-t
ime
oper
a
tin
g
mod
e
s
w
i
th
sign
ifica
n
t
(2
t
o
3
t
i
m
e
s)
h
ig
her
va
l
u
e
t
h
an
t
he
n
e
e
d
ed
o
ne.
Th
is
i
s
done
w
i
t
h
a
t
r
an
sistor
b
ri
d
g
e
r
e
so
nan
t
in
verter
,
for
i
n
duc
t
i
o
n
h
e
a
t
i
n
g
a
pp
lica
tio
n
for
e
x
am
pl
e
.
B
ased
o
n
t
he
a
n
a
ly
sis,
t
he
a
u
t
hors
pr
opose
a
new
so
l
u
t
i
o
n
:
e
xce
p
t
for
a
m
i
nim
u
m
val
u
e,
d
ea
d
tim
e
sh
o
u
l
d
b
e
lim
it
ed
t
o
a
ma
x
i
mu
m
v
a
lu
e,
a
n
d
ma
th
ema
t
i
c
al
depe
n
d
e
n
ce
is
d
eri
v
e
d
.
P
a
rt
2
p
res
e
nt
s
gen
e
ral
theore
ti
cal
i
nformation.
P
ar
t
3
-
the
r
esults
o
f
e
x
p
e
rime
nta
l
r
esea
rche
s,
d
o
n
e
in
a
s
l
i
gh
tl
y
m
o
re
u
n
u
s
u
a
l
a
ppr
oac
h
-
t
he
t
h
e
ore
t
i
c
al
t
i
m
e
di
a
g
ram
s
a
nd
e
xper
i
m
e
nt
o
sc
ill
ogra
m
s
a
r
e
show
n
nex
t
t
o
e
ach
o
t
h
er.
O
n
t
he
b
a
s
is
o
f
t
h
e
exper
i
m
e
n
t
a
l
r
e
s
ults
i
n
P
art
3,
t
heore
t
i
c
al
c
o
n
cl
us
ion
s
a
nd
rec
o
mm
enda
t
i
ons f
or the
c
h
o
i
ce
of
dea
d
-
tim
e
are m
a
de
i
n P
a
rt 4.
2.
T
H
EO
R
E
TIC
A
L
DATA
F
i
g
u
r
e
1
shows
a
po
wer
ci
rcui
t
di
ag
ra
m
of
a
b
ri
dg
e
t
r
a
n
si
st
o
r
r
es
o
n
an
t
i
nve
rter
d
e
s
i
g
ne
d
for
in
duc
t
i
on
hea
t
i
ng,
w
ith
c
on
sta
n
t
v
o
l
t
a
g
e
su
p
p
l
y
.
D
e
pend
in
g
on
the
loa
d
,
by
eq
ui
va
len
t
t
r
a
nsform
atio
ns
t
h
e
dia
g
ra
m
i
n
t
he
d
ia
go
na
l
o
f
t
h
e
b
r
i
d
g
e
ca
n
b
e
t
u
r
ne
d
i
n
to
a
s
eri
es-
r
esonan
c
e
c
i
rcui
t
for
w
h
ic
h
t
h
e
fol
l
o
w
i
n
g
resona
nce
con
d
i
tio
n is
f
ulf
ill
ed.
F
i
gure
1.
Brid
g
e
tra
n
sis
t
or r
esona
n
t
in
v
er
t
e
r sc
hem
e
R
2
.
,
(1
)
It is kn
ow
n
tha
t
t
he ow
n
r
e
s
on
a
n
ce
fre
que
nc
y
of the
c
irc
l
e
is
d
e
t
e
r
m
i
ne
d by
the
d
epe
nde
n
c
e
.
(
2
)
wher
e
.
(3
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
D
e
ad tim
e
in
f
l
ue
nce o
n
o
p
er
at
i
ng
m
o
des o
f
trans
is
tor re
so
na
nt …
(
M
ih
a
i
l
An
tchev
)
1
817
is
t
he
d
a
m
pi
n
g
r
a
tio.
T
h
e
r
e
i
s
a
nothe
r
fr
equ
e
nc
y
f
o
r
the
i
n
ver
t
er
-
s
w
i
t
c
hin
g
f
r
e
que
nc
y
of
t
he
t
r
a
nsist
o
r
s
se
t
b
y
t
he
i
n
v
e
r
t
er
c
on
tr
ol
s
ys
tem
.
T
he
a
dju
s
t
i
ng
of
t
he
o
u
t
pu
t
p
ow
er
i
s
via
P
u
lse
F
r
e
q
u
e
nc
y
M
o
du
l
a
ti
o
n
(
P
F
M
)
-
c
h
ang
e
o
f
the
sw
i
t
ch
in
g
fr
e
q
ue
nc
y
w
h
ile
m
ain
t
a
i
n
i
ng
s
y
m
me
t
r
i
c
c
on
tr
o
l
o
f
the
di
a
g
ona
l
l
y
c
o
n
n
e
c
te
d
transis
t
ors -
50
%
dut
y
c
y
c
l
e
i
f
d
ea
d-
t
i
me
i
s
neg
l
e
c
t
ed.
D
e
pe
n
d
in
g
on
t
h
e
r
a
t
i
o
be
t
w
e
e
n
the
actua
l
reso
nanc
e
f
r
e
q
u
e
nc
y
o
f
t
h
e
cir
c
le
a
nd
the
s
w
i
t
c
h
i
n
g
f
r
e
que
n
c
y
,
dif
f
e
r
ent
o
p
er
a
tio
n
m
odes
ar
e
know
n
-
w
ith
a
f
r
e
quenc
y
be
low
or
a
bove
t
h
e
r
esonan
c
e,
i
n
r
e
sona
nce
m
o
de,
i
n
w
h
i
ch
t
h
e
c
ur
r
e
n
t
t
hr
ou
g
h
t
he
d
iag
o
n
al
c
an
b
e
in
t
e
rrup
t
ed
o
r
con
t
in
uou
s.
B
y
m
a
them
at
ica
l
a
nal
y
sis,
r
e
s
pecti
v
e
m
a
t
h
em
atica
l
d
epe
n
de
n
c
ies
can
b
e
o
b
t
ai
ne
d
an
d
can
b
e
dra
w
n
gr
aph
i
c
a
l
de
pe
n
d
enc
i
e
s
f
or
the
c
o
n
duc
t
i
on
time
s
o
f
t
r
ans
i
st
or
s
an
d d
i
ode
s
in
th
e s
c
heme,
as it
is
don
e in
[
18
],
n
o
t
tak
in
g
in
m
ind
t
h
e
d
ead-
tim
e.
T
he
t
h
e
or
et
ica
l
i
n
f
or
m
a
ti
o
n
p
r
e
se
nt
e
d
h
e
re
i
s
com
p
l
e
te
d
in
P
a
r
t4
w
ith
t
he
oret
ic
a
l
c
onc
l
u
sio
n
s
ba
sed
on
ex
pe
r
i
me
nt
a
l
r
e
s
ear
ch.
D
e
l
i
ber
a
te
l
y
,
the
r
ec
har
g
i
n
g
of
t
he
o
u
t
p
u
t
ca
p
a
ci
ta
nce
s
o
f
t
h
e
si
ng
le le
g
tran
s
is
to
r
s
is ig
n
o
red,
w
h
i
c
h
a
s is kn
o
wn ha
ppe
n
s
a
t
t
he
be
g
inn
i
ng
of
t
he
d
ea
d-
ti
m
e
.
Th
is is
d
o
n
e
t
o
di
ff
er
e
n
tia
te
t
h
e
r
egim
es
i
n
te
r
m
s
of
t
he
c
o
n
duc
tiv
i
t
y
r
a
nge
o
f
t
he
s
e
m
ic
on
duc
tor
dev
i
ce
s
in
t
he
c
ir
c
u
it.
3.
EX
PERIMENT
AL R
E
S
E
A
RC
H
E
S
The
osc
ill
ogr
a
m
s
pr
ese
n
t
e
d
he
r
e
a
r
e
f
r
o
m
e
x
per
i
m
e
n
t
s
un
der
the
fo
llo
wi
n
g
c
ond
iti
o
n
s
:
in
ve
rt
er
sup
p
l
y
vol
t
a
ge
200
,
used
t
r
a
nsis
tor
s
-
I
R
F
450.
T
he
c
apac
ita
nc
es
o
f
these
t
r
ans
i
st
ors
are
as
f
o
l
l
o
ws
:
ou
t
p
u
t
c
apac
ita
nce
-
6
0
0
,
fe
edb
a
c
k
c
apac
i
t
a
n
c
e
-
2
40
.
The
ma
ximum
value
of
d
r
a
in
c
u
r
r
e
nt
i
n
t
h
e
des
i
g
n
a
n
d
i
mple
me
n
t
a
tio
n
o
f
t
he
r
eso
n
an
t
i
nve
r
t
er
i
s
1
.
5
.
A
t
l
oa
d
c
h
a
n
g
i
ng,
t
h
i
s
ma
x
i
mu
m
v
a
lu
e
i
s
15
,
but
a
t
the
d
e
s
i
g
n
t
h
e
s
m
a
ller
valu
e
is
t
ake
n
,
as
d
ead-
tim
e
i
s
i
n
v
e
r
s
e
l
y
pr
opor
ti
ona
l
t
o
t
h
e
m
axim
um
c
ur
r
e
nt
v
a
l
ue.
The
ca
l
c
ul
a
t
ions
b
as
e
d
o
n
t
h
i
s
d
a
t
a
,
u
s
i
n
g
t
h
e
f
o
r
m
u
l
a
s
f
r
o
m
pa
ge
18
o
f
[
11
]
a
n
d
f
o
r
m
ul
a
(
7
)
of
[
7]
g
ive
appr
ox
ima
t
e
l
y
the
s
ame
resu
lt
fo
r
th
e
mi
nimu
m
d
e
ad
-time
v
a
lu
e
by
calc
u
la
ti
on
2
0
0
. In the
prac
t
i
c
a
l
im
pl
e
m
e
n
ta
t
i
o
n
,
the
dea
d
-
tim
e
value
i
s
f
irm
l
y
estab
l
ishe
d
60
0
.
F
o
r
a
l
l
the
o
s
ci
ll
ogr
am
s
show
n
be
low
,
t
h
e
C
H
1
c
ur
r
e
n
t
i
s
m
o
n
i
tor
e
d
w
i
t
h
a
c
ur
r
e
nt
p
r
o
be
wi
th
1
:1
ra
t
io
a
n
d
t
h
e vo
lt
ag
e
o
f
C
H2
wi
t
h
vo
lt
ag
e p
r
ob
e wi
th
1
0:
1
r
a
t
i
o.
(a)
(b
)
F
i
gur
e
2.
O
pera
tin
g
mode
a
t
0
.
5
w
i
t
h
dead-
t
im
e
c
ons
i
d
e
r
at
i
o
n.
(
a)
t
heor
e
t
ic
a
l
t
ime
diagr
a
m
s
o
f
t
h
e
cur
r
ent t
h
ro
ug
h
t
h
e
ser
i
e
s
-re
sona
nce
circ
u
it
and t
h
e
v
o
lta
ge
of the
reso
nan
t
capa
c
itor
;
(
b
)
osci
llo
gr
a
m
s
of
t
he
c
ur
r
e
nt
t
hr
o
u
g
h
t
he
s
er
i
e
s-
r
e
sona
nce
ci
r
c
uit
-
c
h1
and
t
h
e
vo
l
t
ag
e
of
t
he
r
e
s
ona
n
t
ca
p
a
cit
o
r
-
c
h
2
F
i
gur
e
2(
a)
s
h
o
w
s
t
ha
t
dur
i
n
g
t
h
e
dead-
t
im
e
f
or
t
he
c
onse
c
u
t
i
v
e
pair
o
f
dia
g
o
n
a
l
l
y
c
on
ne
c
t
e
d
tr
a
n
sis
t
or
s
t
h
e
con
d
u
c
t
i
o
n
is d
one
by t
h
e
r
e
v
e
r
s
e
dio
d
e
of
t
he
othe
r
pair
o
f
tr
a
n
sist
or
s.
T
hi
s
d
o
es
n
o
t
a
f
f
ec
t
t
h
e
m
ode
o
f
o
p
er
a
tio
n
of
t
he
r
e
s
ona
n
t
i
n
v
e
r
ter
–
F
i
gur
e
2(
b)
.
The
s
am
e
i
s
t
he
case
at
0.5
F
i
g
u
r
e
3(
a)
a
nd
F
i
gur
e
3(
b)
.
Th
e
th
eo
reti
cal
m
o
d
e
o
f
reso
nan
c
e
,
id
e
a
l
l
y,
w
it
ho
ut
d
ea
d-
t
i
m
e
c
ons
i
d
e
r
at
i
on,
i
s
ill
us
t
r
ate
d
w
i
t
h
t
he
t
ime
d
i
a
g
r
a
m
s
i
n
F
i
gur
e
4.
I
t
ca
n
be
s
e
e
n
t
h
a
t
t
h
e
r
e
v
erse
d
io
de
s
d
o
n
ot
c
o
n
d
u
c
t
,
i
.e
.
t
h
ere
i
s
no
r
e
turn
o
f
e
n
erg
y
from
t
h
e
l
o
a
d
c
ircu
it
b
a
c
k
to th
e
power
s
u
ppl
y
.
If
the
c
o
ntr
o
l
system
s
u
p
p
o
rts
t
h
is
t
he
or
et
ical
m
ode,
it
wo
u
l
d
pr
o
v
ide
m
a
x
i
mum
ener
gy
efficie
n
c
y
.
Wh
en
e
n
t
eri
n
g
t
h
e
d
ea
d-
t
i
m
e
i
n
the
r
e
so
na
nc
e
mode
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
815
–
1
822
1
818
im
me
di
a
t
el
y
af
ter
sw
itc
h
i
n
g
o
ff
t
h
e
c
ons
ec
u
t
i
v
e
pa
ir
o
f
di
a
g
o
n
a
lly
c
o
n
n
ected
t
ran
s
is
to
rs,
th
eir
rev
e
rse
diod
es
c
o
n
duc
t
–
F
i
g
u
r
e
5
(
a
)
and
F
i
gur
e
5(
b)
.
I
t
t
ur
ns
o
u
t
t
ha
t
t
h
is
m
ode
i
s
simi
lar
to
t
h
a
t
show
n
in
F
ig
ur
e
3,
r
e
gar
d
l
e
ss
o
f
t
h
e
di
ffe
r
e
nc
e
i
n
r
ati
o
o
f
t
h
e
f
r
e
que
nc
ies
a
nd
.
(a)
(
b
)
F
i
gur
e
3.
O
pera
t
i
n
g
m
ode
a
t
0.5
w
ith
d
ea
d
-
ti
m
e
c
ons
idera
t
i
o
n. (a) theor
e
t
i
c
a
l
t
im
e
dia
g
ram
s
of
th
e c
u
rre
nt
t
hro
u
gh t
h
e
se
ries-r
eson
ance
c
i
r
cu
i
t
a
nd
the
vo
l
t
a
g
e
of
t
he
r
e
s
on
a
n
t
ca
pa
ci
t
o
r
;
(
b
)
osc
i
l
l
ogr
am
s
of
t
he
c
ur
r
e
n
t
t
hr
o
u
g
h
t
he
s
e
r
ies-
r
e
sona
nc
e
c
i
rcu
it
-
c
h1
a
nd
t
h
e
v
o
lta
ge
o
f
t
h
e
r
e
sona
n
t
ca
p
a
cit
o
r
-
c
h
2
F
i
gur
e
4.
O
per
a
ti
n
g
m
ode
a
t
w
itho
u
t
d
e
a
d-
ti
m
e
c
onside
r
at
i
on.
T
he
or
eti
c
a
l
t
i
m
e
dia
g
r
a
ms
o
f
the
curre
nt t
hro
u
g
h
the
s
eries-
re
s
on
a
n
ce
circ
u
i
t
a
nd
t
h
e
vo
lta
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e
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nt
capa
c
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or
L
C
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L
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C
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G1,3
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4
t
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Id
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o
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a
d
t
i
m
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t
J
P
o
w
Elec
&
D
r
i
S
y
st
I
S
S
N
:
2088-
86
94
D
e
ad tim
e
in
f
l
ue
nce o
n
o
p
er
at
i
ng
m
o
des o
f
trans
is
tor re
so
na
nt …
(
M
ih
a
i
l
An
tchev
)
1
819
(a)
(b
)
F
i
gur
e
5.
O
pera
t
i
n
g
m
ode
a
t
w
i
t
h
de
ad-
tim
e
c
onside
r
at
i
o
n
(
t
he
s
t
a
r
t
o
f
t
h
is
t
im
e
i
s
a
fte
r
t
h
e
curr
ent
has
pa
sse
d
t
h
r
o
ug
h
z
e
r
o
v
al
ue
)
.
(
a
)
t
heor
e
tica
l
time
d
i
agr
a
ms
o
f
t
h
e c
u
rre
n
t t
h
rou
g
h
th
e se
ri
es
res
o
n
a
n
c
e
c
i
rcu
it
a
nd
the
r
e
sonan
t
c
apa
c
i
t
o
r
vo
lta
ge
;
(b)
osci
ll
ogr
am
s
of
t
h
e
c
ur
r
e
nt
t
hr
o
ugh
t
h
e
se
r
i
es
r
e
sona
nc
e
c
i
r
c
ui
t
-
c
h1
a
nd
t
h
e
vol
ta
ge
o
f
th
e
r
e
sonan
t
c
a
p
ac
i
t
or
-
c
h2
(a)
(
b
)
F
i
gur
e
6.
O
per
a
ti
n
g
m
ode
a
t
w
it
h
dea
d
-
t
i
m
e
cons
ider
a
t
io
n
(
t
he
b
e
g
in
ni
n
g
o
f
t
h
e
tim
e
is
b
ef
or
e
the
cur
r
ent ha
s pas
s
ed
t
h
r
ou
g
h
ze
r
o va
lue
)
.
(a
) the
o
r
e
tica
l
tim
e
di
ag
rams o
f the cu
rren
t
t
h
r
oug
h
th
e
s
e
ries-
resona
nce
circ
uit
a
nd
t
h
e
r
e
sona
nt
capa
c
i
t
o
r
vol
ta
ge
;
(b
) o
s
cillog
rams o
f
th
e
cu
rr
ent th
ro
ugh
th
e
se
ri
es- re
so
n
a
nc
e ci
rc
u
i
t
-
c
h1
a
nd
t
h
e
v
o
lta
ge
o
f
t
h
e
r
e
son
a
nt
c
apa
c
i
t
or
-
c
h
2
The
oper
a
t
i
n
g
m
odes
s
how
n
in
F
igur
e
6
a
n
d
F
i
gur
e
7
ar
e
n
o
t
desc
r
i
be
d
in
t
he
l
it
e
r
a
t
ur
e
and
ar
e
du
e
on
l
y
t
o
dea
d
-
t
im
e,
a
l
t
h
o
u
g
h
t
he
s
w
itc
h
i
n
g
f
r
e
que
ncy
i
s
h
i
gher
t
han
t
h
e
r
e
so
nanc
e
fr
eq
u
e
nc
y.
T
y
p
ica
l
l
y
,
t
h
i
s
m
ode
o
f
op
er
at
i
o
n
i
n
t
he
a
bse
n
ce
o
f
de
a
d
-
t
i
m
e
,
i
s
e
xpec
t
e
d
t
o
p
r
o
vi
de
Z
V
S
.
The
in
te
r
e
st
ing
in
b
oth
m
ode
s
is
the
a
l
t
e
r
n
a
t
i
o
n
of
c
ond
uc
ti
on
i
n
t
er
va
l
s
o
f
o
n
e
pa
ir
o
f
d
i
a
g
o
n
a
l
l
y
c
on
ne
c
t
ed
d
io
des
w
i
th
t
he
o
t
h
er
p
a
i
r
of
dia
g
ona
lly
c
o
n
n
ec
te
d
d
i
o
d
e
s
.
I
n
F
ig
ur
e
7,
t
h
e
d
ur
at
io
n
of
t
he
t
w
o
i
n
t
e
r
v
a
l
s
i
s
t
h
e
s
a
m
e
.
A
s
y
o
u
c
a
n
s
e
e
,
b
o
t
h
of
t
he
m
ode
s
d
o
n
o
t
p
r
o
v
i
de
Z
V
S
.
I
n
t
he
c
a
s
e
sh
ow
n
i
n
F
i
g
ur
e
8,
w
he
n
t
h
e
de
ad-
time
c
o
i
n
c
i
de
s
in
d
ur
a
tio
n
w
i
t
h
t
he
c
o
n
d
u
c
ti
o
n
i
n
t
er
va
l
of
a
p
air
of
r
ever
se
d
i
ode
s
be
for
e
t
he
s
witc
hi
n
g
o
f
t
h
e
i
r
respec
tive
trans
i
s
t
ors,
ZVS is p
r
o
v
id
e
d
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N: 2
0
8
8
-
86
94
I
n
t
J Po
w El
ec &
D
ri S
y
s
t
Vo
l. 1
0
,
No
. 4
,
D
e
c
2
0
19
:
1
815
–
1
822
1
820
(a)
(b
)
F
i
gur
e
7.
O
pera
tin
g
mode
a
t
w
i
t
h
dead-
tim
e
c
ons
i
d
e
r
at
i
o
n
(
t
he
b
e
g
i
n
ni
ng
and
the
e
nd
of
t
h
i
s time
ar
e symm
etrica
l
l
y
spa
c
e
d
t
o th
e
curre
nt fl
o
w
t
h
r
oug
h
zer
o va
l
u
e
). (а
)
t
h
e
o
r
et
i
cal
ti
m
e
d
i
ag
ra
ms o
f
t
h
e cu
rre
n
t
thr
o
u
g
h
the
s
e
r
ies-
r
esona
nce
circ
uit
a
nd
the
r
e
sonan
t
capa
c
itor
vo
l
t
age
; (b
) o
s
cillog
rams o
f th
e
cu
rrent
t
h
r
o
u
g
h
t
he
s
e
r
ies-
r
esonanc
e
c
i
r
c
u
it
-
c
h1
an
d
the
v
o
lta
ge
o
f
t
h
e
r
e
so
nan
t
c
a
p
ac
it
or
- ch
2
N
a
m
e
ly
t
h
i
s
b
o
r
d
er
l
i
ne
c
a
s
e
is
u
se
d
be
l
o
w
to
s
e
t
t
he
m
a
x
i
m
um
d
e
ad
-t
ime
l
i
m
it
a
tio
n
.
T
hi
s
c
a
se
i
s
take
n
in
m
in
d,
b
eca
use
a
t
t
h
e
f
ur
ther
i
ncr
ease
o
f
t
he
f
r
e
q
u
e
n
c
y
o
f
sw
itc
hi
n
g
dur
in
g
de
ad-
t
ime
alw
a
y
s
t
he
r
e
ver
s
e
dio
d
e
o
f
t
he
r
e
s
pe
c
t
i
v
e
tr
a
n
si
s
t
or
c
on
duc
ts
a
nd
ZV
S
is
i
m
p
l
emen
t
e
d
.
(a)
(b
)
F
i
gur
e
8.
O
pe
rati
n
g
m
ode
a
t
w
it
h
de
ad-
time
c
onsider
at
i
on
(
t
he
e
n
d
o
f
t
h
is
t
i
m
e
is
b
ef
or
e
t
he
c
u
r
r
e
n
t
ha
s
passe
d
thr
o
u
g
h
ze
r
o
v
a
l
ue
)
.
(
a)
t
heor
et
i
c
a
l
tim
e
d
i
agr
a
m
s
o
f
th
e
c
u
r
r
e
nt
t
hr
o
ugh
t
h
e
se
r
i
es-
r
e
sonanc
e
circ
u
i
t
a
nd
the
r
e
sona
nt
capa
c
it
or
v
o
l
tage
;
(
b
)
o
s
cillog
rams o
f th
e
cu
rr
en
t
thr
o
ug
h
t
h
e
ser
i
es-
r
e
sona
nce
c
i
r
c
u
it
-
c
h1
a
nd
t
h
e
v
o
lta
ge
o
f
t
h
e
r
e
sona
n
t
c
apac
i
t
or
-
c
h
2
4.
THE
O
R
E
T
I
C
A
L CONCLUSIONS
F
r
om
t
he
s
how
n
in
P
ar
t
3
c
a
n
be
c
o
n
c
l
u
d
e
d
t
ha
t
a
p
a
r
t
f
r
o
m
the
m
inim
um
limi
t
t
he
d
e
a
d
-time
must
h
a
v
e
m
a
xim
u
m
l
i
m
i
t
to
pr
o
v
i
de
a
Z
V
S
m
ode
i
n a
w
i
der
in
ter
v
a
l
o
f
f
r
e
q
ue
n
c
y
v
a
r
i
at
ion
ar
ou
nd
t
h
e
r
eso
n
a
n
ce
v
a
l
ue
.
I
t
i
s
su
ff
ici
e
nt
t
o
t
h
e r
e
c
h
a
r
gi
n
g
t
ime
of
t
he
o
u
t
p
u
t c
a
p
ac
i
t
a
n
ces of t
h
e
tran
s
i
s
t
o
r
s [7,
11]
t
o a
dd
t
h
e t
i
m
e
f
o
r
sw
itc
h
i
n
g
o
n
the
r
e
ver
s
e
di
ode
s,
i
.
e
.
t
o
e
n
sur
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
E
l
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
D
e
ad t
i
m
e
i
n
f
l
u
ence
o
n
o
p
e
r
a
t
i
ng m
o
de
s o
f
tr
ansis
t
o
r
reso
na
n
t
… (M
i
h
a
i
l An
tche
v)
1
821
(
4
)
The
q
u
e
s
t
i
o
n
i
s
what
i
s
t
h
e
v
a
lue
of
t
i
m
e
.
Re
gardi
n
g
t
h
e
sw
itc
h
i
n
g
t
ime
of
t
he
d
io
de
s
use
d
i
n
t
h
e
D
C
/
D
C
c
o
n
v
e
r
ters,
there
is
a
d
eta
ile
d
st
u
d
y
[1
9]
s
how
in
g
t
h
at
f
or
t
he
d
i
f
fe
rent
t
y
p
es
i
t
ra
nge
s
fr
om
2
t
o
1
5
nS
.
I
n
t
hi
s
ca
se
,
how
eve
r
,
it
is
a
bo
ut
t
he
r
eve
r
se
d
iode
o
f
M
O
S
F
ET,
w
hich
i
s
ac
tu
a
l
l
y
a
p
a
rasitic
t
ra
nsist
o
r
in
the
st
r
u
c
t
ure.
A
t
t
h
e
g
a
te
o
f
the
tra
n
s
i
s
t
or
t
here
i
s
no
s
w
i
t
c
h
-
on
si
g
n
al
a
s
i
t
i
s
i
n
t
he
s
y
n
c
h
ro
no
us
r
ec
ti
fier
s
so
th
i
s
s
ig
na
l
w
ill
b
e
prov
i
d
ed
a
fter
d
e
a
d
-t
ime
.
I
n
thi
s
case
,
t
he
p
ub
l
i
s
h
e
d
s
t
u
d
i
es
o
n
sync
h
r
on
ous
r
ect
ifie
r
s
c
an
no
t
b
e
u
se
d.
F
r
o
m
thi
s
p
oi
n
t
o
f
v
i
e
w
,
it
c
a
n
b
e
sa
id
t
ha
t
in
t
h
e
ma
nu
fa
c
t
u
r
ers
'
d
ocum
enta
t
i
o
n
t
her
e
i
s
n
o
prec
ise
da
ta
o
n
the
t
i
m
e
o
f
sw
itc
h
i
n
g
o
n
o
f
t
h
e
re
verse
di
o
d
e.
F
or
e
xam
p
le
,
w
i
t
h
r
egar
d
t
o
t
he
u
sed
he
r
e
IRF45
0
t
ra
nsis
tors
i
n
[2
0]
i
t
i
s
s
a
i
d
:
“
Intr
i
n
sic
tur
n
-on
ti
me
is
n
e
g
l
i
g
ib
le.
Tur
n
-on
sp
e
e
d
is
s
u
b
s
t
a
n
ti
a
lly
c
o
n
t
r
o
l
l
e
d
b
y
L
S
+
L
D
”
.
A
l
s
o
f
o
r
t
h
e
s
u
m
o
f
t
h
e
i
n
d
u
c
t
a
n
c
e
s
o
f
the
tw
o
t
e
rm
i
n
a
l
s
of
t
h
e
t
ra
nsis
tor,
the va
lue
is 6.
1
nH
.
Tak
i
n
g
i
n
min
d
t
he
a
b
ove,
t
h
e
au
th
ors
of
fers
t
he
f
o
l
low
i
ng
w
a
y
of
d
e
t
erm
i
ning
the
ti
m
e
:
Be
for
e
st
a
r
t
i
n
g
t
he
s
w
i
tc
h
on
of
t
he
M
O
S
F
ET
re
verse
di
o
d
e
,
t
he
capa
c
i
t
y
of
t
he
d
ra
i
n
-
s
o
u
r
ce
tr
ansist
or
n
e
e
ds
t
o
be
curr
ent
d
i
sc
ha
rged
t
hro
u
gh
th
e
dia
g
o
n
a
l
o
f
the
i
nver
t
e
r
b
ri
dge
t
o
a
v
ol
t
a
g
e
o
f
ap
prox
ima
t
e
l
y
0.
6V
.
The
r
e
f
ore
,
it
c
a
n
b
e
as
su
me
d
tha
t
o
n
th
e
sum
of
t
he
i
nd
uc
tanc
e
s
i
s
app
l
i
e
d
v
o
lta
g
e
w
ith
s
uc
h
va
lue.
T
he
n
th
e
rate
of
curr
ent
c
h
a
n
ge
t
hro
u
g
h
t
he
m
and
t
h
e
re
verse
diode
w
il
l
be
:
.
(
5
)
O
r
i
n
t
h
e de
scribe
d
case
.
.
0
.
1
(
6
)
There
f
ore
,
a
t know
n va
l
u
e o
f
the
c
urre
n
t
w
h
i
c
h
m
ust
be r
eac
hed
thro
u
gh
the
re
verse
dio
d
e
.
(
7
)
F
o
r e
x
am
ple,
f
or
t
he c
ase
show
n in F
i
gur
e 8
(
b) fo
r
1
,
1
0
.
A
t
c
urrent va
l
ue
1
0A
the t
i
m
e
w
ou
ld
be
100
nS
.
5.
CONCL
U
S
IONS
As
a
r
esul
t
o
f
t
his
st
u
d
y
for
t
h
e
de
ad-
tim
e
i
m
pa
ct
o
n
t
h
e
o
p
er
a
t
i
n
g
m
o
d
e
s
o
f
brid
ge
t
ra
ns
istor
reso
na
n
t
in
verter
, is es
t
a
b
l
i
s
h
e
d
an
oper
a
t
i
n
g
m
ode aro
un
d
t
h
e
r
e
so
na
nce
f
re
qu
en
cy
wi
t
h
c
o
n
s
ecut
i
v
e
co
nd
u
c
t
i
o
n
o
f
t
he
pairs di
a
g
ona
l
l
y
co
n
n
ec
te
d
r
e
ver
s
e
MO
S
F
ET
di
o
d
es,
w
h
ic
h
has
n
o
t
b
e
e
n
descri
b
e
d
t
ill n
o
w
.
H
ere
is
o
ffer
ed
a
form
ula
for
the
m
a
xim
u
m
l
i
mita
t
i
o
n
o
f
de
a
d
-time
va
l
u
e
be
si
des
t
he
k
n
o
w
n
s
o
fa
r
m
i
nim
u
m
va
l
u
e
l
i
mit
a
ti
o
n
.
A
n
e
xam
p
l
e
o
f
how
to use
i
t
i
s show
n a
s
w
ell.
REFE
RENCES
[1]
X
i
n
g
k
un
Qi,
Yo
ng
lo
ng
P
e
ng
,
Yab
i
n
Li,
“
P
aram
e
t
ers
Des
i
g
n
o
f
S
e
ri
es
R
es
o
n
an
t
Inv
e
rter
C
ircuit”,
Phys
i
c
s
P
r
o
cedi
a
,
2
4
,
pp.
13
3-1
38,
2
0
12.
[2]
M
a
ri
an
K
.
K
azim
i
e
r
czu
k,
D
ari
u
sz
C
zarkow
sk
i,
“
Reson
a
nt
P
ow
e
r
C
on
v
e
rte
r
s”
,
A
Jo
hn
W
i
lle
y
&
Son
s
,
Se
c
o
nd
edition,
2011.
[3]
S
a
n
d
j
a
y
Hanan
u
r
,
“
M
a
t
chi
n
g
S
y
stem
D
ead
Time
t
o
M
O
S
FET
P
a
ram
e
ter
s
in
Z
VS
C
i
r
cuits”,
V
ishay
Si
liconix,
Rev
i
s
i
o
n
:
06
.
1
0
.
20
14
,
A
N
84
5
,
Do
c
um
ent
Nu
mber:
67
527
.
[4]
“
F
ai
rchild
S
e
m
ico
ndu
cto
r
,
A
d
v
a
n
ced
P
uls
e
F
req
u
ency
M
o
dul
ation
(
P
F
M
)
C
ontro
ll
er
f
or
H
alf
-
Bri
d
g
e
R
eso
n
an
t
Converters”,
FA
N
7631, www.
f
a
i
r
childs
e
mi.com
, 2012.
[5]
“
I
n
f
in
eon,
D
esign
G
u
i
d
e
f
o
r LL
C
Con
v
erter
wit
h
ICE
2H
S0
1
G
”,
Appl
icati
on Not
e
,
V1.0
, Ju
l
y 2
0
1
1
.
[6]
J
i
an
gu
ang
M
A
,
X
u
ey
e W
E
I
,
Li
a
n
g
HU
,
W
e
n
t
i
ng J
I
A
,
“
In
vestig
ati
o
n
on
op
t
i
m
a
l
p
aram
e
t
er s
e
l
ecti
o
n
f
o
r LLC h
a
lf
-
b
r
id
ge
r
es
on
ant
con
v
ert
e
r
bas
e
d
o
n
F
H
A
”,
T
u
r
k
ish Jo
ur
nal
o
f
Elect
ri
ca
l
En
g
i
neering
&
Co
mputer
S
c
ience
,
no
2
6,
p
p
.
895
-90
5
,
2018.
[7]
T
e
xas
Ins
t
rum
e
nts,
“
S
u
rv
ey
o
f
Reson
a
nt
C
on
verter
T
op
ol
og
ies”,
2
0
18
Te
xas Inst
rument
s
P
o
wer
Suppl
y Des
i
gn
Se
min
a
r
S
EM
23
0
0
,
SLUP
376
.
[8]
S
ilv
io
d
e
Sim
o
n
e
,
“
L
LC
r
eson
ant
h
a
lf
-bri
dg
e
con
v
ert
e
r
des
i
g
n
g
u
i
d
el
in
e”
,
S
T
Mi
cro
e
lectr
o
n
i
cs
,
AN
24
50
,
Ma
rc
h
,
20
14
.
[9]
Je
ff
J
in,
“
A
pp
lic
a
t
io
n
No
te
f
o
r
a
n
LLC
Re
so
na
n
t
C
on
ve
rte
r
U
sin
g
R
eso
n
an
t
Con
t
rol
l
er
H
R1
00
0”,
The
Fu
t
u
re
of
An
alog
IC
Te
c
h
n
o
lo
gy
,
A
N
05
4,
20
1
3
.
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 :
1
8
1
5
– 1
822
1
822
[10]
Junhao
L
uo,
Jun
h
ua
W
ang,
Z
h
ijian
Fang,
Ji
anwei
Shao,
J
i
anqui
L
i
,
“O
p
tim
a
l
D
esi
g
n
o
f
a
H
i
gh
Eff
i
ci
ency
L
LC
Res
o
n
a
nt
C
onv
erter
wit
a
Narrow
Fre
q
u
e
nc
y Ra
n
g
e
fo
r Vo
lta
ge
R
e
g
ula
t
io
n”
,
E
n
erg
i
es
,
20
18
.
[11]
H
e
len
D
i
ng,
“
Desi
gn
o
f
Reso
n
a
n
t
H
alf-Bri
dg
e
Con
v
ert
e
r
us
ing
IRS
279
5
(1,
2),
Con
t
rol
IC”
,
Interna
tional
R
ectifi
er
AN-11
60
.
[12]
J
.
T
i
a
n
,
G
.
B
e
r
g
e
r
,
T
.
R
e
i
m
a
n
n
,
M
.
S
c
h
e
r
f
,
S
.
P
e
t
z
o
l
d
t
,
“
A
h
a
l
f
-bri
dg
e
s
e
ries
r
es
on
ant
i
nvert
er
f
o
r
i
nd
uct
i
o
n
co
ok
ers
us
in
g
a
no
vel
F
P
G
A
-bas
ed
c
o
n
tro
l
s
t
r
ateg
y”,
Europea
n
Con
f
er
enc
e
on
power
Elect
ro
ni
c
s
an
d
A
p
licat
i
ons
, 20
0
5
,
[13]
Reza
B
e
iran
van
d
,
B
is
han
Ras
h
idian
,
M
oh
a
m
m
a
d
Reza
Zo
lh
adri
,
S
e
y
e
d
Mo
ha
mma
d
Hosse
in
A
la
v
i
,
“
O
pt
im
iz
ing
t
h
e
N
o
rm
ali
zed
D
ead-Ti
m
e
and
M
a
xim
u
m
S
w
itchi
ng
F
requen
c
y
o
f
a
W
i
d
e-
A
djust
a
ble
-
Ran
g
e
L
L
C
Reso
nan
t
Converter”,
IEEE
T
r
a
n
s.
on
Po
wer
Electr
onics
,
v
o
l
2
2
, n
o2
,
p
p
. 4
62
-47
2
, 2
01
1.
[14]
Ya
sse
r
N
ou
r,
A
rn
old
Kno
t
t
,
L
a
r
s
Pre
ss
Pe
te
rse
n
,
“Hig
h
fre
q
ue
n
c
y
S
of
t
swit
c
h
i
ng
S
e
ries-res
onant
C
on
verter
Ut
i
l
i
z
ing
Gal
lium
Nitr
i
d
e
F
e
t
’
s
”
,
Pr
oceedi
n
g
s
of
th
e 1
9
t
h
E
u
rop
e
a
n
Con
f
eren
ce o
n
P
o
wer
El
ectr
o
n
i
cs
an
d
Ap
pl
ic
a
tio
ns
,
2017
.
[15]
X
i
Z
h
a
ng
,
Ziy
ang
L
a
i,
R
u
i
Z
h
i
on
g,
Z
h
e
L
i,
Z
h
i
mi
n
Zh
ang,
L
ian
g
Z
h
ong
,
“S
wit
c
hi
ng
D
e
vic
e
D
ead
T
im
e
Optimi
z
a
tion
o
f
R
esonant
Double-Si
ded
LCC
Wi
rel
e
ss
C
harging
Sys
te
m
f
o
r
El
ectric
Veh
i
cl
e”,
En
er
gi
es
,
vol
10,
n
o
11,
2
0
17.
[16]
L
i
n
g
-F
en
g
S
h
i
,
F
u
Bo
L
i
u
,
Hui
-
S
e
n
H
e
,
Xi
ang-Y
u
M
ao
,
Xi
n-Qu
an
L
a
i,
“
D
e
si
g
n
o
f
Ad
aptive
dead-t
im
e
con
t
rol
ci
rcui
t
f
o
r reson
a
nt hal
f
-
br
i
d
ge d
ri
ver”,
In
ter
nationa
l Jo
ur
nal of
E
l
ect
ronics
,
v
o
l
10
0
,
no
10,
pp.
131
7-13
31
,
2
013
.
[17]
S
u
ros
o
,
Daru
t
o
i
N
ugro
h
o
,
T
os
h
i
hi
k
o
N
og
uchi,
“ New
Dead
-Tim
e
Co
m
p
en
sati
on
M
eth
o
d
at P
owe
r
Invert
er Usin
g
Carri
er
B
ased
S
i
n
u
s
o
i
dal
P
u
lse-Wid
t
h
M
o
du
lati
on
”.
Inter
n
a
tio
na
l Jou
r
na
l
of
E
l
ect
rica
l a
n
d Comp
ut
er
En
gi
ne
e
r
i
n
g
(
I
J
EC
E
)
,
v
o
l
8,
no 6
,
p
p
.
4
88
0-48
9
1
,
2
018
.
[18]
P
l
atek
M
.,
Z.
W
aradzin
,
“
Op
erati
on
m
o
des
of
f
u
ll-bri
d
g
e
voltag
e
-source
resonant
i
nverter
wit
h
PFM
c
ontro
l
f
or
i
n
d
u
ctio
n
h
eating
appl
icatio
ns”,
El
ektrotech
ni
ka i
El
ektr
oni
ka
, 2
5
(
1
)
, pp
. 5
8-6
7
, 2
00
6.
[19]
J
i
m
Willi
a
m
s
, D
avi
s
Beeb
e, “D
i
o
d
e T
u
rn-o
n
T
i
me In
d
u
ces F
ai
lu
re
s
i
n
S
w
it
chin
g Regul
ato
r
s”,
L
i
n
e
ar Te
c
h
n
o
lo
gy
,
AN12
2,
2
00
9.
[20]
International
Re
ctifie
r,
R
epetiti
v
e
A
val
a
nhe
and
dv/dt
Transist
ors
IRF
4
50
,
PD
-330
F
,
2
2.
0
1
.
2001,
d
eri
v
ed
f
rom
ww
w.
ir
f
.
c
o
m.
B
I
OGRAPHIES
O
F AUTHO
RS
M
i
hail
Hrist
ov An
tch
e
v
–
P
rof
e
ss
or,
P
h
D
,
DS
c
-
was
born
in
S
ofia
,
B
u
l
gari
a
,
i
n
195
5.
H
e
aw
ard
e
d
Mas
t
er d
egree at
Tech
nical
Un
i
v
e
rs
ity
–
S
o
f
ia, Bu
lg
aria
, in
1
9
8
1
.
He
is P
rof
e
sso
r
i
n
“
P
ow
er e
lect
ron
i
cs”
in
Tech
nical
un
i
v
e
rsity-S
ofia.
He h
a
s
p
ub
li
sh
e
d
ab
o
u
t
1
00
scie
n
tific pap
ers,
1
2
b
oo
ks
a
nd
o
t
her
s
c
hoo
l
applian
ces.
P
ro
f.
M
.Ant
chev
w
ork
s
i
n
th
e f
i
e
l
d of po
w
er el
ectron
i
c
co
nvert
ers
w
i
t
h
im
p
ro
ved
energy
i
n
d
i
cators,
a
s
we
l
l
a
s
of
d
y
n
am
ic
a
nd
cont
rol
sy
st
em
o
f
p
o
w
e
r
el
ectron
i
c co
nv
erters. E-m
ail
:
a
ntch
ev@t
u-s
o
fi
a
.
b
g
H
r
ist
o
M
ihai
lo
v
A
n
t
c
hev
–
Chief
A
s
sist
an
t
,
P
hD w
as
b
orn
in
S
o
f
i
a,
B
ul
gari
a
,
in
1981
.
H
e
aw
ard
e
d
Bach
elo
r
and
M
as
t
e
r
degrees
at
Techn
i
c
a
l
Univ
e
r
s
i
t
y
– S
of
i
a
, Bu
l
ga
ri
a,
i
n
s
p
ecial
izatio
n “
P
o
w
er El
ectro
ni
c
s
He
is Ch
i
e
f
A
ss
i
s
tant in
“E
le
ct
ron
i
cs
”
in
U
niv
e
rs
it
y
of
Ch
emi
cal T
echn
o
lo
gy
and
M
etallu
rgy. Dr.H.A
n
tch
e
v w
o
rk
s i
n
t
h
e
f
i
e
ld
o
f
pow
er elect
ron
i
cs,
comput
er s
imul
a
tion
a
nd
cont
ro
l
.
E
-
m
ail: hrist
o
_a
nt
c
h
ev@t
u-so
fi
a.bg
Evaluation Warning : The document was created with Spire.PDF for Python.