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ase
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tem
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le
PF
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h
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s
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n
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c
c
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n
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e
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CC B
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e
n
se
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C
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r
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s
p
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A
uth
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r
:
Ma
jd
Gh
az
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s
eh
E
lectr
ical
E
n
g
in
ee
r
in
g
Dep
ar
t
m
en
t,
Prin
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s
s
Su
m
ay
a
Un
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r
s
ity
f
o
r
T
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h
n
o
lo
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Kh
alil A
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-
Sak
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St,
Am
m
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,
J
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ail:
m
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b
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s
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t.e
d
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j
o
1.
I
NT
RO
D
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I
O
N
T
h
e
d
em
an
d
f
o
r
DC
lo
ad
s
lik
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PC
s
,
lap
to
p
s
,
elec
tr
o
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ic
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ev
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es,
an
d
h
o
m
e
ap
p
lian
ce
s
is
r
is
i
n
g
.
T
h
ese
lo
ad
s
o
b
tain
p
o
wer
f
r
o
m
AC
m
ain
s
in
two
s
tag
es,
a
s
s
h
o
wn
in
Fig
u
r
e
1
(
a)
.
First,
AC
i
s
r
ec
tifie
d
in
to
DC
u
s
in
g
a
f
u
ll
-
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e
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ec
tifie
r
a
n
d
th
en
f
ilter
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with
a
ca
p
ac
ito
r
[
1
]
.
T
h
e
s
ec
o
n
d
s
tag
e,
th
e
DC
-
DC
s
tag
e,
u
tili
ze
s
s
witch
es
to
ad
ju
s
t
th
e
v
o
ltag
e
ac
co
r
d
i
n
g
to
th
e
ap
p
licatio
n
.
T
h
ese
s
u
p
p
lies
ar
e
r
ef
e
r
r
ed
to
as
s
witch
ed
-
m
o
d
e
p
o
wer
s
u
p
p
lies
(
SMPSs
)
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d
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o
ast
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ig
h
ef
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icien
cies
th
at
s
u
r
p
ass
9
0
%,
lead
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g
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th
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lace
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en
t
o
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lin
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ly
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eg
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lated
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o
wer
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u
p
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lies
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h
e
DC
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k
in
SMPS,
C
in
,
h
el
p
s
m
ain
tain
t
h
e
o
u
tp
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t
DC
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l
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s
e
to
th
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k
v
alu
e
o
f
th
e
in
p
u
t
v
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ch
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r
ex
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e
r
ien
ce
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ief
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ts
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ig
h
in
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t
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e
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o
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ch
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r
g
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g
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h
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u
s
es
cu
r
r
en
t
s
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ar
o
u
n
d
th
e
in
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u
t
v
o
ltag
e
p
ea
k
s
,
as
d
ep
icted
in
Fig
u
r
e
1
(
b
)
.
T
h
e
n
o
n
-
s
in
u
s
o
id
al
n
atu
r
e
o
f
th
is
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p
u
t
cu
r
r
en
t,
lead
s
to
a
p
o
o
r
p
o
wer
f
ac
to
r
(
PF
)
.
T
h
e
to
tal
h
ar
m
o
n
ic
d
is
to
r
tio
n
o
f
th
e
in
p
u
t c
u
r
r
en
t (
T
HDi)
in
Fig
u
r
e
1
(
b
)
is
1
8
4
%.
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h
e
r
elativ
ely
lar
g
e
n
u
m
b
er
o
f
SMPSs
u
s
ed
d
aily
r
ef
lects
p
o
o
r
ly
o
n
th
e
p
o
wer
q
u
ality
an
d
s
tab
ilit
y
o
f
th
e
g
r
id
.
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h
e
r
ed
u
ctio
n
in
PF
d
u
e
to
th
e
h
ar
m
o
n
ic
c
o
n
ten
t
o
f
t
h
e
d
is
to
r
ted
c
u
r
r
e
n
t
is
n
o
t
d
esira
b
le
as
it
in
cr
ea
s
es
th
e
cu
r
r
en
t
with
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r
awa
l
f
r
o
m
t
h
e
m
ain
s
f
o
r
th
e
s
am
e
am
o
u
n
t
o
f
r
ea
l
p
o
wer
.
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h
u
s
,
th
ese
s
u
p
p
lies
m
u
s
t
co
m
p
ly
with
in
ter
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atio
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al
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tan
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s
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ch
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e
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e
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m
u
s
t
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e
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th
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p
ly
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th
e
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r
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u
o
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with
th
e
in
cr
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ased
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s
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o
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SMPSs
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it th
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h
ig
h
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ar
m
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ic
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ated
.
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I
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t J Po
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&
Dr
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t
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Vo
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16
,
No
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1
,
Ma
r
c
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20
25
:
355
-
368
356
I
m
p
r
o
v
in
g
th
e
PF
b
y
d
r
awin
g
a
s
in
u
s
o
id
al
cu
r
r
e
n
t
in
p
h
ase
with
th
e
v
o
ltag
e
r
ed
u
ce
s
th
e
h
ar
m
o
n
i
c
co
n
ten
t
an
d
en
h
an
ce
s
th
e
p
o
we
r
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u
ality
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h
is
ca
n
b
e
r
ea
lized
t
h
r
o
u
g
h
p
o
we
r
f
ac
to
r
co
r
r
ec
tio
n
(
PF
C
)
tech
n
iq
u
es,
wh
ich
allev
iate
th
e
ef
f
ec
ts
o
f
p
o
o
r
PF
o
n
th
e
g
r
i
d
.
T
h
is
wo
r
k
will
f
o
cu
s
o
n
th
e
f
ir
s
t
s
tag
e
o
f
th
ese
SMPSs
,
n
am
ely
,
a
tec
h
n
iq
u
e
to
r
ec
tify
AC
s
ig
n
als
in
to
DC
q
u
an
titi
es
in
a
r
elativ
ely
h
ar
m
less
way
to
th
e
g
r
i
d
co
m
p
ar
ed
to
th
e
tr
ad
itio
n
ally
u
s
ed
b
r
i
d
g
e
h
ig
h
lig
h
ted
in
Fig
u
r
e
1
(
a
)
.
PF
C
tech
n
iq
u
es
ar
e
class
i
f
ied
in
t
o
p
ass
iv
e
an
d
ac
tiv
e
cir
cu
its
,
wh
er
e
p
ass
iv
e
cir
cu
its
u
s
e
en
er
g
y
s
to
r
ag
e
elem
en
ts
(
in
d
u
cto
r
s
an
d
ca
p
ac
it
o
r
s
)
.
I
n
co
n
tr
ast,
ac
tiv
e
cir
cu
its
u
tili
ze
d
if
f
er
en
t
p
o
w
er
elec
tr
o
n
ic
to
p
o
lo
g
ies
an
d
co
n
tr
o
l
m
eth
o
d
s
to
co
r
r
ec
t
t
h
e
PF
.
Activ
e
PF
C
tech
n
iq
u
es,
w
h
ich
will
b
e
o
v
er
v
iewe
d
in
th
is
wo
r
k
,
ar
e
p
r
ef
er
r
ed
o
v
e
r
p
ass
iv
e
o
n
es
b
ec
a
u
s
e
o
f
th
e
m
u
ch
h
i
g
h
e
r
PF
ac
h
iev
ed
an
d
s
m
aller
cir
c
u
itry
[
1
]
.
Activ
e
PF
C
co
n
v
er
ter
s
u
tili
ze
elec
tr
o
n
ic
elem
en
ts
with
f
ee
d
b
ac
k
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n
tr
o
l,
r
eg
u
latin
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o
u
t
p
u
t
v
o
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e
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d
co
r
r
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tin
g
th
e
PF
to
a
v
alu
e
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clo
s
e
to
u
n
ity
.
T
h
ey
ar
e
s
u
itab
le
f
o
r
h
i
g
h
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p
o
w
er
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p
licatio
n
s
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d
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n
o
p
er
ate
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o
s
s
a
u
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iv
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s
al
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e
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t
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g
e
.
Usi
n
g
h
ig
h
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r
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g
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th
ese
c
o
n
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ter
s
s
h
ap
e
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h
e
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r
r
en
t to
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e
d
esire
d
s
in
u
s
o
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f
o
r
m
,
s
ig
n
if
ican
tly
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ed
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cin
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s
ize
co
m
p
ar
ed
to
p
ass
iv
e
tech
n
iq
u
es.
Ma
n
y
to
p
o
lo
g
ies
a
r
e
u
s
ed
to
ac
h
iev
e
ac
tiv
e
PF
C
,
with
an
d
with
o
u
t
t
h
e
r
ec
tific
atio
n
b
r
i
d
g
e,
as
in
co
n
v
en
tio
n
al
SMPSs
;
th
ey
ar
e
class
if
ied
in
to
b
r
id
g
e
d
an
d
b
r
i
d
g
eless
to
p
o
lo
g
ies
[
2
]
-
[
7
]
.
Fig
u
r
e
2
s
h
o
ws
s
o
m
e
o
f
th
e
m
o
s
t
co
m
m
o
n
to
p
o
lo
g
ies to
ac
h
iev
e
ac
tiv
e
P
FC
.
T
h
e
to
tem
-
p
o
le
t
o
p
o
lo
g
y
is
c
h
o
s
en
h
er
e
f
o
r
th
e
d
esig
n
an
d
s
im
u
latio
n
d
u
e
to
its
n
u
m
er
o
u
s
ad
v
an
tag
es
o
v
er
co
n
v
en
tio
n
al
b
r
i
d
g
ed
PF
C
to
p
o
lo
g
ies
a
n
d
o
th
e
r
b
r
id
g
e
less
to
p
o
lo
g
ies
[
8
]
-
[
1
6
]
.
T
h
e
r
est
o
f
th
e
p
ap
er
is
ar
r
an
g
e
d
as
f
o
llo
ws:
i)
Sectio
n
2
p
r
o
v
i
d
es
a
b
r
ief
o
v
er
v
i
ew
o
f
th
e
ac
tiv
e
PF
C
to
p
o
lo
g
ies,
p
r
esen
ted
in
Fig
u
r
e
2
,
with
em
p
h
asis
o
n
th
e
r
ec
en
tly
r
e
-
em
er
g
in
g
t
o
tem
-
p
o
le
to
p
o
lo
g
y
en
ab
le
d
b
y
ad
v
an
ce
m
en
ts
in
s
tate
-
of
-
th
e
-
a
r
t
g
alliu
m
n
itrid
e
(
GaN
)
tr
an
s
is
to
r
s
;
ii)
Sectio
n
3
o
f
f
er
s
a
s
im
p
le
y
et
th
o
r
o
u
g
h
s
tep
-
b
y
-
s
tep
d
esig
n
g
u
i
d
e
f
o
r
a
T
PP
FC
co
n
v
er
ter
th
at
is
ea
s
y
to
f
o
llo
w
an
d
im
p
lem
en
t
u
s
in
g
th
e
PS
I
M
s
o
f
twar
e
an
d
t
h
e
Sm
ar
tC
tr
l
to
o
l
;
iii)
I
n
s
ec
tio
n
4
,
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
d
esig
n
ed
T
PP
FC
co
n
v
er
ter
is
v
alid
ated
th
r
o
u
g
h
s
im
u
latio
n
a
n
d
test
e
d
u
n
d
er
d
if
f
er
en
t
in
p
u
t
v
o
ltag
e
lev
els
an
d
lo
ad
in
g
c
o
n
d
itio
n
s
.
A
m
o
m
en
tar
y
s
h
o
r
t
cir
cu
it
is
also
in
tr
o
d
u
ce
d
to
v
er
if
y
th
at
t
h
e
o
u
t
p
u
t
v
o
ltag
e
is
m
ain
tain
ed
ab
o
v
e
a
p
r
ed
eter
m
in
ed
lev
el
;
an
d
v
)
L
astl
y
,
th
e
r
e
s
u
lts
ar
e
d
is
cu
s
s
ed
,
an
d
co
n
clu
s
io
n
s
ar
e
d
r
awn
.
(
a)
(
b
)
Fig
u
r
e
1
.
T
y
p
ical
SMPS
:
(
a)
g
en
er
al
p
o
wer
s
u
p
p
ly
ci
r
cu
it d
i
ag
r
am
an
d
(
b
)
in
p
u
t
cu
r
r
e
n
t sp
ik
es v
s
in
p
u
t
v
o
ltag
e
at
V
in
=
2
3
0
V,
5
0
Hz
Fig
u
r
e
2
.
Activ
e
PF
C
to
p
o
lo
g
i
es c
lass
if
icat
io
n
2.
P
O
WE
R
F
AC
T
O
R
CO
RRE
CT
I
O
N
T
O
P
O
L
O
G
I
E
S O
V
E
RVI
E
W
T
h
e
ef
f
icien
cy
,
p
o
wer
d
en
s
ity
,
an
d
ea
s
e
o
f
co
n
tr
o
l
o
f
AC
-
DC
p
o
wer
s
u
p
p
lies
ar
e
co
n
tin
u
o
u
s
ly
b
ein
g
ch
allen
g
ed
.
T
h
er
ef
o
r
e,
in
th
is
s
ec
tio
n
,
th
e
d
if
f
er
e
n
t
PF
C
to
p
o
lo
g
ies
m
en
tio
n
ed
in
Fig
u
r
e
2
a
r
e
b
r
ief
ly
r
e
v
iewe
d
alo
n
g
with
a
d
is
cu
s
s
io
n
o
f
th
eir
p
r
o
s
an
d
co
n
s
.
T
h
e
cir
cu
it
o
f
ea
ch
to
p
o
l
o
g
y
is
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
f
ir
s
t to
p
o
lo
g
y
to
b
e
r
ev
iewe
d
is
th
e
tr
a
d
itio
n
al
b
r
id
g
ed
PF
C
to
p
o
lo
g
y
.
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
P
o
w
er fa
cto
r
co
r
r
ec
tio
n
co
n
ve
r
ters
o
ve
r
v
iew
w
ith
P
S
I
M si
m
u
la
tio
n
-
b
a
s
ed
…
(
Ma
jd
G
h
a
z
i B
a
ta
r
s
eh
)
357
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
3
.
Dif
f
e
r
en
t PFC
to
p
o
l
o
g
ies
:
(
a)
b
r
i
d
g
ed
c
o
n
v
e
n
tio
n
a
l b
o
o
s
t,
(
b
)
class
ical
b
r
id
g
eless
b
o
o
s
t,
(
c)
d
u
al
b
o
o
s
t,
an
d
(
d
)
to
tem
-
p
o
le
2
.
1
.
B
ridg
ed
P
F
C
T
h
e
m
o
s
t
co
m
m
o
n
ac
tiv
e
PF
C
cir
cu
it
is
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
PF
C
s
h
o
wn
i
n
Fig
u
r
e
3
(
a)
,
wh
e
r
e
a
b
o
o
s
t
DC
-
DC
co
n
v
er
ter
is
co
n
n
ec
ted
in
s
er
ies with
th
e
f
u
ll
b
r
id
g
e
d
io
d
e
r
ec
tifie
r
.
T
h
e
r
ea
s
o
n
f
o
r
u
s
in
g
a
b
o
o
s
t
co
n
v
er
ter
is
th
e
in
d
u
cto
r
at
th
e
in
p
u
t,
wh
ich
f
ilter
s
h
ig
h
-
f
r
e
q
u
en
cy
co
m
p
o
n
e
n
ts
in
th
e
in
p
u
t
cu
r
r
en
t.
W
h
en
th
e
s
witch
is
c
lo
s
ed
,
th
e
in
d
u
cto
r
is
ch
ar
g
ed
f
r
o
m
th
e
AC
m
ain
s
with
th
e
in
p
u
t
v
o
ltag
e
ap
p
lied
ac
r
o
s
s
it
an
d
a
p
o
s
itiv
e
lef
t
-
s
id
e
p
o
lar
ity
.
W
h
en
th
e
s
witch
o
p
en
s
,
th
e
in
d
u
ct
o
r
o
p
p
o
s
es
th
e
d
ec
r
ea
s
e
i
n
its
c
u
r
r
en
t
b
y
ch
an
g
i
n
g
p
o
lar
ity
,
a
n
d
to
g
eth
er
with
th
e
r
ec
tifie
d
AC
in
p
u
t,
c
h
ar
g
es
u
p
th
e
o
u
tp
u
t
ca
p
ac
ito
r
,
an
d
t
h
e
o
u
tp
u
t
v
o
ltag
e
is
b
o
o
s
ted
[
2
]
.
T
h
is
PF
C
m
eth
o
d
is
w
id
ely
u
s
ed
f
o
r
its
s
im
p
licity
an
d
h
ig
h
P
F,
r
ea
ch
in
g
u
p
to
0
.
9
9
.
I
n
ad
d
itio
n
,
it
h
as
less
co
m
m
o
n
-
m
o
d
e
(
C
M)
el
ec
tr
o
m
ag
n
etic
in
ter
f
er
en
ce
(
E
MI
)
co
m
p
ar
ed
to
o
th
er
b
r
i
d
g
eless
to
p
o
lo
g
ies.
Ho
wev
er
,
it
h
as
s
ig
n
if
ican
t
d
r
awb
ac
k
s
co
n
ce
r
n
in
g
ef
f
ic
ien
cy
,
s
ize,
a
n
d
c
o
s
t.
C
o
m
p
ar
ed
to
b
r
id
g
eless
to
p
o
lo
g
ies,
th
e
f
u
ll
b
r
id
g
e
r
ec
tifie
r
in
cu
r
s
m
o
r
e
co
n
d
u
ctio
n
lo
s
s
es
d
u
e
to
th
e
h
ig
h
er
n
u
m
b
er
o
f
d
io
d
es
in
th
e
co
n
d
u
ctio
n
p
ath
an
d
th
e
r
el
ativ
ely
m
o
r
e
c
o
m
p
o
n
en
ts
u
s
ed
;
h
e
n
ce
,
it
h
as
a
h
ig
h
er
co
s
t
an
d
a
l
o
wer
p
o
wer
d
en
s
ity
.
I
n
ad
d
itio
n
,
t
h
e
r
ev
er
s
e
-
r
ec
o
v
e
r
y
c
h
ar
ac
ter
is
tics
o
f
th
e
d
io
d
es
in
th
is
to
p
o
l
o
g
y
r
esu
lt
in
lo
wer
ef
f
icien
cy
[
3
]
.
2
.
2
.
B
ridg
eless
P
F
C
T
h
e
p
o
o
r
h
ea
t
m
an
a
g
em
en
t
o
f
th
e
b
r
id
g
e
d
co
n
v
en
tio
n
al
b
o
o
s
t
PF
C
m
ak
es
it
h
ar
d
er
to
a
ttain
h
ig
h
p
o
wer
d
en
s
ities
.
T
h
e
b
r
id
g
e
r
ec
tifie
r
in
th
e
b
r
id
g
e
d
PF
C
ci
r
cu
its
r
esu
lts
in
2
-
3
%
lo
s
s
es
o
f
th
e
o
v
er
all
o
u
tp
u
t
p
o
wer
[
4
]
.
B
r
id
g
eless
PF
C
cir
c
u
its
b
ec
am
e
p
o
p
u
lar
b
ec
au
s
e
o
f
th
e
ab
s
en
ce
o
f
th
e
in
p
u
t
b
r
id
g
e
r
ec
tifie
r
,
r
esu
ltin
g
in
r
ed
u
ce
d
p
o
wer
lo
s
s
es
d
u
e
to
th
e
d
ec
r
ea
s
e
o
f
th
e
o
v
e
r
all
co
n
d
u
ctio
n
lo
s
s
es
o
f
th
e
s
em
ico
n
d
u
cto
r
d
ev
ices
.
T
h
e
m
ain
b
r
id
g
eless
PF
C
to
p
o
lo
g
i
es in
clu
d
e:
2
.
2
.
1
.
Cla
s
s
ica
l
bridg
eles
s
PFC
T
h
is
b
asic
to
p
o
lo
g
y
s
h
o
wn
in
Fig
u
r
e
3
(
b
)
ca
n
b
e
d
er
iv
e
d
f
r
o
m
th
e
b
r
id
g
e
r
ec
tifie
r
b
y
r
e
p
lacin
g
th
e
b
o
tto
m
two
d
io
d
es
with
MO
SF
E
T
s
witch
es,
tak
in
g
ad
v
an
ta
g
e
o
f
t
h
eir
in
tr
in
s
ic
b
o
d
y
d
io
d
e,
an
d
p
lacin
g
t
h
e
b
o
o
s
t
in
d
u
cto
r
,
L
,
at
th
e
i
n
p
u
t
s
id
e
.
I
n
th
e
p
o
s
itiv
e
h
alf
c
y
cle
,
D
1
a
n
d
S
1
wo
r
k
to
g
eth
er
as
a
b
o
o
s
t
co
n
v
er
ter
to
ch
ar
g
e
an
d
d
is
ch
ar
g
e
th
e
in
d
u
c
to
r
,
with
th
e
b
o
d
y
d
i
o
d
e
o
f
S
2
p
r
o
v
id
i
n
g
th
e
r
etu
r
n
p
ath
o
f
th
e
cu
r
r
en
t.
Similar
ly
,
in
th
e
n
eg
ativ
e
h
alf
c
y
cle,
D
2
an
d
S
2
d
o
th
e
b
o
o
s
tin
g
ac
tio
n
wh
ile
th
e
b
o
d
y
d
io
d
e
o
f
S
1
p
r
o
v
id
es
th
e
r
et
u
r
n
cu
r
r
en
t
p
ath
.
T
h
e
co
n
d
u
ctio
n
p
ath
in
th
e
b
r
id
g
eless
to
p
o
lo
g
y
h
as
two
s
em
ico
n
d
u
ct
o
r
d
ev
ices
co
m
p
ar
e
d
to
th
r
ee
s
em
ico
n
d
u
cto
r
s
in
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
PF
C
.
T
h
is
r
e
s
u
lts
in
a
lo
wer
v
o
ltag
e
d
r
o
p
in
th
e
lin
e
cu
r
r
en
t
p
ath
,
in
cr
ea
s
ed
ef
f
icien
cy
an
d
r
ed
u
ce
d
th
e
n
u
m
b
er
o
f
c
o
m
p
o
n
en
t
s
.
On
th
e
o
th
er
h
an
d
,
th
is
to
p
o
lo
g
y
s
u
f
f
er
s
f
r
o
m
in
cr
ea
s
ed
C
M
n
o
is
e
co
m
p
ar
e
d
to
th
e
co
n
v
en
tio
n
al
b
o
o
s
t
PF
C
[
5
]
,
[
6
]
.
2
.
2
.
2
.
Dua
l
bo
o
s
t
PFC
T
o
r
ed
u
ce
th
e
C
M
n
o
is
e,
th
e
class
ical
b
r
id
g
eless
-
b
o
o
s
t
PF
C
'
s
to
p
o
lo
g
y
is
m
o
d
if
ied
b
y
a
d
d
in
g
two
s
lo
w
r
ec
o
v
er
y
d
io
d
es,
D
3
an
d
D
4
,
an
d
an
o
th
er
in
d
u
cto
r
,
L
2
,
as
in
Fig
u
r
e
3
(
c)
.
T
h
is
ar
r
an
g
em
en
t
r
ep
lace
s
th
e
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
.
1
,
Ma
r
c
h
20
25
:
355
-
368
358
h
ig
h
-
f
r
eq
u
e
n
cy
p
u
ls
atin
g
v
o
lta
g
e
s
o
u
r
ce
with
a
lo
w
-
f
r
eq
u
en
c
y
p
ath
b
etwe
en
th
e
ac
in
p
u
t
an
d
o
u
tp
u
t
ter
m
i
n
als,
r
ed
u
cin
g
th
e
C
M
n
o
is
e
to
a
lev
el
s
im
ilar
to
th
e
co
n
v
en
tio
n
a
l
b
o
o
s
t
PF
C
,
b
u
t
th
is
co
m
es
at
th
e
ad
d
itio
n
al
co
s
t
an
d
s
ize
o
f
th
e
ex
tr
a
in
d
u
cto
r
an
d
two
d
io
d
es,
r
ed
u
cin
g
t
h
e
p
o
wer
d
en
s
ity
o
f
th
e
co
n
v
er
ter
[
7
]
.
2
.
2
.
3
.
T
o
t
em
-
po
le
PFC
T
h
e
to
tem
-
p
o
le
PF
C
(
T
PP
F
C
)
to
p
o
lo
g
y
h
as
a
s
im
p
le
d
esig
n
,
as
s
h
o
wn
in
Fig
u
r
e
3
(
d
)
.
T
h
is
to
p
o
lo
g
y
is
s
im
ilar
to
th
e
class
ical
b
r
id
g
eless
-
b
o
o
s
t
PF
C
b
u
t
with
th
e
b
o
tto
m
s
witch
an
d
o
p
p
o
s
ite
d
io
d
e
s
wap
p
ed
.
T
h
e
m
m
f
m
h
f
h
h
h
k
f
h
h
,
k
m
“
m
-
”
[
4
]
.
T
h
e
T
PP
FC
to
p
o
lo
g
y
h
as
th
e
leg
with
th
e
d
io
d
es
o
p
er
atin
g
at
lin
e
f
r
eq
u
e
n
c
y
an
d
th
e
s
witch
es
o
p
er
atin
g
at
h
ig
h
f
r
e
q
u
en
c
y
.
D
u
r
in
g
th
e
p
o
s
itiv
e
h
al
f
cy
cle
o
f
th
e
i
n
p
u
t
v
o
ltag
e,
s
witch
S
1
is
tu
r
n
e
d
o
n
an
d
o
f
f
,
an
d
th
e
d
io
d
e
D
1
alwa
y
s
co
n
d
u
cts
th
e
in
p
u
t
cu
r
r
e
n
t.
T
h
e
in
p
u
t
in
d
u
cto
r
L
,
th
e
s
witch
es
S
1
an
d
S
2,
alo
n
g
with
th
e
d
io
d
e
D
1,
f
o
r
m
a
ty
p
ical
b
o
o
s
t
co
n
v
er
ter
;
S
1
ac
ts
as
th
e
ac
tiv
e
s
witch
,
an
d
th
e
b
o
d
y
d
io
d
e
o
f
S
2
as
th
e
d
io
d
e
o
f
th
e
b
o
o
s
t
co
n
v
e
r
ter
.
T
h
is
r
e
m
ain
s
tr
u
e
in
th
e
n
eg
ativ
e
cy
c
le,
with
S
1
an
d
S
2
r
ev
er
s
in
g
f
u
n
ctio
n
ality
[
8
]
,
[
9
]
.
Fig
u
r
es
4
(
a)
an
d
4
(
b
)
illu
s
tr
ate
th
e
c
u
r
r
en
t
p
ath
s
d
u
r
in
g
t
h
e
p
o
s
itiv
e
h
alf
-
cy
cle
o
f
th
e
in
p
u
t
v
o
ltag
e,
wh
ile
Fig
u
r
es 4
(
c)
an
d
4
(
d
)
d
ep
ict
th
e
cu
r
r
en
t
p
ath
s
d
u
r
in
g
th
e
n
eg
ativ
e
h
alf
-
cy
cle,
r
esp
ec
tiv
ely
.
T
h
e
T
PP
FC
h
as
s
ev
er
al
ad
v
a
n
tag
es
o
v
er
o
th
er
PF
C
to
p
o
lo
g
ies
[
1
0
]
-
[
1
3
]
,
th
ese
m
ain
ly
b
ein
g
t
h
e
f
o
llo
win
g
:
i)
a
ch
iev
es
r
elativ
ely
th
e
lo
west
co
n
d
u
ctio
n
lo
s
s
es
,
ii)
b
etter
C
M
E
MI
p
er
f
o
r
m
an
ce
,
iii)
e
asier
in
p
u
t
-
v
o
ltag
e
m
ea
s
u
r
em
e
n
t
; a
n
d
i
v
)
s
im
p
le
cir
cu
itry
a
t
h
ig
h
d
e
v
ice
u
tili
za
tio
n
,
r
esu
ltin
g
in
h
ig
h
e
r
p
o
wer
d
e
n
s
ities
.
Alth
o
u
g
h
its
co
n
d
u
ctio
n
lo
s
s
es
ar
e
am
o
n
g
th
e
m
i
n
im
u
m
o
f
all
PF
C
to
p
o
lo
g
ies,
th
e
m
ain
i
s
s
u
e
is
th
at
th
is
to
p
o
lo
g
y
ca
n
o
n
l
y
b
e
o
p
er
ated
in
d
is
co
n
tin
u
o
u
s
-
c
o
n
d
u
ctio
n
m
o
d
e
(
DC
M)
o
r
cr
itical
-
co
n
d
u
ctio
n
m
o
d
e
(
C
r
M)
.
I
f
o
p
e
r
ated
in
co
n
tin
u
o
u
s
-
co
n
d
u
cti
o
n
m
o
d
e
(
C
C
M)
with
o
u
t
m
o
r
e
c
o
m
p
lex
co
n
t
r
o
l,
t
h
e
r
ev
e
r
s
e
r
ec
o
v
er
y
o
f
th
e
b
o
d
y
d
io
d
es
o
f
t
h
e
s
ilico
n
MO
SF
E
T
s
ca
n
ca
u
s
e
v
er
y
h
i
g
h
lo
s
s
es.
T
h
is
is
d
u
e
to
t
h
e
m
u
ch
lo
n
g
er
r
ec
o
v
er
y
m
f
h
MO
S
E
’
b
y
h
h
f
f
-
r
ec
o
v
er
y
d
io
d
e,
r
esu
ltin
g
i
n
ex
ce
s
s
iv
e
r
ev
er
s
e
r
ec
o
v
er
y
lo
s
s
es a
n
d
s
ig
n
if
ican
tly
r
ed
u
cin
g
th
e
ef
f
icien
cy
.
Ho
wev
er
,
with
th
e
d
ev
el
o
p
m
e
n
t
o
f
wid
e
-
b
an
d
g
ap
s
em
ico
n
d
u
cto
r
d
e
v
ices,
esp
ec
ially
g
alli
u
m
n
itrid
e
(
GaN
)
tr
an
s
is
to
r
s
,
th
e
T
PP
FC
to
p
o
lo
g
y
is
attr
ac
tin
g
m
u
c
h
m
o
r
e
atten
tio
n
an
d
b
ec
o
m
in
g
th
e
m
o
s
t
p
r
o
m
is
in
g
to
p
o
lo
g
y
.
T
h
e
ab
s
en
ce
o
f
an
i
n
tr
in
s
ic
b
o
d
y
d
io
d
e,
an
d
ef
f
ec
tiv
ely
an
y
PN ju
n
ctio
n
in
th
e
GaN
d
ev
ice,
lead
s
to
n
o
m
in
o
r
ity
ca
r
r
ier
in
jectio
n
a
n
d
,
as
a
r
esu
lt,
n
o
s
to
r
e
d
ch
a
r
g
e.
T
h
is
tr
an
s
lates
to
ze
r
o
r
ec
o
v
er
y
ch
ar
g
e
(
Q
rr
≈
0
)
in
GaN
tr
an
s
is
to
r
s
an
d
n
o
r
ev
er
s
e
r
ec
o
v
er
y
o
p
e
r
atio
n
wh
en
u
s
ed
as
a
r
ec
tifie
r
[
1
4
]
.
F
u
r
th
er
m
o
r
e
,
th
e
later
al
s
tr
u
ctu
r
e
o
f
GaN
s
witch
es,
to
g
eth
er
with
th
e
r
ed
u
ctio
n
in
t
h
e
ch
ip
s
ize
an
d
th
e
r
ed
u
ce
d
R
on
,
r
esu
lts
in
th
e
r
ed
u
ctio
n
o
f
th
e
ju
n
ctio
n
ca
p
a
citan
ce
an
d
th
e
t
o
tal
ca
p
ac
itan
ce
o
f
th
e
d
ev
ice.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
4
.
C
u
r
r
e
n
t p
ath
d
u
r
i
n
g
t
h
e
p
o
s
itiv
e
lin
e
cy
cle
wh
e
n
S1
is
(
a)
o
n
,
(
b
)
o
f
f
,
d
u
r
i
n
g
th
e
n
eg
ativ
e
lin
e
cy
cle
wh
en
S2
is
(
c)
o
n
,
an
d
(
d
)
o
f
f
T
h
is
m
ak
es
th
e
GaN
h
ig
h
-
elec
tr
o
n
m
o
b
ilit
y
tr
an
s
is
to
r
(
HE
MT
)
o
p
e
r
ate
m
o
r
e
lik
e
an
id
ea
l
h
ig
h
-
f
r
eq
u
e
n
cy
s
witch
b
y
d
e
cr
ea
s
in
g
th
e
g
ate
ch
ar
g
e,
wh
ich
allo
ws
f
o
r
f
aster
s
witch
in
g
an
d
l
o
wer
d
r
iv
e
lo
s
s
es
[
1
4
]
-
[
1
6
]
.
T
h
e
d
r
i
v
in
g
s
ch
em
e
o
f
GaN
HE
MT
s
m
u
s
t
b
e
p
r
o
p
er
ly
ad
d
r
ess
ed
,
as
s
ev
er
al
ch
allen
g
es,
lik
e
s
ig
n
al
o
s
cillatio
n
s
an
d
p
o
ten
ti
al
m
alf
u
n
ctio
n
s
,
co
u
ld
a
r
is
e
d
u
e
to
p
ar
asit
ic
ca
p
ac
itan
ce
[
1
7
]
.
T
h
e
a
d
v
an
tag
es
m
en
tio
n
ed
a
b
o
v
e
o
f
GaN
s
witch
es
en
ab
le
th
e
u
tili
za
tio
n
o
f
th
e
T
PP
FC
to
p
o
lo
g
y
in
th
e
C
C
M.
T
h
er
ef
o
r
e,
a
g
r
ea
t
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
P
o
w
er fa
cto
r
co
r
r
ec
tio
n
co
n
ve
r
ters
o
ve
r
v
iew
w
ith
P
S
I
M si
m
u
la
tio
n
-
b
a
s
ed
…
(
Ma
jd
G
h
a
z
i B
a
ta
r
s
eh
)
359
d
ea
l
o
f
atten
tio
n
is
b
ein
g
d
ir
e
cted
o
n
to
th
is
to
p
o
lo
g
y
;
h
en
c
e,
it
is
im
p
o
r
tan
t
to
lay
o
u
t
a
well
-
s
tr
u
ctu
r
ed
an
d
q
u
ick
d
esig
n
g
u
id
e
f
o
r
th
e
co
n
v
er
ter
to
s
h
if
t
th
e
f
o
cu
s
in
to
en
h
an
cin
g
th
e
to
p
o
lo
g
y
an
d
s
o
lv
i
n
g
o
th
er
an
ticip
ated
h
ar
d
war
e
-
r
elate
d
d
if
f
icu
lties
.
T
h
e
d
esig
n
p
r
o
ce
s
s
d
is
cu
s
s
ed
in
th
e
f
o
llo
win
g
s
ec
tio
n
aid
s
i
n
ac
h
iev
in
g
a
s
o
lid
y
et
q
u
ick
d
esig
n
o
f
th
e
T
PP
FC
co
n
v
er
ter
.
3.
T
P
P
F
C
CO
NVER
T
E
R
CO
M
P
L
E
T
E
D
E
SI
G
N
G
U
I
DE
T
h
is
s
ec
tio
n
co
v
er
s
im
p
o
r
tan
t
d
esig
n
co
n
s
id
er
atio
n
s
f
o
r
th
e
T
PP
F
C
.
Firs
t,
th
e
p
lan
t
co
m
p
o
n
en
ts
o
f
th
e
lo
w
-
f
r
eq
u
e
n
cy
leg
an
d
t
h
e
a
v
ailab
le
clo
s
ed
-
lo
o
p
co
n
t
r
o
l
m
eth
o
d
s
ar
e
d
is
cu
s
s
ed
.
T
h
en
,
a
d
etailed
d
esig
n
p
r
o
ce
d
u
r
e
f
o
r
th
e
T
PP
FC
co
n
v
er
ter
is
p
r
esen
ted
.
3
.
1
.
Desig
n
co
ns
idera
t
io
ns
3
.
1
.
1
.
L
o
w
-
f
re
qu
ency
leg
co
m
po
nents
R
ef
er
r
in
g
b
ac
k
to
Fig
u
r
e
3
(
d
)
an
d
as
m
en
tio
n
ed
ea
r
lier
,
th
e
T
PP
F
C
h
as
two
leg
s
;
th
e
o
n
e
o
n
th
e
le
f
t,
co
m
p
r
is
ed
o
f
s
witch
es
S
1
an
d
S
2
,
o
p
er
ates
at
th
e
h
ig
h
s
witch
in
g
f
r
eq
u
e
n
cy
,
w
h
ile
th
e
o
th
er
leg
o
n
th
e
r
ig
h
t,
m
ad
e
u
p
o
f
d
io
d
es
D
1
an
d
D
2
,
o
p
er
ates
at
th
e
lo
w
lin
e
f
r
eq
u
en
cy
.
I
t
is
co
m
m
o
n
p
r
ac
tice
in
th
is
to
p
o
lo
g
y
t
o
r
ep
lace
th
e
d
io
d
es
o
f
th
e
lo
w
-
f
r
eq
u
en
c
y
leg
with
s
ilico
n
MO
SF
E
T
s
to
tak
e
ad
v
an
tag
e
o
f
th
eir
lo
wer
co
n
d
u
ctio
n
lo
s
s
es,
co
m
p
ar
ed
with
s
lo
w
r
e
co
v
er
y
d
io
d
es,
th
er
eb
y
im
p
r
o
v
in
g
ef
f
icien
cy
.
Ho
wev
er
,
th
is
ad
d
s
m
o
r
e
co
n
tr
o
l
r
eq
u
ir
em
e
n
ts
to
tu
r
n
th
ese
s
witch
es
o
n
an
d
o
f
f
an
d
in
cr
ea
s
es
th
e
co
s
t.
An
o
t
h
er
p
r
o
b
lem
with
u
s
in
g
tr
a
n
s
is
to
r
s
in
s
tead
o
f
d
io
d
es
is
th
eir
o
u
tp
u
t
ca
p
ac
itan
ce
,
C
oss
.
T
h
is
o
u
tp
u
t
ca
p
ac
itan
ce
is
o
n
e
o
f
th
e
m
ain
r
ea
s
o
n
s
b
eh
in
d
th
e
in
d
u
cto
r
cu
r
r
en
t sp
ik
es a
t t
h
e
ze
r
o
c
r
o
s
s
in
g
[
1
8
]
,
[
1
9
]
.
R
ef
er
r
in
g
to
Fig
u
r
e
4
(
d
)
,
d
u
r
i
n
g
th
e
n
e
g
ativ
e
h
alf
c
y
cle
o
f
th
e
lin
e
v
o
ltag
e
an
d
wh
en
S
2
is
o
f
f
,
it
is
ev
id
en
t
th
at
D
1
is
s
u
b
ject
to
t
h
e
f
u
ll
o
u
tp
u
t
v
o
ltag
e
in
r
ev
e
r
s
e
b
ias
m
o
d
e.
I
f
th
er
e
we
r
e
a
s
witch
in
s
tead
,
its
o
u
tp
u
t
p
ar
asit
ic
ca
p
ac
itan
ce
C
oss
wo
u
ld
th
u
s
b
e
ch
ar
g
ed
to
th
e
f
u
ll
o
u
tp
u
t
v
o
ltag
e.
W
h
en
th
e
in
p
u
t
v
o
ltag
e
ch
an
g
es
p
o
lar
ity
a
f
ter
t
h
e
ze
r
o
cr
o
s
s
in
g
a
n
d
S
1
tu
r
n
s
o
n
,
as
i
n
Fig
u
r
e
4
(
a
)
,
t
h
e
ch
a
r
g
ed
C
oss
is
n
o
w
allo
wed
to
d
is
ch
ar
g
e
th
r
o
u
g
h
t
h
e
in
d
u
cto
r
,
cr
ea
tin
g
a
p
o
s
itiv
e
cu
r
r
en
t
s
p
ik
e
at
th
e
ze
r
o
-
cr
o
s
s
in
g
m
o
m
en
t.
T
h
e
s
am
e
lo
g
ic
ap
p
lies
to
th
e
s
witch
in
g
b
etwe
en
th
e
n
e
g
ativ
e
an
d
p
o
s
itiv
e
c
y
cles
o
f
th
e
in
p
u
t
v
o
ltag
e.
Sp
i
k
es
o
f
th
is
k
in
d
ar
e
h
u
g
ely
allev
iated
if
d
io
d
es
a
r
e
u
s
ed
b
ec
au
s
e
t
h
eir
ju
n
ctio
n
ca
p
ac
itan
ce
v
alu
es
a
r
e
m
a
g
n
itu
d
es
o
f
o
r
d
er
less
th
an
in
MO
SF
E
T
s
.
Ov
er
all,
d
io
d
e
s
o
f
f
er
f
ewe
r
c
o
n
tr
o
l
r
eq
u
i
r
e
m
en
ts
,
m
o
r
e
m
itig
atio
n
o
f
ze
r
o
-
cr
o
s
s
in
g
c
u
r
r
e
n
t
s
p
ik
es,
an
d
ar
e
ch
ea
p
er
,
wh
ile
MO
SF
E
T
s
p
r
o
v
id
e
h
ig
h
er
ef
f
icien
cy
.
Fo
r
th
e
ad
v
a
n
tag
es
ab
o
v
e,
an
d
s
in
ce
th
e
in
cr
ea
s
e
in
ef
f
icien
cy
is
n
o
t c
o
n
s
id
er
ab
le,
d
i
o
d
es we
r
e
ch
o
s
e
n
f
o
r
t
h
is
d
esig
n
.
3
.
1
.
2
.
Co
ntr
o
l
m
et
ho
d
I
t
is
im
p
o
s
s
ib
le
to
ac
h
iev
e
a
n
e
ar
-
u
n
ity
PF
u
s
in
g
an
ac
tiv
e
PF
C
co
n
v
er
ter
with
o
u
t
an
a
d
eq
u
a
te
co
n
tr
o
l
m
eth
o
d
.
T
h
is
is
ac
h
iev
ed
b
y
h
av
in
g
two
c
o
n
tr
o
l
lo
o
p
s
:
an
in
n
er
cu
r
r
en
t
lo
o
p
t
h
at
s
h
ap
es
t
h
e
in
d
u
cto
r
c
u
r
r
en
t
in
to
th
e
d
esire
d
s
in
u
s
o
id
al
wav
ef
o
r
m
w
h
ile
k
ee
p
i
n
g
it
in
p
h
ase
with
th
e
i
n
p
u
t
v
o
ltag
e
an
d
an
o
u
ter
v
o
ltag
e
lo
o
p
to
k
ee
p
th
e
o
u
t
p
u
t
v
o
ltag
e
at
a
co
n
s
tan
t
lev
el.
T
h
e
in
n
e
r
lo
o
p
ac
h
iev
es
th
e
d
esire
d
s
in
u
s
o
id
al
s
h
ap
e
b
y
p
r
o
d
u
ci
n
g
th
e
p
u
ls
e
wid
th
m
o
d
u
latio
n
(
PW
M)
s
witch
in
g
s
ig
n
als
th
at
co
n
tr
o
l
th
e
two
h
ig
h
-
f
r
e
q
u
en
cy
s
witch
es
o
f
th
e
T
PP
F
C
cir
cu
it
[
2
0
]
.
T
h
e
cu
r
r
en
t
co
n
tr
o
ller
(
in
n
er
c
o
n
tr
o
l
lo
o
p
)
ca
n
r
esu
lt
in
an
y
o
f
th
e
th
r
ee
co
n
d
u
ctio
n
m
o
d
es
d
ep
en
d
in
g
o
n
th
e
d
esig
n
p
ar
am
eter
s
.
DC
M
an
d
C
r
M
b
o
th
r
eq
u
ir
e
a
b
ig
g
er
in
p
u
t
f
ilter
,
wh
ich
r
esu
lts
in
a
h
ig
h
er
in
p
u
t
R
MS
cu
r
r
en
t
th
an
th
e
C
C
M
o
p
er
atio
n
d
u
e
to
th
e
la
r
g
er
r
ip
p
le
in
th
e
cu
r
r
en
t,
m
ak
i
n
g
C
C
M
a
m
o
r
e
d
esira
b
le
m
o
d
e
o
f
o
p
er
atio
n
f
o
r
h
ig
h
e
r
p
o
wer
lev
els.
C
C
M
ca
n
b
e
r
ea
lized
th
r
o
u
g
h
d
if
f
er
en
t
co
n
tr
o
l
m
et
h
o
d
s
,
s
u
ch
as
p
ea
k
c
u
r
r
e
n
t
co
n
tr
o
l,
h
y
s
ter
esis
cu
r
r
en
t
co
n
tr
o
l,
an
d
a
v
er
ag
e
c
u
r
r
e
n
t
co
n
tr
o
l
[
2
0
]
-
[
2
2
]
.
Oth
er
m
eth
o
d
s
,
s
u
ch
as
s
lid
in
g
m
o
d
e
co
n
tr
o
l
(
SMC
)
an
d
p
r
e
d
ictiv
e
cu
r
r
en
t
c
o
n
tr
o
l
(
PC
C
)
,
ar
e
also
u
s
ed
[
2
3
]
-
[
2
5
]
.
T
h
e
av
e
r
a
g
e
cu
r
r
e
n
t
co
n
t
r
o
l
m
eth
o
d
p
r
o
v
id
es
a
co
n
s
tan
t
s
witch
in
g
f
r
eq
u
en
cy
,
d
o
es
n
o
t
n
ee
d
a
r
am
p
co
m
p
e
n
s
ato
r
,
an
d
r
esu
lts
in
a
b
etter
in
p
u
t
cu
r
r
en
t
wa
v
ef
o
r
m
th
an
o
th
er
co
n
tr
o
l
m
eth
o
d
s
;
th
u
s
,
i
t
is
th
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
co
n
tr
o
l
m
et
h
o
d
f
o
r
PF
C
co
n
v
er
ter
s
[
2
5
]
.
Fig
u
r
e
5
d
ep
icts
th
is
m
eth
o
d
'
s
r
esu
ltin
g
in
d
u
cto
r
c
u
r
r
e
n
t
an
d
th
e
cu
r
r
en
t
r
ef
e
r
en
ce
.
Fo
r
th
ese
r
ea
s
o
n
s
,
o
p
er
atio
n
in
th
e
C
C
M
u
s
in
g
th
e
av
er
ag
e
cu
r
r
e
n
t c
o
n
tr
o
l
m
eth
o
d
is
ch
o
s
en
f
o
r
th
is
d
esig
n
.
3
.
2
.
Det
a
iled desi
g
n pro
ce
du
re
h
’
y
y
,
b
y
h
f
.
First
is
th
e
s
izin
g
o
f
th
e
p
la
n
t
co
m
p
o
n
en
ts
,
wh
er
e
th
e
i
n
d
u
ctan
ce
,
ca
p
ac
itan
ce
,
a
n
d
r
esis
tiv
e
lo
ad
v
alu
es
ar
e
ca
lcu
lated
,
an
d
s
ec
o
n
d
is
d
esig
n
in
g
th
e
f
ee
d
b
ac
k
co
n
tr
o
l
lo
o
p
s
.
E
ac
h
o
f
th
ese
s
tep
s
is
ca
r
r
ie
d
o
u
t
in
a
d
ed
icate
d
s
u
b
-
s
ec
tio
n
.
T
h
e
f
lo
w
ch
ar
t
s
h
o
wn
in
Fig
u
r
e
6
illu
s
tr
ates
th
e
o
v
er
all
d
esig
n
p
r
o
ce
s
s
f
o
ll
o
wed
in
th
is
s
ec
tio
n
.
T
h
is
wo
r
k
in
clu
d
es a
ll th
e
d
esi
g
n
s
tep
s
s
h
o
wn
in
th
e
f
ig
u
r
e
u
s
in
g
b
o
ld
b
o
r
d
e
r
lin
es.
Ho
wev
er
,
th
e
f
in
al
s
tep
o
f
p
h
y
s
ical
im
p
lem
en
tatio
n
,
s
h
o
wn
in
a
d
ash
ed
b
o
r
d
er
lin
e,
is
n
o
t in
clu
d
e
d
d
u
e
to
lim
ited
ac
ce
s
s
to
r
eso
u
r
ce
s
.
S
h
h
f
q
m
,
b
1
m
m
z
h
’
s
p
e
c
i
f
i
ca
t
i
o
n
s
t
o
b
e
a
c
h
ie
v
e
d
b
a
s
e
d
o
n
v
a
l
u
e
s
t
y
p
i
c
a
ll
y
u
s
e
d
i
n
d
i
f
f
e
r
e
n
t
i
n
d
u
s
t
r
i
a
l
a
p
p
l
i
c
ati
o
n
n
o
t
e
s
s
i
m
i
la
r
t
o
[
2
6
]
-
[
2
8
]
,
a
c
c
o
r
d
i
n
g
t
o
w
h
i
c
h
th
e
f
i
r
s
t
s
t
e
p
o
f
s
i
z
i
n
g
t
h
e
c
o
m
p
o
n
e
n
t
s
is
c
a
r
r
ie
d
o
u
t
.
F
o
r
t
h
e
c
o
n
t
r
o
l
l
e
r
t
o
f
o
ll
o
w
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
.
1
,
Ma
r
c
h
20
25
:
355
-
368
360
t
h
e
r
e
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e
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lated
to
t
h
e
p
r
e
-
d
eter
m
i
n
ed
r
ef
er
en
ce
v
o
ltag
e.
T
h
e
o
u
te
r
v
o
ltag
e
co
n
tr
o
l
lo
o
p
is
also
r
esp
o
n
s
ib
le
f
o
r
d
eter
m
in
in
g
th
e
am
p
litu
d
e
o
f
th
e
g
en
er
ated
cu
r
r
en
t
r
ef
e
r
en
ce
,
w
h
ich
is
th
en
u
s
ed
in
th
e
in
n
er
cu
r
r
en
t
lo
o
p
[
2
0
]
.
T
h
e
T
PP
FC
co
n
v
er
ter
co
n
tr
o
l
b
lo
c
k
d
iag
r
a
m
is
s
h
o
wn
in
Fig
u
r
e
7
.
I
n
th
is
co
n
tr
o
l
s
ch
em
e,
it
s
h
o
u
ld
b
e
n
o
ted
th
at
th
e
s
en
s
ed
o
u
tp
u
t
v
o
ltag
e,
in
p
u
t
v
o
ltag
e
,
an
d
cu
r
r
en
t
ar
e
n
o
r
m
alize
d
b
y
th
eir
r
esp
ec
tiv
e
R
MS
v
alu
es.
T
h
e
v
o
ltag
e
co
n
tr
o
ller
p
r
o
v
id
es
th
e
cu
r
r
en
t
r
ef
er
e
n
ce
m
a
g
n
itu
d
e
m
u
ltip
lied
b
y
th
e
r
ec
tifie
d
,
n
o
r
m
aliz
ed
in
p
u
t
v
o
ltag
e
to
p
r
o
d
u
ce
th
e
cu
r
r
en
t
r
e
f
er
en
ce
s
ig
n
al.
T
h
is
f
ee
d
f
o
r
war
d
o
f
th
e
in
p
u
t
v
o
ltag
e
g
u
id
es
th
e
in
p
u
t
cu
r
r
en
t
to
tr
ac
k
it
an
d
a
v
o
id
s
p
r
o
p
a
g
atin
g
th
e
i
n
p
u
t
v
o
ltag
e
d
is
tu
r
b
an
ce
th
r
o
u
g
h
th
e
PF
C
f
ee
d
b
ac
k
lo
o
p
s
[
2
0
]
.
T
h
e
o
u
tp
u
t
o
f
th
e
cu
r
r
en
t
c
o
n
tr
o
ller
is
th
e
d
u
ty
r
atio
(
D)
,
wh
ich
is
u
s
ed
to
g
e
n
er
ate
th
e
s
witch
in
g
s
ig
n
als
f
o
r
th
e
co
n
v
er
ter
.
T
o
av
o
id
ex
tr
em
e
v
alu
es
f
o
r
D
(
n
ea
r
1
0
0
%),
wh
ic
h
o
cc
u
r
at
th
e
ze
r
o
cr
o
s
s
in
g
s
,
a
lim
iter
is
u
s
ed
with
a
m
ar
g
in
o
f
2
%,
i.e
.
,
0
.
0
2
–
0
.
9
8
.
a)
I
n
n
er
l
o
o
p
d
esig
n
T
h
e
in
n
er
l
o
o
p
co
n
tr
o
ller
n
ee
d
s
to
b
e
f
ast
e
n
o
u
g
h
to
m
ak
e
th
e
in
p
u
t
cu
r
r
en
t
tr
ac
k
th
e
in
p
u
t
v
o
ltag
e
an
d
as
a
r
esu
lt,
th
e
in
n
er
cu
r
r
en
t
co
n
tr
o
l
lo
o
p
is
r
eq
u
ir
e
d
to
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av
e
a
v
er
y
lar
g
e
b
an
d
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th
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elativ
e
to
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e
o
u
ter
v
o
ltag
e
co
n
tr
o
l
l
o
o
p
.
T
h
u
s
,
ea
ch
l
o
o
p
s
h
all
b
e
d
esig
n
ed
s
ep
ar
ately
[
2
9
]
.
T
h
e
d
esig
n
o
f
th
e
in
n
er
c
u
r
r
en
t
l
o
o
p
an
d
th
e
tu
n
in
g
o
f
th
e
p
r
o
p
o
r
tio
n
al
-
in
te
g
r
al
(
PI)
c
o
m
p
en
s
ato
r
in
th
e
c
o
n
tr
o
l
lo
o
p
will
b
e
illu
s
tr
ated
i
n
th
e
s
tep
s
to
f
o
llo
w
h
er
ea
f
ter
.
˗
I
n
n
er
l
oop
-
Step
1
:
Sin
ce
th
e
P
FC
o
p
er
ates
as
a
b
o
o
s
t
c
o
n
v
e
r
ter
d
u
r
i
n
g
ea
c
h
h
alf
-
lin
e
cy
cle
,
th
e
f
ir
s
t
s
tep
is
to
d
eter
m
in
e
th
e
d
u
ty
r
atio
(
D
)
o
f
th
e
b
o
o
s
t
co
n
v
er
te
r
th
at
r
e
s
u
lts
in
an
o
u
tp
u
t
v
o
ltag
e
o
f
4
0
0
V
as
p
er
th
e
d
esig
n
s
p
ec
if
icatio
n
s
.
T
h
e
b
o
o
s
t
co
n
v
er
ter
is
d
esig
n
ed
to
p
r
o
v
id
e
an
o
u
tp
u
t
o
f
4
0
0
V
f
r
o
m
a
2
3
0
V
DC
in
p
u
t
.
T
h
e
d
u
ty
r
atio
is
f
o
u
n
d
u
s
in
g
(
4
)
,
wh
ich
g
iv
es a
r
esu
lt o
f
0
.
4
2
5
.
=
1
−
(4
)
As
in
th
e
b
o
o
s
t
co
n
v
er
ter
,
th
e
PW
M
s
ig
n
al
is
g
en
er
ated
b
y
c
o
m
p
ar
in
g
a
tr
ian
g
u
la
r
wav
e
with
a
co
n
s
tan
t
DC
r
ef
er
en
ce
th
r
o
u
g
h
a
co
m
p
ar
ato
r
,
wh
er
e
th
e
tr
ian
g
u
lar
wav
e
v
ar
ies
b
etwe
en
0
V
an
d
1
V
at
f
sw
.
T
h
e
r
ef
e
r
en
ce
o
f
th
e
PW
M
m
o
d
u
lato
r
s
h
o
u
l
d
b
e
s
et
at
0
.
4
2
5
an
d
a
s
m
all
s
ig
n
al
p
er
tu
r
b
atio
n
is
in
tr
o
d
u
ce
d
t
o
th
is
r
ef
er
en
ce
as
an
AC
s
in
u
s
o
id
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s
o
u
r
ce
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An
AC
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er
f
o
r
m
ed
o
n
th
e
a
d
d
ed
p
er
t
u
r
b
atio
n
s
o
u
r
ce
,
an
d
th
e
i
n
p
u
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
6
9
4
I
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w
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lec
&
Dr
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s
t
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Vo
l.
16
,
No
.
1
,
Ma
r
c
h
20
25
:
355
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368
362
cu
r
r
en
t
is
m
ea
s
u
r
e
d
to
o
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tain
t
h
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o
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e
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h
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ir
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it
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o
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lo
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PS
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M
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h
o
wn
in
Fig
u
r
e
8
(
a)
,
an
d
t
h
e
r
esu
ltin
g
b
o
d
e
p
lo
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is
p
lay
e
d
in
Fig
u
r
e
8
(
b
)
.
˗
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n
n
er
l
o
o
p
-
Step
2
:
T
h
e
b
o
d
e
p
lo
t
in
Fig
u
r
e
8
(
b
)
is
th
en
im
p
o
r
ted
in
to
th
e
Sm
ar
tC
tr
l
s
o
f
twar
e
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s
ed
in
th
is
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r
k
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ich
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elp
tu
n
e
th
e
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m
p
en
s
ato
r
.
Af
ter
im
p
o
r
ti
n
g
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e
c
u
r
r
en
t
-
co
n
tr
o
lled
m
o
d
e
s
in
g
le
lo
o
p
with
a
cu
r
r
en
t sen
s
o
r
an
d
a
PI
r
eg
u
lato
r
is
ch
o
s
en
.
Fig
u
r
e
7
.
T
PP
FC
co
n
v
er
ter
c
o
n
tr
o
l b
lo
c
k
d
iag
r
am
(
a)
(
b
)
Fig
u
r
e
8
.
I
n
n
er
lo
o
p
-
Step
1
:
(
a
)
in
n
er
c
u
r
r
e
n
t lo
o
p
s
wee
p
cir
c
u
it a
n
d
(
b
)
cu
r
r
en
t
c
o
n
tr
o
l
o
p
e
n
-
lo
o
p
b
o
d
e
p
lo
t
Sm
ar
tC
tr
l
p
r
o
v
id
es
a
s
o
lu
tio
n
m
ap
with
p
air
s
o
f
cr
o
s
s
o
v
er
f
r
eq
u
en
cies
(
f
cv
)
h
m
(
Φ
m
)
.
I
t
id
en
tifie
s
s
tab
le
co
n
tr
o
ller
co
m
b
in
atio
n
s
a
n
d
p
o
ten
tial
in
s
tab
ilit
ies.
A
cr
u
cial
f
ac
to
r
in
s
elec
tin
g
a
s
tab
le
s
o
lu
tio
n
is
en
s
u
r
in
g
th
at
th
e
cl
o
s
ed
-
lo
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p
p
h
ase
r
esp
o
n
s
e
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ea
r
ly
ze
r
o
b
etwe
en
1
0
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a
n
d
1
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h
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g
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d
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to
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.
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h
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ws
t
h
e
in
n
er
lo
o
p
to
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ac
k
th
e
in
p
u
t
v
o
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e,
a
r
ec
tifie
d
s
in
u
s
o
id
at
eith
er
1
0
0
o
r
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
P
o
w
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cto
r
co
r
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tio
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r
ters
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w
ith
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S
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M si
m
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b
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(
Ma
jd
G
h
a
z
i B
a
ta
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)
363
1
2
0
Hz
in
a
u
n
iv
e
r
s
al
in
p
u
t
5
0
-
6
0
Hz
PF
C
d
esig
n
.
Fig
u
r
e
9
d
ep
icts
th
e
i
n
n
er
clo
s
ed
-
lo
o
p
p
h
ase
r
esp
o
n
s
e
[
2
0
]
.
Sm
ar
tC
tr
l
ca
lcu
lates
th
e
PI
co
m
p
en
s
ato
r
c
o
n
s
tan
ts
(
k
p
an
d
k
i
)
b
ased
o
n
t
h
e
ch
o
s
en
cr
o
s
s
o
v
er
f
r
eq
u
e
n
cy
(
f
cv
)
h
m
(
Φ
m
)
.
W
ith
an
in
n
er
lo
o
p
cr
o
s
s
o
v
er
f
r
eq
u
en
cy
o
f
2
0
0
k
Hz
an
d
a
p
h
ase
m
ar
g
in
o
f
4
0
°,
th
e
co
n
tr
o
ller
v
alu
es a
r
e
d
eter
m
in
ed
as k
p
=
2
.
9
9
9
2
9
an
d
k
i
=
6
5
1
.
2
3
5
n
.
b)
Ou
ter
lo
o
p
d
esig
n
T
h
e
o
u
ter
v
o
ltag
e
c
o
n
tr
o
l
l
o
o
p
h
as
two
o
b
jectiv
es:
d
eter
m
i
n
in
g
th
e
p
ea
k
in
d
u
cto
r
cu
r
r
e
n
t
r
ef
er
en
ce
an
d
s
tab
ilizin
g
th
e
o
u
tp
u
t
v
o
ltag
e.
T
h
e
o
u
tp
u
t
v
o
ltag
e
c
o
n
tain
s
a
s
ec
o
n
d
h
a
r
m
o
n
ic
c
o
m
p
o
n
en
t,
ca
u
s
in
g
p
u
ls
atio
n
at
twice
th
e
m
ain
f
r
e
q
u
en
cy
(
5
0
Hz
o
r
6
0
Hz
)
.
T
o
r
eg
u
late
th
e
av
er
a
g
e
o
u
tp
u
t
v
o
ltag
e
at
4
0
0
V,
th
e
v
o
ltag
e
co
n
tr
o
l
lo
o
p
m
u
s
t
s
u
p
p
r
ess
th
e
s
ec
o
n
d
h
ar
m
o
n
ic
r
ip
p
le
f
r
o
m
th
e
f
ee
d
b
ac
k
p
ath
[
3
0
]
-
[
3
1
]
.
T
h
is
r
esu
lts
in
a
lo
wer
b
an
d
wid
th
th
a
n
th
e
in
n
er
lo
o
p
,
with
a
cr
o
s
s
o
v
er
f
r
eq
u
en
cy
b
elo
w
1
0
0
Hz.
T
h
e
v
o
ltag
e
lo
o
p
co
n
tr
o
l
is
d
esig
n
ed
in
two
m
ain
s
tep
s
,
as o
u
tlin
ed
b
elo
w
:
˗
Ou
ter
lo
o
p
-
Step
1
:
T
h
e
cir
cu
it
in
Fig
u
r
e
1
0
(
a)
(
s
ee
Ap
p
en
d
ix
)
g
en
e
r
ates
th
e
o
u
tp
u
t
v
o
ltag
e'
s
b
o
d
e
p
lo
t
with
a
1
V
r
ef
er
en
ce
an
d
a
s
m
all
s
ig
n
al
p
er
tu
r
b
atio
n
,
s
im
ilar
to
th
e
cu
r
r
en
t
lo
o
p
.
T
h
e
r
esu
ltin
g
b
o
d
e
p
lo
t
is
s
h
o
wn
in
Fig
u
r
e
1
0
(
b
)
(
s
ee
Ap
p
en
d
ix
)
.
˗
O
u
t
e
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.
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2
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C
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tr
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l d
esig
n
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
.
1
,
Ma
r
c
h
20
25
:
355
-
368
364
4.
SI
M
UL
A
T
I
O
N
R
E
S
UL
T
S
AND
DIS
CUSS
I
O
N
Af
ter
d
eter
m
in
in
g
co
m
p
o
n
en
t
s
izes
an
d
d
esig
n
in
g
th
e
two
co
n
tr
o
l
lo
o
p
s
,
th
e
PF
C
co
n
v
e
r
ter
d
esig
n
was
s
im
u
lated
u
s
in
g
PS
I
M.
I
d
ea
l
MO
SF
E
T
s
r
ep
r
esen
ted
t
h
e
GaN
s
witch
es,
an
d
all
o
th
er
co
m
p
o
n
en
ts
wer
e
co
n
s
id
er
ed
id
ea
l
f
o
r
th
e
r
esu
lt
s
in
th
is
s
ec
tio
n
.
T
h
e
co
n
v
er
t
er
u
n
d
e
r
wen
t
test
s
f
o
r
f
u
ll
lo
a
d
in
g
at
r
ated
in
p
u
t
r
eq
u
ir
em
e
n
ts
an
d
v
ar
io
u
s
s
ce
n
ar
io
s
to
v
alid
ate
th
e
s
y
s
tem
s
p
ec
if
icatio
n
s
.
All
d
ata
was
o
b
tai
n
ed
f
r
o
m
PS
I
M
an
d
g
r
ap
h
e
d
in
MA
T
L
AB
.
4
.
1
.
F
ull
lo
a
d t
ests a
t
v
a
ri
o
us
inp
ut
v
o
lt
a
g
e
lev
els a
nd
f
re
qu
encie
s
I
n
th
e
f
ir
s
t
s
im
u
latio
n
,
t
h
e
p
e
r
f
o
r
m
a
n
ce
o
f
t
h
e
T
PP
FC
co
n
v
er
ter
was
ass
ess
ed
u
n
d
er
v
ar
io
u
s
in
p
u
t
v
o
ltag
es,
r
ep
r
esen
tin
g
th
e
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n
i
v
er
s
al
an
d
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m
m
o
n
r
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g
es
wo
r
ld
wid
e.
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h
e
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n
v
er
ter
was
test
ed
with
f
o
u
r
in
p
u
t
v
o
ltag
es: 8
5
V
a
n
d
1
2
0
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at
6
0
Hz
a
n
d
2
3
0
V
an
d
2
6
5
V
at
5
0
Hz.
At
ea
ch
lev
el,
g
r
a
p
h
s
wer
e
o
b
tain
e
d
f
o
r
th
e
in
p
u
t
c
u
r
r
en
t
an
d
o
u
t
p
u
t
v
o
lta
g
e.
Fas
t
Fo
u
r
ier
tr
an
s
f
o
r
m
(
F
FT)
was
u
s
ed
to
ca
lcu
late
th
e
p
er
ce
n
ta
g
e
o
f
to
tal
h
ar
m
o
n
ic
d
is
to
r
ti
o
n
(
T
HD)
o
f
th
e
in
p
u
t
cu
r
r
en
t.
T
h
e
p
o
wer
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ac
to
r
(
PF
)
was
f
o
u
n
d
to
b
e
eq
u
al
to
t
h
e
d
is
to
r
tio
n
f
ac
t
o
r
(
DF)
s
in
ce
th
er
e
was
n
o
p
h
ase
d
if
f
er
en
ce
b
etwe
en
th
e
in
p
u
t
cu
r
r
en
t
an
d
v
o
ltag
e.
I
n
p
u
t
cu
r
r
en
t
an
d
o
u
tp
u
t
v
o
ltag
e
r
i
p
p
les
wer
e
also
m
ea
s
u
r
ed
.
Fig
u
r
e
1
3
d
is
p
lay
s
th
ese
g
r
ap
h
s
f
o
r
t
h
e
2
3
0
V
at
5
0
Hz
i
n
p
u
t
v
o
ltag
e.
T
ab
le
3
s
u
m
m
ar
izes th
e
r
esu
lts
f
o
r
th
e
f
o
u
r
lev
els p
r
e
v
io
u
s
ly
m
en
t
io
n
ed
to
h
elp
in
ter
p
r
et
th
e
o
u
t
co
m
es o
f
th
is
test
.
(
a)
(
b
)
(
c)
(
d
)
Fig
u
r
e
1
3
.
Stead
y
-
s
tate
o
p
er
ati
o
n
r
esu
lts
at
V
in
=
2
3
0
V,
5
0
Hz:
(
a)
in
p
u
t
v
o
ltag
e
a
n
d
cu
r
r
en
t,
(
b
)
in
p
u
t c
u
r
r
en
t r
ip
p
le,
(
c)
o
u
t
p
u
t v
o
ltag
e
,
an
d
(
d
)
in
p
u
t c
u
r
r
en
t h
ar
m
o
n
ics
I
n
th
is
test
,
th
e
o
u
tp
u
t
lo
a
d
r
esi
s
tan
ce
was
v
ar
ied
to
s
im
u
late
d
if
f
er
en
t
lo
ad
in
g
lev
els:
1
0
%
to
1
0
0
%
in
1
0
%
in
cr
em
en
ts
an
d
o
v
e
r
lo
ad
in
g
lev
els
o
f
1
2
5
%
an
d
1
5
0
%.
Fo
r
ea
ch
lev
el,
th
e
in
p
u
t
cu
r
r
en
t'
s
T
HD
an
d
PF
wer
e
ca
lcu
lated
an
d
p
lo
tted
a
g
ain
s
t
th
e
lo
ad
le
v
el,
r
esu
ltin
g
in
Fig
u
r
es
1
4
(
a)
an
d
1
4
(
b
)
.
L
o
o
k
i
n
g
at
th
e
PF
v
ar
iatio
n
,
it
is
o
b
v
io
u
s
th
at
as
t
h
e
p
o
wer
lo
ad
in
g
in
cr
ea
s
es,
th
e
PF
in
cr
ea
s
e
s
.
I
t
co
u
ld
also
b
e
s
ee
n
th
at
it
r
em
ain
s
ab
o
v
e
0
.
9
5
f
o
r
all
lo
ad
in
g
p
er
c
en
tag
es
at
all
in
p
u
t
v
o
ltag
e
lev
els
ex
ce
p
t
f
o
r
2
3
0
V
an
d
2
6
5
V
,
wh
er
e
it
is
s
lig
h
tly
u
n
d
er
at
0
.
9
4
6
an
d
0
.
9
4
7
,
r
esp
ec
tiv
ely
,
f
o
r
1
0
%
lo
ad
in
g
.
As
f
o
r
th
e
o
v
e
r
lo
ad
i
n
g
co
n
d
itio
n
s
,
th
e
PF
im
p
r
o
v
es,
g
o
in
g
f
r
o
m
1
0
0
%
to
1
2
5
%
an
d
1
5
0
%
lo
ad
i
n
g
f
o
r
all
lev
els,
ex
ce
p
t
f
o
r
th
e
8
5
V,
wh
er
e
it
r
em
ain
ed
co
n
s
tan
t.
T
h
e
m
ax
im
u
m
PF
with
a
v
alu
e
o
f
0
.
9
9
9
8
9
is
ac
h
iev
e
d
f
o
r
1
5
0
% lo
ad
in
g
at
1
2
0
V
in
p
u
t v
o
ltag
e.
T
ab
le
3
.
Su
m
m
a
r
y
o
f
s
im
u
latio
n
r
esu
lts
f
o
r
t
h
e
T
PP
FC
co
n
v
er
ter
m
ain
o
p
er
atio
n
V
o
l
t
a
g
e
l
e
v
e
l
a
n
d
f
r
e
q
u
e
n
c
y
8
5
V
,
6
0
H
z
1
2
0
V
,
6
0
H
z
2
3
0
V
,
5
0
H
z
2
6
5
V
,
5
0
H
z
I
n
p
u
t
c
u
r
r
e
n
t
r
i
p
p
l
e
(
A
)
1
.
6
7
5
1
.
9
5
1
.
9
1
.
7
2
5
P
e
r
c
e
n
t
a
g
e
i
n
p
u
t
c
u
r
r
e
n
t
r
i
p
p
l
e
(
%)
3
.
3
5
6
5
.
5
1
5
1
0
.
3
0
0
1
0
.
7
7
5
O
u
t
p
u
t
v
o
l
t
a
g
e
r
i
p
p
l
e
(
V
)
1
2
.
2
5
1
2
.
5
15
15
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n
p
u
t
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r
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e
n
t
TH
D
(
%)
1
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n
p
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t
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F
0
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9
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.
9
9
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8
1
0
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9
9
9
3
9
0
.
9
9
9
3
6
Evaluation Warning : The document was created with Spire.PDF for Python.