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.
2, June
2
01
9, pp.
625~
6
3
5
IS
S
N
: 2088-
86
94,
D
O
I
:
10.11
59
1
/ij
ped
s
.
v10
.
i
2.pp
6
25-
63
5
625
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
Hardware implementati
on
of sing
le phase th
ree-level cascaded
H-bridge m
ultilevel inverter
using sinusoidal pulse
width m
o
dulation
A
. Shamsu
l
R
ahim
i
A
.
S
ubki
1
, M
o
hd
Z
a
i
d
i Mo
hd
T
u
m
a
ri
2
,
Wan
N
o
rh
isya
m
A
bd Rash
id
3
,
A
i
m
a
n
Za
k
w
a
n
J
i
d
i
n
4
,
Ah
mad
Niz
a
mmu
dd
in
M
uh
ammad
Mustafa
5
1
,
2,
3,
4,
5
Dep
a
rt
em
ent
o
f
E
lectri
onic an
d Co
m
puter E
ngi
neeri
ng, U
TeM
, M
a
l
a
ysia
1,
2
Center f
or Ro
b
oti
c
s
a
n
d
Indus
t
ria
l
Automation
,
U
niversiti
T
e
kni
k
a
l
M
a
lay
s
i
a
Melak
a, M
alay
si
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
R
e
c
e
i
v
e
d
No
v
2
7
,
2
018
Re
vise
d Jan
1
2
, 2019
A
c
c
e
pte
d
F
eb 3,
201
9
In
t
hi
s
p
a
per
a
h
a
rd
ware
i
mp
lemen
t
ati
o
n
o
f
s
in
g
l
e-p
h
as
e
casc
a
de
d
H-brid
ge
th
ree
lev
e
l
m
u
lt
il
evel in
v
erter
(ML
I)
us
ing
s
i
nus
o
idal
p
uls
e
w
i
d
t
h
m
o
du
la
ti
on
(S
PWM
)
i
s
pre
s
en
ted
.
T
here
a
re
a
f
ew
i
nt
eresti
ng
f
eatu
r
es
o
f
u
s
i
n
g
this
con
f
ig
urati
on,
w
here
l
es
s
com
p
on
ent
cou
n
t,
l
es
s
s
w
itch
in
g
lo
ss
e
s,
a
nd
im
p
r
oved
o
u
tp
u
t
v
o
l
t
a
ge/
c
urrent
w
av
ef
orm.
T
he
o
ut
pu
t
o
f
p
o
w
er
i
nv
erter
con
s
i
s
t
s
o
f
t
h
ree
f
o
rm,
t
h
at
i
s,
s
quare
w
av
e,
m
o
d
ified
squ
a
re
w
av
e
an
d
p
u
re
si
ne w
ave. The pu
r
e si
ne w
ave an
d
m
o
d
i
fi
ed s
qu
are wav
e
are
m
ore
e
xp
e
n
sive
th
an
s
qu
are
w
a
ve.
The
f
o
cus
p
a
per
is
t
o
g
e
nerate
a
P
W
M
s
ig
nal
w
hich
c
o
ntrol
the
sw
itc
h
in
g
o
f
M
O
S
F
E
T
po
we
r
se
m
i
c
o
nd
uc
tor.
T
h
e
s
in
e
w
av
e
can
be
c
rea
t
ed
by
using
t
h
e
concept
of
S
chmit
t
-Tr
i
g
g
er
o
scillator
a
nd
l
o
w
-
p
a
s
s
filter
topol
ogy
fol
l
owed
b
y
half
o
f
the
wavef
o
rm
w
i
l
l
be
e
li
min
ated
b
y
usi
n
g
th
e
ci
rc
u
i
t
of
p
reci
si
on
half
-wave
recti
f
ier.
W
avefo
r
m
was
i
nve
rt
e
d
w
it
h
18
0º
by
c
i
r
cui
t
o
f
invert
in
g
op
-amp
a
mp
lifier
in
o
rder
t
o
com
p
ar
e
sa
w-
to
oth
wav
e
f
o
rm.
Tw
o
of
P
WM
s
i
gnal
were
p
rod
u
ced
b
y
circui
t
of
P
WM
a
nd
u
s
e
d
di
gital
in
vert
er
t
o
i
n
v
e
rt
t
he
t
w
o
P
W
M
s
i
g
n
a
l
be
fore
t
h
i
s
PWM
s
ig
nal
w
i
l
l
b
e
pas
s
ed
t
o
2
M
O
S
F
ET
d
ri
ver
and
a
3
-
level
ou
tpu
t
w
av
ef
orm
with
4
5
H
z
w
a
s
pro
d
u
ced.
As
a
co
nclu
si
on
,
a
3-lev
e
l
ou
tput
w
av
efo
r
m
is
p
rod
u
ce
d
with
ou
tp
ut
v
o
l
t
a
ge
a
n
d
c
u
rrent
r
ecor
d
ed
a
t
22
.
5
V
rms
and
4.
5
A
r
ms.
Th
e
val
u
e
of
m
easu
r
e
d
r
esi
s
tance
i
s
0
.01
5
Ω
t
hat
cause
vol
tag
e
d
ro
p
aro
und
0
.0
4
3
V
.
Ba
se
d
o
n
t
he
r
e
s
ult
ob
ta
in
e
d
,
th
e
po
we
r
fo
r
de
s
i
g
n
e
d
in
v
e
rte
r
i
s around
1
00W
and
eff
i
ci
ency
r
e
c
orded
at
75%
.
K
eyw
ord
s
:
Mu
ti
leve
l
Inve
rte
r
PSIM Implem
enta
t
i
o
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:
A
Sh
a
m
s
u
l
R
a
h
i
m
i
B
in
A
S
u
b
ki
,
Fac
u
l
t
y
of
El
ect
ri
c
a
l
a
n
d
El
ec
tro
n
i
c
En
g
in
e
e
ri
ng
Tec
hno
lo
gy
FTK
EE,
U
n
i
v
ersi
ti
T
e
k
ni
ka
l Ma
la
ysia
M
ela
k
a
(U
TeM),
76
1
00 Duria
n
T
u
n
g
g
a
l
,
M
a
la
cc
a,
M
alays
i
a
Em
ail:
sha
m
su
lra
h
i
m
i@
u
t
e
m
.edu.
my
1.
I
N
TR
OD
U
C
TI
O
N
P
o
w
e
r
se
mic
onduc
tor
de
vice
s
i
s
v
e
r
y
imp
o
rta
n
t
i
n
t
he
p
ow
e
r
e
le
c
tro
n
i
c
s
fiel
d.
I
t
w
ill
for
m
o
f
a
mat
r
i
x
o
f
on
o
r
of
f
s
wit
c
h
e
s
an
d
h
e
lp
t
o
conv
e
r
t
t
h
e
p
o
w
er
fro
m o
n
e to an
o
t
h
er
one
suc
h a
s
A
C t
o
D
C,
D
C t
o
A
C
,
D
C
t
o
D
C
a
nd
A
C
t
o
A
C
.
Rece
n
t
t
ec
h
n
o
l
o
gie
s
r
eq
uire
a
h
i
g
h
d
em
an
d
in
p
r
act
ice
a
n
d
fas
t
d
e
v
e
l
o
p
in
g
of
hi
gh
p
o
w
e
r
de
vi
c
e
s
[
1].
Th
us
,
re
se
arc
h
ers
and
i
n
d
u
str
i
al
c
om
pan
ies
i
n
ter
e
ste
d
i
n
mu
lt
i
l
e
v
el
i
n
v
er
t
e
r
d
u
e
t
o
its
rela
tio
n
w
i
th
c
on
tro
l
t
ec
hn
i
q
ue.
Mu
l
t
i
l
e
v
el
i
n
v
erte
r
(MLI)
can
i
m
prove
t
he
o
utp
u
t
v
o
l
ta
ge
i
n
ter
m
o
f
reduc
e
to
t
a
l
ha
rm
onic
dis
t
ort
i
o
n
a
n
d
d
ec
rea
s
es
e
l
e
c
t
r
o
ma
gne
t
i
c
i
n
ter
f
e
re
n
c
e
p
r
ob
l
e
ms.
Conv
e
n
ti
on
al
t
w
o
l
e
v
e
l
s
in
verter
o
n
l
y
g
e
nera
t
e
s
tw
o
st
age
s
o
f o
u
t
p
u
t
vo
lta
ge,
w
h
i
l
e
m
u
l
ti
le
ve
l
i
nve
rter
s
ca
n
pr
ovi
de
m
ore,
d
e
p
e
nds
o
n
the
i
r
des
i
g
n
e
d
s
truc
t
u
r
e
.
There
f
ore
,
t
he
M
LI
i
s
use
d
t
o
pro
duce
m
u
l
t
i
l
e
ve
l-o
u
t
put
v
o
l
tag
e
s
w
h
i
c
h
are
pure
l
y
sinus
o
i
da
l
or
s
yn
t
h
es
is
a
s
t
a
ir
case
vo
l
t
age
w
a
vefor
m
a
nd
t
hus
r
e
duce
h
a
rmonic
c
o
n
t
e
n
t
.
H
ig
he
r
fre
que
nc
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
625
–
6
35
62
6
harm
on
ics
are
easier
t
o
f
i
l
t
e
r
th
a
n
h
arm
o
n
i
c
s
n
e
a
r
the
fu
nda
me
n
ta
l
fr
e
que
nc
y.
M
LI
h
as
t
he
a
d
v
an
t
a
ges
of
gene
ra
ti
n
g
b
et
t
e
r
outpu
t
qua
l
i
t
y
by
usi
n
g pu
ls
e
w
i
dth
modu
l
a
ti
o
n (P
WM)
t
e
chn
i
que.
The
m
o
st
c
om
mon
MLI
to
p
o
lo
g
i
es
a
re
c
las
s
ifie
d
i
n
to
t
hree
t
y
p
es
w
h
ic
h
ar
e
ne
u
t
r
a
l
p
o
i
nt
c
lam
p
e
d
MLI
(NP
C
-
M
LI
),
f
lying
capacitor
M
L
I
(F
C-MLI)
a
nd
c
a
s
c
a
de
d
H
-
br
i
dg
e
M
L
I
(
C
HB
-M
LI).
P
o
w
er
r
at
ing
o
f
in
verter
i
s
i
n
c
r
ea
se
d
w
ith
i
nc
rea
s
e
i
n
numb
e
r
of
l
e
v
e
l
i
n
the
i
n
v
erter
[2].
T
he
i
n
v
er
t
e
r
i
s
t
he
o
ne
t
ype
o
f
t
h
e
bas
i
c
c
onve
rsi
on
w
h
i
c
h
w
i
l
l
t
ra
nsform
a
l
ow
D
C
pow
er
t
o
a
h
i
g
h
v
o
l
t
a
g
e
A
C
p
o
w
e
r
.
T
h
e
i
n
v
e
r
t
e
r
s
a
r
e
alw
a
ys
m
a
k
e
use
o
f
r
e
n
ew
a
b
l
e
e
ne
rg
y
so
urce
s
uch
a
s
w
in
d,
f
uel
c
e
ll
a
nd
so
on.
T
hese
e
n
v
ir
onm
e
n
t
a
ll
y
frie
nd
ly e
ner
g
y
source
c
a
n
be
co
n
v
e
r
t i
n
t
o
A
C s
ourc
e
a
n
d
u
sed i
n ma
n
y
a
ppl
ica
tio
n. Bes
ide
s
, the
i
n
v
erte
r
s
are
w
i
de
ly used in
dustria
l ap
p
lic
ati
o
ns suc
h as
v
a
r
ia
ble s
p
eed A
C
m
ot
or
, i
n
d
u
c
t
i
on he
at
i
ng and s
o
o
n.
T
he ou
t
p
u
t
A
C
source
is d
e
pen
d
s o
n
t
he
i
npu
t
D
C
s
ourc
e
[
3].
P
u
lse
w
i
dt
h
m
o
d
u
l
at
i
on
is
t
h
e
m
ain
c
o
n
t
r
o
l
stra
te
gy
im
ple
m
e
n
t
e
d
i
n
t
h
e
pow
e
r
e
l
e
c
t
ro
n
i
cs.
Th
i
s
i
s
the
b
e
s
t
w
a
y
of
dri
v
in
g
m
ode
rn pow
er
e
lec
t
r
o
n
i
c
de
vi
c
e
s
.
Mo
st
o
f t
h
e
p
o
w
e
r
e
lectro
nic
circ
u
i
ts
a
re
c
on
tro
lle
d
by
P
W
M si
g
n
a
l
s of var
io
us fo
r
m
s
s
uch as m
ul
t
i
ca
rrier
P
WM
[
1-
4]
.
Th
e
ef
fi
c
i
en
cy
p
a
r
amet
e
r
s
o
f
a
m
ul
t
i
l
e
vel
in
verter
s
uc
h
as
s
w
itc
hi
n
g
l
osses
a
nd
harm
onic
re
d
u
c
tion
a
r
e
pr
inc
i
p
a
lly
d
e
p
e
n
ded
on
the
m
o
du
la
t
i
o
n
st
r
a
te
gie
s
u
sed
to
c
o
n
t
ro
l
t
h
e
in
ver
t
e
r
.
In
a
ddi
t
i
o
n
t
o
t
h
e
s
e
t
o
p
o
l
o
gi
e
s
,
the
m
o
d
u
la
t
i
on
c
o
ntr
o
l
schem
e
s
for
the
mult
i
l
e
v
el
i
n
v
e
r
ter
ca
n
be
d
i
v
ide
d
i
n
t
o
t
w
o
cate
g
o
r
ies
w
h
i
c
h
a
r
e
fun
d
am
enta
l
swi
t
c
h
in
g
freq
ue
nc
y
a
n
d
h
i
g
h
sw
it
c
h
i
n
g
fr
e
q
uenc
y
P
W
M.
F
igure
1
sh
ow
s
t
h
e
mu
l
t
i
l
e
v
e
l
c
o
n
v
erte
r
m
o
d
u
l
at
ion
m
e
t
h
o
d
s.
A
mong
var
i
ous
con
t
ro
l
sche
m
e
s,
t
he
s
i
nuso
i
dal
P
W
M
(S
PW
M
)
i
s
the
mos
t
c
om
m
o
n
l
y
u
se
d
control
schem
e
s
for
the
co
ntrol
of
m
u
l
t
ile
ve
l
i
nver
t
er
s
due
t
o
ma
ny
ad
va
nt
a
g
es
i
nc
lu
d
i
ng
ea
sy
i
mp
lem
e
n
t
at
i
on,
l
ow
er
h
a
r
m
oni
c
o
u
t
pu
t
an
d
low
sw
i
t
ch
i
ng
lo
ss
[
5].
F
i
gure
1. Mu
l
t
ile
ve
l co
nv
e
r
ter
modula
t
io
n m
e
th
o
d
s
The
m
u
lt
i
l
e
v
el
c
a
rrier
b
ase
d
o
n
PWM
,
S
e
l
ect
i
v
e
Ha
rm
oni
c
El
i
m
i
n
a
ti
on
a
nd
S
p
ace
V
ec
t
o
r
P
u
l
s
e
Wi
d
t
h
M
o
dula
t
i
o
n
(
S
VP
WM
)
a
r
e
the
sw
i
t
c
h
i
n
g
co
n
t
ro
l
m
e
th
o
d
s
a
nd
a
l
w
a
ys
u
se
d
in
i
ndus
tria
l
ap
p
l
i
c
atio
ns
and pow
er elec
t
ro
ni
c
s
[8-
9]. The mul
t
i
l
e
v
e
l
c
arr
i
e
r
based on
P
W
M
me
t
h
o
d
i
s
t
h
e
mo
st
pop
ul
ar
m
et
ho
d
du
e
to
ea
si
ly
i
mp
lem
e
nte
d
.
Th
i
s
m
et
ho
d
ca
n
be
c
a
t
e
g
o
r
i
e
s
in
to
S
P
W
M
an
d
S
V
P
W
M
[
8
]
.
T
h
e
S
P
W
M
i
s
c
o
m
p
a
r
i
n
g
t
h
e
re
f
e
re
n
c
e
s
w
av
e
an
d
th
e
ca
rri
er
w
av
e
t
o
p
ro
du
c
e
t
h
e
p
u
l
s
e.
Th
e
ca
rri
e
r
b
a
s
e
d
o
n
P
W
M
s
c
h
eme
are
class
i
fie
d
i
n
t
o pha
se
shi
fted
m
ult
i
c
a
rr
i
e
r
mod
u
l
at
i
on a
nd
le
vel
s
hi
fte
d
m
ul
t
i
c
a
rr
i
e
r
modula
t
io
n.
M
u
lti
l
e
v
e
l
i
n
vert
e
r
s
t
r
u
c
tu
re
s
are
b
e
c
o
mi
ng
i
n
c
r
ea
si
ng
l
y
p
o
pul
a
r
f
o
r
hi
gh
p
o
w
e
r
a
p
p
l
i
c
a
t
i
on
s,
t
h
e
i
r
s
w
i
t
c
h
e
d
o
u
t
p
u
t
v
o
l
t
a
g
e
h
a
r
m
o
n
i
c
s
c
a
n
b
e
r
e
d
u
c
e
d
s
in
c
e
s
e
m
i
c
o
n
d
uc
t
o
r
s
.
The
MLI
is
t
he
i
mpr
ovem
e
n
t
o
f
th
e
in
verter
w
hic
h
w
il
l
trans
f
or
m
a
h
i
gh
A
C
so
urc
e
p
ow
er.
T
h
e
r
e
a
r
e
t
hree
t
y
p
e
o
f
t
h
e
m
u
lti
le
ve
l
in
verter
,
th
a
t
i
s,
di
ode
c
lam
p
e
d
m
ultile
ve
l
i
n
v
e
r
t
e
r
,
fl
yi
n
g
c
a
p
ac
it
or
m
ulti
le
vel
in
ver
t
e
r
a
n
d
c
asca
de
d
H
-
bri
dge
M
LI
[
6
]
.
Thi
s
pro
j
ec
t
foc
u
se
s
on
ca
scad
e
d
H
-
b
ridge
M
LI
w
h
i
c
h
c
o
n
n
e
c
t
a
ll
the
H
-
br
idg
e
i
n
t
h
e
se
ries
f
orm
t
o
o
b
t
ai
n
a
high
A
C
s
ource
p
o
w
e
r
.
The
sw
i
t
c
h
in
g
c
o
n
t
ro
l
m
e
tho
d
i
s
ver
y
i
mpor
ta
n
t
t
o
c
o
n
t
rol
t
h
e
po
we
r
se
mi
c
ond
u
c
to
r
dev
i
ce
s.
The
sw
itc
hi
n
g
con
tr
ol m
eth
o
d
w
il
l re
duce
t
h
e ha
rm
oni
c
c
o
nte
n
t
s
i
n
t
h
e
o
u
t
p
u
t
A
C [7-
10]
.
I
n
t
his
pa
pe
r,
a
s
t
e
p
b
y
s
te
p
des
i
g
n
t
he
n
implem
en
ta
t
i
o
n
o
f
t
h
e
S
P
W
M
s
w
itc
hi
n
g
p
u
l
se
c
ircu
it
b
y
us
i
n
g
M
u
ltiSi
m
s
oftw
are
is
p
rese
nt
e
d
.
Later
on,
a
c
om
ple
t
e
prot
ot
ype
o
f
ca
sc
a
d
e
d
H
-b
ri
d
g
e
m
ult
i
l
e
v
e
l
i
n
v
e
rt
e
r
b
y
u
s
i
ng
a
p
r
ot
oty
p
e
of
s
i
n
e
w
a
ve
g
en
era
t
o
r
a
nd
t
ri
an
g
ul
a
r
w
av
e
g
e
n
e
ra
t
o
r
a
s
g
ati
ng
pul
se
i
s
deve
l
ope
d
an
d
t
h
e
fina
l
l
y
t
h
e
result
is
c
om
par
e
d
a
nd
a
n
al
yze
d
f
or
both
si
m
u
la
te
d
r
e
sul
t
s
an
d
pr
oto
t
y
p
e
results.
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
H
a
rd
ware
im
p
l
e
m
ent
a
t
i
on
o
f
s
i
n
g
l
e
ph
ase t
h
r
e
e
-
leve
l casc
a
d
e
d H
-
brid
ge
…
(A.
Sham
su
l Rah
i
m
i
A.
Su
bki
)
62
7
2.
RESEARCH
M
ETH
O
D
2.1.
S
in
e
wave ge
n
e
r
ator
The
F
i
gur
e
2
sh
ow
s
the
c
i
r
c
ui
t
t
h
at
g
e
n
e
r
ate
s
t
h
e
s
i
n
e
w
a
ve
i
s
c
o
m
pose
d
o
f
a
S
c
hmi
t
t
-
Tri
g
ger
osc
illa
t
o
r
a
nd
a
four
th-
o
r
d
er
B
ut
ter
w
ort
h
l
o
w
-pa
s
s
ac
t
i
ve
f
i
l
t
e
r
w
ith
a
S
all
e
n
-
K
e
y
to
po
l
o
g
y
.
The
S
c
hm
itt
tri
gger osc
illa
t
o
r ca
n
pr
od
uce
a
s
quar
e
w
a
v
e
b
y
ha
v
i
n
g a
sy
m
m
e
t
ric st
im
ulus a
n
d
the
low
-pass
f
i
l
t
er
w
i
ll fil
t
er
all
t
h
e
h
a
rm
onic
s
e
xce
p
t
the
fu
n
d
a
m
e
n
t
a
l
fre
que
nc
y
w
h
i
c
h
is
s
i
n
e
w
a
ve.
The
fre
que
n
c
y
of
t
he
f
un
dam
e
nt
a
l
w
a
ve
is e
q
ua
l t
o
fr
e
que
nc
y of
s
qu
a
r
e
w
a
ve
an
d
a
l
l
-n
um
bere
d
harm
on
ics mul
t
i
p
l
i
e
d
by
1
/
k
.
Th
e
lo
w-p
a
ss
fi
lt
e
r
w
il
l
miti
gat
e
t
h
e
h
armo
ni
cs,
l
eav
in
g
t
h
e
f
u
nda
me
nt
a
l
w
ave
w
h
ic
h
is
s
ine
w
a
ve
w
i
t
h
a
b
o
u
t
2
%
o
f
T
H
D
.
T
h
e
f
r
e
q
u
e
n
c
y
o
f
t
h
e
s
q
u
a
r
e
w
a
v
e
c
a
n
b
e
controll
e
d
b
y
resistor
(
R3
)
a
nd
cap
a
c
i
t
o
r
(C1)
on
the
in
ve
rt
i
n
g
term
in
al.
The
capa
c
i
t
o
r
w
ill
c
h
arge
t
hro
u
g
h
t
he
r
e
s
is
tor
(R
3)
i
f
the
o
u
t
p
ut
i
s
in
h
ig
h
st
a
t
e
.
T
h
i
s
co
nd
iti
o
n
w
i
l
l
c
on
tin
u
e
u
nti
l
t
he
vol
t
a
g
e
a
t
ne
g
a
ti
v
e
t
e
r
mi
na
l
i
s
h
ig
h
e
r
tha
n
t
h
e
n
on
-i
nvert
i
n
g
t
e
rmi
n
al
.
Th
e
c
y
cl
e
con
t
i
n
u
e
s
a
n
d
resul
t
i
s
a
squ
a
re
w
av
e
.
T
h
e
sq
uar
e
w
a
v
e
co
ns
ists
o
f
fun
d
a
m
e
nta
l
fre
que
nc
y
s
i
ne
w
ave
an
d
od
d
num
ber
of
h
arm
onic,
s
o,
t
he
l
ow
-pa
s
s
f
ilter
w
a
s
desi
gn
t
o
f
i
l
t
e
r
o
u
t
a
ll
t
h
e
harm
on
ics e
x
c
e
pt
f
u
ndam
e
n
t
al si
n
e
w
a
ve
.
F
i
gure
2.
C
ir
cu
it
o
f si
ne
w
ave
gene
ra
tor
2.2.
P
re
cis
i
on r
ec
tifier
The
r
e i
s
no
le
v
e
l-sh
i
f
tin
g o
f
t
he saw
-t
oo
t
h
w
a
v
e i
n
t
h
e
I
C
T
L
4
9
4, so,
t
he c
irc
u
i
t
o
f pr
ecis
i
on re
ct
ifier
is
n
ee
ded
t
o
e
limi
n
a
t
e
t
h
e
n
e
ed
t
o
l
e
ve
l-s
h
i
f
tin
g
the
sa
w
-
too
t
h
w
a
v
e
.
B
e
f
o
r
e
t
h
e
s
i
n
e
w
a
v
e
p
a
s
s
t
o
t
h
e
prec
isio
n
re
ct
i
f
ier,
one
o
f
th
e
sine
w
a
v
e
w
i
l
l
b
e
flow
t
o
t
h
e
i
nver
t
i
n
g
am
pl
ifier.
T
here
fore
,
the
i
nve
r
t
i
n
g
am
plif
i
e
r
w
i
ll
i
nver
t
t
he
s
i
n
e
w
a
ve
a
n
d
a
m
p
lif
i
e
r
t
h
e
am
p
l
itu
de
o
f
t
h
e
s
i
ne
w
av
e
with
R
f
/
R1
.
Th
e
inv
e
rt
s
in
e
w
a
ve
m
e
a
ns
t
h
e
pha
se
o
f
the
si
ne
w
ave
is
1
80
°o
u
t
o
f
pha
se
o
f
th
e
orig
in
a
l
s
ine
w
a
ve
.
The
n
,
bo
th
o
f
t
h
e
s
i
ne
w
a
ve
w
ill be
p
assed i
n
t
o
t
he
c
irc
u
i
t
o
f pre
c
is
ion
rec
t
i
f
i
e
r in
order
to o
bta
i
n hal
f
-
w
ave
.
F
i
gure
3
sh
ow
s
the
c
i
rc
ui
t
o
f
p
rec
i
s
i
o
n
r
ec
tifier
i
n
cl
u
d
i
n
g
of
in
ver
tin
g
a
m
pl
i
f
ie
r.
I
n
this
c
a
s
e,
t
he
am
plit
ud
e
o
f
t
he
s
ine
w
a
ve
w
a
s
n’
t
en
lar
g
e
d
b
e
c
a
u
se
t
w
o
o
f
t
h
ose
a
m
p
lit
u
d
e
of
s
i
n
e
w
a
ve
m
ust
be
i
n
sam
e
r
e
a
d
i
n
g
,
s
o
,
t
h
e
R
f
a
n
d
R
1
a
r
e
i
n
s
a
m
e
v
a
l
u
e
w
h
i
c
h
i
s
1
0
k
Ω
.
T
h
e
n
,
t
h
e
sine
w
ave
inc
l
ud
i
ng
of
o
r
i
g
i
n
a
l
s
i
n
e
w
a
ve
a
n
d
1
80
°o
ut
o
f
ph
a
s
e
of
s
ine
w
a
ve
w
il
l
be
f
l
o
w
e
d
t
h
rou
g
h
t
he
p
rec
i
si
on
r
ec
tifi
e
r
c
i
rcui
t
i
n
o
rder
t
o
ob
ta
in
t
he
h
a
l
f
-
w
a
ve
o
f
the
s
i
ne
w
a
v
e.
W
h
e
n
the
pos
iti
ve
c
ycle
of
t
he
s
ine
w
a
ve,
the
dio
d
e
D
3
a
nd
D
4
a
re
forw
a
r
d
b
i
ase
d
,
so,
t
h
e
forw
a
r
d
b
i
a
s
e
d
o
f
d
i
ode
D
3
ma
ke
s
shor
t
ou
t
p
u
t
o
f
the
I
C
T
L0
84
t
o
t
he
i
nv
e
r
t
i
ng
term
ina
l
a
nd
b
ypa
ss
t
he
R
1
2
.
Whe
n
t
he
n
e
g
a
t
i
v
e
c
y
c
l
e
of
t
he
s
in
e
w
a
ve,
t
h
e
di
o
d
e
D
3
a
nd
D
4
are
ne
gat
i
v
e
bia
s
ed
a
nd
th
is
m
ake
an
ope
n
circ
uit.
S
o,
t
he
n
e
g
a
t
i
v
e
sine
w
a
v
e
w
i
l
l
b
e
flow
t
o
the
in
ve
rti
ng
am
p
l
i
f
ie
r
w
i
t
h
gai
n
–
R
12
/
R
1
3
.
There
f
ore,
t
he
o
u
t
pu
t
of
t
he
I
C
TL
084
w
i
l
l
b
e
p
osi
t
i
v
e
as
t
he
i
npu
t
of
t
he
s
i
n
e
w
a
ve
i
s
nega
t
i
ve
a
nd t
h
e
out
put
o
f t
h
e
IC TL08
4
w
i
l
l be
ze
r
o a
s
the
i
np
u
t
of t
h
e
si
n
e
w
ave
is posi
tive.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
625
–
6
35
62
8
F
i
g
u
r
e
3.
Circuit of precision
rect
ifier
2.3.
I
n
v
e
r
tin
g
g
a
i
n
am
p
lifier
F
i
gure
4
be
lo
w
show
s
t
h
e
c
i
r
c
u
it
o
f
i
n
v
e
r
t
i
n
g
g
a
i
n
a
m
pl
i
f
ier
.
T
h
i
s
type
o
f
cir
c
ui
t
fu
nc
tio
n
a
s
t
o
pro
duce
a
m
a
xim
u
m
of
t
he
P
W
M
d
ut
y
c
y
cl
e.
T
he
h
a
l
f-w
a
ve
o
f
the
s
i
n
e
wa
v
e
w
a
s
i
nv
e
r
t
e
d
i
n
t
hi
s
ci
rcu
i
t
and
t
h
e
a
m
pli
t
ud
e
o
f
h
al
f-wa
v
e
i
n
cl
ud
ing
of
180
°
ou
t
of
p
h
a
se
h
a
l
f
-
w
a
ve
w
as
e
nl
a
r
ged
by
–
R1
5/
R
14.
I
n
th
i
s
circ
u
i
t,
t
he
f
r
e
que
nc
y
o
f
t
he
bot
h
i
nve
rt
ing
hal
f
-
w
ave
re
ma
in
u
ncha
n
g
ed
a
s
pr
evi
o
us
h
alf-w
ave
fre
qu
enc
y
.
Be
s
i
de
s,
t
he
v
ol
ta
ge
d
i
v
i
d
er
w
as
c
onstr
u
c
t
beh
i
nd
the
ou
t
p
u
t
o
f
I
C
L
M
3
5
8
.
T
h
e
v
o
l
t
a
g
e
d
i
v
i
d
e
r
w
i
l
l
r
e
d
u
c
e
the D
C
l
e
v
e
l
of
the in
ver
t
i
ng h
a
lf-wa
v
e i
n
or
d
er
t
o
ma
ximize
th
e
PWM
d
u
ty
c
ycle
.
F
i
gur
e 4.
Circu
it o
f
i
nv
e
r
t
i
ng
gai
n
a
mpl
i
fier.
2.4.
P
WM
c
irc
u
it
The
n
e
x
t
s
te
p
i
s
p
a
s
s
t
h
e
in
ve
rti
ng
ha
lf-s
ine
w
a
ve
t
o
th
e
P
W
M
c
i
r
c
u
i
t
.
T
h
e
c
ons
truc
t
i
o
n
o
f
P
W
M
as
F
i
gure
5.
T
he
s
i
n
g
l
e
-
en
de
d
a
p
p
lic
at
io
n
w
a
s
app
l
i
e
d
in
t
his
c
i
rc
u
it,
s
o,
t
he
p
i
n
o
utp
u
t
c
o
ntr
o
l
mu
st
c
o
n
n
ec
t
t
o
gro
u
n
d
.
The freque
nc
y of sa
w
-
t
oo
t
h
w
avef
o
r
m
ca
n be
calc
u
l
a
t
e
d b
y
usi
n
g Eq
ua
ti
on 1.
13
24
1
C
R
f
(
1
)
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
H
a
rd
ware
im
p
l
e
m
ent
a
t
i
on
o
f
s
i
n
g
l
e
ph
ase t
h
r
e
e
-
leve
l casc
a
d
e
d H
-
brid
ge
…
(A.
Sham
su
l Rah
i
m
i
A.
Su
bki
)
62
9
F
i
gure
5.
P
ulse
w
idth
m
odu
la
t
i
o
n
circ
u
it
2.5.
C
ascad
e
d
H-b
r
id
ge
m
u
l
t
i
le
v
e
l in
ve
rte
r
The
sim
p
le
c
irc
u
it
of
c
asca
d
e
d
H
-
bri
dge
m
u
lti
lev
e
l
i
nver
t
e
r
w
it
h
M
O
S
F
E
T
a
n
d
d
r
i
v
e
r
a
r
e
s
h
o
w
n
i
n
F
i
gure
6.
D
ue
t
o
h
i
g
h
s
w
itc
h
i
ng
s
p
eed
s,
t
he
N
-c
hanne
l
M
O
S
F
ET
w
a
s
chosen
a
s
t
h
e
sw
it
che
s
i
n
t
h
e
H
-
bridge
.
Be
s
i
de
s, the
N
-c
han
n
e
l
M
O
S
FET
w
ill
a
lso m
i
nim
i
ze
t
h
e
p
o
w
e
r
loss
a
nd
p
reve
n
t
t
he da
m
a
g
e.
F
i
gure
6.
T
hre
e
leve
l
H
-br
i
d
g
e
MLI
3.
RESULT
S
A
N
D
ANALY
S
IS
The
s
i
n
e
w
ave
is
s
ucce
ss
fu
ll
y
cr
ea
t
e
d
u
s
in
g
c
i
r
c
ui
t
c
o
m
p
ose
d
o
f
a
S
c
h
mitt
Tri
gger
o
s
c
illa
t
o
r
a
n
d
a
fo
urt
h
-or
d
e
r
But
terw
or
th low
-pass
act
i
v
e
fi
l
t
e
r
w
i
t
h
a
S
a
lle
n
-
K
ey t
o
p
o
l
o
gy
a
s
s
how
n
in
F
igure
7.
T
he
w
ho
le
circ
u
i
t
is
m
ad
e
with
a
s
in
g
l
e
a
n
d
pa
ssi
v
e
com
p
one
n
t
.
The
Sc
hmit
t
Trig
ger
i
s
b
a
s
ic
a
lly
a
c
o
m
pa
rator
w
ith
h
y
s
t
e
res
i
s
U
s
in
g
t
h
i
s
t
o
p
o
lo
gy,
t
he
o
u
t
p
u
t
s
i
ne
w
ave
f
o
r
m
a
m
plit
ude
a
nd
fre
qu
e
n
cy
c
re
at
ed
i
s
rec
o
rd
ed
a
t
5
.
36
V
at
4
1
H
z
a
s
i
n
d
i
ca
te
s
in
F
i
g
ur
e
8
be
l
o
w
.
T
he
s
ig
na
l
ge
n
e
ra
t
i
o
n
circ
uit
for
3-Leve
l
P
W
M
c
i
rc
l
e
a
r
o
un
d
t
h
e
TL4
94,
d
ev
ice
inc
o
rp
ora
t
e
s
al
l
the
func
t
i
ons
re
q
u
i
r
e
d in
the
co
n
s
truc
t
i
o
n
o
f a p
u
l
se
-w
id
th-
m
odu
la
ti
o
n
(P
W
M)
con
t
ro
l
circ
uit
on
a
s
i
n
g
le
c
h
i
p.
TL4
94
ge
ne
ra
tes
a
P
W
M
s
i
g
n
a
l
by
c
o
m
pa
ri
ng
a
n
i
n
t
e
rna
l
ly
g
e
n
erat
e
d
s
aw-
to
oth
w
a
ve
w
it
h
a
n
e
rr
or
s
ig
na
l.
I
n
ma
ke
o
u
t
D
C/A
C
c
o
n
v
e
rter
,
t
he
e
rr
or
a
m
p
lifiers
w
i
th
n
o
feedbac
k
f
r
o
m
the o
u
t
p
u
t
is us
ed
s
o
t
h
at t
he
e
rr
or signal i
s
th
e
s
i
g
na
l
re
qui
r
e
d is e
nc
ode
d
in
t
he
P
WM ou
t
pu
t
.
TL4
94
w
o
rks
in
t
he
s
am
e
fash
io
n
as
t
he
P
WM
g
e
n
e
r
at
i
on
of
t
he
2
-
L
e
vel
P
W
M
c
i
rcui
t,
a
f
ew
modi
fic
a
t
i
on
s and tw
e
a
k is r
equ
i
red.
The
m
od
ifi
c
a
t
io
n i
s
d
iv
ide
d i
n
t
o thre
e parts w
h
ic
h
is (1)
exte
r
nal
l
y le
ve
l
sh
i
f
t
i
n
g
t
he
s
i
n
e
wa
ve
r
e
f
er
ence
b
y
cr
eati
ng
refere
nce
ha
lf-wa
v
es
t
o
e
limi
n
a
t
e
t
h
e
n
eed
t
o
le
ve
l-
shi
f
t
t
h
e
c
a
r
r
i
e
r
w
a
v
e
,
(
2
)
i
n
v
e
r
t
i
n
g
t
h
e
m
t
o
p
r
o
d
u
c
e
t
h
e
m
a
x
i
m
u
m
P
W
M
d
u
t
y
c
y
cle,
a
nd
(3)
usi
ng
pa
irs
of
T
L
4
9
4
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
625
–
6
35
63
0
pro
duce
ea
c
h
h
a
l
f
o
f
t
he
s
in
e
w
a
ve
o
u
t
pu
t.
T
he
t
yp
ica
l
l
e
v
el
s
h
iftin
g
c
a
rr
i
e
r
w
a
ve
i
n
3
-
l
e
ve
l
P
W
M
s
y
ste
m
s
requ
ire
d
usi
n
g
op-a
m
p rec
t
i
f
ie
rs on
the
re
fer
e
nce
s
i
ne
w
ave.
Ba
se
d
on F
i
g
u
re
3,
t
h
e
op-am
p pr
ecis
i
o
n
re
c
tif
i
e
r
w
o
rks
by
t
u
r
n
i
n
g
o
n
d
i
o
de
D
3
w
h
e
n
eve
r
t
he
i
n
put
i
s
gr
ea
t
e
r
t
h
a
n
s
igna
l
gro
u
nd.
T
hi
s
ha
s
the
eff
e
ct
o
f
b
y
p
a
ssi
n
g
a
n
y
c
u
rre
n
t
th
a
t
w
ou
l
d
g
o
t
h
roug
h
R
13
,
preve
n
ti
n
g
i
t
from
d
e
v
e
l
opi
ng
a
vol
tag
e
.
S
i
nce
t
h
e o
u
t
p
u
t
i
s
con
n
ec
ted t
o
th
e
v
ir
t
u
a
l
gr
o
u
nd,
it is
eq
u
a
l
to
it.
W
h
en t
he i
n
p
u
t is less tha
n
sig
na
l
,
t
he ci
r
c
u
it ac
t
s
like a
fi
xe
d
in
vert
i
ng
am
p
l
ifier w
ith the g
a
i
n e
q
ua
l
t
o
r
a
tio of
-
R
13
/R
12
.
Si
n
c
e
th
is
c
i
r
cu
it
r
ec
ti
fi
e
s
o
nly
th
e
h
a
lf
o
f
t
h
e
si
n
e
w
a
ve
t
ha
t
is
l
e
s
s
tha
n
s
ig
na
l
gr
oun
d,
a
n
i
n
v
e
r
t
e
d
s
ine
w
a
v
e
i
s
use
d
w
ith
a
no
the
r
p
re
cis
i
on
r
ect
ifier
t
o
c
re
ate
the
se
c
o
nd
ha
l
f
-
w
ave
for
P
W
M
sig
n
a
l
c
om
paris
on.
F
ig
ure
9
sh
ow
s
t
h
e
ou
t
p
u
t
s
ine
w
a
vefor
m
t
he
p
re
cis
i
o
n
hal
f
-
w
ave
rec
tifi
e
r.
F
i
gur
e 7.
S
i
n
e
w
a
ve
g
e
n
era
t
io
n
circu
i
t
F
i
gure
8. O
utp
u
t s
i
ne
w
avef
o
r
m
F
i
gur
e 9.
H
a
l
f-si
ne w
ave
ou
t
p
ut s
ine
w
a
ve
fo
rm
Base
d
on
o
ur
o
u
t
pu
t
w
a
vefo
r
m
,
the
v
o
l
t
a
g
e
su
ffe
ri
n
g
m
il
d
d
i
s
t
or
t
i
o
n
.
T
h
i
s
d
is
tor
tio
n
i
s
c
rea
t
ed
b
y
the
ne
ga
tive
fe
edbac
k
c
om
pe
nsa
t
i
n
g
for
t
h
e
forw
ar
d
dr
op
a
c
ross
t
h
e
ou
tpu
t
d
i
o
de,
h
o
w
eve
r
,
the
s
i
g
n
al
s
ar
e
stil
l
o
p
e
r
at
io
na
l.
T
hese
s
ig
na
l
s
s
h
o
u
l
d
p
r
o
d
u
c
e
t
he
p
ro
duce
t
h
e
n
ec
essar
y
P
WM
s
i
gna
ls
w
hen
s
a
m
p
l
e
d
w
i
t
h
a
ca
rrier
w
a
v
e,
but
t
he
T
L
4
94
p
r
od
uces
a
s
ma
l
l
e
r
d
u
t
y
c
y
cl
e
a
s
t
h
e
err
o
r
sig
n
al
g
e
t
s
la
rger.
T
h
is
c
a
n
b
e
t
h
ou
ght
o
f
a
s
a
n
i
n
c
re
asi
n
g
DC
l
ev
el
a
t
t
h
e
ou
t
p
ut
,
and
t
h
e
TL49
4
c
o
m
p
e
nsa
t
es
b
y
pr
o
v
i
d
in
g
sh
or
t
e
r
p
u
lse
s
.
S
ubseq
ue
n
t
l
y
, as ea
c
h
o
f
t
he hal
f-w
a
ves rea
c
hes its peak a
m
p
lit
ude,
m
i
n
i
m
u
m
dut
y
c
y
c
l
e hap
p
e
n
s. Thi
s is
t
h
e
con
f
lic
t
i
n
g
o
f
t
h
e
des
i
re
d
e
ffec
t
.
Ther
efor
e,
t
o
o
v
erc
o
me
t
h
i
s,
t
he
h
a
l
f
w
a
ves
c
r
ea
t
e
d
pre
v
i
o
us
l
y
w
i
ll
be
in
verte
d
.
Ba
se
d
on
F
ig
ure
3,
LM
3
5
8
is c
hos
e
n
for
the
in
v
er
tin
g
g
a
in
st
a
g
e
o
f
th
e h
a
l
f
waves
du
e
t
o t
h
i
s
dev
i
ce
abi
l
i
t
y
t
o
dra
w
a
n
ou
t
p
u
t
v
ol
t
a
ge
v
ery
cl
os
e
to
n
e
g
a
t
ive
r
a
il
s
v
o
l
t
a
ge,
a
n
d
w
i
ll
ha
ve
f
ree
dom
f
or
a
d
j
us
tin
g
ma
ximum
du
t
y
c
yc
le
,
a
s
t
h
e
TL4
94
re
ac
he
s
ma
ximum
P
W
M
d
u
ty
c
ycle
a
s
the
i
n
pu
t
rea
c
hes
0
V
,
w
h
ile
minim
u
m
du
t
y
c
yc
le
o
cc
urs
w
h
en
t
he
i
n
p
u
t
is
a
t
ab
o
u
t
3V
.
It
s
h
o
u
l
d
be
n
ote
d
t
hat
R
16
a
n
d
R
17
a
d
j
u
s
t
t
h
e
D
C
Leve
l
of
t
he
h
al
f-w
a
ve
a
nd
R
14
a
n
d
R
15
a
dj
us
t
t
h
e
a
m
pl
i
t
ude
o
f
the
ha
l
f
w
a
v
e
.
T
he
v
a
l
u
e
s
ab
o
v
e
w
e
re
expe
r
i
me
n
t
a
lly
d
eter
mi
ned
t
o
p
rod
u
ce
t
he
l
e
a
s
t
c
r
oss
o
ver
d
i
s
t
or
ti
on
o
f
t
he
o
u
t
pu
t
s
i
ne
w
ave
w
h
ile
s
us
t
a
in
in
g
a
rea
l
ist
i
c a
m
pl
it
ude
.
F
i
gure
10
show
s t
h
e
i
n
vert
in
g ha
lf-
s
in
e
out
p
u
t
w
a
ve
f
o
rm
of
i
nve
r
tin
g
gai
n
a
mpl
i
fie
r
.
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
H
a
rd
ware
im
p
l
e
m
ent
a
t
i
on
o
f
s
i
n
g
l
e
ph
ase t
h
r
e
e
-
leve
l casc
a
d
e
d H
-
brid
ge
…
(A.
Sham
su
l Rah
i
m
i
A.
Su
bki
)
63
1
F
i
gure
1
0
.
Inve
rting
ha
lf-s
in
e
w
a
ve
o
u
t
p
u
t
A
t
t
hi
s
i
n
stan
t,
t
he
s
i
g
n
a
ls
a
r
e
r
ea
dy
t
o
u
se
i
n
t
h
e
TL
494.
U
si
n
g
E
qua
t
i
o
n
1
,
t
h
e
sw
itc
hin
g
f
re
que
nc
y
is
p
ro
gra
m
m
e
d
t
o
b
e
at
4
0
k
H
z
w
i
t
h
s
e
l
ect
io
n
of
R
24
e
q
u
a
l
t
o
2
5
k
Ω
a
n
d
C
13
e
qu
al
t
o
1
0
00p
F
.
Fi
g
u
r
e
11
show
s
the
fre
que
nc
y
an
d
am
pl
i
t
ude
o
f
t
h
e
saw
-
t
o
ot
h
w
a
ve
form
g
en
er
ate.
T
he
o
u
t
pu
t
at
t
he
p
u
ll-d
o
wn
t
r
a
n
si
st
o
r
w
ere
th
e
i
n
v
e
rse
as
e
x
p
e
ct
ed
.
Th
e
d
u
t
y
cy
cl
e
s
w
e
r
e
p
re
cise,
b
u
t
w
here
w
e
ex
pe
c
t
ed
a
l
o
g
i
c
1,
t
her
e
w
a
s
a
l
o
g
i
c
0.
T
here
fore
.
To
over
c
om
e
t
h
i
s
i
ssue,
t
h
e
v
o
l
t
a
ge
i
n
ha
lf
a
t
the
T
L
4
9
4
c
o
lle
ct
ors
is
d
i
v
id
ed
t
o
ma
ke
t
he
o
u
t
p
u
t
c
o
m
p
a
t
i
b
le
w
it
h
7
4
-serie
s
l
o
g
i
c
ga
te
i
n
v
e
r
te
rs.
T
h
e
s
i
g
n
a
l
a
t
t
h
e
T
L
4
9
4
c
o
l
l
e
c
t
o
r
w
o
u
l
d
b
e
su
i
t
a
b
le
t
o
dri
v
e
t
h
e
l
o
w
-
si
de
g
a
t
es
o
n
our
M
O
S
F
E
T
H
-
br
i
dge
,
w
i
t
h
t
he
i
n
v
er
t
e
d
s
i
g
n
a
l
d
r
i
v
i
ng
t
h
e
hi
gh-
side
gat
e
s
.
F
i
gure
1
1
.
Freque
nc
y
and
A
m
pli
t
ude
o
f
S
a
w
-
Toot
h Wa
ve
for
m
A
s
s
how
n
i
n
F
igure
1
2
,
by
c
ompa
rin
g
t
h
e
i
npu
t
(in
v
er
se
s
ine
w
a
v
e
f
orm
)
w
ith
t
he
s
aw
-
t
oo
th
w
a
ve
form
,
P
W
M
si
g
n
a
l
i
s
pr
oduc
e
d
.
F
i
gur
e
1
3
s
how
s
the
P
W
M
si
g
n
a
l
prod
uce
d
a
fter
c
ompa
ri
ng
ste
p
a
s
me
ntio
n
in
F
ig
ure
12.
T
h
i
s
P
W
M
si
gna
l
w
i
ll
b
e
fe
d
i
n
t
o
b
o
t
h
low
s
ide
gate
o
f
c
a
sca
d
e
H
-
bridge
M
O
S
F
E
T
con
f
ig
ura
tio
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
625
–
6
35
63
2
Figure
1
2
.
C
o
m
p
ariso
n
be
t
w
e
en
s
a
w
-too
t
h
w
a
v
e
form
a
nd in
vert
i
ng ha
lf-sine w
a
ve
F
i
gure
1
3
.
P
W
M
S
i
gn
al from
TL4
94 f
o
r bo
t
h
low
-
sid
e
g
at
e
F
o
r
both
h
i
gh
side
g
a
t
e
ha
l
f
-
c
yc
l
e
s,
a
n
a
l
t
e
rnat
in
g
P
W
M
si
gna
l
as
s
ho
w
n
i
n
Fi
gu
re
1
4
i
s
a
pp
li
e
d
.
A
f
ter
t
h
e
n
P
WM w
as suc
ce
ss
fu
l
l
y
ge
nera
t
e
d
,
now
the
se P
W
M
s
ig
na
l
i
n
f
e
tch
in
t
o
the
t
h
r
ee
-level
casc
a
d
ed
H-
bri
dge
M
LI
t
opo
l
o
g
y
t
o
tes
t
w
he
the
r
t
h
i
s
P
W
M
s
i
gna
l
s
u
itab
l
e
i
n
t
e
r
m
of
s
wit
c
h
i
ng
t
h
e
I
R
2
304
M
O
S
F
E
T
hal
f
b
ri
dge dr
i
ve
r. F
or
t
hi
s
prot
o
t
y
p
e
, tw
o
h
alf br
id
ge
dri
v
e
r
s
i
s used
a
s show
n in
F
ig
ure
6.
F
i
gure
1
4
.
P
W
M
signa
l
from
TL
494
for
bo
th
h
ig
h-
si
de
g
at
e
The
bo
ots
t
rap
c
a
pac
i
t
o
r
w
a
s
adde
d
a
nd
c
o
n
n
ecte
d
b
e
t
w
e
en
t
he
p
i
n
6
a
n
d
p
i
n
8
o
f
t
h
e
M
O
S
F
E
T
d
r
iv
e
r
.
Th
e
f
unc
t
i
on
o
f
b
oot
s
t
rap
ca
p
acit
o
r
is
t
o
act
iv
at
e
the
h
i
gh-s
i
de
o
f
t
h
e
H
-
brid
ge
i
n
v
er
t
e
r.
N
or
ma
l
l
y,
t
h
e
gate
v
ol
ta
ge
o
f
th
e
MO
S
F
ET
requ
ire
d
a
h
i
g
h
v
o
l
ta
ge
a
nd
m
o
re
t
ha
n
in
p
u
t
v
o
l
t
a
g
e
s
u
p
p
ly.
For
t
h
e
c
o
nd
i
tio
n
of
h
ig
h-
si
de
o
f
H
-
br
i
dge
i
n
v
e
r
t
e
r,
t
he
v
o
l
t
a
g
e
s
up
p
l
y
sho
u
l
d
co
nnec
t
w
i
t
h
MO
S
F
ET
pow
er
s
e
m
icon
d
u
ct
or
befor
e
co
n
n
ec
tin
g
w
i
t
h
l
oa
d
.
D
ue
t
o very lo
w
re
s
ista
nce
of
M
O
S
F
ET d
r
ive
r
, the loa
d
vo
l
tage
is ver
y
hi
gh a
n
d
a
l
mo
st
e
q
u
a
l
to
v
o
l
t
a
g
e
s
upp
ly
.
So
,
th
e
gat
e
-sou
rc
e
volt
a
g
e
i
s
l
a
rg
e
r
t
h
a
n
th
e
th
re
sh
old
vo
lt
ag
e
o
f
t
he
MO
S
F
ET
and
the
s
ourc
e
v
ol
ta
ge.
The
s
ourc
e
v
o
l
ta
ge
i
s
e
q
ual
to
l
oa
d
vol
tage
a
nd
t
he
g
ate-
so
urce
v
olt
a
ge
i
s
gate v
olta
ge
m
in
us
t
he
s
o
u
rce
vo
l
t
age.
F
rom
these
s
t
a
t
em
en
ts,
t
he ga
t
e
v
o
ltage
i
s
e
qua
l
to
s
ource
v
o
lta
ge
p
lu
s
the
thres
h
o
l
d
v
o
l
t
a
g
e,
s
o,
t
h
e
b
o
o
ts
trap
c
a
p
a
c
itor
is
u
se
d
in
o
rde
r
t
o
so
lve
t
h
is
p
r
oble
m
.
F
i
rstly,
the
b
o
o
t
s
trap
ca
paci
t
o
r
cha
r
ges
from
V
cc
t
hr
o
u
g
h
d
i
o
de
w
hen
the
l
o
w
e
r
M
O
S
F
ET
pow
e
r
s
em
icond
u
c
tor
is
t
ur
n
o
n
a
nd
t
h
e
up
per
MO
S
F
ET
p
o
w
e
r
sem
i
c
o
n
d
u
c
t
or
i
s
t
u
rn
o
ff.
T
he
f
unc
t
i
o
n
o
f
d
io
de
i
s
to
p
r
e
ve
nt
t
he
c
a
p
aci
t
o
r
fr
om
di
sc
harg
i
ng
int
o
V
cc
.
Whe
n
uppe
r
MO
S
F
ET
pow
er
s
em
ico
n
d
u
c
t
or
i
s
t
u
rn
on,
t
he
b
oo
ts
tr
ap
c
a
p
aci
t
o
r
will
un
derg
o
d
i
sc
ha
rgi
ng
pr
oce
s
s
a
nd
th
i
s
p
r
o
ce
ss
w
ill
c
a
u
se
g
a
t
e
vo
lta
ge
g
oes
up
to
overc
ome
the
e
f
fec
t
o
f
hi
g
h
-
side
of
t
h
e H
-
brid
ge in
v
e
r
ter.
Th
e
fa
b
r
i
c
at
ed
p
roto
typ
e
h
as
b
e
e
n
t
e
st
ing
f
o
r
l
o
w-vol
t
a
ge
t
e
s
t
i
n
g
m
ec
ha
nism
.
The
l
o
w
-
vo
l
t
a
g
e
tes
tin
g
w
a
s
co
nd
uc
t
e
d
us
i
ng
t
h
e
1
2
V
DC
l
e
a
d
ac
i
d
b
a
t
ter
y
b
o
t
h
a
s
t
he
V
CC
r
e
gul
a
t
or
s
ourc
e
a
nd
a
s
t
he
H
-
bri
dge
D
C
ra
il
.
A
s
s
uch,
t
he
o
ut
p
u
t
w
a
s
a
12
V
P
WM
s
i
gna
l,
w
hic
h
wa
s
f
i
l
t
ered
a
nd
u
se
d
t
o
p
o
w
er
u
p
a
1
2
V
hal
o
gen
bu
lb.
Test
in
g
a
t
l
ow
-
volta
ge
a
l
l
ow
ed
u
s
to
s
afe
l
y
tes
t
o
u
r
s
e
t
u
p
a
nd
p
erf
o
rm
b
a
s
i
c
t
ro
ubl
e
s
ho
oti
n
g
befor
e
m
ovin
g
on
to
h
i
gh
v
o
lta
g
e
.
F
i
g
u
r
e
1
5
show
s
t
h
e
o
u
t
pu
t
of
H
-
b
ri
dge
i
nve
rter.
Cha
nne
l
1
sh
ow
s
o
u
t
put
vo
lta
ge
f
or t
he
h
i
gh
gate
o
f th
e ha
lf-
b
r
i
d
g
e
.
S
om
e di
s
t
orti
o
n
c
a
n
be see
n
,
bu
t t
h
e w
a
ve
fo
rm
s other
w
i
s
e
lo
o
k
a
s
the
y
s
h
o
u
l
d.
T
hi
s
d
i
s
t
or
t
i
o
n
w
as
c
om
p
l
e
m
e
n
t
e
d
b
y
s
ever
e
over
h
ea
t
i
n
g
o
f
M
O
S
F
E
T
s
a
n
d
c
a
u
s
e
d
q
u
i
t
e
a
b
i
t
o
f
t
r
ou
bl
e
un
til
i
t
wa
s f
i
gu
re
d
o
u
t
.
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
H
a
rd
ware
im
p
l
e
m
ent
a
t
i
on
o
f
s
i
n
g
l
e
ph
ase t
h
r
e
e
-
leve
l casc
a
d
e
d H
-
brid
ge
…
(A.
Sham
su
l Rah
i
m
i
A.
Su
bki
)
63
3
F
i
gure
1
5
. O
ut
pu
t o
f
three
le
v
e
l
H
-bridge
i
n
v
e
rter
Du
ri
ng
l
o
w
-vol
t
a
g
e
t
e
s
ti
ng
m
e
c
h
ani
s
m,
t
h
e
v
olt
a
g
e
a
nd
c
urre
n
t
a
re
r
e
c
orde
d
as
s
how
n
in
T
ab
le
1
.
F
i
gure
1
6
s
ho
w
s
t
he
o
utp
u
t
vo
l
t
age
w
a
ve
form
acr
oss
the
12
V
hal
o
g
e
n
b
u
l
b
w
i
t
hou
t
c
a
pa
ci
t
o
r
filter
.
W
i
t
h
t
h
e
ca
paci
t
o
r
re
mo
ve
d,
t
he
p
rev
i
o
u
s
d
i
stort
i
on
a
l
so
g
one,
t
hou
g
h
t
h
e
vo
lta
ge
s
til
l
sl
ope
s
t
o
s
ome
degre
e
a
t
b
o
t
h
pos
it
ive
an
d
n
e
gat
i
ve
c
yc
le
.
The
s
i
ne
o
u
t
pu
t
w
a
s
e
n
o
u
g
h
w
ith
t
h
e
f
ilter
and
t
h
a
t
t
he
o
utp
u
t
w
i
t
ho
u
t
t
h
e
f
il
ter
w
a
s
e
s
se
n
tia
ll
y
t
h
e
sam
e
a
s
b
e
fo
r
e
,
b
u
t
w
ith
t
he
d
i
s
t
o
r
tio
n
go
n
e
,
c
an
b
e
ta
k
e
n
t
o
m
ea
n
th
a
t
out
put
w
oul
d
be
idea
l i
f
we
had
t
h
e
fi
l
t
er.
Ta
b
l
e
1.
Recor
d
ed da
t
a
d
u
ri
n
g
low
v
olta
ge
t
est
i
ng
me
cha
n
ism
Me
a
s
ure
d
V
olt
a
ge
M
ea
sure
d C
u
rr
e
n
t
O
u
tput
P
ow
e
r
18.
8
V
3.
69
A
70
W
F
i
gure
1
6
.
O
u
tpu
t
v
olta
ge
w
a
v
efor
m
acr
oss hal
o
gen
bu
lb
Ta
b
l
e
2
s
how
s
t
h
e
ou
tc
om
e
of
t
he
t
hre
e
l
e
v
e
l
H
-brid
g
e
inve
r
t
er
w
h
e
n
t
h
e
s
y
s
t
e
m
i
s
f
e
d
f
r
o
m
2
0
V
pow
er
su
p
p
l
y.
The
va
l
ue of m
e
asur
e
d
re
s
is
ta
nce
is 0.
0
1
5
Ω tha
t
c
a
u
s
e v
o
lt
a
g
e dr
o
p
ar
o
u
nd 0.0
43 V
. Ba
s
e
d
o
n
the
re
sul
t
o
b
t
ai
ned,
t
he
p
ow
er
f
or
d
es
ig
ne
d
i
nver
t
e
r
i
s
arou
nd
1
00W
a
nd
e
f
f
i
c
i
e
n
c
y
rec
o
rd
ed
a
t
75
%.
F
i
g
u
r
e
17
b
e
l
ow
s
how
s
t
h
e
F
F
T
for
t
h
e
o
u
tp
ut
v
o
l
ta
ge
w
a
v
ef
orm
,
p
erform
e
d
a
c
t
i
v
e
l
y
b
y
t
h
e
o
s
c
i
l
l
o
s
c
o
p
e
.
T
h
e
l
a
r
g
e
pea
k
,
w
h
ich
is
a
ll
the
w
a
y
t
o
t
he
l
eft
in
t
hi
s
ima
g
e,
i
s
t
h
e
4
5
H
z
s
ine
w
a
ve
f
u
n
d
am
enta
l
fre
que
nc
y
.
T
hi
s
prima
r
y
freque
ncy w
h
ic
h w
i
ll
be
r
etaine
d
by
fil
ter
and
go
t
h
ro
u
g
h
t
o the
loa
d
.
Tab
l
e
2. Thr
ee leve
l
H
-
brid
ge
i
n
v
e
r
ter
at 2
0V
D
C
pow
er
s
upply
M
eas
ured V
oltag
e
M
eas
ured
C
u
rre
nt
O
utp
u
t
P
o
w
e
r
22
.
5
V
4
.5 A
1
00 W
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SSN: 2088-
8694
Int J
P
o
w
El
e
c
&
D
ri S
yst
,
V
ol.
10,
N
o.
2
, June
20
1
9
:
625
–
6
35
63
4
F
i
gure
1
7
.
O
u
tpu
t
v
olta
ge
F
FT
4.
CONCL
U
S
ION
F
o
r
furthe
r
i
m
provem
e
n
t
s,
t
o
im
pro
v
e
to
ta
l
har
m
o
n
i
c
d
ist
o
rt
ion
a
nd
impr
o
v
e
o
u
t
p
ut
pow
e
r
efficie
n
c
y
,
a
t
l
east thre
e
i
m
provem
e
n
t
s ca
n
be d
o
n
e
. Firstly,
t
he
f
ilt
e
r
cir
c
uit
s
u
ch as RC
f
ilter,
R
L filter or
L
C
f
ilt
er
s
ho
uld
b
e
c
on
st
ru
c
t
e
d
i
n
th
e
l
o
a
d
b
ec
au
se
t
h
e
h
armo
n
i
c
c
o
n
t
en
t
s
w
i
l
l
be
f
il
ter
e
d
ou
t
or
a
tte
nua
t
e
d.
Se
cond
l
y
,
t
h
e
switc
h
i
n
g
f
r
e
q
u
enc
y
c
a
n
b
e
i
n
cr
ease
d
o
ver
tha
n
4
0
k
H
z
b
e
c
a
u
s
e
t
h
e
s
w
i
t
c
h
i
n
g
f
r
e
q
u
e
n
c
y
c
a
n
minim
i
z
e
t
he
h
ar
monic
c
o
n
t
e
n
ts.
S
o
,
the
h
i
g
h
er
t
he
s
w
itc
h
i
ng
f
r
e
q
ue
ncy,
t
he
l
ow
e
r
t
he
h
arm
onic
c
o
nte
n
t
s
o
f
the
3-le
vel
ou
t
p
u
t
w
a
v
e
f
orm
.
T
his
in
cre
a
sing
sw
itc
h
i
n
g
f
reque
nc
y
wi
ll
als
o
d
ecr
ease
the
f
i
l
t
er
c
omp
o
n
e
nt
si
z
e
.
F
i
na
l
l
y,
a
h
ig
h-le
ve
l
o
f
t
he
H
-bri
d
g
e
m
u
lti
le
vel
in
ve
rter
w
i
l
l
r
e
d
u
c
e
m
o
r
e
t
h
e
T
H
D
o
f
t
h
e
o
u
t
p
u
t
w
a
ve
form
c
ompa
re
t
o
the
low
-
le
ve
l
o
f
t
he
H
-brid
g
e
m
u
l
t
i
l
e
v
el
i
n
v
e
rter.
For
exa
m
ple,
5
-
l
e
v
el
H
-bridge
mult
i
l
e
v
el
i
n
v
e
rter
w
ill
br
in
g
w
i
th
h
i
g
h
effic
i
e
n
cy,
low
di
stor
tio
n
a
nd
ea
si
e
r
f
i
l
t
e
r
.
S
o
,
a
5-
l
e
ve
l
H
-
brid
ge
mult
i
l
e
v
el i
n
v
e
r
t
e
r is ve
r
y in
te
re
st
e
d
t
o be
pu
r
sued
i
n the
fu
t
ur
e.
ACKNOW
LEDG
E
MEN
T
S
The
au
th
ors w
o
u
l
d li
ke
t
o
tha
nk Fa
ku
lti Te
k
n
o
l
og
i K
e
jur
u
te
raa
n
U
T
e
M
and
U
n
ivers
iti
T
e
kn
i
k
al
M
ala
y
s
i
a
Me
laka
f
or
s
po
nsor
i
n
g
thi
s
w
or
k u
nder
the s
hor
t-te
rm
gra
nt,
U
T
e
M
,
P
P
J
P
/
201
8/
F
T
K (1
1
A
)/
S0
1
612
.
REFE
RENCES
[1]
P.
V
.
Kum
a
r,
et
a
l
.
,“S
i
n
g
le
P
hase
C
as
cad
ed
M
u
l
t
i
l
e
vel
In
vert
er
Using
M
u
lticarrier
P
W
M
Techn
i
qu
e.”
ARP
N
J
o
urna
l o
f
Eng
i
n
e
e
r
in
g a
n
d
Ap
pl
ie
d
Sc
ie
nc
e
s
,
v
ol.
8
,
no.
1
0
,
pp.
796-7
9
9
,
2
0
1
3
.
[2]
P
.
P
.
Raj
eevan
,
et al.
,
“
A
S
ev
en
-L
evel
I
n
v
ert
e
r
To
pol
og
y
f
o
r
In
d
u
ct
ion
M
o
t
o
r
D
r
iv
e
Us
ing
Two-L
e
vel
Invert
ers
a
n
d
Floa
ting
Ca
pa
c
i
tor
F
e
d
H-brid
ge
s,”
IEEE
Transaction
s
on
Power Elect
ron
i
c
s
,
vo
l.
26,
n
o
.
6
,
p
p
.
17
33
–1
74
0,
20
11
.
[3]
W.
A
.
Halim,
et
a
l
.,
“Revi
e
w
of
M
ultile
vel
Inverter
T
opologi
es
and
Its
Ap
plicati
o
n
s
.”
J
o
ur
na
l o
f
T
e
leco
mmu
ni
catio
n, Elect
ronic
a
n
d
Com
puter
Engi
neeri
n
g
(
J
TEC)
,
vo
l
.
8
,
n
o
.
7,
pp.
5
1
-
56,
2
0
1
7
.
[4]
A
.
N
a
m
b
o
o
d
i
r
i
a
n
d
H
.
S
.
W
a
n
i
,
“
U
n
i
p
o
l
a
r
a
n
d
B
i
p
o
l
a
r
P
W
M
I
n
v
e
r
t
e
r.
”
Inter
n
a
t
i
onal Jo
ur
na
l f
o
r
Inno
vat
i
v
e
Res
e
ar
ch i
n
S
c
ie
n
ce
&
T
echn
o
logy (
I
JIR
S
T
)
,
v
o
l
.
1
,
n
o
.
7
,
p
p
.
237-24
3,
201
4.
[5]
L.
M
.
T
o
l
b
ert,
et
a
l
.
“
M
u
ltil
e
vel
Co
nv
ert
e
rs
f
or
L
arg
e
E
lect
ric
D
r
i
v
es
”,
IE
E
E
T
r
an
s.
Ind
.
Ele
c
t
ro
n,
v
o
l
.
3
5
,
p
p
.
3
6
-
44
,
1
99
9.
[6]
M.K.
K
u
m
a
r
,
et
a
l
.
,
“Cas
caded
M
u
l
til
evel
I
nvert
er
w
ith
P
WM
C
on
tro
l
M
e
t
h
o
d
.
”
Int
e
rnati
o
n
a
l
Jour
na
l o
f
En
gi
neer
ing Tren
ds
an
d
T
ech
no
lo
gy
(
I
JET
T
)
,
vol.
4
,
n
o
.
5,
pp.
1491-1
4
9
6
.
2
01
3.
[7]
V.
M
.
Re
dd
y,
et
a
l
.
,
“
C
o
m
pre
h
ens
i
v
e
R
evi
e
w
o
n
S
ingle-P
h
ase
F
i
ve-lev
el
I
nvert
er
T
o
p
olog
ie
s”
International
Jou
r
n
a
l
o
f
En
g
i
n
eer
ing
Res
e
ar
ch &
T
ech
no
log
y
(
I
JER
T
),
v
o
l
. 4
, n
o. 6
, p
p.
21
1
-
21
6, 20
1
5
.
[8]
D.
S
u
b
ram
a
ni
an
a
nd
R
.
R
a
sh
ee
d,
2
0
1
3
.
“
Fi
ve
L
ev
el
C
ascaded
H
-bri
dge
Mul
t
ilevel
Inverter
Usi
ng
M
ulticarrier
P
u
l
s
e
Wi
d
t
h
Mo
du
lation
T
echn
i
q
u
e.”
Inter
n
a
t
i
o
n
a
l Jou
r
n
a
l
of Eng
i
n
eeri
ng and Inn
o
va
tive T
echn
o
lo
gy
(
I
JEIT)
,
vo
l.
3
,
no
.
1,
p
p
. 4
38
-4
41
.
[9]
P
.
Irai
a
nb
u
an
d
M
.
S
iv
ajum
ar,
“A
S
i
ngle
D
C
S
ou
rce
B
a
sed
C
a
scad
e
d
H
-
brid
ge
5
L
evel
I
nv
erte
r.
”
In
ter
nat
io
nal
Jou
r
n
a
l
o
f
Inn
o
v
a
tive Resea
r
ch
in
Sci
e
nce,
Engineeri
ng
and
T
echn
o
l
o
g
y
, v
o
l
. 3
,
n
o
. 1
, p
p.
99
5
-
10
00
,
2
0
1
4
.
[10]
T.
S
ingaravelu,
et
al
.
,
“
D
esi
gn
an
d
Imp
l
em
en
tati
on
o
f
S
e
ven
Lev
e
l
Cascaded
H
-b
rid
g
e
I
nvert
er
Usin
g
L
o
w
f
r
equ
e
ncy
t
r
a
n
sfo
r
m
e
r
with
S
i
ngle
DC
S
ource,
”
Int
e
rn
atio
na
l
Jo
ur
na
l o
f
E
ngineer
in
g an
d Tech
no
lo
gy (
I
J
E
T)
.
v
o
l
.
5,
n
o
.
3
,
pp
.
3
068-3
076
.
2
01
3
Evaluation Warning : The document was created with Spire.PDF for Python.