TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 14, No. 3, June 20
15, pp. 420 ~ 4
2
7
DOI: 10.115
9
1
/telkomni
ka.
v
14i3.789
3
420
Re
cei
v
ed Ma
rch 2, 2
015;
Re
vised Ap
ril
15, 2015; Accepte
d
May 1
,
2015
A Power Factor Corrected Bridgeless Type III Cuk
Derived Converter fed BLDC Motor Drive
J. Pearly
Catherine*
1
, R. Balamuruga
2
Dep
a
rtment of Po
w
e
r El
ectron
ics and Dr
ives,
K.S.Rangas
a
m
y
Co
lle
ge of
T
e
chnolog
y (A
utonom
ous),
K.S.R Kalvi Na
gar, T
i
rucheng
ode, Nam
a
kkal
,
T
a
milnad
u, India, Ph./F
ax: 0
428
8 27
474
1-4
4
/042
88 2
7
4
8
6
0
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: pearl
y
k
p
m@
gmail.c
o
m
1
, nrbals@
gma
il.co
m
2
A
b
st
r
a
ct
T
h
is pap
er dea
ls w
i
th the power factor correcti
on in BLD
C
motor dr
ive w
i
th different cuk deriv
e
d
converter to
pol
ogi
es an
d the
best on
e is si
mu
late
d fo
r po
w
e
r factor correction
oper
atio
n. Pow
e
r qua
li
t
y
issue
is the
ma
jor co
ncern
in t
he BL
DC
mot
o
r drive
due
to r
e
co
mme
nde
d l
i
m
its of
har
mo
n
i
cs in th
e su
ppl
y
current. C
onve
n
tion
ally
the B
L
DC
motors ar
e p
o
w
e
red w
i
th
the h
e
l
p
of
dio
de
brid
ge r
e
ctifiers w
h
ich
res
u
lt
s
in hi
ghly d
i
sto
r
ted supp
ly cu
rrent and
poor
pow
er fact
or. So mo
dificati
on in co
nverte
r topolo
g
y is th
e
researc
h
hotsp
ot in rece
nt ye
ars.
Alternativ
e
l
y brid
gel
ess c
onverter to
pol
o
g
ies ar
e use
d
i
n
plac
e of di
od
e
brid
ge rectifier
s
(DBR). Amo
ng t
he brid
ge
l
e
ss topol
ogi
es
cuk derived c
onverters suit
e
d
w
e
ll
for pow
er
factor correctio
n. In this pap
e
r
the different
cuk t
opol
og
ies
are inv
e
stig
ate
d
an
d the b
e
st one is si
mulat
e
d
w
i
th the help of
neuro-fu
zz
y
c
ontrol
l
er in MA
T
L
AB/Simuli
nk
platform
.
Ke
y
w
ords
: p
o
w
er factor corr
ection
(PF
C
), brid
gel
ess C
u
k
conv
erters, to
tal h
a
rmon
i
c d
i
stortions (T
HD
),
pow
er qua
lity, dio
de bri
d
g
e
re
ctifier (DBR), BLDC
motor dr
iv
e
Copy
right
©
2015 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The BL
DC
motors a
r
e
becoming
m
o
re
popul
ar
in many lo
w and m
ediu
m
po
wer
appli
c
ation
s
. They are
wid
e
ly used i
n
h
ousehol
d ty
pes of eq
uipm
ent like fan
s
,
air conditio
n
e
r
s,
water
pump
s
, refrige
r
ators, wa
shin
g machi
n
e
s
et
c. [1-3]. It also find
s app
lication in m
any
indu
strial to
o
l
s, medi
cal
e
quipme
n
t’s,
heating,
vent
ilation an
d ai
r conditio
n
in
g, rob
o
tics a
n
d
pre
c
ise moti
on control
sy
stem
s. As th
e name i
ndi
c
a
t
e
s it
ha
s n
o
bru
s
h
e
s f
o
r co
mmut
a
t
i
o
n
.
Based
on th
e roto
r p
o
siti
on the
po
wer elect
r
oni
c
switch
es
are
comm
utated.
Hen
c
e
it is
also
kno
w
n a
s
an
electroni
cally comm
utated
motor [4-5].
Powe
r qu
ality proble
m
s
have be
com
e
impo
rtant i
s
sue
s
in the
s
e m
o
tors d
ue to th
e
recomme
nde
d limits of harmo
nics in
sup
p
ly cu
rre
nt by variou
s internation
a
l power q
u
a
lity
stand
ard
s
su
ch a
s
the Int
e
rnatio
nal El
ectrote
c
h
n
ica
l
Commi
ssio
n (IEC) 61
00
0-3
-
2 [6]. So
the
power fa
ctor
corre
c
tion
ha
s led th
e ci
rcuit desi
gne
rs
to look
clo
s
el
y at all se
ctio
ns of the
ci
rcuit
and d
e
velop
possibl
e lo
we
r lo
ss
altern
a
t
ives. A conv
entional PF
C schem
e ha
s lowe
r effici
e
n
cy
due to sig
n
ificant lo
sses in
the diode b
r
i
dge. One
se
ction that contributes
signifi
cantly to redu
ce
the lo
sses in
the in
put b
r
i
dge
re
ctifier. Conve
n
tionall
y
boo
st
conv
erters
are
u
s
ed a
s
front-e
n
d
rectifie
rs [10
-
11]. For low
voltage appli
c
ation
s
su
ch as tele
comm
unication or
compute
r
indu
stry
an addition
al conve
r
ter o
r
isolatio
n tran
sformer i
s
req
u
ired to ste
p
down the voltage. As a re
sult,
the alte
rnativ
es to
elimi
n
a
t
e the
diode
bridg
e
o
r
co
nvert it into
a du
al-u
se
ci
rcuit
have
be
en
explore
d
fo
r
many yea
r
s.
The el
i
m
inati
on/co
nversio
n
of
Diod
e Br
i
dge brin
gs
ab
out
its own set
of
chall
enge
s.
To overcome
these d
r
a
w
ba
cks several b
r
idgel
es
s top
o
logie
s
suitab
le for step u
p
or ste
p
down appli
c
a
t
ions in orde
r to incre
a
se
the powe
r
factor at the
ac main
s. Th
e distingui
shi
n
g
cha
r
a
c
teri
stic of a b
r
idg
e
le
ss PFC converter is th
at the pa
rtial
elimination
of di
ode
s in th
e di
od
e
bridg
e
at the input. This re
duces po
we
r
losse
s
that normally occu
r in
a diode bridge; hen
ce the
overall syste
m
efficien
cy is
imp
r
oved
with
comp
arable
co
st sa
vings. Bri
dge
less PF
C bu
ck
conve
r
ters are limited for step do
wn a
pplicatio
n
s
[12-13]. Input li
ne cu
rrent ca
nnot follow t
h
e
input voltage
arou
nd zero
cro
s
sing
s of
the input
line voltage. O
u
tput to input voltage ratio
is
limited to half
resulting in i
n
crea
sed
THD an
d re
du
ce
d PF. Bridgel
ess bu
ck-b
oo
st co
nverte
r h
a
s
both step u
p
and step d
o
w
n op
eratio
n
in a single
circuit [15-16
]. It has the disa
dvantag
e
s
:
Disco
n
tinuou
s in
put
curre
n
t, high
pea
k cu
rrent in
p
o
we
r
com
pon
ents, p
oor tra
n
sie
n
t re
sp
on
se
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Power Fact
or Corrected Bri
dgel
ess Type III Cuk Deri
ved Convert
e
r… (J.
Pearl
y
Catherine)
421
mak
e
it less
effic
i
ent. Power Fac
t
or
Correc
tion
rectifi
e
rs
are u
s
ed
to improve th
e re
ctifier p
o
w
er
den
sity
and
to
red
u
ce
n
o
i
se emissio
n
s
via soft switchi
ng
te
ch
nique
s or co
upled
mag
n
e
t
ic
topologi
es [7-9].
2. Cuk Deriv
e
d PFC Co
n
v
erters
Powe
r Fa
cto
r
Co
nverte
rs used fo
r b
o
th
step
-up
and ste
p
do
wn ap
plications a
r
e
analyzed Cu
k converte
r h
a
s b
o
th input
and outp
u
t
currents with a
low cu
rre
nt
ripple,
the Cuk
conve
r
ter
see
m
s to be a potential can
d
i
date in
the basi
c
co
nverte
r topologi
es.
Hen
c
e it can
be
use
d
for appli
c
ation
s
re
sulti
ng in
lower in
put and outp
u
t
current rippl
e.
The th
ree
ne
w Cuk de
rived topol
ogie
s
a
r
e d
e
rive
d from th
e
convention
a
l
PFC
Cu
k
rectifie
rs [1
7-19] as
sh
own
in Fi
gu
re 1.
The b
r
idg
e
le
ss Cuk
derive
d
conve
r
ter i
s
a com
b
inatio
n of
two dc-d
c co
nverters. On
e for each h
a
lf line per
io
d (T/2) is the
input voltage. The numb
e
r of
semi
con
d
u
c
tor switche
s
in the cu
rrent
flowing p
a
th
is
r
e
du
ce
d
.
C
u
rr
en
t s
t
r
e
ss
es
in
th
e
activ
e
and pa
ssive
switche
s
are further red
u
ce
d. Circ
uit
efficiency is improved a
s
com
p
a
r
ed
to
conve
n
tional
Cu
k rectifie
r. They d
o
n
o
t
suffer from
high
comm
on mo
de
noi
se
pro
b
lem
and
comm
on mod
e
emission p
e
rform
a
n
c
e is sim
ilar to the
conventio
nal
PFC topologi
es.
(a)
(b)
(c
)
Figure 1. CUK Derived
Co
nverter T
opol
ogie
s
(a) Type I, (b) Type II, (c
) Type III
The thre
e new Cu
k recti
f
iers a
r
e co
m
pared ba
se
d on com
p
o
nents
count,
mode of
operation
i
n
DCM
and dri
v
er circuit complexity
. From the
comparison
results
the type III cuk
conve
r
ter
pro
v
ides le
ss co
mpone
nt co
u
n
t and
sw
it
ches
co
ndu
cte
d
in current f
l
owin
g path i
s
minimum. It utilizes t
w
o power switches
(
Q
1 and
Q
2
and the t
w
o
p
o
we
r
swit
che
s
can b
e
d
r
iven
by the same
control sig
nal
, which
signifi
cantly simplifi
e
s the control
circuitry.
3. Opera
t
ion of T
y
pe III BL Cuk Conv
e
r
ter
The choi
ce of
mode of o
p
e
r
ation
of a PF
C converte
r i
s
a
critic
al issue be
cau
s
e it
dire
ctly
affects the
cost and
ratin
g
of the com
pone
nts u
s
ed
in the PFC
conve
r
ter [20
-
21]. Co
ntinu
ous
Con
d
u
c
tion
Mode
(CCM
) and
Disco
n
t
inuou
s Con
ductio
n
Mod
e
(DCM
) a
r
e
widely u
s
e
d
in
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 14, No. 3, June 20
15 : 420 – 42
7
422
pra
c
tice. In
CCM o
r
DCM,
the indu
ctor’
s
curre
n
t or th
e voltage a
c
ross intermedi
ate ca
pa
citor
in
a PFC conve
r
ter
rem
a
in
s
contin
uou
s o
r
di
scontin
u
o
u
s
i
n
a switching peri
od resp
ectively. To
operate a PF
C convert
e
r i
n
CCM, on
e requires th
re
e
sen
s
o
r
s (two
voltage, one
curre
n
t)
while
a
DCM o
p
e
r
ati
on ca
n be a
c
hieved u
s
ing
a singl
e vo
ltage se
nsor. T
he stresse
s
o
n
PFC co
nve
r
ter
swit
ch
ope
rat
i
ng in
DCM
a
r
e
com
paratively highe
r
a
s
com
pared with
its
op
era
t
ion
in CCM. By
operating the
rectifie
r in DCM, several a
d
v
antage
s ca
n
be gaine
d su
ch a
s
:
1)
Natural nea
r-unity powe
r
factor.
2)
The p
o
wer
switch
es
are turne
d
O
N
at
zero
curre
n
t and the
outp
u
t diode
s a
r
e
turne
d
OFF at z
e
ro current.
The mo
de of
operation i
s
an ap
plication de
pen
den
t. CCM i
s
su
itable for hi
g
h
po
wer
appli
c
ation
s
and
DCM fo
r
low p
o
wer a
p
p
licatio
ns. Th
us, the lo
sse
s
du
e to the t
u
rn
-on
switch
ing
and the
reve
rse
re
cove
ry of the outp
u
t diode
s
a
r
e co
nsid
erab
ly redu
ced.
Conve
r
sely, DCM
operation si
g
n
ificantly increases
the condu
ction lo
sses d
ue to
the incre
a
sed cu
rre
nt stress
throug
h
circui
t com
pon
ents. As a
result, this l
ead
s to
one
di
sadva
n
tage
of the
DCM
o
peration,
whi
c
h limit
s it
s u
s
e
to lo
w-power
appli
c
ations
(le
s
s
t
han 300 W). Hen
c
e, DCM
is prefe
r
red for
low-po
we
r ap
plicatio
ns [22]
.
(a)
Duri
ng po
sitive half cycle
(b)
Duri
ng ne
gative half cycle
Figure 2. Circuits
of Type III Cuk
rec
t
ifier
4. Design of
Neuro
-
Fu
zz
y
Contr
o
ller
The
co
st of
a
BLDCM
driv
e ha
s two
m
a
in
com
pone
nts; on
e i
s
th
e moto
r
and
other is
the cont
rolle
r. The co
st of the co
ntrolle
r
and comple
xi
ty of control b
e
com
e
the ke
y factor for th
e
comm
erciali
z
ation of these drives
. Th
e
r
efore, the co
ntrolle
r de
si
g
n
for a parti
cular ap
plication
plays a maj
o
r role in th
e perfo
rman
ce
and effici
e
n
cy of the drive. Hen
c
e the
acceptability
of
BLDC moto
rs in
a va
riet
y of appli
c
ati
ons solely d
epen
ds upo
n
the resea
r
ch in th
e a
r
e
a
of
simplified a
n
d
low cost co
ntrolle
r de
sig
n
havi
ng imp
r
oved po
we
r
quality at the input mains
o
f
the drive.
Figure 3. Neu
r
o-fu
zzy Logi
c Co
ntrolle
r
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
A Power Fact
or Corrected Bri
dgel
ess Type III Cuk Deri
ved Convert
e
r… (J.
Pearl
y
Catherine)
423
Neu
r
al n
e
two
r
ks a
r
e u
s
e
d
to desi
gn m
e
mbe
r
ship fu
nction
s of fu
zzy
system
s
that are
employed a
s
deci
s
ion
-
ma
king
system
s for cont
rol
ling equi
pme
n
t as sh
own
in Figure 3
.
Although fu
zzy logi
c ca
n
encode exp
e
r
t kno
w
le
dge
dire
ct
ly usin
g
rule
s with lin
guisti
c
label
s,
it
usu
a
lly takes a lot
of time
to de
sig
n
a
n
d
tune
the
m
e
mbe
r
ship fu
nction
s
whi
c
h
qua
ntitatively
define the
s
e
lingui
stic lab
e
ls. Ne
ural n
e
twork
lea
r
ni
ng tech
niqu
e
s
ca
n autom
ate this pro
c
ess
and sub
s
tanti
a
lly redu
ce d
e
velopme
n
t time and cost
while imp
r
ovi
ng perfo
rma
n
ce.
A fuzzy neu
ral syste
m
combi
n
e
s
the adv
antag
e
s
of fuzzy
system
s and
neural
netwo
rks. As
a fuzzy sy
ste
m
, it does no
t requi
re
a large data
set a
nd it provide
s
tran
spa
r
en
cy,
smooth
n
e
ss,
and re
pre
s
e
n
t
ation
of prio
r
kn
owl
edg
e.
As a
ne
ural
system, it p
r
ov
ides pa
ram
e
tric
adapta
b
ility.
5. Simulation Circuits
A compute
r
simulatio
n
model for P
F
C Cuk
con
v
erter fed B
L
DC motor
drive is
develop
ed u
s
ing the MAT
L
AB/SIMULINK softwa
r
e i
s
sho
w
n i
n
Fig
u
re
4. The
switching
pul
se f
o
r
Cu
k
conve
r
te
r is ge
nerate
d
with th
e h
e
l
p
of hal
l
si
gn
als obtaine
d
f
r
om hall sen
s
ors. The sp
e
e
d
of the motor i
s
co
ntroll
ed b
y
controlli
ng the DC lin
k vo
ltage of the in
verter with th
e help of Neu
r
o
fuzzy l
ogic co
ntrolle
r. Singl
e pha
se
a
c
v
o
ltage i
s
give
n a
s
inp
u
t to the Cuk rectifi
e
r. Th
e volta
g
e
sou
r
ce invert
er boo
st the
DC voltag
e of the
rec
t
ifier and is
fed to the BLDC Motor.
Figure 4. Simulink bl
ock of BLDC m
o
tor
dr
iv
e wit
h
N
e
uro
-
Fu
zzy
log
i
c co
nt
rolle
r
Figure 5. Simulink Blo
ck fo
r Rule
s F
r
ami
ng with Neuro-Fu
zzy Algorithm
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046
TELKOM
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KA
Vol. 14, No. 3, June 20
15 : 420 – 42
7
424
Input and out
put para
m
ete
r
s a
r
e chose
n
as tw
o me
mbershi
p
function
s as
spe
ed error
and ch
ang
e in spee
d error are de
signe
d
with the help
of neural net
work. Rul
e
s f
o
r co
ntrollin
g of
swit
che
s
are
framed with
the knowl
e
dge of fuzzy
logic as sh
own in Tabl
e 1. These two
combi
nation
s
are impl
eme
n
ted in ne
uro
-
fuzzy co
ntrol
l
er a
s
sho
w
n
in Figure 5.
The two i
npu
ts
are ta
ken
as
spe
ed e
r
ror a
nd chan
ge in
spe
ed e
r
ror f
o
r fuzzy logi
c controlle
r. Thus th
e de
cision
makin
g
rule
s
for FLC for o
b
taining controlled sig
nal comp
ri
se
s of 11x3 matri
c
e
s
. Based u
p
o
n
these
rule
s th
e switching
p
u
lse
for cuk
converte
r
i
s
ge
nerate
d
co
rre
s
po
ndin
g
to speed
variatio
n.
The cu
k
con
v
erter re
gulat
es the suppl
y given to
th
e inverter, so that the sp
eed shoul
d be
maintaine
d
at the referen
c
e value.
Table 1. Rul
e
s table for FL
C
The sim
u
latio
n
block for A
C
main
s po
wer fact
o
r
cal
c
ulation blo
c
k is sh
own in F
i
gure 6.
The di
spl
a
y
sho
w
s the A
C
mai
n
s po
wer facto
r
which
could
b
e
affecte
d
when th
e mot
o
r i
s
con
n
e
c
ted to the mains. With the help of cuk c
onvert
e
r with ne
uro
-
fuzzy logic
switchi
ng pul
se,
the power factor has
been i
m
prove
d
to 0.98 whi
c
h i
s
n
eare
r
to unity.
Figure 6. Power F
a
cto
r
Calcul
ation Blo
c
k
The
sub
blo
c
k of p
o
wer fa
ctor
cal
c
ul
ation is sho
w
n i
n
Figu
re
7. T
he line
si
de
voltage
and current i
s
take
n a
s
in
put and it is
conve
r
ted int
o
co
rre
sp
ond
ing re
al and
rea
c
tive po
wer
usin
g re
al an
d rea
c
tive po
wer Sim
u
lin
k
block. T
he
p
o
we
r facto
r
o
f
the AC mai
n
s i
s
calculat
ed
with the help
of math operator blo
c
ks.
Figure 7. Sub block for po
wer fa
ctor
cal
c
ulatio
n
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TELKOM
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ISSN:
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046
A Power Fact
or Corrected Bri
dgel
ess Type III Cuk Deri
ved Convert
e
r… (J.
Pearl
y
Catherine)
425
6. Results a
nd Discu
ssi
ons
As
said earlier com
pared
to other bri
dgeless
conv
erte
rs, the type III cuk
converter
effectively re
gulate
s
the i
n
verter
su
ppl
y and imp
r
ov
es the
po
we
r factor at AC main
s ne
ar
to
unity. The a
c
-dc bri
dgel
ess conve
r
ter t
hus
red
u
ce
s the cond
uctio
n
losse
s
a
nd
the use of P
W
M
inverter ma
kes it possibl
e to operate
at the f
und
amental swit
chin
g frequ
e
n
cy. The arti
ficial
intelligent fuzzy logic
controller ge
ne
rate
s t
he switchi
n
g pulses for t
he Cu
k conve
r
ter.
The speed
i
s
cont
rolled
effectively by
co
ntrolling the DC li
nk voltage.
For the
perfo
rman
ce
evaluation of
the
propo
se
d drive
und
e
r
inp
u
t ac voltage vari
ation, the DC lin
k
voltage is kep
t
consta
nt.
Figure 8. Speed Re
sp
on
se
The spee
d should b
e
lin
early varie
d
and settled to the refe
re
nce valu
e at 0.056s.
Comp
ared to
other
cont
roll
ers, th
e settling time of
the
artificial intell
igent controll
ers is mi
nimu
m.
The sp
eed va
riation is al
so
smooth
e
r. Th
ere is n
o
dip
and ri
se in th
e spe
ed waveform.
Figure 9. Electrom
agn
etic
Torq
ue waveform
The ele
c
trom
agneti
c
torqu
e
waveform i
s
sho
w
n in Fi
gure 9. The p
eak ove
r
shoo
t of
the
torque
is
0.3
2
Nm
at 0.0
08s. T
he g
e
nerate
d
el
e
c
t
r
oma
gneti
c
torqu
e
contai
ns
ripple
s
in
its
waveform. Th
e torqu
e
attain its nomin
al
value at 0.03
ms. Du
e to torque
rippl
e, the BLDC mot
o
r
prod
uce EMI and pe
rform
a
nce of the mo
tor is deg
ra
de
d due to noi
se.
The trap
ezoi
dal sh
ape ba
ck EMF
wav
e
form is
sho
w
n in Figu
re
10. The sh
ap
e of the
back EMF waveform get
s collap
s
e
d
at the time of starting. Up to 0.1s the ba
ck EMF wavefo
rm
is ideal a
nd a
fter that there
shoul
d be so
me disto
r
tion
s in the wavef
o
rm.
The stato
r
cu
rre
nt wavefo
rm is sh
own in
Figure 11
Comp
ared to
other controllers, the
distortio
n
i
n
i
n
the
wavefo
rm i
s
mi
nimu
m. The
pe
ak overshoot
of the
curr
ent
is 2.3A at
0.00
7s.
Due to th
e le
ss
disto
r
tion
s in the waveform, the h
eat
ing of the p
h
a
se
win
d
ing i
s
minim
u
m. T
he
curre
n
t sho
u
l
d
attain the nominal value
at 0.017ms.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 14, No. 3, June 20
15 : 420 – 42
7
426
Figure 10. Back EMF
Wav
e
form
Figure 11. Stator Cu
rrent Wavefo
rm
Figure 12. To
tal Harm
oni
c Disto
r
tion
The Total
Ha
rmoni
c Di
sto
r
tion (THD) is
achi
ev
ed a
s
5.46% is represe
n
ted in Fi
gure
12.
For any type of load the ha
rmoni
c level i
s
almo
st con
s
tant.
Referen
ces
[1]
Gieras JF
, W
i
n
g
M. Permane
nt magnet motor tec
hno
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atio
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w
York: Marcel
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.
[2]
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ot JR, Miller T
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[3]
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. Brushl
ess per
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t
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an R. El
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o
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u
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iss
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ment In
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w
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t rectifier
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i
t
h
l
o
w
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d
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07;
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TELKOM
NIKA
ISSN:
2302-4
046
A Power Fact
or Corrected Bri
dgel
ess Type III Cuk Deri
ved Convert
e
r… (J.
Pearl
y
Catherine)
427
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o
vi´c MM. Bridgel
ess hig
h
-po
w
e
r-factor buc
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2-61
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pou
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nove
l
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i
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e
ctifier
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it
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e
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d
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a
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e
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i W
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p
eng
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g
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n
g
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ang
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l
br
id
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a
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