Internati
o
nal
Journal of P
o
wer Elect
roni
cs an
d
Drive
S
y
ste
m
(I
JPE
D
S)
V
o
l.
7, N
o
. 1
,
Mar
c
h
20
16
,
pp
. 15
9
~
17
2
I
S
SN
: 208
8-8
6
9
4
1
59
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJPEDS
Comparative Steady State Anal
ys
is of
B
o
ost and Cas
c
ad
ed
Boost Converter with In
ducti
ve ESR Losses & Capacitor
Current Behaviour
Byam
ake
s
h
Nayak
,
T
a
nm
oy Roy Choudh
ury
School of
Electr
ical Eng
i
neering
,
KIIT
University
, Bhuban
e
swar
– 24, Odisha, In
dia
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 17, 2015
Rev
i
sed
D
ec 12
, 20
15
Accepte
d Ja
n
4, 2016
In this p
a
per
,
an overall comparison between
the Boost Conv
erter (BC)
&
Cascaded Conv
erter/ Cas
caded B
oost Converter (
CBC) has been
depicted in
term
s of idea
l
condition
,
as w
e
ll
as w
ith th
e
considera
tion of
Equiva
lent
S
e
ries
Res
i
s
t
an
c
e
(ES
R
) of ind
u
ctor(s
).
The
lo
s
s
com
p
aris
on in the two
converters due
to the
ESR is also includ
ed
in
this paper. It
can b
e
seen
that in
CBC, voltage g
a
in is more bu
t the power
loss due to
ESR is
also more
compared to BC. The par
a
meters of the converters are d
e
rived with a
consideration of
per unit ripple quantity
of ind
u
ctor cur
r
ent
an
d capacitor
voltag
e
. A boundar
y
condition
between
th
e continuous cond
uction mode
(CCM) & disco
n
tinuous condu
ction mode
(DC
M
) of the indu
ctor curren
t
is
also shown. The behaviour of
the cap
acitor cu
rrent for the
co
nverters is
discussed during ON and
OF
F condition of the
switch(es) durin
g DCM. At
the end, th
e simulation results
of both the converters are g
i
ven for a
20V/100V, 100 W output. Th
e analy
s
is a
nd simulation
results ar
e presented
in this
pape
r for
the v
e
rifi
ca
tion
of the
fe
asibil
it
y.
Keyword:
Bo
und
ary co
nditio
n
Capacitor current
Cascad
ed conver
t
er
D
C
-D
C conv
erter
ESR loss
com
p
arison
I
ndu
ctiv
e ESR
Copyright ©
201
6 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Tan
m
o
y
Ro
y Ch
oud
hu
r
y
,
Sch
ool
o
f
El
ec
t
r
i
cal
En
gi
neer
i
ng,
KI
IT Uni
v
er
si
t
y
,
B
h
uba
nes
w
a
r
– 24
,
Odis
ha,
I
N
D
I
A.
Em
a
il: tan
m
o
y
.
n
ita20
09@rediffm
ai
l.co
m
1.
INTRODUCTION
DC
- DC
c
o
n
v
e
rsi
o
n i
s
bec
o
m
i
ng very
i
m
port
a
nt
i
n
va
ri
o
u
s p
o
r
t
a
bl
e ap
pl
i
cat
i
ons
no
w
a day
s
. M
a
ny
po
rt
abl
e
de
vi
c
e
s use po
we
r at
di
ffere
nt
l
e
v
e
l
s
of vol
t
a
ge.
The
m
oder
n
t
echn
o
l
o
gy
i
s
m
a
ki
ng t
h
e re
newa
bl
e
ener
gy
s
o
u
r
ces
(R
ES
) t
o
bec
o
m
e
an al
t
e
rna
t
i
v
e o
f
t
h
e
co
m
bust
i
on e
ngi
nes
fo
r
p
o
we
r
gene
rat
i
o
n as
t
h
e c
o
s
t
and t
h
e en
vi
r
o
nm
ent
a
l
i
ssues are conc
er
ne
d. [
1
]
-
[
6
]
B
u
t
t
h
e
m
a
i
n
hi
n
d
ra
nce be
hi
n
d
R
E
S i
s
l
e
ss
vol
t
a
ge
g
e
n
e
ration
p
e
r cell. [7
] So
t
o
fu
lfill th
e req
u
i
rem
e
n
t
o
f
h
i
gh
v
o
ltag
e
ap
p
lication
s
, a
n
u
m
b
e
r
o
f
cell
s
to
be
con
n
ect
ed
i
s
s
e
ri
es o
r
pa
ral
l
e
l
com
b
i
n
at
i
on.
It
f
u
rt
her
re
du
ces t
h
e e
n
e
r
gy
gene
rat
i
o
n
due
t
o
s
h
a
d
o
w
e
f
f
ect
o
n
th
e PV cells. [8
]-[11
]
So
a v
o
ltag
e
st
ep up
proces
s can be
used with a fuel
cel
l
(FC
)
or P
hot
ov
ol
t
a
i
c
(P
V) cel
l
to boost the
output voltage a
nd t
hus t
h
e efficiency can
also be inc
r
ease
d
. [12], [13] As
the dc-dc c
o
nverter
in
j
ects less curren
t
ripp
le in
to th
e so
urce, the
efficiency a
s
well as the
life
spa
n
ca
n
be increased with that for
t
h
e P
V
or
FC
a
rray
.
[
14]
,
[
15]
Th
e
v
o
ltag
e
bu
ild
u
p
can b
e
po
ssib
l
e
b
y
B
C
an
d CBC. [1
6
]
,
[1
7
]
BC
can
no
t
g
i
v
e
t
h
e sig
n
i
fican
t
b
u
ild
u
p
of
ou
tp
u
t
vo
ltag
e
fo
r th
e sam
e
du
ty ratio as
co
m
p
ared to CBC as th
e
ou
tpu
t
v
o
ltag
e
of t
h
e later
o
n
e
is a quadratic function of dut
y
cycle. Again for BC as hi
g
h
v
o
l
t
a
ge ge
ne
rat
i
on re
q
u
i
r
es
a large duty cycle, so
i
t
furt
he
r i
n
c
r
e
a
ses t
h
e re
ver
s
e reco
very
e
ffe
ct
of t
h
e
di
o
d
e
s
. [
18]
,
[1
9]
R
e
fere
nce [
1
]
ha
s di
scu
ssed a
b
out
t
h
e
clo
s
ed loo
p
operatio
n.
The w
o
r
k
s o
n
di
ffe
re
nt
dc – dc co
nve
rt
ers h
a
ve bee
n
p
ubl
i
s
he
d i
n
di
ffe
re
nt
Jou
r
nal
s
and
prese
n
t
e
d i
n
vari
ous c
o
nfe
r
ences,
but a com
p
le
te steady state analysis
is no
wh
ere presen
t with
re
fe
r
e
nce t
o
vari
ou
s
l
o
sses.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
: 1
5
9
–
17
2
16
0
Thi
s
pape
r
i
s
not
foc
u
si
ng o
n
a
n
y
ki
n
d
of
m
odi
fi
cat
i
o
n or
c
h
a
nge
s
re
qui
red f
o
r
t
h
e
im
pro
v
em
ent
of
t
h
e
con
v
e
r
t
e
r
ope
r
a
t
i
on,
b
u
t
t
h
i
s
onl
y
s
h
ows
a c
o
m
p
ara
tiv
e v
i
ew
with
a
prop
er
steady
state analysis.
The c
o
m
p
arative study
of t
h
e
two c
onv
erters is fo
cused
i
n
th
is p
a
p
e
r along
with
th
e con
s
id
eration
o
f
ESR
of t
h
e i
n
duct
o
r
(
s) i
n
se
ct
i
on 3 an
d p
o
w
er l
o
sse
s due
t
o
t
h
e ESR
effect
i
s
di
scus
sed i
n
sect
i
on
4. I
n
section 5, converter pa
ram
e
ter
s
are designe
d
with a di
scussi
on a
b
out the stresses on the s
w
itch(es
). Sect
ion
6
d
e
p
i
cts abo
u
t
th
e
bo
und
ary con
d
ition
between con
tinu
o
u
s
cond
u
c
ti
o
n
m
o
d
e
(CCM) & d
i
scon
tin
uo
us
con
d
u
ct
i
on m
ode
(DC
M
)
o
f
i
n
d
u
ct
o
r
cu
rre
nt
. B
e
ha
vi
o
r
of t
h
e ca
pa
ci
t
o
r cur
r
e
n
t
and t
h
e si
m
u
l
a
t
i
on
perform
a
nces are s
h
own in se
ction
7 & 8 res
p
ectively.
2.
OPERATION OF THE
CONVE
RTERS
2.
1.
Casc
ade
d
B
o
o
s
t
Co
nver
ter
(a)
(b
)
(c)
Figu
re
1(a
)
,
(
b
)
,
(c
). Casca
d
e
d
Bo
ost Co
n
v
ert
e
r,
Switches
are in
ON state,
Switches
are i
n
OFF state
Th
e CBC is sho
w
n
in
Figu
re
1
(
a) wh
ere
is th
e in
pu
t vo
ltag
e
,
Q
1
, Q
2
– are t
w
o active switche
s
,
D
1
,
D2 a
r
e the passive
swit
ches a
nd
L
1
, L
2
& C
1
, C
2
are the c
o
rres
ponding va
l
u
e
s
of
Inductanc
e
and
Cap
acito
r
of the con
v
e
rter. The ou
tpu
t
vo
ltage is rep
r
esen
ted
b
y
v
0
=
v
C2
. Th
e du
ty
ratio
is
term
ed
as
k
h
e
re.
The steady sta
t
e param
e
ters of the convert
e
r can
be f
o
u
nd
o
u
t
by
co
n
s
i
d
eri
n
g t
h
e
O
N
an
d
OFF
co
ndu
ctio
n m
o
d
e
o
f
th
e switch
e
s, Q
1
& Q
2
.
Th
e ON state o
f
th
e
switches is sh
own
in
Figu
r
e
1(
b)
. I
n
th
is con
d
i
t
i
o
n
indu
ctor
cu
rr
en
t
1
is
f
l
ow
ing
thr
ough
th
e sw
itch
Q
1
and
2
thr
oug
h Q
2
. So
switch
cu
rren
t
1
=
1
and
2
=
2
. The
di
ode
s, D
1
&
D
2
are
reve
rse
biased as
shown
by light c
o
lor. T
h
e ca
paci
tor C
1
d
i
sch
a
rges th
ro
ugh
th
e
in
du
ctor
L
2
-
Q
2
, as
well as C
2
discharges t
h
rough the loa
d
resist
an
ce R. The
load c
u
rrent is
shown as
i
0
.
During
th
e OFF m
o
d
e
of th
e
switch
e
s, no
cu
rren
t is
flowi
n
g th
rou
g
h
t
h
e switch
Q
1
an
d Q
2
as s
h
own
i
n
Fi
gu
re 1
(
c)
. The di
odes
D
1
, D
2
b
eco
m
e
s f
o
rw
ard
b
i
ased
n
o
w
.
Cur
r
e
n
t
passin
g
thro
ugh th
e d
i
o
d
e
s ar
e
1
&
2
respectively
.
T
h
e
out
put
voltage across t
h
e
lo
ad is sam
e
as th
e cap
acitor
v
o
ltag
e
,
2
.
To
fin
d
the
ste
a
dy
state pa
ra
m
e
ters
I
,
I
and
V
,
V
th
e fo
llowing
m
e
th
od
h
a
s b
e
en
fo
llo
wed
:
Du
rin
g
ON
&
OFF
tim
e
of t
h
e switches
,
A
v
er
ag
e
v
o
ltage dr
op
acr
o
ss i
n
du
ctor
L
1
,
V
=
kV
,
V
=
1k
V
V
A
v
er
ag
e
v
o
ltage dr
op
acr
o
ss i
n
du
ctor
L
2
,
V
=
kV
,
V
=
1k
V
V
A
v
er
ag
e
cu
rr
en
t p
a
s
s
i
ng
throu
g
h
c
a
p
a
c
itor
C
1
,
I
= -
kI
,
I
=
1k
I
I
A
v
er
ag
e
cu
rr
en
t thr
ough the
capacitor C
2
,
I
= -
kI
,
I
=
1k
I
I
T
h
e
av
e
r
ag
e vo
lta
g
e
d
r
op
a
c
ro
s
s
a
n
y inductor is zero, i.e.,
V
+
V
= 0.
Sol
u
t
i
o
n
o
f
t
h
i
s
ab
o
v
e e
x
p
r
es
si
on
gi
ves as
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
SN
:
208
8-8
6
9
4
C
o
m
p
a
r
at
i
ve
S
t
eady
St
at
e
An
al
ysi
s
of
Bo
ost
an
d C
a
sc
ade
d
Bo
ost
C
o
nvert
e
r w
i
t
h
I
n
duct
i
ve …
(Ta
n
mo
y RC)
16
1
V
V
1
k
(1
)
V
V
1
k
(2
)
A
v
er
ag
e
cu
rr
en
t p
a
s
s
i
ng
throu
g
h
an
y c
a
p
a
c
i
to
r
is
z
e
ro
,
i.e
.
,
I
+
I
= 0.
Fr
o
m
th
e so
lu
tio
n of
t
h
e ab
ove exp
r
ession
,
1
(3
)
1
(4
)
O
u
tp
u
t
vo
lta
g
e
of
th
e c
a
s
c
a
d
ed
co
nv
er
te
r
,
1
2.
2.
B
oos
t Co
nve
r
t
er
(a)
Fi
gu
re
2(a
)
.
B
o
ost
c
o
n
v
ert
e
r i
n
ON
m
ode
(b
)
Fi
gu
re
2(
b
)
. B
oost
co
n
v
ert
e
r
i
n
O
FF m
ode
Th
e B
o
o
s
t conv
er
ter is sho
w
n in
Figu
r
e
2(
a), (b
) wh
er
e
V
is th
e i
n
pu
t
v
o
ltage, Q
–
an
active switch,
D
is th
e p
a
ssi
ve sw
itch
and
L & C ar
e th
e cor
r
e
spo
n
d
i
ng
v
a
lu
es o
f
I
ndu
ctan
ce and
Cap
aci
to
r
of
th
e conver
t
er
.
The
output vol
t
age is re
prese
n
ted
by
v
=
v
. Th
e
d
u
t
y
ratio
is termed
as
d
h
e
re.
Th
e
On
state of
th
e boo
st conv
er
ter is sh
own
in Figur
e
2
(
a)
an
d OFF stat
e in
Fi
g
u
r
e
2
(
b)
. Th
e
bo
ost
co
nv
erter is also
op
erating
in
th
e sam
e
way
as th
e Cas
cade
d
boost conve
r
ter. The i
ndu
cto
r
cu
rr
en
t is f
l
o
w
i
n
g
t
h
r
o
u
g
h
t
h
e
sw
i
t
c
h Q
d
u
ri
ng
ON
t
i
m
e
and t
h
r
o
ug
h t
h
e
di
o
d
e
du
ri
n
g
OF
F
t
i
m
e
of t
h
e
swi
t
ch.
Th
e ou
tpu
t
v
o
l
tag
e
eq
u
a
ls th
e cap
acito
r vo
ltag
e
as
sh
own
in
th
e Figu
r
e
2(
a)
and 2(b). Steady state
param
e
t
e
rs of
t
h
e c
o
n
v
e
r
t
e
r ca
n
be
fo
u
n
d
o
u
t
by
f
o
l
l
o
wi
n
g
t
h
e m
e
t
hod
st
at
ed a
b
o
v
e.
V
V
1
d
(5
)
I
V
1
d
R
(6
)
O
u
t
p
u
t
vo
ltag
e
of
th
e boo
st co
nv
er
ter
,
V
V
V
1
d
Th
e
relatio
n b
e
tween
t
h
e
d
u
t
y
ratio
s
o
f
th
e t
w
o
co
nv
erters
with
a sam
e
v
o
ltag
e
g
a
in
can be g
i
v
e
n
as-
d1
1
k
(7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
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:
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94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
: 1
5
9
–
17
2
16
2
Fig
u
re. 3 Co
mp
ariso
n
b
e
t
w
een
BC an
d CBC du
ty ratio
at t
h
e sam
e
v
o
ltag
e
g
a
in
It is seen
fro
m
th
e cu
rv
e
o
f
Fig
u
re 3
t
h
at fo
r th
e
sam
e
v
o
ltag
e
g
a
i
n
, less du
ty ratio
is requ
ired
in
CBC co
m
p
ared
to
BC. So
a
cascad
ed
boo
st co
nv
erter can
p
r
ov
id
e m
o
re v
o
ltag
e
bu
ild
up
co
m
p
ared
to
b
o
o
s
t
co
nv
erter
with
a less du
ty rati
o
.
3.
EFFECT
OF INDUCTIVE
ESR
In section
2
,
th
e
d
i
scussion
i
s
related to the id
eal
c
o
nve
rters. B
u
t
practi
cally in all conve
rters
,
the
inductance is
unde
r the i
n
fl
ue
nce of a
se
ries connected
resi
stor or ESR. Du
e to t
h
e prese
n
ce of s
u
c
h
ESR, the
conve
r
ter pe
rform
a
nce or t
h
e efficiency
ca
nnot be
practi
cally sa
m
e
as that
o
f
th
e i
d
eal co
nv
erters.
In
th
is
sect
i
on t
h
e ES
R
effect
of t
h
e
t
w
o c
o
nve
rt
er
s i
s
di
sc
usse
d
wi
t
h
t
h
e l
o
ss c
a
l
c
ul
at
i
on
due
t
o
t
h
e sai
d
ES
R
effect
i
n
t
h
e
ne
xt
sect
i
on.
3.
1.
Ca
scaded Boo
s
t Co
nv
ert
e
r
Fig
u
re
4
.
In
du
ctiv
e ESR in
cas
caded boost c
o
nve
rter
To fi
nd the st
eady state para
m
e
ters of the
cascaded
B
o
ost co
nv
er
ter
du
e to
the ESR
effect of the
in
du
ctor, t
h
e
follo
wing
m
e
th
od
is app
lied
:
Du
rin
g
ON
&
OFF
tim
e
of t
h
e switches
,
A
v
er
ag
e
v
o
ltage dr
op
acr
o
ss t
h
e indu
ctor
L
1,
(8
)
1
(9
)
A
v
er
ag
e
v
o
ltage dr
op
acr
o
ss i
n
du
ctor
L
2
,
(1
0)
1
(1
1)
A
v
er
ag
e
cu
rr
en
t p
a
s
s
i
ng
throu
g
h
c
a
p
a
c
itor
C
1
,
(1
2)
1
(1
3)
A
v
er
ag
e
cu
rr
en
t thr
ough the
capacitor C
2
,
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
0
0.
2
0.
4
0.
6
0.
8
1
Bo
os
t
Co
n
v
er
t
e
r
Du
t
y
Ra
t
i
o
C
as
c
ade
d C
onv
er
t
e
r
D
ut
y
R
at
i
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
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6
9
4
C
o
m
p
a
r
at
i
ve
S
t
eady
St
at
e
An
al
ysi
s
of
Bo
ost
an
d C
a
sc
ade
d
Bo
ost
C
o
nvert
e
r w
i
t
h
I
n
duct
i
ve …
(Ta
n
mo
y RC)
16
3
(1
4)
1
(1
5)
Ave
r
a
g
e v
o
l
t
a
ge d
r
op a
c
r
o
ss
any
i
n
duct
o
r
i
s
zero a
n
d t
h
e avera
g
e c
u
rrent passi
ng
thro
ugh
th
e cap
a
cito
r is
also zero. So,
0
(1
6)
0
(1
7)
So
lu
tion
of the equ
a
tio
ns (16
)
&
(17
)
wit
h
refe
ren
ce to equ
a
tio
ns (8
)
–
(15), the s
t
eady state
param
e
ters of t
h
e casca
de
d c
o
nve
rter
due to
ESR effect ca
n be
obtained as
-
1
1
1
(1
8)
1
1
(1
9)
1
1
1
(2
0)
1
1
1
(2
1)
3.
2.
Bo
ost
C
o
n
v
er
ter
Fig
u
re
5
.
In
du
ctiv
e ESR in Boo
s
t co
nv
erter
The stea
dy state pa
ram
e
ters of th
e Boo
s
t co
nv
er
ter can be fo
und
as,
1
1
1
(2
2)
1
1
(2
3)
Figure 6 s
h
ows the com
p
arative analysis of the
Cascaded Boost and the Boost conve
rter voltage
g
a
in
wh
en
equ
a
l ESR
o
f
al
l th
e in
du
ctor is con
s
id
ered
. It is clearly u
n
d
e
rstoo
d
from
the curve t
h
at the
attain
ab
le v
o
l
t
a
g
e
g
a
in
in
Cascad
ed
Bo
o
s
t
co
nv
erter is
even m
o
re as com
p
ared to
Boost conve
r
ter even if
with
th
e lo
sses
o
f
du
e t
o
th
e ESR effect.
Bo
th
th
e con
v
erters can
wo
rk
with
i
n
th
e
Qu
asi –
Li
n
ear
reg
i
on
on
ly. Beyo
nd
th
at th
e
Non
–
Lin
e
ar
regi
on a
p
pears
,
where
the
pe
rform
a
nce of t
h
e c
o
nver
t
e
rs i
s
di
st
u
r
be
d
&
t
h
ey
can
not
be
o
p
erat
ed
. T
h
e
du
ty
cycle for the
operating
poin
t
o
f
t
h
e cascad
e
d
co
nv
erter is
less with
co
m
p
ar
ison
to boo
st con
v
e
r
t
er
op
er
atin
g
poi
nt duty cycle.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
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-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
: 1
5
9
–
17
2
16
4
Fig
u
re
6
.
Sh
ows th
e
Vo
ltag
e
gain
ratio with
ESR (0
.1
Ω
)
fo
r the
tw
o c
o
n
v
e
rters
4.
LOSSES
DUE TO INDUCTIVE ESR
Th
eo
retically DC-DC con
v
e
rters can
provid
e
a in
fin
ite
v
o
ltag
e
g
a
in.
Bu
t p
r
actically it is n
e
v
e
r
p
o
s
sib
l
e as th
ere are so
m
e
in
h
e
ren
t
p
a
rasitic elem
en
ts p
r
es
en
t su
ch th
at
ESR.
In th
is sectio
n
t
h
e lo
sses du
e t
o
ESR effect of
the inductor is cons
ide
r
e
d
. T
h
e losses ha
ve
m
o
re im
pact
whe
n
the de
vi
ce is used for any low
po
we
r a
ppl
i
cat
i
on.
[
2
0]
-[
21]
So t
h
e l
o
ss cal
cul
a
t
i
on i
s
di
sc
usse
d as
u
n
d
er:
The
value
of t
h
e inductor,
∝
(24)
w
h
er
e,
N
=
no
.
of
tur
n
s in
t
h
e indu
ctor
,
A = c
r
oss secti
onal a
r
ea
of the inductor
L
= leng
th of
t
h
e indu
ctor
Ag
ai
n
th
e length
,
∝
So
equ
a
tio
n (24
)
can b
e
written
as,
∝
(25)
Si
nce t
h
e
cu
rr
e
n
t
pa
ssi
n
g
t
h
r
o
ug
h t
h
e c
o
n
d
u
c
t
or,
∝
Cross
sectional area,
∝
∝
(2
6)
whe
r
e,
x
is th
e
d
i
am
e
t
er of th
e con
d
u
c
tor.
The e
q
uation (25)
now
can be
re-a
rra
nged as
,
∝
⁄
(2
7)
The E
S
R
value
,
∝
∝
⁄
⁄
(
2
8
)
So
t
h
e ESR p
e
r un
it In
du
ctor
i
s
,
∝1
⁄
⁄
(2
9)
Fo
r Boo
s
t conv
erter, ESR of
th
e ind
u
c
t
o
r L,
∝
⁄
⁄
(3
0)
For
C
a
sca
d
ed
B
oost
c
o
nve
rt
e
r
,
ESR of
t
h
e indu
ctor
L
1
,
∝
⁄
⁄
(3
1)
ESR of
t
h
e indu
ctor
L
2,
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
0.
8
0.
9
1
0
5
10
15
20
25
30
35
D
u
ty R
a
ti
o
V
o
lt
a
g
e
G
a
in
B
oost
C
a
sca
de
d B
oost
Q
u
a
s
i
-
Li
n
e
a
r
R
egi
on
N
o
n
-
Li
n
e
a
r
R
egi
on
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
PED
S
I
S
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:
208
8-8
6
9
4
C
o
m
p
a
r
at
i
ve
S
t
eady
St
at
e
An
al
ysi
s
of
Bo
ost
an
d C
a
sc
ade
d
Bo
ost
C
o
nvert
e
r w
i
t
h
I
n
duct
i
ve …
(Ta
n
mo
y RC)
16
5
∝
⁄
⁄
(3
2)
Since, i
n
the ca
scade
d
c
o
nvert
e
r,
1
, e
quat
i
o
n
(
3
2
)
ca
n
be
wri
t
t
e
n as,
∝
1
⁄
⁄
(3
3)
Si
nce t
h
e i
n
p
u
t
powe
r
fo
r t
h
e B
oost
as wel
l
as C
a
scaded con
v
e
r
t
e
r i
s
sam
e
. So for t
h
e
sam
e
i
nput
vol
t
a
ge
,
.
Th
us t
h
e rel
a
t
i
on
bet
w
ee
n t
h
e ESR
val
u
es of L
1
inductor in cascaded to
t
h
e ESR
val
u
e of B
oost
co
nv
er
ter
inducto
r
L can be
giv
e
n
as,
(3
4)
In
the sam
e
wa
y
,
1
(3
5)
Power l
o
sses in
th
e Boo
s
t con
v
e
rter,
(3
6)
Power l
o
ss i
n
t
h
e inductors
of cascade
d
B
o
ost conve
rter,
To
tal lo
ss in
t
h
e cascad
ed
bo
ost con
v
e
rter
due to
indu
ctiv
e
ESR,
1
(3
7)
So t
h
e
po
we
r l
o
ss
rat
i
o
of
t
h
e
cascade
d
b
oos
t
con
v
e
r
t
e
r t
o
t
h
e
bo
ost
c
o
nve
rt
er ca
n
be
deri
ved
as,
1
1
1
1
1
(3
8)
Figure
7 shows the power l
o
s
s
ratio c
u
rve in Cascad
ed to
B
o
o
s
t con
v
e
rter
with
a ch
ang
e
in
th
e
d
u
t
y
ratio of the
cas
caded boost conve
rter. It
is seen
th
at
with
an
in
crem
en
t o
f
th
e du
ty ratio
, th
e vo
ltag
e
g
a
in
of
the casca
ded c
o
nve
r
ter inc
r
ea
ses. But
t
h
e power l
o
ss
due to the inducti
ve
ES
R effect also inc
r
eases c
o
m
p
ared
t
o
t
h
e c
o
nve
nt
i
onal
B
o
ost
co
n
v
ert
e
r
.
Fig
u
r
e
7
.
Sh
ows po
w
e
r
l
o
ss
r
a
tio
cur
v
e du
e t
o
indu
ctiv
e ESR
The
on state l
o
ss
of the
Cas
caded
co
nv
erter is less co
m
p
ared to
t
h
e B
o
o
s
t co
nv
erter
fo
r th
e
sam
e
voltage
gai
n
.
Whe
r
eas t
h
e
off state loss
is
m
o
re in Bo
o
s
t
c
o
nv
er
te
r
co
mp
a
r
ed
to
Ca
s
c
ad
e
d
Boo
s
t co
nv
e
r
te
r.
0
0.
1
0.
2
0.
3
0.
4
0.
5
0.
6
0.
7
1
2
3
4
5
6
7
C
a
s
cad
ed
D
u
ty
R
a
ti
o
(
k
)
P
c/
P
b
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
: 1
5
9
–
17
2
16
6
5.
PA
RA
METE
R
DESIG
N
The desi
gni
ng
of t
h
e
param
e
ters o
f
t
h
e casc
a
ded
bo
os
t conv
erter is con
s
i
d
ered
h
e
re in
term
s o
f
p
e
r
u
n
it
ripp
le in
t
h
e indu
ctor cu
rren
t
⁄
and
p
e
r un
it ripp
le in th
e cap
acitor
v
o
l
t
a
g
e
⁄
.
During
ON time of th
e switches,
v
o
ltag
e
drop
acro
ss th
e ind
u
c
t
o
r L
1
,
(3
9)
Co
n
s
i
d
eri
n
g the ripp
le cu
rren
t
in
th
e ind
u
cto
r
as
, equ
a
tion
(3
9)
g
i
v
e
s th
e
so
lu
tion
as,
(4
0)
Th
e i
n
du
ctor
valu
e can be foun
d in
ter
m
s o
f
p
e
r un
it r
i
pp
le
f
r
o
m
eq
u
a
tion
(
4
0
)
as,
(4
1)
Equation (3) c
a
n
be
placed in
equation (41)
and thus,
1
(4
2)
whe
r
e,
T
s
i
s
t
h
e swi
t
c
hi
ng
pe
r
i
od =
1
⁄
Seco
nd
i
n
duct
o
r
L
2
v
a
l
u
e can also
b
e
f
oun
d
o
u
t
i
n
th
e sam
e
w
a
y as,
1
(4
3)
Cu
rren
t
p
a
ssi
ng
thro
ugh
th
e cap
acito
r C
1
durin
g
t
h
e
ON ti
me of th
e switches,
1
1
(4
4)
The capa
c
i
t
o
r
val
u
es ca
n be
fo
u
nd
out
by
consi
d
eri
ng a
p
e
r u
n
i
t
ri
ppl
e i
n
t
h
e capa
c
i
t
o
r
vol
t
a
ge i
n
t
h
e
sam
e
way
as,
1
(4
5)
(4
6)
A cascade
d
b
o
o
st
con
v
e
r
t
e
r as sho
w
n i
n
Fi
g
u
re 1
(
a)
whe
r
e
t
h
e nom
i
n
al
val
u
es con
s
i
d
e
r
ed as:
i
nput
vol
t
a
ge
V
in
= 20
V
,
ou
tpu
t
vo
l
t
ag
e
V
0
=
10
0
V, t
h
e
n
o
m
in
al du
ty ratio
k
=
0.
55
.
C
o
nsi
d
eri
n
g
a 2% ri
p
p
l
e
i
n
t
h
e
inductor curre
n
t and the
capacito
r vo
ltag
e
as well with
switch
i
ng
frequen
c
y
f
s
=
20
k
H
z. To m
a
ke a 10
0
W
co
nv
er
ter
,
t
h
e
p
a
r
a
m
e
ter
s
can b
e
fo
und
o
u
t
by th
e equ
a
tion
s
(4
2)
,
(4
3)
,
(4
5)
& (4
6)
is
show
n in
Tab
l
e
2
.
Du
ri
n
g
B
o
ost
C
o
n
v
ert
e
r desi
gni
ng t
h
e val
u
e of t
h
e i
n
d
u
ct
or a
nd t
h
e cap
aci
t
o
r can al
so
be fo
u
nd
o
u
t
b
y
th
e
sam
e
w
a
y as show
n abo
v
e
.
1
(4
7)
(4
8)
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I
J
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S
I
S
SN
:
208
8-8
6
9
4
C
o
m
p
a
r
at
i
ve
S
t
eady
St
at
e
An
al
ysi
s
of
Bo
ost
an
d C
a
sc
ade
d
Bo
ost
C
o
nvert
e
r w
i
t
h
I
n
duct
i
ve …
(Ta
n
mo
y RC)
16
7
Whe
n
t
h
e s
w
itches a
r
e
ON, t
h
e c
u
rrent
pas
s
ing t
h
ro
u
g
h
t
h
em
is th
e cu
rren
t st
ress
o
n
th
e switch
e
s.
Wh
ereas
d
u
ring
OFF co
nd
itio
n
of th
e switch
e
s th
e
vo
ltag
e
stress
can
b
e
o
b
t
ain
e
d
.
Th
e cu
rren
t
stress will
b
e
th
e m
a
x
i
m
u
m
p
eak
cu
rr
en
t passin
g
thro
ugh th
e r
e
sp
ectiv
e sw
itch
.
Bu
t si
n
ce th
e vo
ltage r
i
p
p
l
e is consid
er
ed
as v
e
ry sm
all,
so
t
h
e
v
o
ltag
e
stress
will b
e
as sam
e
as
th
e av
erag
e
v
a
lu
e of th
e vo
ltag
e
ap
p
lied to
t
h
e switch
.
In cascade
d
boost c
o
nverte
r,
t
h
e cu
rren
t
stress on
t
h
e switches is as
fo
llows:
i
Q
1pe
ak
= i
L1
pe
ak
;
i
Q
2
peak
= i
L2
pe
ak
i
D
1pe
ak
= i
L1
pe
ak
;
i
D
2
pe
ak
= i
L2
pe
ak
In Fi
gu
re 8 t
h
e
i
n
d
u
ct
or c
u
r
r
e
n
t
wi
t
h
t
h
e m
a
xi
m
u
m
and t
h
e
m
i
nim
u
m
value o
f
t
h
e ri
ppl
e i
s
sho
w
n
.
The pea
k
val
u
e
o
f
t
h
e
i
n
duct
o
r
can be f
o
u
n
d
out
a
s
:
I
I
L
∆
I
2
(4
9)
Tak
i
ng
t
h
e referen
c
e of eq
u
a
ti
o
n
(40
)
, th
e curren
t
stress equatio
n
o
f
th
e i
n
du
ctor can
b
e
written
as,
ILmax
I
2
(5
0)
Fi
gu
re
8.
S
h
o
w
s i
n
duct
o
r c
u
rr
ent
ri
ppl
e
wi
t
h
m
i
nim
u
m
and
m
a
xim
u
m
peak
So
t
h
e
cu
rren
t stress o
n
th
e switch
Q
1
& D
1
,
2
(5
1)
Current
st
ress on
the switch Q
2
an
d D
2,
2
(5
2)
In case
o
f
th
e
Bo
o
s
t con
v
e
rter, t
h
e cu
rren
t st
ress
o
n
th
e swi
t
ch
and
t
h
e
d
i
od
e
will b
e
as,
2
(5
3)
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I
S
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:
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088
-86
94
I
J
PED
S
Vo
l. 7,
No
.
1,
Mar
c
h
2
016
: 1
5
9
–
17
2
16
8
Table 1. Param
e
ter
com
p
arison of
Boo
s
t & Cascad
ed
Boo
s
t
Co
nv
erter
Para
m
e
ters
Boost Converter
Cascaded Boost
Voltage
Gain
1
1
1
1
I
nductor
value(
s)
1
1
1
Capacitor
value(
s)
Voltage
stress on
switch
1
1
=
I
nductor
Cu
rren
t
1
1
1
Cu
rren
t
stress on
switch
2
2
2
Cu
rren
t
stress on
Diode
2
2
2
Tabl
e
2.
Param
e
t
e
r com
p
ari
s
o
n
of
B
o
ost
&
C
a
scade
d
B
o
ost
C
o
n
v
ert
e
r f
o
r
10
0
W
Para
m
e
ters
Boost Converter
Cascaded Boost
Duty
Ratio
0.
80
0.
55
I
nductor
value(
s)
L
= 4
m
H
L
1
=
2.
82 m
H
L
2
=
6.
26 m
H
Capacitor
value(
s)
C = 40 µF
C
1
=
136 µF
C
2
=
27.
5 µF
Load Resistance R
50
Ω
50
Ω
Voltage str
e
ss on s
w
itch
V
Q
=
100 V
V
Q1
= 50 V
V
Q2
= 100 V
Cur
r
e
nt str
e
ss on s
w
itch
i
Qp
ea
k
=
10.
1 A
i
Q
1
peak
=
9.
85 A
i
Q
2
peak
= 4.
43 A
Cur
r
e
nt str
e
ss on
Diode
i
Dp
ea
k
=
10.
1 A
i
D
1peak
=
9.
85 A
i
D
2peak
= 4.
43 A
6.
BOUNDARY BETWEEN
CCM &
DCM
The
b
o
u
n
d
ary
bet
w
ee
n t
h
e
C
C
M
& DC
M
can
be
deri
ved
o
n
l
y
w
h
en
t
h
e i
n
d
u
ct
o
r
c
u
r
r
e
nt
t
o
uche
s
zero. During the OFF state of
the
switc
hes, t
h
e inductor c
u
rrent
gra
d
ually reduces t
o
a m
i
nim
u
m
value
I
Lmin
as
sho
w
n i
n
Fi
gu
r
e
8.
The
val
u
e
o
f
t
h
e l
o
we
st
i
n
duct
o
r
cu
rre
nt
ca
n
be
fo
u
n
d
as,
∆
2
(5
4)
Equ
a
tio
n
(5
4) can
b
e
re-written
with
reference to
eq
u
a
ti
o
n
(50
)
as,
2
(5
5)
Fo
r th
e Boo
s
t co
nv
erter, equ
a
t
i
o
n
(5
5) can
b
e
written as,
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