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il
it
y
o
f
a
d
etailed
P
ar
eto
o
p
tim
al
s
et,
al
o
n
g
w
it
h
g
iv
in
g
to
th
e
d
esig
n
er
m
o
r
e
in
s
i
g
h
t
a
n
d
f
lex
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ili
t
y
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n
t
h
e
c
h
o
ic
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is
g
r
ea
tl
y
h
elp
f
u
l
w
h
en
t
h
e
ca
l
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lated
o
p
ti
m
al
p
ar
a
m
eter
s
h
av
e
to
b
e
tr
an
s
lated
in
to
t
h
e
d
is
cr
ete
v
al
u
es
o
f
co
m
m
er
cial
co
m
p
o
n
e
n
t
s
.
T
h
e
p
o
s
s
ib
ilit
y
o
f
a
m
o
r
e
ac
cu
r
ate
m
o
d
elin
g
ap
p
r
o
ac
h
,
b
y
i
n
cl
u
d
in
g
SP
I
C
E
s
i
m
u
lat
io
n
s
f
o
r
t
h
e
e
v
al
u
atio
n
o
f
t
h
e
d
esi
g
n
g
o
a
ls
w
i
ll
b
e
al
s
o
d
is
cu
s
s
ed
,
g
iv
in
g
a
n
e
s
ti
m
a
tio
n
o
f
t
h
e
r
eq
u
ir
ed
ad
d
itio
n
al
co
m
p
u
tatio
n
al
ef
f
o
r
t.
2.
ST
O
CH
AS
T
I
C
O
P
T
I
M
I
Z
AT
I
O
N
AL
G
O
R
I
T
H
M
S
AND
P
AR
E
T
O
O
P
T
I
M
AL
F
RO
N
T
T
RAC
I
N
G
Mo
s
t
o
f
t
h
e
r
ea
l
-
w
o
r
ld
o
p
ti
m
i
za
tio
n
p
r
o
b
lem
s
i
n
v
o
l
v
e
m
u
lt
ip
le
co
n
f
lic
tin
g
o
b
j
ec
tiv
es
t
h
a
t
m
u
s
t
b
e
m
u
tu
al
l
y
r
ec
o
n
ciled
.
T
h
ese
p
r
o
b
lem
s
ar
e
ca
lled
m
u
l
ti
o
b
jectiv
e
o
p
ti
m
izatio
n
p
r
o
b
lem
s
(
MO
O)
,
o
r
v
ec
to
r
o
p
tim
izatio
n
p
r
o
b
lem
s
,
i
n
co
n
tr
ast
to
s
i
n
g
le
o
b
j
ec
tiv
e
o
p
ti
m
izatio
n
(
SOO)
,
o
r
s
ca
lar
o
p
ti
m
izatio
n
p
r
o
b
le
m
s
[
1
6
]
.
I
f
w
e
d
ef
in
e
a
s
12
,
,
.
.
.
kM
f
x
x
x
th
e
f
it
f
u
n
ctio
n
a
s
s
o
ciate
d
to
th
e
k
-
t
h
g
o
al
in
a
p
r
o
p
er
p
ar
am
eter
s
s
p
ac
e,
th
e
o
p
ti
m
izat
io
n
p
r
o
b
lem
i
s
o
f
ten
ex
p
r
es
s
ed
as:
12
m
i
n
(
)
,
(
)
,
.
.
.
(
)
N
M
f
f
f
x
x
x
xX
(
1
)
w
h
er
e
X
is
th
e
f
ea
s
ib
le
s
et
o
f
th
e
d
ec
is
io
n
v
ar
iab
les
v
ec
to
r
x
.
I
n
m
u
lti
-
o
b
j
ec
tiv
e
o
p
ti
m
iza
tio
n
,
u
s
u
al
l
y
i
t
d
o
es
n
o
t
ex
i
s
t
a
f
ea
s
ib
le
s
o
l
u
tio
n
th
at
m
i
n
i
m
izes
a
ll
o
b
j
ec
tiv
e
f
u
n
ctio
n
s
s
i
m
u
ltan
eo
u
s
l
y
.
T
h
er
ef
o
r
e,
eith
er
t
h
e
p
r
o
b
lem
i
s
r
ed
u
ce
d
to
a
s
ca
la
r
o
n
e
b
y
m
ea
n
s
o
f
a
w
ei
g
h
ted
s
u
m
[
1
7
]
o
f
i
n
d
iv
id
u
al
o
b
j
ec
t
iv
es,
o
r
a
d
i
f
f
er
e
n
t
n
o
tio
n
o
f
o
p
ti
m
al
h
as
to
b
e
d
ef
i
n
ed
,
th
at
is
th
e
w
ell
k
n
o
w
n
P
ar
eto
o
p
tim
al.
A
(
f
ea
s
ib
le)
s
o
lu
tio
n
is
“
P
ar
eto
o
p
tim
a
l”
if
it
ca
n
n
o
t
b
e
i
m
p
r
o
v
ed
in
an
y
o
f
t
h
e
o
b
j
ec
tiv
es
w
i
th
o
u
t
d
eg
r
ad
in
g
at
least
o
n
e
o
f
th
e
o
th
er
o
b
j
ec
tiv
es.
I
n
s
u
ch
ter
m
s
,
d
if
f
er
en
t P
ar
eto
o
p
tim
a
l so
l
u
tio
n
s
ca
n
b
e
f
o
u
n
d
,
an
d
a
t
h
eir
s
et
i
s
d
ef
in
ed
a
s
“
P
ar
eto
o
p
tim
a
l f
r
o
n
t”.
I
n
t
h
e
last
y
ea
r
s
,
Mu
lti
-
Ob
j
ec
tiv
e
E
v
o
lu
t
io
n
ar
y
A
l
g
o
r
ith
m
s
(
MO
E
A
)
h
a
v
e
d
e
m
o
n
s
tr
ated
to
b
e
ex
tr
ao
r
d
in
ar
y
f
ac
il
ities
f
o
r
s
o
lv
in
g
o
p
ti
m
izat
io
n
p
r
o
b
lem
s
in
d
if
f
er
en
t
ar
ea
s
.
E
v
o
l
u
tio
n
ar
y
alg
o
r
ith
m
s
s
u
c
h
as
th
e
Ge
n
etic
A
l
g
o
r
ith
m
[
1
8
]
h
as
b
ec
o
m
e
a
s
ta
n
d
ar
d
ap
p
r
o
a
ch
,
an
d
s
c
h
e
m
e
s
b
ased
o
n
Si
m
u
lated
An
n
ea
l
in
g
[
1
9
]
an
d
P
ar
ticle
Sw
ar
m
Op
ti
m
izat
io
n
[
2
0
]
,
[
2
1
]
a
r
e
n
o
w
f
a
m
iliar
.
C
u
r
r
en
tl
y
,
m
o
s
t
ev
o
lu
tio
n
ar
y
m
u
lti
-
o
b
j
ec
tiv
e
o
p
ti
m
izatio
n
(
E
MO
)
alg
o
r
ith
m
s
ap
p
l
y
P
ar
eto
-
b
ase
d
r
an
k
in
g
s
c
h
e
m
es.
Su
c
h
p
o
w
er
f
u
l,
s
y
s
te
m
atic
an
d
n
o
w
ad
a
y
s
w
ell
as
s
es
s
ed
ap
p
r
o
ac
h
to
o
p
tim
al
d
esi
g
n
,
i
s
s
till
n
o
t
s
o
co
m
m
o
n
l
y
ad
o
p
ted
i
n
th
e
e
le
ctr
o
n
ic
cir
cu
it
d
e
s
ig
n
ar
ea
.
M
ain
g
o
al
o
f
t
h
i
s
p
ap
er
is
s
h
o
w
t
h
e
p
o
s
s
ib
ilit
y
o
f
ex
ten
d
i
n
g
th
e
u
s
e
o
f
MO
E
A
o
p
ti
m
izatio
n
to
o
ls
to
th
e
s
w
itc
h
in
g
co
n
v
er
ter
s
d
esi
g
n
.
As
s
i
m
u
latio
n
en
v
ir
o
n
m
e
n
t
w
e
ad
o
p
ted
a
p
u
b
lic
d
o
m
a
in
M
A
T
L
A
B
to
o
l,
k
n
o
w
n
as
t
h
e
GOD
L
I
KE
p
ac
k
ag
e
[
2
2
]
w
h
ic
h
allo
w
s
,
in
a
u
n
iq
u
e
en
v
ir
o
n
m
en
t,
to
u
s
e
d
i
f
f
er
e
n
t
al
g
o
r
ith
m
s
an
d
to
co
m
p
ar
e
d
ir
ec
tly
t
h
ei
r
p
er
f
o
r
m
a
n
ce
s
b
y
p
r
o
d
u
cin
g
o
p
ti
m
al
r
an
k
i
n
g
s
ch
e
m
e
s
.
T
h
e
test
ca
s
e
p
r
o
p
o
s
ed
in
th
i
s
p
ap
er
co
n
f
ir
m
t
h
e
v
iab
ilit
y
a
n
d
th
e
ef
f
ec
tiv
e
n
e
s
s
o
f
t
h
i
s
p
ac
k
a
g
e
in
th
e
d
ef
i
n
itio
n
o
f
t
h
e
P
ar
eto
o
p
ti
m
al
f
r
o
n
t
f
o
r
a
t
y
p
ical
elec
tr
o
n
ic
d
esi
g
n
p
r
o
b
lem
.
I
n
t
h
is
w
a
y
w
e
s
u
g
g
est
h
o
w
,
at
p
r
ese
n
t,
it
’
s
q
u
i
te
r
ea
lis
tic
to
in
tr
o
d
u
ce
th
e
E
M
O
alg
o
r
it
h
m
s
in
th
e
s
tan
d
ar
d
o
p
ti
m
al
d
esi
g
n
o
f
ele
ctr
o
n
ic
d
ev
ices.
3.
O
P
T
I
M
AL
DE
S
I
G
N
O
F
AN
H
YB
RID CO
NVER
T
E
R
T
h
e
ef
f
ec
ti
v
e
n
es
s
o
f
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
is
s
h
o
w
n
b
y
p
u
r
s
u
i
n
g
t
h
e
o
p
ti
m
a
l
d
esi
g
n
o
f
h
y
b
r
id
co
n
tr
o
l
lo
w
p
o
w
er
b
u
ck
DC
-
D
C
co
n
v
er
ter
.
W
e
alr
ea
d
y
m
e
n
t
io
n
ed
h
o
w
s
o
m
e
b
asic
i
m
p
o
r
tan
t
r
eq
u
ir
e
m
en
t
s
i
n
th
eir
o
p
ti
m
al
d
es
ig
n
ar
e
to
ac
h
iev
e
h
ig
h
p
o
w
er
e
f
f
icie
n
c
y
,
f
o
r
b
est
e
x
p
lo
itatio
n
o
f
b
atter
i
es,
an
d
at
t
h
e
s
a
m
e
ti
m
e
h
i
g
h
p
o
w
er
d
en
s
it
y
,
to
r
e
d
u
ce
v
o
l
u
m
e
a
n
d
w
ei
g
h
t o
f
t
h
e
d
ev
ice.
T
h
e
c
h
o
ice
o
f
t
h
e
cir
cu
it p
ar
a
m
eter
s
a
n
d
co
n
tr
o
l stra
teg
y
to
f
u
l
f
ill b
o
t
h
r
eq
u
ir
e
m
en
ts
is
n
o
t tr
iv
ial.
I
n
th
e
s
tan
d
ar
d
d
esig
n
o
f
f
ix
ed
f
r
eq
u
en
c
y
co
n
v
er
ter
s
,
it
is
w
e
ll
k
n
o
w
n
h
o
w
h
i
g
h
s
w
itc
h
i
n
g
f
r
eq
u
en
c
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is
r
eq
u
ir
ed
in
o
r
d
er
to
ac
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v
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h
ig
h
p
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w
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d
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s
it
y
,
s
i
n
ce
th
e
h
ig
h
er
is
th
e
f
r
eq
u
e
n
c
y
,
th
e
s
m
aller
i
s
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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8
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694
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Op
timiz
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a
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Desig
n
o
f H
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DC
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381
in
d
u
cta
n
ce
an
d
ca
p
a
citan
ce
[
5
]
.
A
t
th
e
s
a
m
e
ti
m
e
t
h
er
e
is
a
tr
ad
e
o
f
f
p
r
o
b
lem
in
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f
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eq
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en
c
y
c
h
o
ice,
s
in
ce
lo
s
s
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n
cr
ea
s
e
s
ig
n
i
f
ica
n
tl
y
at
h
i
g
h
f
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eq
u
e
n
cies.
C
o
n
v
er
ter
s
o
p
er
atin
g
at
f
i
x
ed
f
r
eq
u
e
n
c
y
h
as th
e
ad
v
an
tag
e
o
f
s
i
m
p
le
d
e
s
ig
n
,
b
u
t
th
e
ir
ef
f
icie
n
c
y
r
ap
id
l
y
d
ec
a
y
s
at
lo
w
lo
ad
s
s
i
n
ce
t
h
e
s
w
itc
h
in
g
lo
s
s
es a
r
e
co
n
s
t
a
n
t o
v
er
t
h
e
w
h
o
le
lo
ad
r
an
g
e
(
F
i
g
u
r
e
1
a)
;
o
n
th
e
o
th
er
h
a
n
d
,
as
s
h
o
w
n
i
n
[
6
]
,
co
n
v
er
ter
s
o
p
er
atin
g
at
v
ar
iab
le
f
r
eq
u
e
n
c
y
ex
h
i
b
it
lo
w
er
lo
s
s
e
s
at
lo
w
lo
ad
s
(
F
ig
u
r
e
1
b
)
,
b
u
t
th
e
d
esig
n
b
ec
a
m
e
m
o
r
e
d
if
f
icu
lt
b
ec
au
s
e
t
h
e
r
an
g
e
o
f
t
h
e
s
w
itc
h
in
g
f
r
eq
u
e
n
c
y
ca
n
b
e
r
elativ
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e.
I
n
Fig
u
r
e
1
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etc
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ar
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1
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u
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2
[7
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[1
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Ha
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T
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1
8
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3
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M
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3
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0
]
P
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g
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h
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;
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;
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,
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H.;
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a
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.
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.
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in
Co
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ter
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1
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tern
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2
0
1
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1
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k
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2
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2
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S
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3
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;
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2
5
7
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2
6
6
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5
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S
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De
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M
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jec
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2
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1
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9
4
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6
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M
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tern
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8
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J.;
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9
5
)
.
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tern
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v
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tri
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ter
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2
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Ro
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y
Old
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is,
“
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ro
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ize
r”
,
Av
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t:
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tt
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:
//
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3
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---
m
u
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ti
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r
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rs.
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