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SYSTEMATIC
DERIVATION
OF
TWO-STATE SWITCHING DC-DC
C O N V E 3 R T E R
STRUCTURES
A . Pietkiewicz D . Tollik
Instytut
Technologii
Elektronicznej
Politechnika G d a u i s k a
M i a j a k o w s k i e g o
11/12
80-952
Gdatsk,
2oland.
Abstract: T h e new
method
of
derivation
of
t w o - s t a t e - & c - d c
co nv e rte r st ructu r es
i s
pro-
posed.
I n
contrast
t o
t h e
available
techniq-
ues
this method
o ri gi na te s f ro m
t h e set of
general
r e q ui r em ents c o nce r ning both structu-
r e
a n d operation of a switching converter.
T h es e r eq u ir e me nt s coupled
with
a n adopted
definition of a
minimal
n u rm b e r o f
elements,
are
converted into
t h e f o r - m
o f
topological
graph
properties a n d applied i n t h e proposed
synthesis
procedure. A s a
r e s u l t ,
twelve
ba-
s i c two-state
converter structures, including
four
n ew t op ol og ie s, are
obtained.
1 .
Introduction
I n
recent
years,
owing
t o t h e
gr eat inte-
rest
i n a
switched-mode
p o w i e r conversion, t h e
family
o f
switching
converters
has been con-
siderably
increased,
C U K [ 1 ]
S E P I C [ 2 ]
,
UP and
D O ' W N
1 6 1
and many
o t h e r s .
While
t h e
most impor-
tant
source
f o r
t h e
new
structures i s still
t h e
designer s
i n t u i t i o n ' ,
t h e e xt en si ve s ea r-
ches
for
t h e
s ui ta bl e s yn th es is t ec hn iq ue s
have no t remained i ne ff ic ie nt . T he se
m e t h o d s ,
which are
co m pr e hensiv el y r e viewe d i n
[ 3 ] ,
consist i n :
1 /
Application of t h e
duality
principle
to
the
existing
structures
4 ]
.
2 / Application
of
t h e b il at er al i nv er si on
transformation
t o
t h e e x is t in g s t ru c tu r es
1 . 5 ]
3 / Combination
o f
t h e b a s i c converters
/ b u c k o r
b o o s t /
with t h e d c
transformers
L 3 ] .
4 /
Combination
of
t h e
basic
converters
/ b u c k and b o o s t / , paralleling,
cascading
[ 3 ]
5 / Extension of
t h e canonical switching
cell
[ 6 ]
[ 7 1 ,
i e are
based o n t h e
v ar i ous t r ansf o rm a ti ons
of
the
existing structures.
I n
contrast,
t h e
new m ethod
presented
i n
this
p ap er c on si st s i n generation o f
all
t h e
possible
L I ,
C
and
S
elements configurations
s a t i s f y ing some
d e finite t o po l og ica l
rules
derived from t w o
following
sets o f
require-
m t e n t s
ensuring
that t h e obtained structure
i s :
I-Two-state dc-dc
converter,
I I- Ba si c v er si on
o f this converter
i e
built
of a
minimal
number
of elements.
I t i s
then assumed that
two-state
conver-
ter
i s a
circuit
t h a t :
1 /
H a s
t h e
general
form
o f
that shown
i n
F i g . 1 , ie
a
single-input / V
E /
a n d
s i n g l e - o u t p u t
/ V O /
loaded
b y
t h e
r e s i s t a n c e
R
i n
p a -
rallel
with t h e
smoothing capacitance
C ,
where b o t h terminals
are
connected
i n
t h e common
g r o u n d
n o d e ,
and
b /
built o f t h e r ea ct an ce e le me nt s
/ L
and C / and
switches / S / .
2 / Converts o n e
d c i np ut v ol ta ge
to ano-
ther d c
output v o l t a g e ,
a/ op er ati ng
on t h e
principle
of
switching two
topologies
o f
the
reac-
tance
elements,
while
b /
t h e conversion
process
i s loss l e s s
and
c/ t h e d c voltage
turn-ratio V E / V O i s
controllable
b y
t h e
duty-ratio
varia-
t i o r n s .
V E I
F i g .
1 .
Assumed
general
structure
ing d c-d c co nv er ter .
v o
o f a switch-
The
second
set
of
requirements,
that
i s
equally important here,
eliminates
fro m
the
synthesis p ro ce du re m an y
extended
versions
of the b a si c s tr u ct ur e s.
These requirements
are
derived fro m
the
adopted
definition
of
minimal
num ber of
L C elements.
M o r e o v e r ,
sin-
c e
the
num ber of
switch
elements
i s
assumed
t o b e
minimal,
t o o ,
t h e
structures
containing
two
a l te rna ti ve l y o p era te d
switches are con-
sidered.
The two
above sets
o f requirements are
jointly
transformed
into t h e
topological
graph properties
i n
Section
2 .
O n that base
the
practical
rules
determining
the
admissib-
l e
arrangements
of
L , C
and
S elements
are
fo rmu l ated
i n
Section
3 .
F i n a l l y ,
these
rules
are
directly
applied
i n
t h e
synthesis proce-
dure
generating
th e
complete
class
of the
b as ic t wo -s ta te
dc-dc
converters,
i n
Section
4 . The
o bt ai ne d r es ul ts
are briefly
s u n m . a r i -
z e d
i n
Section
5 .
2 .
T o p o l o g i c a l
graph p r o p e r t i - e s
The
structure
of
any
s w r i t c h i n g
dc-dc con-
verter
i n e a c h
interval
o f
a switching period
can
b e
represented
in
th e
form
of a
topologi-
cal
graph
where
th e
vertices
correspond
t o
the
nodes
and
t h e
edges
correspond t o
the
branches
of t h e
initial structure,
a s exem-
plified
i n
F i g . 2 b .
Clearly, t h e edges o f a
graph
c a n
b e
d iv id ed into
five groups,
so
that
th e
E , C ,
C R , L I ,
S
and
S
- t y p e e d g e s
on
S o f f - t p
de
correspond t o
t h e
e l e r r e n t s
of i de al v ol ta ge
sources, c a p a c i t o r s , c a p a c i t o rs
i n
p a r a l l e l
with
resistances i n d u c t o r s ,
closed
and
open
s w i t c h e s ,
respechively.
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1 }
V E
I i f
0 2
V
edges / C o n d i t i o n
2 /
does
not vio l ate
the
h i g h
i m p e d a n c e
p a t h s
i n
t h e
respective
c i r c u i t s ,
for
example
consider
t h e
cutset
I f - L f 2
i n
F i g . 3 .
f f
2
L l
3
C i
4
2
5
2 )
S j
-
o f f
S 2
-
on
2
3
C 1
4
5
E
V
c R
c
2
3 C 1 4
5
1
F i g .
2 .
Basic
CUK
converter
/ a /
represented
b y
topological
grapb
/ b /
r e d u c e d ,
i n
e a c h
i n t e r v a l ,
t o
ECC
S trees
/ c /
t h a t
fall
i d e n t i c a l l y
?Bto
two ECCR
pieces
/ d / .
2 . 1 .
Definition
of th e
basic
converters
Then,
using
the
topological
graph
descri-
p t i o n ,
t h e
definition
of basic
structures,ie
built
o f minimal
number
o f
L C
e l e m e n t s ,
c a n
b e
i n t r o d u c e d .
Definition
1 .
I t
i s assumed
that
t h e
basic
converter
structures
are
represented
b y t h e
graphs
that
contain
n o :
1 /
Circuits
composed
o n l y
o f t h e
C a n d / o r
E
a n d / o r
C R - t y p e
edges,
2 /
C ut se ts c om po se d
o n l y
of
t h e L-type
edges,
3 /
Circuits
composed
o n l y
o f t h e L - t y p e
edges,
4 / Cutsets
composed
o n l y
o f t h e C - t y p e
e d g e s ,
5 /
C u t s e t s
composed
o n l y
o f t h e
C-type
edges
and
o n e L-type
e d g e ,
6 /
P a t h s
composed
only
of t h e
L-type
ed-
ges and
joining
t w o
vertices
o f
t h e
same
piece
o f t h e
E C C R - s u b g r a p h .
To
justify
t h e
s u c c e s s i v e
conditions
o f
t h e
above
definition
i t
should
b e realized
t h a t
t h e role
o f C and L
elements
can
b e vie-
wed
a s t h e
effective
s h o r t c i r c u i t
o r opencir-
c u i t ,
respectively,
for
t h e
a c
currents
o f
a
s w i t c h i n g
frequency,
and
therefore
their
physical
values
should
b e adequately
l a r g e .
H e n c e ,
a
removal
of
any C-type
edge
from
t h e
circuit composed
only
of t h e
C
and/or E
a n d /
o r
C R - t y p e
edges
/ C o n d i t i o n
1 /
does
no t vio-
l a t e
t h e
l o w impedance
path
seen
from
t h e ver-
tices o f
t h e
removed C-type
e d g e .
Consequent-
l y ,
such
a n edge
can
b e
eliminated
a s illus-
trated
b y
example
o f
t h e
circuit
C
3 - C 4 - C 5
i n
F i g . 3 .
Similarly,
a
removal
of
a n y
l - t y p e
e d g e
from
t h j e cutset
composed
only
o f the
L - t y p e
F i g .
3 .
E x t e n d e d
vers ion
o f
C U K
con verter
/ a /
an d i t s
topological
g r a p h
/ b /
illust-
rating
definition
o f
basic converter.
The
C o n d i t i o n s
3
and
4
are
q u i t e
obvious
a s t h e y eliminate
eccessive
elements
o f
t h e
same type
c o n n e c t e d ,
for
example,
i n
serious
/ C /
o r
i n
parallel
/ L / .
The
Condition 5
results
from
t h e observa-
tion
that t h e presence
o f
such a cutsets
would i n v o l v e
zero
d c current
i n t h e L - t y p e
e d g e ,
t h a t
c o u l d
be
c o n s e q u e n t l y
o m i t t e d ,
as
for example
i n t h e cutset
C 1
-C2-L3
i n
F i g - 3 .
The
Condition
6 can
b e
j u s t i f i e d
b y
n o t i n g
that
s u c h
a
p a t h
would
involve
ze r o d c
volta-
g e
difference between
b o t h
i t s
terminal
ver -
tices.
Since
both
vertices
a re embraced
i n
t h e
same
piece
of
t h e
E C C R - s u b g r a p h ,
t h e y
can
b e
simply
contracted
and
t h e
eccessive L - t y p e
e d g e
e l i m i n a t e d , s e e
p a t h
L f 3
i n
F i g . 3
for
e x a m p l e .
2 , 2 A
T o y o l o g j c a l
c o n - s e q u e n c e s
o f t h e
defini-
tion
of
a two-state
dc-dc converter
The
relevant
definition
consists
of
two
sets
o f
requirements
concerning
b o t h : 1 / ge-
neral
structure
and
2 /
operation
of
a conver-
t e r .
The first
s e t
i s
directly a p p l i c a b l e
t o
formulate
some
useful
rules
influencing
a
to-
pology
of
t h e
s y n t h e t i z e d
structures.
H o w e v e r ,
t h e
second
set
r e q u i r e s
an
intermediate
trans-
formation
into
t h e
form
o f
t o p o l o g i c a l g r a p h
properties.
F i r s t ,
t h e
n e c e s s a r y
c o n d i t i o n s
e l i m i n a -
t i n g
p o s s i b l e
power
lossess
i n
t h e
s w i t c h i n g
converters
composed
o f
lossless
L C
e l e m e n t s
are examined.
Assuming
t h a t :
1 /
P ow er l oss es s
can
arise
o n l y
i n
t h e
s w i t c h
elements
during
switching
a c t -
i o n s ,
2 /
Switch
resistances
i n t h e
on-state
Rson
0
and
i n
t h e off-state
RsofT,
it i s e v i d e n t
that
t h e abo ve
hssumptions
e x -
4 7 4
b )
1 )
S i
-on
S 2 - o f f
2
3
C 1 4
5
E
S i
R
2
3
C 1
4
E~~~
I
w
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c l u d e
both
t h e infinite
current
pulses i n
the
closed
switches
and
the
infinite
voltage
pul-
s e s i n
t h e
o p e n
switches.
T h u s ,
i t can be
con-
cluded
that a
topological
graph
representing
a n y converter
structure
i n
each interval
of a
switching period
m ay
contain
n o :
/ i / Circuits
composed
o n l y
o f t h e
S o n - t y -
p e e d g e s
together
with
E
and/or
C
a n d / o r
C R - t y p e e d g e s
/ o t h e r w i s e
infi-
nite current
pulses
would
occur during
closing
a
s w i t c h b
/ii/
Cuteets composed
only
o f t h e
S o f f - t y -
p e a n d
L-type
edges
/otherwise
infi-
nite
voltage
pulses
would occur
during
opening
a switch.
Furthermore,
assuming
t h a t Conditions
1
a n d
2
o f
Definition 1
are satisfied
i t
can b e
stated
also t h a t
t h e s e
topological
grapbs
con-
tain n o :
/ i i / Circuits
composed
only
o f t h e
C
and/
o r
E and/or CR-type
edges,
/iiii/
C u t e e t s
composed
o n l y o f
t h e L - t y - p e
e d g e s .
Removing
all
t h e
L and
S o f f - t y p e
edges
from t h e
graph
representing
t h e
converter
structure
i n
each
interval
of
a
switching
p er-
iod and
satisfying
conditions
/ i / - / i i i / ,
the
subgraphs
containing
only t h e E ,
C ,
C R
and
s -type
edges
are obtained
/ Fi g
2 b / . These
s R i g r a p h s
i n virtue
o f /i/
and /iii/
d o
not
contain any
circuits
and i n
virtue
of
/ i i /
and / i i i i /
are
connected
/ o n e
piece
g r a p h s / .
Thus,
Property
1 .
The
E C C B
Sn-
subgraphs
o f a given
conver-
t e r , for
all the intervals
of
a
s w i
tching
p e r i o d ,
constitute
the
trees of
the
initial
g 8 r a p h s
whereas
t h e
remaining
L
and S
- f f
type
edges
are
t h e chords
of
these trees.
I n
order
to proceed
with t h e formulation
of another essential
graph
property
that
re-
sults
from
t h e
requirement
of t h e
output vol-
tage
controllability,
i t i s
advisable
t o
note
some
inter esting c o nse quence
of Property
1 .
Namely,
i t ca n
b e seen
that
t h e r em ova l
o f
t h e
S o n - t y p e
edges from
the
E C C B R S o n - s u b g r a p h s
causes
these
subgraphs
to
fall
into two ECCR
pieces
/ F i g . 2 c / .
I n
t h e
initial graphs
both
pieces
are
connected
b y
S o n So ff
and
L-type
edges,
where
the averaged
over t h e
whole p er-
iod va lue of
all
the
L-type e d g e
voltages
a re
zero.
S o ,
if
any
L-type
e d g e voltage
in
either
interval
were forced
to
zero,
i t
would
remain
zero also
i n another
interval.
Moreover,
ta-
king into
account
t h e
f a c t
t h a t
t h e p o t e n t i a l s
corresponding
t o
t h e
vertices
o f
both
E C C B
p i e c e s
are
k e p t
approximately
c o n s t a n t ,
i t
can b e concluded
that
t h e
voltages
of
all
t h e
remaining
1 - t y p e
edges
i n b o t h
intervals
would
b e z e r o ,
t o o .
A s a
result
t w o
ECC
pieces
would b e
permanently
connected
mating
t h e
controllof
t h e
tree-edges
voltages
b y
duty-
ratio variations
i m p o s s i b l e .
Similarly,
i t
c a n
b e
s h o w n
t h a t
i f
a n y
C-type
e d g e
current
i n
either
interval
were
forced to
z e r o ,
i t would
remain
zero also
i n
another
interval.
H e n c e ,
the
averaged
current
o f
all
t h e
L-type
e d g e s
would
b e
zero,
causing
the tree-edge
voltages
be
i n d e p e n d e n t
on
the
duty-ratio
v a r i a t i o n s .
S u m m a r i z i n g ,
t h e
a b o v e
d i s s c u s s i o n
proves
t h a t :
Property
2 .
T h e
topological
g r a p h s
of
a
two-state
switching
converter
contain
n o :
/ 1 /
circuits
c o m p o s e d
o n l y
o f L a n d
S o n -
t y p e
e d g e s
and
/ 2 /
c u t s e t s
c o m p o s e d
o n l y
o f C a n d
S o f f -
t y p e
e d g e s .
3 .
The
rules
o f
admissible
LCS
c o n f i g u r a t i o n s
The
definition
o f
t h e
basic
converters
and
t h e
p r o p e r t i e s
derived
from
the
a d o p t e d
definition
of
a two-state
s w i t c h i n g
dc-dc
converter
can
b e
e a s i l y
used
to
for mulate
t h e
set
o f
rules
determining
al l
admissible
c o n f i g u r a t i o n s
o f
t h e
E ,
C ,
C R ,
L ,
S o n
and
S o f f - t y p e
e d g e s .
F r o m t h e
definition
o f
a
switching
con-
verter / S e c . 1 , i t e m
l a
a n d
b /
i t
i s
obvious
t h a t :
R u l e
A .
The g r a p h s
of t h e
switching
converters
a r e
composed
i n
general
o f
t h e
E , C ,
C a ,
L o
S o n
and
S o f f - t y p e
e d g e s
where
t h e
E
and
C R -
t y p e
edges
are
single
a n d connected
i n
the
common
vertex.
F r o m
Property
1
i t c a n
b e concluded
t h a t :
Rule B .
The
E C C R - s u b g r a p h s
a r e
composed
o f two
d i s j o i n t
p i e c e s ,
e a c h
o f
them
having t h e
f o r r m
o f t h e
subtree / s i n g l e
vertex
i n the
simplest
c a s e / ,
and
Rule C .
The
S on
-type
edges
occur
only
between
t h e
vertices
embraced
i n
two
different
p i e -
ces
of
th e
E C C . - s u b g ; r a p h .
F r o m
Definition
1
/ S e c . 1 , i t e m
6 /
i t can
b e
obtained
that:
Rule
D .
The L - t y p e
edges
occur
o n l y
between
t h e
vertices
embraced
i n
tw o
different pieces
o f
t h e
E C C . - s u b g r a p h
a n d a t
mo s t one
L - t y p e
e d g e
is
connected
with
each
vertex.
T o
formulate
t h e
remaining rules
all
t h e
vertices
of
t h e
E C C R - s u b g r a p h
are
divided
into
two following
types:
Type
I -
V erti ce s c on ne ct ed
with
t h e E-
a n d / o r
C R - t y p e
edge.
Type
I I - Vertices
c o n n e c t e d
only
w i t h
the
C -t ype e dges
o r ,
in
th e simplest
case,
isolated
/ n o
E , C
or
C R -
t y p e
e d g e i n c i d e n t / .
Then,
t o ensure
a power
transfer
i t
i s
required
t h a t :
Rule
E .
Eacb
o f Type
I
vertex
i s connected
a t
l e a s t
w i t h
one L
o r
S-type
e d g e .
Taking
into
account
Definition
1
/ S e c . 2 ,
i t e m
5 / ,
Property
2
a n d
a d d i t i o n a l l y
I R u l e
D
i t
c a n
b e concluded
t h a t :
R u l e
P .
Each
of T y p e
I I
vertex
i s
connected
with
a t
least
o n e S-type
edge
together
with
exac-
tly
o n e
L-type
e d g e .
F i n a l l y , ,
using
Property
2
i t
can
b e
noted
t h a t s
475
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Rule
G .
T h e L-type
edges
do
not
occur
i n parallel
with
t h e
S
O-type
edges.
4 - . - Z n t h e s i s
procedure
of basic
two-state
converter topologies
Basing
o n
the above
rules
o f
admissible
topological
configurations
i n
this section
th e
systematic
procedure
o f
derivation
o f
basic
two-state
converter
structures
i s developed.
The procedure
i s outlined
i n the
flow
chart
of Fig.4.
Step
1 .
I n t h e
first
step minimal
number
o f
switches required
i n
two-state
switching
converters
i s determined.
According to Sect-
i o n 1
two switches
are indispensable.
Step 2 .
I n t h e second
step
number
o f
ECC
-subtrees
/pieces
of
ECC
-subgraph/
i s
d e t i r n i n e d .
According
to R u l g
B
two
such
a
subtrees
are t o b e
considered.
Step
3 . I n the third step nu mb er s
a n d
types
of
vertices i n
each
particular
subtree
are determined.
From
Rule
A
i t results
t h a t
all
three
Type
I
vertices
are grouped
i n o n e
common
EB C -subtree
called
henceforth
t h e
main s u b t r A e .
Consequently,
t h e
second
subtree
called
henceforth
th e
subsidiary
subtree
con-
tains o n l y Type
II
vertices.
Additionally,
accounting
for Rule
F
i t i s
evident
that
i n
t h e
case o f two
S-type
edges t h e
subsidiary
subtree
contains
o n e
o r
two
vertices.
These
vertices
are
connected
totally with
three
or
four
L
a n d
S-type
edges,
respectively.
This
i n turn,
together
with
R u l e F ,
leads
t o
t h e
conclusion
that
the main subtree
beside
t h e
aforementioned
three vertices
o f Type
I
can-
not contain any
other
vertices
/ t o
generate
one
extra
Type
II
vertex
a t
least
t j i v e
I
and
S-type
edges
are
r e q u i r e d / .
F i g .
4 .
The
flow
chart o f
t h e
thesis
procedure.
proposed
syn-
i _ i
t y p e
I
v e r t e x
I n p u t , '
1
a )
n
y
r -
t y p e
I I v e r t e x
o u t p u t
t
1 1
AI\
c
B
OS
BUC K BOOST
B U C K / B 0 0 S T
o l
m a i n
A
X
s u b s i d i a r y
s u b t r e e
I
I , 0 H s u b t r e e
II
UP
C U K
DOWN
D L J A L - S E P I C
NEW1
S E P I C N E W 2
N EW3
NEW4
F i g .
5 .
S u b s e q u e n t
steps
o f
t O h e
procedure:
possible
vertices
distributions
/ & / ,
t w o - s w i t c h
configurations
/ b / ,
admissible
L S structures
/ c /
and
final
two-state
converters / d / .
476
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Summarizing,
there
ar e
two
possible dis-
tributions
o f vertices
i n the E C C 2 - s u b g r a p h ,
shown
i n
F i g . 5 a :
/ i /
L a i n
subtree-three
Type
I
v e r t i c e s ,
subsidiary
subtree-one
Type
I I vertex
/ i /
M i a i n
subtree-three
Type
I
v e r t i c e s ,
s u b s i d i a r y
s u b t r e e - t w o
T y p e
I I
ver-
t i c e s .
Step
4 .
I n
t h e fourth
s t e p ,
considering
b o t h
intervals
a t t h e
s a m e
time,
a l l
the
p o -
ssible
configurations
o f
t h e
S-type
edges
a r e
g e n e r a t e d , F i g . 5 b .
A s
a
r e s u l t ,
nine
configu-
rations a r e
o b t a i n e d .
Step
5 .
I n t h e
f i f t h
s t e p ,
f o r
each
o f
t h e
S - t y p e
e d g e s
configurations,
t h e possible
L t y p e
e d g e s
p o s i t i o n s
a r e
generated.
This
p r o c e s s
a c c o u n t s
for
Rule
D ,
E ,
F
and
G
a n d
leads
t o twelve
different
L S
structures
a s
shown
i n
F i g . 5 c .
Step
6 .
I n t h e
s i x t h
step
t h e
obtained
L S
structures
a r e completed
b y
C-type
e d g e s
which
i n
t h i s
c a s e
c a n occur
only
i n the
sub-
sidiary
subtree
o f
nine
structures
o f F i g . 5 d .
L l - 0
VEE
L
2
c
v o
NE W
I
L i
i
V E t
D 0 2 v
NEW
4
F O R
NE W
1
AND
4
V Q
-
1 - 2 D
V E
1 - D
1 1
t
V o
i V o
N E W
2
NE W
3
F O R
1
NEW 2 A N D 3 :
V O
1 - D
V E
1 - 2 D
- - -
1
_
I
F i g .
6 .
P o u r
new
two-state
dc-dc
converters
with
t h e i r
ideal
static
c h a r a c t e r i s t i c s .
A s a
r e s u l t ,
a t
t h e o u t p u t
o f
t h e
proce-
dure
overall
t w e l v e
basic
t w o - s t a t e
converter
structures
a r e d e r i v e d ,
w h e r e
e i g h t
o f
t h e m
a r e
already
k n o w n
w h i l e
f o u r ,
most
l i k e l y ,
still
u n k n o w n .
These
four n e w
s t r u c t u r e s ,
a s
c a n
b e easily
p r o v e d ,
have
t h e
static
chara-
c t e r i s t i c s
V
/ V
being
t h e n o n - c o n s t a n t
fun-
ctions
o f
t h 8
d g t y - r a t i o
D .
T h u s ,
t h e
rules
f o r m u l a t e d
i n
Section 3 c o n s t i t u t e
t h e
s e t
o f
both
necessary
and
s u f f i c i e n t conditions
equi-
valent
t o
t h e a d o p t e d
definition
of
basic
t w o - s t a t e
c o n v e r t e r .
I n
F i g . 6
four
new
converter structures
with their
static
c h a r a c t e r i s t i c s
ar e redrawn
i n
a more
s t a n d a r d
form.
A s
s e e n ,
these c o n -
verters
prove
t h e
p o s s i b i l i t y
of
o b t a i n i n g
b o t h
i n v e r s e d
a n d
non-inversed
p o l a r i t y
o f
t h e
o u t p u t
v o l t a g e .
V i r t u a l l y ,
i n or der
to
exploit
this
feature
two
ideal
s y m m e t r i c a l
s w i t c h e s
would
b e
involved.
H o w e v e r ,
the
im-
p l e m e n t a t i o n
o f
u n i - d i r e c t i o n a l
s w i t c h e s
/ t r a n s i s t o r s
and
d i o d e s /
would
r e q u i r e
a n
i n t e r c h a n g e
o f
their
p o s i t i o n s
a t
D = 0 . 5 .
5 .
Conclusions
T h e
systematic
method
o f
t o p o l o g i c a l
syn-
thesis
o f
basic
t w o - s t a t e
dc-dc
converters
allowed
t o
a c h i e v e
t h e
c o m p l e t e
class
of
t h e -
s e
c i r c u i t s ,
i n c l u d i n g
four
n e w
structures.
The
derived
structures
a r e
basic
in
that
sense
that
e a c h
element
i s
a b s o l u t e l y
e s s e n t i a l
from
t h e
v i e w p o i n t
o f
their
static
p r o p e r t i e s .
S u c h
a
basic
structure
can
b e ,
a c c o r d i n g
t o
some
o p t i o n a l
r e q u i r e m e n t s ,
modified
b y
addi-
tion
of
filters
/ a t
i n p u t
a n d / o r
o u t p u t / ,
t a p p e d
i n d u c t o r s ,
transformers
a n d
p a r a l l e l
or series
L C
a r r a n g e m e n t s .
I t ca n
b e
p o i n t e d
o u t
that
i n
a
number
of
structures
/ C U K ,
U P ,
D U A L - S E P I C
a n d
NEW
1 / ,
b y
removal
of
t h e
C-
type
edge p a r a l l e l
to
t h e
l o a d
resistance
r i ,
the o u t p u t
i m p e d a n c e
ca n
b e
c h a n g e d
f r o m r
t h e
high
t o
the
low
l e v e l .
6 . R e f e r e n c e s
[ 1 ]
S.Cuk
and
R - . D . S i d d l e b r o o k ,
A
new
o p t i m u m
t o p o l o g y
s w i t c h i n g
dc-dc
converter ,
i n
1977
IEEE
Power
Electronics
S p e c i a l i s t s
C o n f e r e n c e
R e c o r d , p p .
1 6 0 - 1 7 9 .
[ 2 ]
R . P . M g a s s e y
and
E . C . R y d e r ,
H i g h
v o l t a g e
s i n g l e - e n d e d
d c - d c c o n v e r t e r ,
i n
1 9 7 7
IEEE
r o w e r
Electronics
S p e c i a l i s t
Conferen-
ce R e c o r d , p p .
1 5 6 - 1 5 9 .
[ 3 ]
R . S e v e r n s ,
S w i t c h m i i o d e
converter
t o p o l o g i e s
make
them work
for y o u t ,
I n t e r s i l ,
I n c . ,
Application
B u l l e t i n
A 0 3 5 ,
1 9 8 0 .
[ 4 ]
S . C u k ,
General
t o p o l o g i c a l
p r o p e r t i e s
o f
switching
s t r u c t u r e s ,
i n
1 9 7 9
I E 2 r
Power
Electronics
Specialist
Conference
R e c o r d ,
p p .
1 0 9 - 1 2 9 .
[ 5 1
G.Cardwell
a n d W . N e e l ,
B i l a t e ra l
p o w e r
c o n d i t i o n e r ,
i n
1 9 7 3
I E E E
Power
Electro-
nics O p e c i a l i s t
C o n f e r e u i c e
R e c o r d , p p .
2 1 4 -
2 2 1 .
[ 6 ]
E . E . L a n d s m a n n ,
A
u n i f y i n g
d e r i v a t i o n
of
switching
dc-dc
converter
t o p o l o g i e s ,
i n
1979
I 2 2
t v c w e r
Electronics
S p e c i a l i s t s
Conference
R 2 e c o r d ,
p p .
2 3 9 - 2 4 3 .
[ 7 ]
N . R . M . R a o ,
Aunifying
p r i n c i p l e
behind
s w i t c h i n g
c o n v e r t e r s
and
s o m e
n e w
basic
c o n f i g u r a t i o n s , ,
I E E E
Transactions
on
r o n -
s u m e r E l e c t r o n i c s ,
v o l .
C E - 2 6 ,
r p .
1 4 2 - 1 4 3 ,
F e b . 1 9 8 0 .
477
