IEEE
TRANSACTIONS
ON
INDUSTRIAL
ELECTRONICS,
VOL.
IE-30,
NO.
1,
FEBRUARY
1983
prototype
of
the
new
switching
power
amplifier
and
the
later
improvements.
REFERENCES
[1]
Slobodan
Cuk
and
R.
D.
Middlebrook,
"A
new
optimum
topology
switching
dc-to-dc
converter,"
in
1977
IEEE
Power
Elec.
Spe-
cialists
Conif.
Rec.,
pp.
160-179.
[2]
Slobodan
Cuk,
"Modelling,
analysis,
and
design
of
switching
converters,"
Ph.D.
thesis,
California
Inst.
Technology,
Nov.
1976.
Also,
NASA
Rep.
CR-135174.
[31
Slobodan
Cuk
and
R.
D.
Middlebrook,
"Coupled-inductor
and
other
extensions
of
a
new
optimum
topology
switching
dc-to-dc
converter,"
in
1977
IEEE
Industry
Applications
Soc.
Ann.
Meet.
Rec.,
pp.
1110-1126.
[4]
R.
D.
Middlebrook
and
Slobodan
Cuk,
"Isolation
and
multiple
output
extensions
of
a
new
optimum
topology
switching
dc-to-dc
converter,"
in
1978
IEEE
Power
Electronics
Specialists
Conf.
Rec.,
pp.
256-264.
[51
R.
D.
Middlebrook,
Slobodan
Cuk,
and
W.
Behen,
"A
new
battery
charger/discharger
converter,"
in
1978
IEEE
Power
Electronics
Specialists
Conf.
Rec.,
pp.
251-255.
[6]
L.
Shaeffer,
"VMOS-A
breakthrough
in
power
MOSFET
tech-
nology,"
Siliconix
Applications
Note
AN76-3,
Santa
Clara,
CA,
1976.
[7]
R.
D.
Middlebrook
and
Slobodan
Cuk,
"Modelling
and
analysis
methods
for
dc-to-dc
switching
converters,"
(invited
review
paper)
in
1977
IEEE
Int.
Semiconductor
Power
Converter
Conf.
Rec.,
pp.
90-111.
[8]
Slobodan
Cuk
and
Robert
W.
Erickson,
"A
conceptually
new
high-
frequency
switched-mode
amplifier
technique
eliminates
current
ripple,"
in
Proc.
Fifth
Nat.
Solid-State
Power
Conversion
Conf.,
May
1978,
pp.
G3.I-G3.22.
Advances
in
Switched-Mode
Power
Conversion
Part
II
SLOBODAN
CUK,
MEMBER,
IEEE,
AND
R.
D.
MIDDLEBROOK,
FELLOW,
IEEE
Abstract-A
number
of
important
practical
extensions
to
the
basic
Cuk
converter
are
presented.
They
include
dc
isolation,
multiple-
output
power
sources,
and
a
physical
realization
of
the
sought
for
hypothetical
dc-to-dc
transformer,
a
device
which
converts
from
pure
dc
(no
voltage
or
current
ripple)
at
one
terminal,
to
pure
dc
(at
a
different
voltage)
at
the
other
terminal.
The
application
of
the
circuit
in
a
highly
efficient
amplifier
for
the
servo
control
of
a
dc
motor
or
other
loads
is
also
presented.
1.
INTRODUCTION
IN
PART
I
of
this
series
we
provided
a
review
of
the
basic
types
of
switched-mode
power
converters
and
showed
how
the
effort
to
solve
the
characteristic
problems
of
these
earlier
designs
led
to
the
development
of
a
fundamentally
new
con-
verter
configuration.
Fig.
1
shows
a
summary
of
the
basic
con-
verter
types
and
a
physical
realization
of
the
new
converter
in
its
simplest
forn.
The
new
converter
topology
embodies
all
of
the
desirable
features
of
previous
types
while
retaining
none
of
their
liabilities.
Whereas
other
converters
rely
upon
the
in-
ductive
coupling
of
energy
between
the
input
and
output,
the
new
converter
uses
a
capacitor
to
transfer
stored
energy
be-
tween
input
and
output
inductors
as
shown.
Due
to
the
presence
of
inductors
on
both
the
input
and
output,
the
current
on
either
terminal
remains
continuous
Manuscript
received
October
15,
1982.
The
authors
are
with
the
California
Institute
of
Technology,
Pasa-
dena,
CA
91125.
This
article
is
reprinted
from
Robotics
Age
Magazine.
avoiding
the
electrical
noise
problems
associated
with
switch-
ing
either
the
input
or
output
current
and
resulting
in
in-
creased
conversion
efficiency.
The
new
converter
has
the
de-
sirable
property
that
its
output
voltage
can
be
either
higher
or
lower
than
that
of
the
input
supply,
as
determined
by
the
duty
ratio
of
the
switching
transistor
(the
fraction
D
of
the
switch-
ing
period
(Ti)
that
the
transistor
is
turned
on).
Also
presented
in
Part
I
were
several
important
extensions
to
the
basic
converter
design.
These
include
adding
the
capability
for
bidirectional
power
flow
between
input
and
output,
coup-
ling
the
input
and
output
inductors
via
a
single
transformer
core,
and
a
high-performance
switched-mode
power
amplifier
configuration
using
parallel
converters
driving
a
differentially
connected
load.
An
important
result
of
the
coupled-inductor
extension
of
the
new
converter,
apart
from
the
further
reduction
in
the
number
of
components,
is
that,
by
proper
adjustment
of
the
magnetic
coupling
between
the
input
and
the
output
induc-
tors,
the
residual
current
and
ripple
at
one
of
the
terminals
can
be
reduced
exactly
to
zero,
resulting
in
pure
dc.
Naturally,
this
motivated
the
search
for
a
converter
configuration
which
would
achieve
the
desired
characteristic
of
having
zero
current
ripple
at
both
input
and
output
simultaneously,
thus
resulting
in
a
physical
realization
of
an
ideal
dc-to-dc
"transformer."
(See
Fig.
8
in
Part
I.)
In
this
article,
we
will
show
how,
by
pursuing
the
desirable
property
of
dc
isolation
between
the
input
and
the
output
cir-
0278-0046/83/0200-0019$01
.00
©
1983
IEEE
19
IEEE
TRANSACTIONS
ON
INDUSTRIAL
ELECTRONICS,
VOL.
IE-30,
NO.
1,
FEBRUARY
1983
BUCK
POWER
STAGE
L
v
L
v
C
R
R
'T'
(a)
BOOST
POWER
STAGE
L
v
L
v
VgC
R
C
R
(b)
BUCK-
BOOST
POWER
STAGE
V9
C
R
L
L
R
(C)
Li
C1
L2
-V
i2-
A
B
0
R
(d)
NEW-SWIT-CHIG
DC-TO-DC
CONVERTER
Li
Ci
L2
-V
ii
~~~~~~~~~2~
Vi
(e)
Fig.
1.
(a)-(d)
The
family
of
four
basic
switching
converter
topologies
and
(e)
a
practical
implementation
of
the
Cuk
converter
using
a
transistor-diode
combination.
(a)
Buck
power
stage.
(b)
Boost
power
stage.
(c)
Buck-boost
power
stage.
(d)
New
converter
topology.
(e)
New
switching
dc-to-dc
converter.
cuits,
the
sought
for
solution
for
the
ideal
converter
was
found
inherently
derived
from
the
new
converter
topology.
Since
the
new
topology
provides
higher
performance
than
all
other
converter
types,
but
may
be
implemented
using
fewer
com-
ponents
than
comparable
solutions,
it
may
be
said
to
be
an
optimal
design.
To
illustrate this
point,
we
will
present
the
de-
sign
of
a
working
circuit
that
shows
the
ease
of
employing
the
new
topology
in
practical
applications.
II.
DC
ISOLATION
IN
THE
NEW
SWITCHING
CONVERTER
All
the
basic
switching
dc-to-dc
converter-types
reviewed
in
Part
I,
along
with
the
newly
introduced
converter
topology,
are
distinguished
by
the
elegant
method
by
which
conversion
is
accomplished
through
the
operation
of
a
single
switch
(double-pole,
single-throw)
in
an
otherwise
passive
energy
stor-
age
network,
as
shown
in
the
converters
in
Fig.
1.
Despite
this
simple
structure,
which
results
in
the
high
con-
version
efficiency
characteristic
of
"switchers,"
the
basic
con-
verter
configurations
all
lack
one
of
the
properties
often
re-
quired
of
power
suppliers:
dc
isolation
between
the
input
and
output
ports.
There
is
therefore
a
strong
incentive
to
find
a
12~~~-
!
-w
-
-
I
ip
Ts2
1s
'S
-
2V
I
~~~~~~~~~~I
..
V
-2V
Ig
FI--]I
I
.-
F
- -
2
Ts
2-w
(a)
_
I
-v
I
*-
Ts
I
TS
I
-V
I
Ij
Ts
be2
.
-2I
(b)
Fig.
2.
Isolated
versions
of
the
(a)
basic
buck
("forward")
and
(b)
buck-boost
("flyback")
switching
converters.
way
to
introduce
an
isolation
transformer
into
the
new
con-
verter
design.
One
could
of
course,
immediately
proceed
in
a
conventional
manner
and
try
a
"push-pull"
configuration
using
an
isolation
transformer
with
a
center-tapped
primary.
However,
the
consequent
doubling
of
the
number
of
compon-
ents,
along
with
other
practical
problems
inherent
in
such
a
design,
favor
the
search
for
a
less
complex
single-switch
imple-
mentation
using
a
"single-ended"
isolation
transformer.
For
example,
dc
isolation
can
be
introduced
into
the
basic
"buck"
converter
as
shown
in
Fig.
2(a),
which
is
usually
known
as
the
"forward
converter."
Similarly,
simple
modification
of
the
"buck-boost"
converter
results
in
a
"flyback"
converter
(Fig.
2(b))byreplacing
the
original
single
inductor
with
a
"single-ended"
isolation
transformer.
The
resulting
configura-
tion
also
allows
the
output
polarity
inversion
of
the
buck-
boost
type
to
be
reversed
as
shown,
where
the
transformer
terminals
of
like
polarity
are
indicated
by
the
dots.
One
is
therefore
motivated
to
try
a
similar
approach
to
modify
the
new
converter
topology.
The
obvious
place
to
insert
the
1:2
vp
Ir
v
I
vp
v
20
lVS
,
Z'
,
Z)
vs
Fv
CUK
AND
MIDDLEBROOK:
SWITCHED-MODE
POWER
CONVERSION
PART
II
(b)
Li
C.
Cb
L2
+
T
-v
Vg
f9
C2
R
(C)
Fig.
3.
Three
keys
steps
leading
to
the
dc-isolated
version
of
the
Cuk
converter.
(a)
Separation
of
the
coupling
capacitance
into
two
series
capacitors.
(b)
Floating
potential
set
to
zero.
(c)
Separation
of
the
extra
inductance
into
two
equal
windings.
isolation
transformer
is
somewhere
in
the
inner
loop
con-
taining
the
coupling
capacitor,
transistor,
and
diode,
in
which
the
actual
energy
transfer
is
accomplished.
There-
are
three
key
steps
leading
to
a
simple,
elegant
solution
to
this
prob-
lem.
The
first
step
is
to
separate2
the
coupling
capacitance
C
into
the
two
series
capacitors
Ca
and
Cb,
thus
making
the
original
symmetrical
switching
structure
divisible
into
two
halves,
as
shown
in
Fig.
3(a),
without
affecting
the
opera-
tion
of
the
converter.
The
second
step
is
to
recognize
that
the
connection
point
between
these
two
capacitors,
due
to
its
iso-
lation
has
an
indeterminate
dc
(average)
voltage.
This
floating
potential
can
then
be
set
at
zero
by
placing
an
inductance
be-
tween
this
point
and
ground
(Fig.
3(b)).
If
the
new
inductance
is
sufficiently
large,
it
diverts
a
negligible
current
from
that
passing
through
the
series
capacitors,
so
that
the
converter's
operation
is
still
unaffected.
The
final
step
is
merely
the
sepa-
ration
of
the
extra
inductance
into
two
equal
transformer
windings,
thus
providing
the
desired
dc
isolation,
resulting
in
the
basic
isolated
version
of
the
new
converter
shown
in
Fig.
3(c)
[11.
One
of
the
main
features
of
the
introduction
of
the
isolat-
ing
transformer
is
that
it
has
brought
the
least
disturbance
to
the
original
converter
operation.
In
fact,
with
a
1:1
trans-
forner,
the
voltages
and
currents
in
the
input
and
output
cir-
cuits
are
the
same
as
in
the
original
nonisolated
version.
The
only
difference
is
that
the
original
switched
current
loop
now
has
evolved
into
two
loops
with
equal
currents
circulating
in
the
same
direction.
It
is
instructive
to
consider
the
current
paths,
voltage
distri-
butions,
and
energy
movements
during
the
two
portions
of
the
switching
cycle.
Fig.
4(a)
shows
the
conditions
during
the
in-
terval
D'T'
when
the
switch
transistor
is
off
(open
circuit).
The
input
current,
having
previously
stored
energy
in
input
inductor
L1,
must
now
pass
through
capacitor
C,
and
the
t
vg
1:1
(a)
Vg
.i4-
-
t
I
I
~~~~t
Dv
K
L
c
1
2.
-
.
~~~(b)
Fig.
4.
Current
and
energy
distribution
in
the
dc-isolated
Cuk
conver-
ter:.
(a)
interval
D'TS
when
the
transistor
switch
is
open;
(b)
interval
DTs
when
the
switch
is
closed.
transformer
primary
as
shown.
This
transfers
energy
from
L1
(in
the
form
of
current)
to
Ca
(in
the
fonn
of
voltage,
or
charge).
An
equal
reflected
current
in
the
transformer
second-
ary
charges
Cb
through
the
now
conducting
diode.
During
this
interval
the
output
inductor
L2
is
releasing
its
stored
en-
ergy
to
the
load
as
shown
and
the
diode
thus
carries
the
sum
of
both
the
input
and
output
currents.
In
Fig.
4(b),
the
transistor
is
turned
on
(closed
circuit)
during
intervalDT,,,and
the
input
current
is
allowed
to
store
energy
in
L1.
Since
Ca
(as
well
as
Cb)
was
charged
to
a
posi-
tive
voltage
(viewed
from
left
to
right)
during
DTx,
it
now
dis-
charges
through
the
transistor
and
the
transformer
primary,
transferring
the
stored
energy
to
the
output
circuit.
Note,
however,
that
when
the
transistor
grounds
the
positive
side
of
C4,
the
voltage
drop
across
the
capacitor
must
(instan-
taneously)
remain
the
same,
so
that
its
right
side
is
pulled
down
to
a
negative
voltage.
This
sudden
drop
is
passed
by
the
transformer
to
the
positive
(left)
side
of
Cb,
and
hence
to
the
anode
of
the
diode,
cutting
it
off.
Since
the
output
cur-
rent
must
now
pass
through
Cb
and
the
transforner
second-
ary,
it
must
match
the
current
through
the
primary,
so
that
both
C4
and
Cb
discharge
their
energy
into
L2
and
the
load.
One
sees
that,
during
this
phase
of
the
cycle,
it
is
the
transis-
tor
that
carries
the
sum
of
both
the
input
and
output
cur-
rents.
Some
of
the
additional
advantages
of
this
new
dc-isolated
converter
become
apparent
upon
reexamining
the
steps
which
led
to
the
inclusion
of
the
isolation
transformer.
Since
both
windings
of
the
transformer
are
dc-blocked
by
Ca
and
Cb,
there
can
be
no
dc
in
either
winding.
In
fact,
an
automatic
volt-second
balance
is
achieved
in
the
steady
stage,
so
that
there
is
no
problem
with
"creep"
of
the
transformer
core
op-
erating
point
as
can
occur
in
push-pull
isolation
arrange-
ments.
Isolation
has
thus
been
achieved
in
the
simplest
possible
21
IEEE
TRANSACTIONS
ON
INDUSTRIAL
ELECTRONICS,
VOL.
IE-30,
NO.
1,
FEBRUARY
1983
BIDIRECTIONAL
POWER
FLOW
Li
Ca
Cb
r~~~~
I
Vg
-IsI
Fig.
5.
Comparison
of
the
isolation
transformer
utilization
in
the
(a)
forward
(small
gap)
and
(b)
flyback
(large
gap)
converters,
and
in
the
(c)
new
(Cuk)
converter.
Twice
the
flux
swing
is
available
in
the
tuk
converter.
manner
by
the
addition
of
only
the
necessary
transformer
(which
is
single-ended)
and
the
separation-of
the
original
coup-
ling
capacitance
into
two.
Thus,
it
is
apparent
that
an
opti-
mum-topology
dc-isolated
converter
has
been
obtained
which
retains
all
the
advantages
of
the
original
topology
upon
which
itis
based.
Other
advantages
become
apparent
upon
comparison
of
the
new
design
with
the
other
popular
isolated
converters
shown
in
Fig.
2.
Specifically,
for
the
forward
converter,
the
core
of
the
isolation
transformer
must
be
gappe.d,
since
the
magnetiz-
ing-current
is
available
in
only
one
direction
(with
an
average
dc
value).
The
size
of
the
core
must
be
chosen
so
that
the
total
flux
excursion
is
no
greater
than
the
saturation
flux
B,
of
the
core
material,
as
shown
in
Fig.
5(a)
[1].
In
contrast,
in
the
new
converter
(Fig.
5(c)),
magnetizing
current
in
the
transformer
is
available
in
both
directions,
and
so
a
core
that
is
fully
utilized
(in
terms
of
flux
swing)
in
buck
forward..converter
is
only
half-utilized
in
the
new
converter.
Therefore,
an
ungapped
core
of
half
the
cross
section
could
be
used,
with
the
result
that
the
total
flux
excursion
would
be
2B.,
and
the
core
losses
would
be
correspondingly
halved.
Similarly,
the
copper
losses
would
be
greatly
lowered
due
to
the
reduced
winding
lengths.
From
the
general
point
of
view,
these
benefits
all
stem
from
the
fact
that
in
the
new
converter
power
is
transmitted
through
the
transformer
during
both
in-
tervals
of
the
switching
cycle,
whereas
the
same
average
power
has
to
be
transmitted
during
only
one
interval
in
the
forward
converter.
Comparison
of
the
transformer
properties
between
the
new
converter
and
the
flyback
converter
shows
that
the
disparity
is
even
more
extreme,
because
in
the
flyback
the
core
gap
must
be
larger
than
in
the
forward
converter,
as
illustrated
in
Fig.
4(b).
This
is
because
the
transformer
is
really
an
inductor,
and
the
energy
transferred
through
the
converter
is
stored
in
the
magnetic
field
(principally
in
the
air
gap)
during
one
part
of
the
cycle
and
released
during
the
other.
Consequen
tly,
the
magnetizing
current,
which
is
again
available
in
only
one
direc-
tion,
constitutes
the
total
primary
or
secondary
current
in-
stead
of
just
a
small
fraction
of
it.
III.
THE
MULTIPLE-OUTPUT
EXTENSION
Once
an
isolation
transforner
has
been
introduced
into
the
new
converter,
several
other
extensions
become
obvious.
There
Fig.
6.
DC-isolated
noninverting
bidirectional
current
Cuk
switching
converter,
using
all
n-p-n
bipolar
transistors.
Compare
this
with
Fig.
9
in
Part
I.
1lXl~
~~~-
=-N3
Fig.
7.
Extension
of
the
dc-isolated
Cuk
converter
to
multiple
outputs
with
arbitrary
ratios
and
polarities.
is
no
reason
why
the
transformer
should
be
limited
to
a
1:1
turns
ratio,
and
therefore
a
turns
ratio
factor
Ns/Np
is
avail-
able
for
either
step-up
or
step-down
in
addition
to
gain
control
obtained
by
varying
the
duty
ratio
D.
Thus
V
Ns
D
Vg
Np
l-D
Also,
as
in
the
case
of
the
isolated
buck-boost
converter
in
Fig.
2(b),
an
output
voltage
of
the
same
polarity
as
the
input
voltage
may
be
easily
obtained
by
reversing
the
polarity
of
the
isolation
transformer
secondary
and
changing
the
direction
of
the
diode
and
polarity
of
the
coupling
capacitor
on
the
sec-
ondary
side
accordingly,
as
shown
in
Fig.
6.
It
is
interesting
to
note
that
this
polarity-preserving
configuration
leads
to
an
im-
plementation
of
the
bidirectional
current
(two-quadrant)
ver-
sion
of
the
dcisolated
converter
using
all
n-p-n
bipolar
tran-
sistors,
requiring
only
positive
switch
drive
signals.
(Compare
this
with
the
complementary
pair,
n-p-n
and
p-n-p
transistor,
version
of
the
bidirectional
converter
presented
in
Part
I.)
The
same
holds
for
the
power
MOSFET
implementation
in
which
only
n-channel
devices
are
needed.
This
is
of
signficant
practi-
cal
importance,
since
n-p-n
transistors
and
n-channel
MOS-
FET's
come
in
all
current
and
voltage
ranges,
while
p-n-p
and
p-channel
devices
are
very
limited,
usually
to
lower
current,
voltage,
and
power
ratings.
Multiple
outputs
of
different
voltages
and
polarities
are
easily
obtained
from
multiple
secondary
windings,
or
from
a
tapped
secondary
winding
as
shown
in
Fig.
7.
All
of
the
bene-
L2
C2-
22
,f
-.L
7-
CUK
AND
MIDDLEBROOK:
SWITCHED-MODE
POWER
CONVERSION
PART
II
fits
of
the
basic
new
converter
topology
are
retained
in
the
multiple-output
versions;
in
particular,
all
the
output
currents
and
the
input
current
are
nonpulsating.
When
compared
to
the
conventional
approach
of
designing
an
isolated
multiple
out-
put
power
supply
using
a
tapped
60-Hz
transformer
followed
by
several
linear
regulators,
the
high
performance
and
cost
ef-
fectiveness
of
the
new
method
is
obvious.
The
lower
the
op-
erating
frequency,
the
more
massive
a
transformer
must
be.
In-
stead
of
a
bulky
60-Hz
transformer,
a
much
smaller
trans-
former
designed
to
operate
at
the
switching
frequency
(20
kHz,
for
example)
is
used.
Instead
of
the
wasteful
power
dissipation
of
linear
regulation,
requiring
heatsinks,
fans,
etc.,
the
new
converter
typically
operates
at
over
90-percent
efficiency.
An
additional
side
benefit
is
that
the
latter
design
is
also
insensi-
tive
to
the
input
line
frequency
(50
Hz,
60
Hz,
400
Hz,
etc.),
since
the
input
voltage
is
supplied
by
rectifying
the
ac.
Thus,
by
introducing
dc
isolation
into
the
new
converter,
we
have
substantially
increased
its
range
of
application.
IV.
THE
COUPLED-INDUCTOR
DC-ISOLATED
CONVERTER
The
isolation
transformer
was
imbedded
in
the
basic
con-
verter
without
altering
its
mode
of
operation,
thus
all
the
modifications
and
extensions
applicable
to
the
basic
con-
verter
are
valid
in
the
isolated
case
as
well.
For
example,
the
input
and
output
inductors
can
be
coupled
on
the
same
core
as
shown
in
Fig.
8.
As
discussed
in
Part
I,
zero
current
ripple
may
be
obtained
on
either
the
input
or
the
output
through
ap-
propriate
design
of
the
coupled
inductor.
The
configuration
in
Fig.
8
may
at
first
seem
significantly
different
from
the
isolated
converter
of
Fig.
3(c)
apart
from
the
coupling
of
the
inductors.
This
is
because
the
transfer
ca-
pacitors
Ca
and
Cb
have
been
relocated
to
the
other
side
of
their
respective
transformer
windings.
This
change
neither
al-
ters
the
converter
topology
nor
affects
its
conceptual
opera-
tion.
From
the
practical
viewpoint,
however,
this
alteration
has
important
noise
reduction
advantages.
Since
the
case
of
an
electrolytic
capacitor
is
usually
common
to
its
negative
termi-
nal,
this
design
effectively
grounds
the
cases
of
the
capacitors,
significantly
reducing
the
radiation
produced
by
the
switching
currents.
While
magnetic
coupling
of
the
input
and
output
inductors
is
very
desirable
for
the
reduction
of
ripple,
size,
and
cost,
it
does
introduce
an
undesirable
characteristic,
namely
the
transient
reversal
of
output
polarity
on
start-up.
Note
that
in
the
steady
state
shown
in
Fig.
8,
the
average
dc
currents
flow
into
the
dots
on
the
coupled
inductors,
contrary
to
the
be-
havior
of
an
ordinary
ac
transformer.
During
the
turn-on
tran-
sient,
however,
the
ac
coupling
of
the
inductors
causes
the
initial
current
pulse
from
the
input
to
be
reflected
in
the
secondary
in
the
opposite
direction
from
the
steady-state
cur-
rent,
as
shown
in
Fig.
9.
Although
the
pulse
is
of
short
dura-
tion
(50
p,s
typically),
it
could
result
in
damage
to
sensitive
loads.
The
simple
addition
of
an
output
clamp
diode
as
shown
limits
the
reverse
transient
to
about
a
volt,
or
less
if
a
Schottky
diode
is
used.
Just
as
in
the
single-output
case,
the
same
opportunity
for
coupling
exists
in
the
multiple-output
isolated
converter:
any
or
all
of
the
inductors
can
be
coupled
on
the
same
core,
as
Fig.
9.
Polarityreversal
at
start-up
in
a
coupled-inductor
Cuk
converter.
The
output
diode
provides
a
safe
path
for
the
transient.
R3
Fig.
10.
Transformer-isolated
Cuk
converter
with
all
inductors
coupled
on
a
single
core.
shown
in
Fig.
10.
The
resulting
converter
has
only
two
mag-
netic
lumps,
one
for
dc
isolation
and
the
other
for
input
and
output
filtering.
Again,
by
judicious
selection
of
the
turns
ratios
and
coupling
coefficients,
the
current
ripple
may
be
eliminated
on
the
input
or
any
of
the
outputs
[1].
These
advances
notwithstanding,
the
possibility
of
zero
cur-
rent
ripple
on
only
one
side
leaves
one
with
a
feeling
of
incom-
pleteness
and
a
desire
to
accomplish
this
ideal
goal
of
zero
rip-
ple
on
both
input
and
output
ports.
That
this
can
indeed
be
accomplished,
with
an
even
further
reduction
in
the
size
and
cost
of
the
circuit,
will
once
again
dramatically
illustrate
the
optimality
of
the
new
topology.
V.
THE
IDEAL
ZERO-RIPPLE
SWITCHING
DC-TO-DC
CONVERTER
In
pursuit
of
the
goal
just
posed,
there
may
be
many
ap-
proaches
to
follow:
for
example,
two
coupled-inductor
con-
verters
could
be
cascaded,
with
one
set
for
zero
input
ripple
i'
2
0
23