484
IEEE
TRANSACTIONS ON
POWER
ELECTRONICS, VOL.
3.
NO.
4,
OCTOBER
I988
Transformerless DC-to-DC Converters
with
Large
Conversion Ratios
R. D. MIDDLEBROOK, FELLOW,
IEEE
Abstract-A new switching dc-to-dc converter
is
introduced in which
large voltage step-down ratios can be achieved without a very small
duty ratio and without a transformer. The circuit is an extension of
the Cuk converter to incorporate a multistage capacitor divider. A par-
ticularly suitable application would he a 50-V to 5-V converter in which
dc isolation is not required. The absence of a transformer and a larger
duty ratio permits operation at a high switching frequency and makes
the circuit amenable to partial integration and hybrid construction
techniques. An experimental 50-W three-stage voltage divider Cuk
converter converts 50 V to
5
V
at 500
kHz,
with efficiency higher than
for a basic Cuk converter operated at the same conditions. A corre-
sponding voltage-multiplier Cuk converter is described, and also dual
buck-boost-derived step-down and step-up converters.
I. INTRODUCTION
HE NEED is growing for a converter/regulator to
T
provide +5-V output from a nominal
-48-V
input
and with a low profile capable of assembly on a plug-in
card. An obvious motivation exists to use a switching fre-
quency at least in the hundreds of kHz to reduce magnet-
ics sizes and to take advantage of hybrid construction
techniques. With the advent of power MOSFETs, the
switching frequency is limited by the magnetics rather
than by the switch.
More specifically,
it
is a transformer that limits the fre-
quency, rather than an inductor, because the ratio of leak-
age
to magnetizing inductance increases as the physical
size decreases. A transformer commonly provides two
functions in a dc-to-dc switching converter: it provides dc
isolation, and it provides an additional voltage conversion
ratio over and above that available from the switch duty
ratio.
In applications where dc isolation is not needed, a
transformer (or an autotransformer) would normally still
be required if the necessary voltage conversion ratio is
large. For example, in a 50-to-5-V converter, the switch
duty ratio would have to be about
0.1
if
a transformer
were not used, which severely limits the switching fre-
quency and the dynamic range, and also has undesirable
implications with respect to peak currents, loss of effi-
ciency, and noise. On the other hand, if a transformer
were used, the switching frequency would also be se-
verely limited by the transformer itself. This paper sug-
Manuscript received January 29, 1988; revised May 23, 1988. This pa-
per was presented in part at INTELEC ’84, New Orleans,
LA,
Nov. l
l-
14, 1984.
The author is with the Power Electronics Group, Electrical Engineering
116-81, California Institute of Technology, Pasadena,
CA
91
125.
IEEE
Log
Number 88228%.
gests a way to avoid both these undesirable solutions by
introducing a voltage-divider property that does not re-
quire a transformer.
11.
THE VOLTAGE-DIVIDER CUK CONVERTER
The new circuit is another extension of the basic Cuk
converter
[I,
vol
11,
sec.
181,
introduced
in
1976 as a
so-
lution to the problem of achieving nonpulsating current at
both input and output with a minimum number of com-
ponents. In the Cuk converter, shown in Fig.
1,
the ca-
pacitor is charged by the input inductor current when the
transistor is
off
and the diode is on and is discharged
through the output inductor when the transistor is on and
the diode is
off.
As
far as the basic conversion property is concerned,
the converter may be considered a coalesced boost fol-
lowed by a buck converter, in which the capacitor average
voltage
V,
corresponds to the output of the boost stage,
given by
V,/
(I
-
D
)
and also to the input of the buck
stage whose output Vis
DV,..
Hence the overall input-to-
output conversion ratio is
M
=
V/VK
=
D/(
1
-
D)
where
D
is the fractional on-time of the transistor and
Vg
is the input voltage. This is the same functional relation-
ship as in the flyback converter and permits either up or
down conversion.
Polarity inversion between input and output occurs be-
cause during charge the positive capacitance terminal
is
grounded through the diode, and during discharge the
negative end
is
grounded through the transistor. The cir-
cuit is normally designed to operate in the “continuous
capacitance voltage mode” in which the polarity of the
capacitance voltage does not reverse
[
1,
vol. 11, sec.
271.
The Cuk converter is unique compared with the con-
ventional buck, flyback, and other converters
in
that
it
utilizes capacitive rather than magnetic energy transfer. It
is this property that permits the capacitance voltage-di-
vider feature to be incorporated. The new circuit, shqwn
in its simplest form in Fig.
2,
is a “voltage-divider
Cuk
converter,” in which two energy transfer capacitors are
charged in series when the transistors are
off
and dis-
charged in parallel when the transistors are on. Thus, ef-
fectively, a two-to-one voltage division is introduced, and
the overall conversion ratio is
M
=
D/2
(
1
-
D
)
where
D
is the duty ratio of the two transistors driven on and
off
simultaneously.
This concept can be generalized to where
N
capacitors
0885-8993/88/1000-0484$01
.OO
O
1988 IEEE
MIDDLEBROOK:
TRANSFORMERLESS
DC-TO-DC
CONVERTERS
485
Fig.
1.
Basic Cuk converter
Fig.
2.
New voltage-divider Cuk converter with two stages
are charged in series and discharged in parallel, as shown
in Fig.
3,
so
that the overall conversion ratio is
DIN(
1
-
0).
The circuit configuration is shown in Fig.
4
for
the two intervals that comprise the switching cycle. The
transistors and diodes are assumed to be ideal switches.
During the fractional off-time
(
1
-
D
)
of the transistors,
shown in Fig. 4(a), the
N
energy transfer capacitors are
charged in series by the input current
Zg.
During the tran-
sistor fractional on-time
D,
shown in Fig. 4(b), each ca-
pacitor supplies one Nth of the output current
I.
By volt-
second balance across the input inductor
L,,
the voltage
across all
N
capacitors in series is
V,
=
Vg
/(
1
-
D
)
(the
same expression as for the basic
Cuk
converter), and this
voltage is shared equally by the
N
capacitors as a result
of
automatic self-adjustment when the capacitors are par-
allelled during the transistor fractional on-time
D.
In comparison with the basic
Cuk
converter, the new
converter operates at a higher duty ratio for the same
overall conversion ratio
M
=
V/ Vg
.
The relation between
the respective duty ratios
DN
and
D,
is obtained from
which leads to
NDI
D-
N-l
+DI(N-
1)
and
Thus
DN
is larger than
DI
and permits a higher switching
frequency to be used with transistors having given switch-
ing times.
Stress levels are also lower on some of the components,
partly as a result
of
sharing between the extra elements
where
N
is greater than unity. In particular, transistor
Q,
carries only the input current plus one Nth
of
the output
current, and the extra transistors carry only one Nth of the
output current. On the other hand, the voltage stress on
Q,,
which is
Vg
/(
1
-
D
),
is higher because of the higher
N
tronslstors
Fig.
3.
Generalized N-stage voltage-divider Cuk converter
(b)
Fig.
4.
N-stage converter.
(a)
During driving transistor off-time,
N
capac-
itors
are
charged in series.
(b)
During transistor on-time,
N
capacitors
are discharged in parallel.
D.
The output diode still carries the sum
of
the input and
output currents, but for a shorter fractional time
(
1
-
D
);
its voltage stress level
V/D
is also lower.
Previously described extensions of the basic
Cuk
con-
verter can also be incorporated into the new circuit. For
example, the input and output inductors may be coupled,
with the attendant ripple steering properties
[l,
vol.
11,
secs.
19,
201.
Transformer isolation may be introduced
between the two capacitors that result from splitting the
first energy transfer capacitor into two
in
series
[I,
vol.
11, secs. 22, 26; vol. 111, secs. 12, 181, in which case all
the magnetics may be integrated
[l,
vol. 11, sec.
28;
vol.
111, secs, 2, 15, 211.
Of course, introduction of an isolation transformer may
obviate the advantage obtained by the voltage divider cir-
cuitry, but it may be beneficial in some applications since
the required transformer turns ratio would be smaller by
the voltage division ratio.
Also,
in multiple outputs the
relative volts-per-turn constraints would be eased. On the
other hand, the dc isolation transformer would require
486
IEEE TRANSACTIONS ON POWER ELECTRONICS,
VOL.
3,
NO.
4,
OCTOBER
1988
AG-
f7--
I I
I
I
I+'
I
ND' D
Fig.
5.
Small-signal model
of
N-stage voltage-divider Cuk converter. (a)
In
form
resembling buck converter preceded by input
filter.
(b)
In
ca-
nonical
form.
separate drives for the first transistor on the primary side
and for the others on the secondary side.
The small-signal model of the new voltage-divider Cuk
converter can be obtained by straightforward application
of the state-space averaging analysis method [l, vol.
I,
sec. 61. The result
is
shown in Fig.
5
in two forms: in
Fig. S(a) the model is presented in the form that exposes
the similarity to the model of the buck converter with in-
put filter; in Fig. 5(b) the model is in the canonical form
in
which the modulation generators are in front of the two-
section filter. As would be anticipated, both these forms
are the same as for the original Cuk converter except that
certain element values are modified by the voltage-divider
ratio N. Interpretation and utilization of both models have
been extensively discussed elsewhere
[
1,
vol. 11, sec. 251.
111.
EXPERIMENTAL RESULTS
A
three-stage voltage-divider Cuk converter
(N
=
3)
has been constructed to demonstrate feasibility. The cir-
cuit, shown in Fig.
6,
is constructed on a printed circuit
board with short length, large area connections. The cir-
cuit
is
designed for a nominal conversion ratio
M
=
V/ Vx
=
5
V/50
V
=
0.1. Because only N-channel MOSFET
transistors were conveniently available, the polarities are
positive
in,
negative
out.
All the diodes are Schottkys.
The component list is as follows:
Q,,
Q2, Q3
RFPlON15 RCA N-channel MOSFET
S,,
S3,
S,
s2
so
(150
V,
10
A, 0.3
a),
1N5822 (40
V,
3
A),
Fuji ERC88-099
(90
V,
S
A),
Unitrode USD945 (45 V,
16
A),
\
Fig.
6.
Experimental three-stage voltage-divider Cuk converter operated
at
500
kHz.
Cl,
Cz,
C3
Ll
LO
TRW-35 1-pF 100-V polypropylene, par-
alleled by two 0.1-pF ceramics,
124-pH 56-mQ (25T #22 on Ferroxcube
1811
PA
250 387 pot core),
5-pH
3-mQ (6T 1.4 mm
x
5.0
mm rect-
angular wire on Magnetics Inc. F ma-
terial 1811 pot core),
100-pF 35-V, paralleled by a I-pF ce-
ramic,
1
-pF ceramic.
CO
Cl
The circuit operates as expected at a switching fre-
quency of
500
kHz. The drain voltage
V,,
and current
ID
waveforms for each transistor are shown in Fig. 7. The
calculated (ideal) duty ratio for
M
=
0.1 and
N
=
3 is
NM
03
=
~
=
0.23
1
+
NM
compared with the value 0.28 observed in Fig. 7.
The waveforms shown in Fig. 7 are direct plots taken
from a Tektronix 7854 digital sampling oscilloscope. The
waveforms are quite clean, although ringing
is
very sen-
sitive to the wire loop added for insertion of the current
probe.
All
the voltage waveforms were taken without any
such
loops,
and the current waveforms were taken with a
loop only for the current being measured.
Efficiency measurements on the N
=
3 converter were
made over a range of input voltage with the output main-
tained constant at
5
V.
The input current was measured
with a Triplett 630-NA. The results, shown in Fig. 8,
indicate a broad maximum in the range 72-74 percent
from about
Vg
=
40-100 V.
Of more interest than the actual efficiency value, how-
ever, is whether, for a given conversion ratio
M,
the mul-
tistage converter has higher efficiency than the original
single-stage converter. To effect as close a comparison as
possible, the same components in the three-stage con-
verter (and in the same layout) were reconnected in par-
allel, and the energy transfer capacitor consisted of
C1
and
C,
in parallel;
C,
and SI through
S4
were omitted. The
MIDDLEBROOK:
TRANSFORMERLESS
DC-TO-DC CONVERTERS
-
Elficiency
-
72%
-
70%
-
68%
487
ov
OA
OV
04
(C)
Fig.
7.
Drain voltage
VDs
and drain current
ID
waveforms for circuit
of
Fig.
6
operated at
500
kHz.
(a) For
Q,.
(b) For
Q,.
(c) For
Q,.
three-stage
74%
/
66%
1
Input Volloqe
i
20
30
40
50
60
70
eo
90
Fig.
8.
Efficiency as function of input voltage for three-stage
Cuk
con-
verter of Fig.
6,
and for same components reconnected as two-stage and
single-stage converters. Output maintained at
5
V,
50
W
in all cases.
drain voltage and drain current waveforms are shown in
Fig.
9.
The duty ratio necessary to realize the conversion
ratio
50
to
5
V
is reduced to
0.11.
The efficiency measurements for the single-stage con-
verter are also shown in Fig.
8,
as well as those for the
intermediate two-stage converter. The broad maximum in
efficiency does indeed move to higher input voltages for
a greater number of stages, confirming the expectation that
the multistage converter can deliver higher efficiencies for
large step-down ratios.
ov
OA-
Fig.
9
Drain voltage and current waveforms for three pdrdllelled transis
tors when circuit
of
Fig
6
is reduced to basic (single-stdge)
Cuk
con
verter
Fig.
10.
Principle of three-stage voltage-multiplier
Cuk
converter.
~~
Fig
11
Principle of three-stage voltage step-down buck-boost converter
IV.
OTHER LARGE-RATIO STEP-UP
AND
STEP-DOWN
CONVERTERS
The previously described voltage step-down Cuk con-
verter is based
on
the energy transfer capacitor being di-
vided into
N
capacitors which are charged
in
series and
discharged in parallel. Each extra energy transfer capac-
itor requires one extra transistor and two extra diodes;
An analogous extension leads to a voltage step-up
Cuk
converter, in which
N
capacitors are charged in parallel
and discharged in series (Fig.
IO,
for
N
=
3).
Each extra
capacitor requires two extra transistors and one extra
diode.
A dual procedure leads to voltage step-down and volt-
age step-up extensions of the buck-boost converter. In the
voltage step-down buck-boost converter (Fig.
11
for
N
=
3),
the energy-transfer inductor is divided into
N
induc-
tors which are charged in series and discharged in paral-
lel. Each extra inductor requires two extra transistors and
one extra diode.
488
IEEE TRANSACTIONS
ON
POWER ELECTRONICS,
VOL.
3,
NO.
4,
OCTOBER
1988
I
Fig. 12. Principle of three-stage voltage step-up buck-boost converter.
In the voltage step-up buck-boost converter (Fig.
12
for
N
=
3),
the
N
inductors are charged in parallel and
discharged in series. Each extra inductor requires one ex-
tra transistor and two extra diodes.
In either the voltage step-up or the step-down buck-
boost converter, one or more of the inductors may be cou-
pled to give the additional ripple-steering feature. The
buck-boost-based multiple-inductor converters compare
less favorably with the conventional transformer-coupled
versions because they require additional magnetics, con-
trary to the original motivation to reduce the magnetics.
V.
CONCLUSIONS
The voltage-divider Cuk converter permits large overall
step-down conversion ratios to be achieved without
a
transformer and yet with switch duty ratios that are not
crunched at the low end, permitting higher switching fre-
quencies to be used that take full advantage of power
MOSFET fast switching speeds. Other advantages are that
all the transistors have a common ground and can be
driven in parallel from a single drive source, each addi-
tional transistor and shunt diode carries only one Nth of
the output current, and each series diode carries only the
input current. The circuit is particularly suitable for par-
tial integration and hybrid construction techniques.
Experimental results confirm the basic operation of a
50-5 V
50
W
three-stage voltage-divider Cuk converter.
Reconnection as a single-stage and as a two-stage con-
verter, still delivering
50
W
at
5
V,
verifies that the effi-
ciency maximizes at larger conversion ratios for a greater
number of stages.
A
corresponding voltage-multiplier Cuk converter is
described in Section IV, and also dual step-down and step-
up converters based on the buck-boost circuit. A
U.S.
patent (4 654 769) has been issued for the voltage-divider
Cuk converter.
ACKNOWLEDGMENT
All of the experimental work, and the derjvation of the
small-signal model, for the voltage-divider
Cuk
converter
was done by Steve Freeland, a graduate student in the
Caltech Power Electronics Group, now at Rockwell In-
ternational.
REFERENCES
[I]
R. D. Middlebrook and S. Cuk,
Advances in Switched-Mode Power
Conversion,
vols.
1-111.
Pasadena, CA: TESLAco, 1983.
R.
David Middlebrook
(S’55-M’56-SM’58-
F’78) was born in England on May
16,
1929. He
received the B.A. and M.A. degrees from Cam-
bridge University, England, and the M.S. and
Ph.D. degrees from Stanford University, Stan-
ford, CA, in 1952, 1954, 1953, and 1955, respec-
tively.
He is a Professor of Electrical Engineering at
the California Institute of Technology, Pasadena.
His interests include solid-state device modeling,
circuits and systems, and power processing elec-
tronics in which he is both Lecturer and Consultant. He is especially in-
terested in design-oriented circuit analysis and measurement techniques
which he teaches at Caltech and through short courses in both Europe and
the
U.S.
Dr. Middlebrook is the recipient of the 1982 IEEE William E. Newell
Power Electronics Award for Outstanding Achievement
in
Power Elec-
tronics and a 1982 Award for Excellence in Teaching, presented by the
Board of Directors of the Associated Students of Caltech. He is the author
of numerous papers, a book on solid-state device theory, and one on dif-
ferential amplifiers.