buck-boost-pwm-converters having two independently controlled switches
TRANSCRIPT
-
7/28/2019 Buck-boost-pwm-converters Having Two Independently Controlled Switches
1/6
1Buck-Boost PWM Converters Having
Two Independently Controlled Switches
-LQJTXDQ&KHQ'UDJDQ0DNVLPRYLDQG5REHUW(ULFNVRQ
Colorado Power Electronics Center
Department of Electrical and Computer EngineeringUniversity of Colorado at Boulder
Boulder, CO 80309-0425, USA
1 This work is supported by Philips Research, Briarcliff Manor, NY, through Colorado Power Electronics Center
Abstract Single-switch step-up/step-down converters, such
as the buck-boost, SEPIC and Cuk, have relatively high
voltage and current stresses on components compared to the
buck or the boost converter. A buck-boost converter with
two independently controlled switches can work as a boost or
as a buck converter depending on input-output conditions,
and thus achieves lower stresses on components. Using the
converter synthesis method from [1], families of two-switch
buck-boost converters are generated, including several newconverter topologies. The two-switch buck-boost converters
are evaluated and compared in terms of component stresses
in universal-input power-factor-corrector applications.
Among them, one new two-switch converter is identified that
has low inductor conduction losses (50% of the boost
converter), low inductor volt-seconds (72% of the boost
converter), and about the same switch conduction losses and
voltage stresses as the boost converter.
I. INTRODUCTION
Dc-dc converters with step-up/step-down characteristic are
required in all applications where the input and the output
voltage ranges overlap. For example, in power factorcorrection (PFC) applications, the use of step-up/step-down
converters such as the buck-boost, SEPIC or Cuk, allows one
to set the output dc voltage to an arbitrary intermediate value.
For one given dc operating point, it is well known that the
buck (if the input is greater than the output), or the boost
converter (if the input is lower than the output) perform
conversion with lower component stresses and energy storage
requirements than the single-switch step-up/step-down
converters.
Paralleling [2] and multilevel techniques [3][4] can be used
to share current or voltage stresses at the expense of more
switching components. However, neither of these approaches
aims at reducing the current and voltage stresses at the sametime. In this paper we show how converters with buck-boost
characteristic can be constructed using two active switches to
achieve low component stresses, low energy storage
requirements, and therefore size and efficiency performance
comparable to the performance of the simple buck or boost
converters.
In Section II, we begin with an introduction of how the
power transfer mechanisms in switching converters affect the
component stresses. The converter synthesis method
described in [1] is adopted to derive all possible two-switch
buck-boost topologies that are capable of achieving minimum
indirect power. The synthesis method is briefly reviewed in
Section III. Families of two-switch buck-boost converters are
presented in Section IV. Selected topologies are compared
against the boost converter and the buck-boost converter inSection V, and new converters that outperform previously
known topologies are highlighted.
II. POWER TRANSFER MECHANISMS IN
SWITCHING CONVERTERS
In the boost and buck converters, there are two
mechanisms that cause transfer of power from the converter
input to the load, and hence the dc output power P is
composed of two components [5]. A part of the power,
Pindirect, is processed by the switching devices using the
(a)
D (Q)
Energy Storage
ElementsQ D
Boost (buck)
Converter
Pdirect
Pindirect
Pindirect
P P
Input Load
(b)
Energy Storage
Elements
Pindirect
Pindirect
P P
Single-switch Buck-
Boost Converter
Input LoadDQ
Fig. 1 Energy flow chart (a) boost and buck converter; (b) single-switch
buck-boost converter.
-
7/28/2019 Buck-boost-pwm-converters Having Two Independently Controlled Switches
2/6
inductor for intermediate energy storage. The remainder of
the input power, Pdirect, flows directly to the output, bypassing
the intermediate process. Fig. 1(a) illustrates the energy flow
process in the boost and buck converters. The ability of
providing direct energy path leads to lower componentstresses, lower energy storage and higher efficiency. In
single-switch step-up/step-down converters, such as the buck-
boost, SEPIC and Cuk, the direct power is equal to zero. All
of the input power is processed by the switching devices, as
illustrated in Fig. 1(b). As a result, component stresses and
energy storage requirements are higher. Figure 2(a) illustrates
the relative indirect power Pindirect/P for the dc-to-dc buck,
boost and single-switch step-up/step-down converters, as a
function ofVin/Vo.
In universal-input (85Vrms-264Vrms) power-factor-
correction (PFC) applications, the boost converter is usually
preferred because of its simplicity, relatively low component
stresses and relatively high efficiency. However, an output
voltage higher than the peak input voltage must be chosen to
satisfy the functional limit of the boost converter. Single-
switch step-up/step-down converters can be used in
applications that require an intermediate output voltage level,
but since the direct power is equal to zero, component
stresses and energy storage requirements are higher. For a
converter in the PFC application, the theoretical minimum
indirect power is shown in Fig. 2(b) as a function of the
Vm/Vo, where Vm is the peak ac line input voltage and Vo is the
output dc voltage. From the discussion above, it follows that
voltage and current stresses can be reduced provided that
there is a direct path for energy delivery. It istherefore of practical interest to find buck-boost
configurations that process minimum indirect power and have
reduced component stresses.
Two simple examples of cascade connection of the buck
and the boost converter in Fig. 3 have the ability to provide
direct energy path and have a widely adjustable output
voltage. In both cases, if the transistors are driven by the
same control signal, there is no direct energy path. To
approach the minimum indirect power process, the transistors
must be independently and optimally controlled. When the
instantaneous input voltage is less than the dc output voltage,
the transistor of the boost converter operates with PWM,
while the transistor of the buck converter is always on. Whenthe instantaneous input voltage is greater that the dc output
voltage, the buck converter is PWM controlled and the boost
transistor is always off. This can lead to a converter system
with capability of intermediate output voltage and with the
theoretically minimum indirect power characteristic shown in
Fig. 2(b).
Although the circuits of Fig. 3 can approach the theoretical
lower limit of indirect power and have lower semiconductor
voltage stresses, the converter in Fig. 3(b) exhibits increased
(a)
Ro
L2
C2Vg
D1
D2Q1
Q2
C1
L1
(b)
Ro
L
CVg D2
D1
Q2
Q1
Fig. 3 Cascaded two-switch buck-boost topologies: (a) boost-buck-
cascaded, (b) buck-boost-cascaded.
(a)
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3
Vin/Vo
P indirect/P
Boost
Buck
single-switch buck-boost, flyback, Cuk or SEPIC
(b)
0
0.2
0.4
0.6
0.8
1
0 0.5 1 1.5 2 2.5 3
Vm/Vo
P indirect/P
Fig. 2 (a) Relative indirect power for dc-to-dc converters; (b) minimum
relative indirect power for low harmonic rectifiers.
(a)
S11 S12
S12
S11
(b)
S21 S22
S21
S22
Fig. 4 Ac (left) and dc circuits (a) boost cell, (b) buck cell
-
7/28/2019 Buck-boost-pwm-converters Having Two Independently Controlled Switches
3/6
-
7/28/2019 Buck-boost-pwm-converters Having Two Independently Controlled Switches
4/6
conduction loss at low ac line input because of the additional
conduction loss of the buck transistor. It is desired to find out
other two-switch buck-boost converter topologies and
compare their performances in terms of component
conduction losses and stresses.
III. SYNTHESIS OF PWM DC-TO-DC
CONVERTERS
The synthesis method introduced in [1] is based on the
equivalent circuits of a PWM dc-to-dc converter at ac and dc,
which are, in the limit, valid for switching frequency
components and dc components, respectively. In ac
equivalent circuits, the voltage sources and filter capacitors
are shorted, while the current sources and filter inductors are
removed. In dc equivalent circuits, the filter capacitors are
removed and the filter inductors are shorted. Therefore, only
the switches remain in both equivalent circuits of a PWM dc-
to-dc converter. For example, Fig. 4 represents the ac and dc
circuits of simple boost and buck converters. Compared to
earlier synthesis methods [6][7], instead of dealing with thelarge number of possible connections of switches, reactive
elements, supplies and loads, this method considers possible
ac and dc circuits having only switch elements. Furthermore,
there are formulation rules of ac circuits and topological
connections between ac and dc circuits that can quickly
narrow down the scope. Also, a method of inserting the
minimum number of inductors and capacitors to realize
complete PWM converters from respective ac and dc circuits
is described in [1].
IV. DERIVATION OF TWO-SWITCH BUCK-BOOST
TOPOLOGIES
The two-switch converters investigated in this paper can
work functionally as either a boost or a buck converter
depending on the input/output conditions. Such converters
can therefore be considered connections of the buck and the
boost converter. For example, the converters in Fig. 3 are
cascade connections of the buck and the boost converter.
Their equivalent dc circuits, shown in Fig. 6(a),(b)
respectively, are cascade connections of those of the buck and
the boost cells of Fig. 4. Their ac circuits, shown in Fig. 5(a),
are those of the boost and the buck cells connected at a single
node.
Following the considerations above, new buck-boost
converters that meet the minimum indirect power objectivecan be found by identifying other possible connections of the
boost and the buck cells, together with the appropriate control
schemes. In addition to the cascade connections, we have
found that interleaved and superimposed connections lead to
several new two-switch buck-boost converters. Cascaded,
interleaved and superimposed classes of two-switch buck-
boost converters are summarized in this section. Their ac and
dc circuits are presented in Fig. 5 and Fig. 6 respectively.
A. Cascaded connectionIn addition to the converters shown in Fig. 3, there are two
other configurations shown in Fig. 7 and 8 respectively,
having the same equivalent ac and dc circuits, and two
inductors. For converters of these two families, the following
control sequence is applied to achieve the minimum indirect
power delivery: (1) when the input voltage is smaller than the
output voltage, PWM control applies to the boost cell, while
the transistor (S21) of the buck cell is always on. The
converter works as a boost converter; (2) when the input
voltage is greater than the output voltage, PWM control
applies to the buck cell, while the diode (S12) of the boost cell
is always on. The converter works as a buck converter. All
these converters share the same overall conversion ratio:
1
21
d
dM
= (1)
where d1 and d2 are the duty ratio of the boost and the buckcell, respectively.
B. Interleaved connectionTwo families of topologies are derived from interleaved
connection. In the dc circuits of this class, shown in Fig.
6(c),(d), the buck (boost) cell is separated from the boost
(buck) cell, and would regain its functionality provided that
one of the boost (buck) switches is closed. The interleaved
topologies have the same ac circuits as the cascaded
topologies and thus have the same control sequence applied
to achieve the minimum indirect power. The family of
converters in which the boost cell is separated is named Boost
Interleaved Buck-Boost converter (BoIBB), and has the
following overall conversion ratio:
1
12
1 d
ddM
+= (2)
There is only one BoIBB with two inductors. The
converter is shown in Fig. 9.
The family of converters where the buck cell is separated is
named BuIBB, and has following overall conversion ratio:
)1
(
1
1
12
d
dd
M
+
= (3)
There is only one BuIBB with two inductors. It is shown in
Fig. 10.
C. Superimposed connectionFig. 5(b) shows another possible ac circuit and the control
sequence that meet the requirement of minimum indirect
power delivery. In each subinterval, there is one and only one
switch conducting. The duty ratios obey:
122211211 =+++ dddd (4)
-
7/28/2019 Buck-boost-pwm-converters Having Two Independently Controlled Switches
5/6
where d11, d12, d21, and d22 are the duty ratio of S11, S12, S21and S22 switch, respectively. Fig. 6(e) is the equivalent dc
circuit that can be identified as superimposed connection of
the buck and the boost cells. Notice that in both ac and dc
circuits, S12 and S21 are in parallel. One of these switches is
redundant. Fig. 5(c) and Fig. 6(f) show the ac and dc circuits
obtained by removing this redundant switch. The control
scheme then becomes:
1321 =++ ddd (5)
with d1 to d3 representing duty ratio of the switches S1 to S3 in
Fig. 5(c) and Fig. 6(f). The switch S2 is playing the role ofS12when the boost cell is active, and S21 when PWM control is
applied to the buck cell. The overall conversion ratio is:
32
21
dd
ddM
+
+= (6)
The results from the realization procedure are two two-
switch converters with two inductors shown in Fig. 11. A
voltage-bidirectional switch is needed to realize S2. The
converter with continuous output current is named BuSBB,
while the converter with continuous input current is named
BoSBB.
V. PERFORMANCE COMPARISONS IN PFC
APPLICATIONS
In this section, the performance of two-switch buck-boost
converters as universal-input power-factor-correctors will be
evaluated and compared to performance of the boost and the
single-switch buck-boost converters in terms of component
stresses, conduction losses and size of magnetics. It is
assumed that converters are operating in continous
conduction mode (CCM).
A. InductorsTwo items are considered here: (1) volt-seconds applied
during a switching period and (2) rms current. These are the
main factors that determine the inductor size.
An inductor in a two-switch buck-boost converter can play
one of three possible roles: (1) as the input inductor of the
boost cell, (2) as the output inductor of the buck cell, (3) asan inactive low-frequency filter. Table I shows the
functionality that the inductors take in two parts of the ac line
input: boost mode, when the input voltage is lower than the
output, and buck mode, when the input voltage is higher than
the output. It is interesting to note that L1 in all topologies
works as the boost inductor in the boost mode, and L2 as a
buck inductor in the buck mode. Their roles in the other
mode are quite different. For those converters where L1 and
L2 always have the same functionality, the inductors can be
coupled on the same magnetic core.
The equations of volt-seconds applied in a switching
period for all three inductor types are shown in Table II,
where the last row stands for the inductor(s) in single-switch
buck-boost converters (SSBB). Using these equations, the
total volt-seconds applied for boost, single-switch buck-boost
and two-switch buck-boost converters are ploted in Fig 12 as
functions of time over one half of the ac line cycle. Three
curves are shown, based on different rms input voltages and a
fixed switching frequency of 100 kHz. For single-switch and
two-switch buck-boost converters, the output voltage is set to
325V, while the boost dc output voltage is 450V. The peak
volt-seconds applied to the inductors for all two-switch buck-
boost converters has the smallest value of 0.812 (mvs),
compared to 1.8 (mvs) for all single-switch buck-boost
converters, and 1.125 (mvs) for boost converter.
TABLE ITHE FUNCTIONALITY OF INDUCTORS IN TWO-SWITCH BUCK-
BOOST CONVERTERS
L1 (L) L2
BoostMode
BuckMode
BoostMode
BuckMode
BuCBB Boost Buck Boost Buck Cascaded
BoCBB Boost Filter Filter Buck
BuIBB Boost Buck Filter Buck Interleaved
BoIBB Boost Filter Boost Buck
SuperposedBuSBB and
BoSBBBoost Buck Boost Buck
0
0.5
1
1.5
2
2.5
3
3.5
150 200 250 300 325 350 400 450
Output Voltage(V)
BoIBB
BoSBB, BuIBB and
BuCBB
Single-Switch Buck-
Boost
BoCBB
Fig. 13 Worst-case inductor conduction losses compared to the boost
(a) (b) (c)
0
0.0004
0.0008
0.0012
0 0.5 1 1.5 2 2.5 3
Radian
vs
Vin=90Vrms
Vin=220Vrms
Vin=305Vrms
0
0.0004
0.0008
0.0012
0.0016
0.002
0 0.5 1 1.5 2 2.5 3
Radian
vs Vin=90Vrms
Vin=220Vrms
Vin=305Vrms
0
0.0002
0.0004
0.0006
0.0008
0.001
0 0.5 1 1.5 2 2.5 3
Radian
vs Vin=90Vrms
Vin=220Vrms
Vin=305Vrms
Fig. 12 The volt-seconds applied to the inductors (a) boost, (b) single-switch buck-boost, (c) two-switch buck-boost
-
7/28/2019 Buck-boost-pwm-converters Having Two Independently Controlled Switches
6/6
The different roles of inductors also lead to different
conduction losses. Numerical results of worst-case inductor
copper losses for all two-switch topologies are plotted in Fig.
13 and compared to the boost converter and the single-switch
buck-boost (SSBB) converter. The results are shown as
functions of the dc output voltage and normalized to the
copper losses in the boost converter with fixed 450V output.
Compared to the single-switch buck-boost converters, all
two-switch topologies exhibit significantly lower stresses
(volt-seconds and rms current) on inductors and can therefore
have significantly reduced size of magnetics. By
appropriately selecting the output voltage, the peak volt-seconds of inductors in all the two-switch converters can be
45% of that in the single-switch buck-boost converter and
72% of the boost converter. The inductor conduction loss in
BoIBB can be as low as 50% of the boost converter loss.
B. SwitchesThe switch voltage stress comparison is shown in Table III.
The switches in the boost cells of superimposed topologies
have the same voltage stress as the single-switch buck-boost
converters, while all other two-switch converters have lower
voltage stresses.
The worst-case main-switch conduction losses are plotted
in Fig. 14 in comparison to the boost converter and thesingle-switch buck-boost converter. In this comparison, we
assume all devices have the same on-resistance, and so we
compare the total transistor rms currents. In practice, for
same die size, the on-resistance for higher voltage rating
would be higher.
BoIBB and BoCBB have significantly lower conduction
losses (50%-70% when the output is set between 200-400V)
on switches compared to the single-switch buck-boost.
Furthermore, BoIBB shows performance comparable to the
boost converter in terms of switch voltage stresses and
conduction losses, while it has lower inductor conduction
losses (50% of the boost converter) and lower inductor volt-
seconds (72% of the boost converter). These results lead to
smaller magnetic size. Low stresses and high efficiency over
universal-input voltage range have been demonstrated in an
experimental BoIBB rectifier [8].
VI. CONCLUSIONS
Several families of two-switch buck-boost converters that
can achieve minimum indirect energy delivery are generated
through a synthesis method based on equivalent ac and dc
circuits. Two-switch converters can function as a boost or as
a buck depending on the input/output operating conditions.
Among generated two-switch converters there are several
new topologies that significantly outperform single-switch
buck-boost converters in terms of switch and inductor
stresses. One of the new two-switch buck-boost converters
(Boost Interleaved Buck-Boost, or BoIBB) is identified with
switch stresses significantly smaller than in cascaded buck-
boost converters, and with lower copper losses and smaller
magnetic size compared to the boost converter. In powerfactor correction applications, further advantages of this new
configuration include the ability to choose the output dc
voltage arbitrarily, and the absence of the inrush current
problem.REFERENCES
[1] D. Zhou, "Synthesis of PWM Dc-to-Dc Power Converters, Ph.D.
thesis, California Institute of Technology, October 1995.[2] P. Lee, Y. Lee, D. Cheng, and X. Liu, Steady-State Analysis of an
Interleaved Boost Converter with Coupled Inductors, IEEE Trans. on
Industrial Electronics, Vol. 47, No. 4, August 2000, pp787-795.
[3] B. Lin and H. Lu, A Novel PWM Scheme for Single-Phase Three-Level Power-Factor-Correction Circuit, IEEE Trans. On Industrial
Electronics, Vol. 47, No. 2, April 2000.
[4] D. Maksimovic and R. Erickson, Universal-Input, High-Power-Factor,Boost Doubler Rectifiers, Proc. IEEE APEC, 1995 Record, pp. 459-
465.
[5] D. Wolaver, Fundamental Study of Dc to Dc Conversion System,Ph.D. thesis, Massachusetts Institute of Technology, January 1969.
[6] R. Erickson, Synthesis of Switched-Mode Converters, Proc. IEEE
PESC, June 1983, pp. 9-22.[7] D. Maksimovic, Synthesis of PWM and Quasi-Resonant Dc-to-Dc
Power Converters, Ph.D. thesis, California.
[8] J. Chen, D. Maksimovic and R. Erickson, A New Low-Stress Buck-Boost Converter for Universal-Input PFC Applications, Proc. IEEE
APEC, March 4-8 2001, pp. 343-349.
TABLE IIVOLT-SECONDS OF DIFFERENT INDUCTORS
Boost So
MM Tt
V
VtVsv = )sinsin( 2
2
Buck SM
oo T
tV
VVsv = )
sin(
2
Filter 0
SSBB SMo
Mo TtVV
tVVsv +
=
sinsin
Vo : output voltage, VM: peak input voltage, Ts : switching period
0.5
1
1.5
2
2.5
150 200 250 300 325 350 400 450
Output Voltage(V)
BoSBB
Single-Switch
Buck-BoostBoCBB and
BoIBBBuCBB and
BuIBB
Fig. 14 Worst-caseswitch conduction losses compared to the boost
TABLE IIICOMPARISON OF SWITCH VOLTAGE STRESS
Q1 Q2 D1 D2
Boost Vo VoSingle-
switch Buck-boost Vm+Vo Vm+Vo
BuCBB Vo Vm Vo VmCascaded
BoCBB Vm Vm Vo Vm
BuIBB Vm Vm Vo VmInterleaved
BoIBB Vo Vm Vo Vm
Superposed BuSBB andBoSBB
Vm+Vo Vm D3:Vm+VoVm