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1Buck-Boost PWM Converters Having

Two Independently Controlled Switches

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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.


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


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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)


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


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

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