Buck-Boost PWM Converters Having Two Independently Controlled Switches

I

Jingquan Chen, Dragan MaksimoviC and Robert Erickson

Energy Storage ElenleNs I

Colorado Power Electronics Center Department of Electrical and Computer Engineering

University of Colorado at Boulder Boulder, CO 80309-0425. USA

Abstract - Single-switch step-uplstep-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 111, families of two-switch buck-boost converters are generated, including several new converter 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 factor correction (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 same time. 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 11, we begin with an introduction of how the power transfer mechanisms in switching converters affect the component stresses. The converter synthesis method described in [l] 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 111. 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 in Section V, and new converters that outperform previously known topologies are highlighted.

11. 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, Pindirec,, is processed by the switching devices using the

L--------------- U I (b) r---------------

I Single-switch Buck- I I Boost Converter I

I

Input #FiT,f$ Load

Pmdvrcl P z n d m o 1 I I I I I I

Fig. 1 Energy flow chart (a) boost and buck converter; (b) single-switch

_ _ _ _ _ _ _ _ _ _ _ _ _ _ - -

buck-boost converter.

This work is supported by Philips Research, Briarcliff Manor, NY, through Colorado Power Electronics Center

0-7803-7067-8/01/$10.00 02001 IEEE 736

single-wltch buck-boost, flyback, Cuk or SEPIC

I

V l o ! 0.5 1 1.5 2 2.5

1

0.8

0.6

0.4

0.2

0 I 0 0.5 I I .5 2 2.5 3

Fig. 2 (a) Relative indirect power for dc-to-dc converters; (b) minimum relative indirect power for low harmonic rectifiers.

inductor for intermediate energy storage. The remainder of the input power, Pdjrecf, flows directly to the output, bypassing the intermediate process. Fig. l(a) illustrates the energy flow process in the boost and buck converters. The ability of providing direct energy path leads to lower component stresses, lower energy storage and higher efficiency. In single-switch step-uplstep-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. l(b). As a result, component stresses and energy storage requirements are higher. Figure 2(a) illustrates the relative indirect power Pin~irecJP for the dc-to-dc buck, boost and single-switch step-up/step-down converters, as a function of Vj,,/Vo.

In universal-input (85Vm,-264V,,) 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-uplstep-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 V,lV,, where V , is the peak ac line input voltage and V, is the

1 I

Fig. 3 Cascaded two-switch buck-boost topologies: (a) boost-buck- cascaded, (b) buck-boost-cascaded.

"'v".. .\

Fig. 4 Ac (left) and dc circuits (a) boost cell, (b) buck cell

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 is therefore 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. When the 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

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Fig. 5 Ac circuits for two-switch buck-boost converters: (a) cascaded connection and interleaved connection, (b) superimposed connection, (c) superimposed connection topologies with reduced number of switches.

JE I 0,

Fig. 6

Vg(] Fig. 7

1 Y 1 U m

1 ii 4

c, I\ 77% f: R.

JE a, L1

Dc circuits for two-switch buck-boost converters: (a) buck cascaded by boost, (b) boost cascaded by buck, (c) buck interleaved by boost, (d) boost interleaved by buck, (e) buck boost superimposed, (f) reduced order of buck boost superimposed.

Other buck-cascaded-by-boost (BuCBB) converters with two inductors.

Fig. 8 inductors.

two

Fig. 9

Fig. 10

(a)

(b)

Fig. 1

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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.

111. SYNTHESIS OF PWM DC-TO-DC CONVERTERS

The synthesis method introduced in [l] 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 the large 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 [I].

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 objective can 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 connection In 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 (SZ,) 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 (SIz) of the boost cell is always on. The converter works as a buck converter. All these converters share the same overall conversion ratio:

(1)

where dl and d2 are the duty ratio of the boost and the buck cell, respectively.

1-d2 M = - dl

B. Interleaved connection Two 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:

(2) dl M =d2 +- 1 - dl

There is only one BoIBB with two inductors. The

The family of converters where the buck cell is separated is

(3)

converter is shown in Fig. 9.

named BuIBB, and has following overall conversion ratio: 1

1-dl

M = dl (4 +-I

There is only one BuIBB with two inductors. It is shown in Fig. 10.

C. Superimposed connection Fig. 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:

(4) d , , + d I 2 + d , , +d, , = 1

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TABLE I THE FUNCTIONALITY OF INDUCTORS IN TWO-SWITCH BUCK-

BOOST CONVERTERS

I I LI (L) I L? I Boost I Buck I Boost I Buck

Mode Mode Mode Mode BuCBB Boost Buck Boost Buck

Cascaded BoCBB Boost Filter Filter Buck

Interleaved BoIBB Boost Filter Boost Buck

Buck Boost Buck BoSBB Superposed BuSBB and Boost

where dl l , d12, d2], and d22 are the duty ratio of SI1, SI2, S2] and 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 S?1 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:

d , + d 2 + d 3 =1 ( 5 ) with d l to d3 representing duty ratio of the switches SI to S3 in Fig. 5(c) and Fig. 6(f). The switch S2 is playing the role of SI2 when the boost cell is active, and S21 when PWM control is applied to the buck cell. The overall conversion ratio is:

(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.

M = - dl + d2 d 2 + d 3

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).

t BoSBB. BulBB and BuCBB

-4-SwkSwitch B u d - Barst

Fig. 13 Worst-case inductor conduction losses compared to the boost

A . Inductors Two 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) as an 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 LI 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.

+ W ~ V r m . M +vln.9ovn. - - C W r n V r m S om- ..._.. Wh305vnn

--cvn-z2ovrm* . ._. . . .-. -vn9ffivn. ___. _.-. .-. . .__ M

om12

0 0 1 2 -

.. 1 ... d. 1 .

Fia. 12 The volt-seconds applied to the inductors (a) boost, (b) single-switch buck

140

Boost

V, : output voltage, VM : peak input voltage, T, : switching period

TABLE111

v . s=~ , l s in~I - - s in v; . 2 w).T, vn

COMPARISON OF SWITCH VOLTAGE STRESS

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 . Switches The 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 the single-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 200-4OOV) on switches compared to the single-switch buck-boost. Furthermore, BoIBB shows performance comparable to the

0.5 4 ! 150 200 250 300 325 350 400 450

Fig. 14 Worst-case switch conduction losses compared to the boost

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 inputloutput 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 power factor 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

D. Zhou, “Synthesis of PWM Dc-to-Dc Power Converters,” Ph.D. thesis, California Institute of Technology, October 1995. 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. 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. D. Maksimovic and R. Erickson, “Universal-Input, High-Power-Factor, Boost Doubler Rectifiers,” Proc. IEEE APEC, 1995 Record, pp. 459- 465. D. Wolaver, “Fundamental Study of Dc to Dc Conversion System,” Ph.D. thesis, Massachusetts Institute of Technology, January 1969. R. Erickson, “Synthesis of Switched-Mode Converters,’’ Proc. IEEE PESC, June 1983, pp. 9-22. D. Maksimovic, “Synthesis of PWM and Qua.i-Resonant Dc-to-Dc Power Converters,” Ph.D. thesis, California. 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.

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