A Zero-Voltage Switching Two-Inductor Boost Converter With an Auxiliary Transformer Quan Li and Peter Wolfs Central Queensland University Rockhampton Mail Center, QLD 47, Australia Abstract-The two-inductor boost converter with an auxiliary transformer has been previously proposed for the applications where a large difference between the input and the output voltages is required. In the isolated version of the converter implementation, however, the leakage inductance of the high frequency isolation transformer presents an adverse effect and will cause significant voltage ringing on the primary switches. This paper presents a resonant version of this converter which is able to actively utilize the transformer leakage inductance as well as the MOSFET drain source capacitance. The resonant arrangement produces soft-switching conditions for both the primary MOSFETs and the output rectifier diodes. The detailed resonant state analysis is provided in the paper. The simulation waveforms are also produced for one specific operating condition. Finally, the experimental waveforms of a 1-MHz 1-W converter are provided to verify the theoretical analysis. I. INTRODUCTION The two-inductor boost converter was developed by applying the duality principle to the conventional voltage-fed half bridge converter [1]. This converter presents the boost feature and has extensive applications where an input of a low voltage and a high current is required to be transformed to an output of a high voltage []-[11]. In order to achieve the voltage regulation over a wide load or input voltage range, a variation of the converter has been proposed by employing an auxiliary transformer with a unity turns ratio to couple the two input inductor currents. The non-isolated version of the converter is shown in Fig. 1 [1], [13]. This topology is suitable for the applications where the difference between the input and output voltages is large. In the applications such as uninterrupted power supplies and grid interactive photovoltaic (PV converters, dual grounding is normally required and this is better dealt with the converter topology galvanically isolated by a high frequency transformer [14], [15]. The isolated version of the two-inductor boost converter with an auxiliary transformer is shown in Fig. [1], [13]. However, this topology does not tolerate high transformer leakage inductance, which causes higher voltage stress on the primary switches. This adverse effect will be exacerbated with higher switching frequencies and reasonable converter efficiency can be hardly achieved. This paper presents a resonant version of the converter shown in Fig. by employing additional resonant inductor and capacitors. The arrangement is able to absorb the transformer leakage inductance and the MOSFET drain source capacitance into the resonant tank and create a zero voltage across the primary switches at turn on. Consequently, zero-voltage switching (ZVS condition can be achieved and the switching loss at switch turn on will be completely removed. A detailed resonant state analysis is provided for the ZVS two-inductor boost converter with an auxiliary transformer for one complete switching period. Simulation waveforms are produced for one operating condition. In order to verify the theoretical analysis, the experimental waveforms of a 1-MHz 1-W converter are also given at the end of the paper and they agree reasonably well with the simulation waveforms. T E L 1 L R V O Q 1 Q D 1 D C 1 C Fig. 1. Two-inductor boost converter with an auxiliary transformer E L 1 L R V O T T D 1 T 1 C 1 Q 1 Q Fig.. Isolated two-inductor boost converter with an auxiliary transformer D C II. ZVS TWO-INDUCTOR BOOST CONVERTER WITH AN AUXILIARY TRANSFORMER Fig. 3 shows the ZVS two-inductor boost converter with an auxiliary transformer. Three resonant components including one resonant inductor and two resonant capacitors are 8 Australasian Universities Power Engineering Conference (AUPEC'8 Paper P-76 page 1
employed in addition to the original converter shown in Fig.. In Fig. 3, the resonant inductance L r is the lump sum of the additional resonant inductance in series with the transformer T primary winding and the transformer leakage inductance reflected to the transformer primary winding. The resonant capacitance C 1 = C = C r is the lump sum of the additional resonant capacitance in parallel with each MOSFET and the drain source capacitance of each MOSFET. D Q1 and D Q are respectively the reverse body diodes of the MOSFETs Q 1 and Q. When the MOSFET turns off, L r resonates with C 1 or C, producing quasi-sinusoidal voltage waveform across the MOSFET. The MOSFET drain source voltage naturally falls back to zero and at this instant the MOSFET will turn on to achieve ZVS operation. In order to simplify the converter analysis, Fig. 4 shows the equivalent circuit of the converter shown in Fig. 3. In Fig. 4, the transformer T 1 is modelled by an ideal transformer with 1:1 turns ratio. The transformer T 1 leakage inductance is small enough to be considered as a short circuit and its magnetizing inductance is large enough to be considered as an open circuit. T 1p and T 1s are respectively the auxiliary transformer primary and secondary windings. All other semiconductor components are also considered to be ideal components. As the auxiliary transformer T 1 is an ideal transformer, the following voltage and current relationships can be obtained: vt p vt1s 1 = (1 dil 1 dil = ( dt dt T 1 D 1 C 3 E L 1 L R V O L r T T Q 1 D Q1 C 1 C D Q Fig. 3. ZVS two-inductor boost converter with an auxiliary transformer v T1p Q D Q 1 C 1 v C1 v C C Q D C 4 T 1p T 1s v T1s D 1 C 3 i L1 i L E v L1 L 1 v L R V O i Lr L r T T C 4 Fig. 4. Simplified ZVS two-inductor boost converter Applying KVL to the circuit diagram in Fig. 4 yields: E = vt1p vl1 vc1 (3 E = v v v (4 T1s L C The voltages across the two inductors v L1 and v L can be written as: dil1 vl1 = L1 dt (5 dil vl = L dt (6 If L 1 = L, manipulations of (1 to (6 yield: v T1p vc vc1 = vt1s = (7 Eq. (7 confirms that the voltage across the primary or the secondary winding of the auxiliary transformer is half of the difference of the two MOSFET drain source voltages at all times. III. RESONANT STATE ANALYSIS In the resonant state analysis, the following two further assumptions are made: The two input inductors L 1 and L are large enough so that they can be modelled by the dc current source I. The two output capacitors C 3 and C 4 are large enough so that their voltages reflected to the transformer primary winding can be modelled by the dc voltage source V d. In the operation of the two-inductor boost converter, it is required that the switching duty ratio be greater than 5% to provide a continuous current path for the two input inductors [1]. The ZVS two-inductor boost converter will go through up to eight resonant states within one switching period and these are shown in Fig. 5. Fig. 6 shows the key resonant waveforms. In the following resonant state analysis, the angular resonance frequency ω and the characteristic impedance Z of the resonant tank are respectively defined as: 1 ω = L (8 r C r Lr Z = (9 C According to Fig. 5, MOSFET Q is on in States (a to (d and v C (t = while MOSFET Q 1 is on in States (e to (h and v C1 (t =. State (a ( t t 1 This state starts when Q 1 turns off. The initial conditions in State (a are i Lr ( = I La and v C1 ( =, where I La >. In this state, the current in the resonant inductor is still negative. This current and the current source I charge the capacitor C 1 and the resonant inductor current decreases. r 8 Australasian Universities Power Engineering Conference (AUPEC'8 Paper P-76 page
I C 1 L r v C1 i Lr V d v C C I I L r i Lr V d C 1 v C1 v C C I conditions in State (c are i Lr (t = and v C1 (t = V Cc. In this state, the capacitor C 1 resonates with the inductor L r. v GQ1 I State (a L r i Lr V d C 1 v C1 v C C I I State (b L r i Lr V d C 1 v C1 v C C I v GQ t t State (c State (d v C1 I L r i Lr V d L r i Lr V d C 1 v C1 v C C I I C 1 v C1 v C C State (e State (f I V Cc V Cb I L r i Lr V d L r i Lr V d C 1 v C1 v C C I I C 1 v C1 v C C I v C t State (g Fig. 5. Eight resonant states State (h The capacitor voltage v C1 and the inductor current i Lr are respectively: vc1 = ( I I La Z sinω t cosωt (1 ilr = sin ω t ( I I La cosωt I Z (11 This state does not exist if I La =. State (b (t 1 t t This state starts when the current in the resonant inductor reaches zero and V d reverses its polarity. If the capacitor voltage v C1 is still lower than V d, the diode D 1 in voltagedoubler rectifier is reverse biased. The resonant inductor and the transformer primary winding are decoupled from the remaining primary circuit and the current source I linearly charges the capacitor C 1. The initial conditions in State (b are i Lr (t 1 = and v C1 (t 1 = V Cb. The capacitor voltage v C1 and the inductor current i Lr are respectively: I v C1 = ( t t1 VCb (1 Cr i Lr = (13 V Cc V Cb i Lr I Ld I La I La I Ld v T1p t t t This state does not exist if I La is large enough to cause v C1 to exceed V d at the end of State (a. State (c (t t t 3 This state starts when v C1 reaches V d at the end of State (b or i Lr reaches zero if State (b does not exist. The initial t 1 t t 3 t 4 t 5 t 6 t 7 t 8 Fig. 6. Key resonant waveforms 8 Australasian Universities Power Engineering Conference (AUPEC'8 Paper P-76 page 3
The capacitor voltage v C1 and the inductor current i Lr are respectively: v C1 i Lr = I Z sinω ( t t ( V V = Cc I Cc Z V cosω ( t t V V d d cosω ( t t sin ω ( t t I d (14 (15 State (d (t 3 t t 4 This state starts when v C1 reaches zero and Q 1 can turn on at any instant between t 3 and t 4. The initial conditions in State (d are i Lr (t 3 = I Ld and v C1 (t 3 =. In this state, the resonant inductor is discharged by V d and the inductor current linearly decreases. The capacitor voltage v C1 and the inductor current i Lr are respectively: v C 1 = (16 ilr = I Ld ( t t3 L (17 State (e (t 4 t t 5 This state starts when Q turns off. As the converter operation is half cycle symmetrical, the initial conditions in State (e are i Lr (t 4 = I La and v C (t 4 =. The capacitor voltage v C and the inductor current i Lr are respectively: vc = ( I I La Z sin ω ( t t4 cosω ( t t4 ilr = sinω ( t t4 Z ( I I cosω ( t t I Same as State (a, this state does not exist if I La =. La r 4 (18 (19 State (f (t 5 t t 6 This state starts when the current in the resonant inductor reaches zero and V d reverses its polarity. If the capacitor voltage v C is still lower than V d, the diode D in voltagedoubler rectifier is reverse biased and this decouples the resonant inductor and the transformer primary winding from the remaining primary circuit. The current source I linearly charges the capacitor C. The initial conditions in State (f are i Lr (t 5 = and v C (t 5 = V Cb. The capacitor voltage v C is: I v C = ( t t5 VCb ( Cr The inductor current i Lr is given by (13. Same as State (b, this state does not exist if I La is large enough to cause v C to exceed V d at the end of State (e. State (g (t 6 t t 7 This state starts when v C1 reaches V d at the end of State (f or i Lr reaches zero if State (f does not exist. The initial conditions in State (g are i Lr (t 6 = and v C (t 6 = V Cc. In this state, the capacitor C resonates with the inductor L r. The capacitor voltage v C and the inductor current i Lr are respectively: v C i Lr = I Z sinω ( t t6 ( VCc cosω ( t t6 VCc = sin ω ( t t6 Z I cosω ( t t I 6 (1 ( State (h (t 7 t t 8 This state starts when v C reaches zero and Q can turn on at any instant between t 7 and t 8. In this state, the resonant inductor is charged by V d and the inductor current linearly increases. The initial conditions in State (h are i Lr (t 7 = I Ld and v C (t 7 =. The capacitor voltage v C and the inductor current i Lr are respectively: v C = (3 ilr = I Ld ( t t7 L (4 IV. SIMULATION WAVEFORMS The simulation of the ZVS two-inductor boost converter with an auxiliary transformer is performed with SIMULINK. The simulation circuit model can be obtained from [16]. The key circuit parameters are listed as follows: Input voltage E = V and output voltage V O = 34V. Auxiliary transformer T 1 turns ratio 1:1. Input inductor L 1 = L = 67.6 µ H. Resonant inductance L r =.8 µ H. Resonant capacitance C1 = C = 7. 85 nc. Isolation transformer T turns ratio 1:3.96. Load resistance R = 1156 Ω. Initial inductor current I La =. Device switching frequency f s = 5 khz or the converter switching frequency f c = 1 MHz. Switching duty ratio D = 61.6%. s Fig. 7 shows the selected simulation waveforms in the ZVS two-inductor boost converter with an auxiliary transformer. They respectively show the waveforms of the gate and drain source voltages of the MOSFETs Q 1 and Q, the resonant inductor or the transformer T primary winding current and the auxiliary transformer primary or secondary voltage. It can be seen that under the selected operating condition, the converter only goes through six resonant states including States (b, (c, (d, (f, (g and (h defined in Section III. r 8 Australasian Universities Power Engineering Conference (AUPEC'8 Paper P-76 page 4
MOSFET Q 1 Gate Voltage v GQ1 (V 15 1 5 1 1 3 4 5 6 7 8 t (µs MOSFET Q Gate Voltage v GQ (V 15 1 5 1 1 3 4 5 6 7 8 t (µs Capacitor C 1 Voltage v C1 (V 8 6 4 Capacitor C Voltage v C (V 8 6 4 Inductor L r Current i Lr (A 1 3 4 5 6 7 8 1 8 6 4 - -4-6 -8 t (µs -1 1 3 4 5 6 7 8 t (µs Transformer T 1 Primary Voltage v T1p (V 1 3 4 5 6 7 8 5 4 3 1-1 - -3-4 Fig. 7. Simulation waveforms t (µs -5 1 3 4 5 6 7 8 t (µs V. EXPERIMENTAL WAVEFORMS In order to verify the theoretical analysis, a prototype 1-W converter was built in the laboratory. The converter has an input voltage of V and an output voltage of 34 V. The key components used in the converter are listed as follows: Auxiliary transformer T 1 Core type Ferroxube ETD39, gapped, ferrite grade Ferroxube 3F3, primary winding 8 Australasian Universities Power Engineering Conference (AUPEC'8 Paper P-76 page 5
N T1 p = 14 turns, secondary winding N 14 turns. T1 s = Inductors L 1 and L Core type Siemens RM1, A L = 4 nh, ferrite grade Siemens N48, inductor winding N L = 13 turns. Isolation transformer T Core type Ferroxube ETD9, gapless, ferrite grade Ferroxube 3F3, primary winding N T p = 5 turns, secondary winding N T s = turns, leakage inductance reflected to the transformer primary L le =.15 µh. Additional Resonant Inductor Core type air core toroidal,.65 µh inductance. Additional Resonant Capacitors Cornell Dubilier surface mount mica capacitor MCFD1J, 1 nf, 7 nf capacitance in parallel with each MOSFET. MOSFETs Q 1 and Q ST STB5NE1, V DS = 1 V, I D = 5 A, R DS(on =. 7 Ω, C oss =. 675 nf. Diodes D 1 and D ST STTA16U, I F = 1. A, V RRM = 6 V, V F = 1. 5 V. Capacitors C 3 and C 4 Murata Electronics multilayer ceramic chip capacitors GRM55DR7E15KW1L, 1 µf, rated dc voltage 5 V. Fig. 8 shows the experimental waveforms of the converter. From top to bottom, Fig. 8 respectively shows the waveforms of the MOSFET Q 1 gate voltage, the MOSFET Q 1 drain source voltage, the auxiliary transformer T 1 primary winding voltage and the resonant inductor L r current. The waveforms compare well with the simulation waveforms and confirm that the MOSFET turns on at zero voltage. When both MOSFETs are on, the voltage across the auxiliary transformer primary winding is not zero as shown in the waveform in Fig. 7. This is due to parasitic components in the auxiliary transformer such as leakage inductance and winding capacitance. VI. CONCLUSIONS This paper proposes a ZVS two-inductor boost converter with an auxiliary transformer. The converter employs a resonant tank made up from one resonant inductor and two resonant capacitors. The arrangement is able to actively utilize the parasitic components including the transformer leakage inductance and the MOSFET drain source capacitance and the switching loss can be removed. All eight possible resonant stages are studied in detail in the converter analysis. Both of the simulation and the experimental waveforms of the key resonant waveforms in a prototype 1-MHz 1-W converter are provided at the end of the paper and they can validate the theoretical analysis. REFERENCES [1] P. J. Wolfs, A current-sourced dc-dc converter derived via the duality principle from the half-bridge converter, IEEE Trans. Ind. Electron., Vol. 4, No. 1, pp. 139-144, Feb. 1993. [] G. Ivensky, I. Elkin and S. Ben-Yaakov, An isolated dc-dc converter using two zero current switched IGBTs in a symmetrical topology, in Proc. IEEE PESC, 1994, pp.118-15. [3] W. C. P. De Aragao Filho and I. Barbi, A comparison between two current-fed push-pull dc-dc converters analysis, design and experimentation, in Proc. IEEE INTELEC, 1996, pp. 313-3. [4] J. Kang, C. Roh, G. Moon and M. Youn, Phase-shifted parallelinput/series-output dual converter for high-power step-up applications, IEEE Trans. Ind. Electron., Vol. 49, No. 3, pp. 649-65, Jun.. [5] Y. Jang and M. M. Jovanovic, A new soft-switched dc-dc front-end converter for applications with wide-range input voltage from battery power sources, in Proc. IEEE INTELEC, 3, pp. 77-777. [6] Y. Jang, M. M. Jovanovic and Y. Hu, Non-isolated two-inductor boost converter with improved EMI performance, in Proc. IEEE INTELEC, 5, pp. 491-496. [7] L. Yan and B. Lehman, Isolated two-inductor boost converter with one magnetic core, in Proc. IEEE APEC, 3, pp. 879-885. [8] L. Yan and B. Lehman, An integrated magnetic isolated two-inductor boost converter: analysis, design and experimentation, IEEE Trans. Power Electron., Vol., No., pp. 33-34, Mar. 5. [9] X. Gao and R. Ayyannar, A novel buck-cascaded two-inductor boost converter with integrated magnetics, in Proc. IEEE INTELEC, 4, pp. 19-197. [1] Q. Li and P. Wolfs, The analysis of the power loss in a zero-voltage switching two-inductor boost cell operating under different circuit parameters, in Proc. IEEE APEC, 5, pp.1851-1857. [11] Q. Li and P. Wolfs, A current fed two-inductor boost converter with lossless snubbing for photovoltaic module integrated converter applications, in Proc. IEEE PESC, 5, pp. 111-117. [1] Y. Jang and M. M. Jovanovic, "Two-inductor boost converter," U.S. Patent 6 39 584, 9 May 1. [13] Y. Jang and M. M. Jovanovic, New two-inductor boost converter with auxiliary transformer, in Proc. IEEE APEC,, pp. 654-66; also IEEE Trans. Power Electron., Vol. 19, No. 1, pp. 169-175, Jan. 4. [14] Y. Xue, L. Chang and P. Song, Recent developments in topologies of single-phase buck-boost inverters for small distributed power generators: an overview, in Proc. IPEMC, 4, pp. 1118-113. [15] Y. Xue, L. Chang. S. B. Kjær; J. Bordonau and T. Shimizu, Topologies of single-phase inverters for small distributed power generators: an overview, IEEE Trans. Power Electron., Vol. 19, No. 5, pp. 135-1314, Sept. 4. [16] Q. Li and P. Wolfs, Variable frequency control of the zero-voltage switching two-inductor boost converter, in Proc. IEEE PESC, 5, pp. 667-673. 5.V Fig. 8. Experimental waveforms 8 Australasian Universities Power Engineering Conference (AUPEC'8 Paper P-76 page 6