A RESONANT HALF BRIDGE DUAL CONVERTER Quan Li and Peter Wolfs Central Queensland University Abstract The half bridge dual converter has been previously presented by the authors for applications in photovoltaic module integrated power converters (MIC). While this relatively new converter is potentially very suitable for converting high current low voltage supplies to higher voltage levels, it does require very low transformer leakage inductance when operated in a hard-switched mode. This paper presents a resonant form of this converter which can actively utilise the primary-secondary leakage inductance as well as the mosfet drain-source capacitance. Experimental results are presented for a 1MHz, 85W converter for a MIC application. 1.

INTRODUCTION

In the design of the pulse-width-modulated DC-DC converters, a high power packing density and a high power conversion efficiency are extremely desirable. In order to obtain a high power packing density, engineers prefer increasing the switching frequency to minimise the size of the magnetic components in the converter. However, significant switching loss can occur due to high voltage and high current overlaps during the switching period. The advantage of high switching frequency can easily be cancelled out by the low conversion efficiency. Resonant switching techniques have been used in high frequency DC-DC converters for more than fifty years, [1]. Theoretically, resonant converters have no switching loss and are more suitable for high frequency operations. The switches in resonant converters turn on and off under zero current and/or zero voltage and there is no switching loss. According to the underlying operation principles of the resonant converters, there are three main approaches, [2]: • Load-Resonant Converter (LRC), it includes a resonant tank leading to oscillating load voltage and current. • Quasi-Resonant Converter (QRC), its resonant network shapes the current or voltage waveform of the main switch. Each switching period has resonant and non-resonant segments and is suitable for the operation in the low megahertz range. • Multi-Resonant Converter (MRC), resonant operation is applied to both the main switch and output rectifier diodes. It is more suitable for very high frequency operation.

Resonant conversion approaches can also be characterised by the use of a zero-voltage or zerocurrent switching condition. A zero-voltage switching (ZVS) quasi-resonant half bridge dual converter, that can actively utilise the drain-source capacitance and the transformer leakage inductance, is introduced in this paper. The authors believe that this is the first resonant version of the half bridge dual converter. During the development of this converter it became clear that a range of operational modes exist. A theoretical discussion on different possible resonance conditions is presented. To verify the theoretical discussion, a resonant half bridge dual converter was designed and constructed. It is used to demonstrate the existence of one of three possible resonant operating modes. Also, operational issues for different load conditions will be discussed.

2.

RESONANT CONVERTER

Half bridge dual converters are well suited to low voltage, high current inputs. They have been proposed by the authors as attractive candidates for photovoltaic module integrated power conditioning applications, where a relatively low module voltage must be boosted to a level, typically 360Vdc, suitable for a grid interconnected inverter, [3]. In the hard-switched implementations, an important barrier to operating efficiency and high frequency operation are losses associated with parasitic circuit elements especially primary-secondary leakage inductance, transformer capacitance and mosfet drain-source capacitance. Figure 1 shows a zero-voltage switching (ZVS) topology that actively exploits the converter parasitic components. As with other ZVS converters the mosfets turn on and off when the capacitor voltage is zero and no switching loss exists, [4].

where L1

1 Lr C1

ω0 =

L2 D2 D1 Lr

E

R C1

frequency and

Z0 =

D3 D4

C2 Q2

Q1

3.

V

is the angular resonance

Lr C1

is the characteristic

impedance. vC1 reaches its peak of Vd + I0 Z0 and iLr is

t 2 = t1 +

π π . And then at t 3 = t 1 + , vC1 2ω 0 ω0

Figure 1. ZVS Half Bridge Dual Converter

I0 at

RESONANCE CONDITIONS

is Vd and iLr reaches its peak of 2I0 . In order for the capacitor voltage vC1 to reach zero at t4 , I0 Z0 must be greater than Vd . At t 4 , v C1 is zero and iLr is I2 .

An equivalent resonant circuit that can be used to analyse the switching behaviour of Q1 is shown in Figure 2. The voltage and current waveforms are shown in Figure 3. The diode D and the voltage source Vd , correspond to secondary side diodes and output filter capacitor voltage as reflected to the primary side. These components present load components to resonant currents. An initial analysis assumes at t0 that Q1 and Q2 are conducting, L1 carries a constant current I0 , the current in the resonant inductor ILr0 = 0 and the voltage across the resonant capacitor VC10 = 0. i Lr i Q1

C1

I0 Q1

D Q1

+ vC1 −

Lr

D Vd

• Stage 3 (t4 ≤ t ≤ t6 ): At t4 Q1 (or the inverse body diode) turns on and the inductor current iLr is

i Lr = I 2 −

Vd (t − t4 ) Lr

(4)

iL linearly discharges to zero at t6 . The current in Q1 would be the difference between I0 and the inductor current. In the period from t4 to t5 the inverse mosfet diode conducts as the remaining current in the inductor is greater than I0 . For this condition it is required that I0 Z0 > Vd . The mosfet must be gated on during period t5 to t6 to maintain a zero drain source voltage. In a practical implementation, turn on between t4 and t5 is easily achieved and places the mosfet into the on state when required. • Stage 4 (t6 ≤ t ≤ t7 ): After t6 , iLr stays at zero until Q2 turns off at t 7 .

Figure 2. Equivalent Resonant Circuit • Stage 1 (t0 ≤ t ≤ t1 ): Q1 is turned off at time t0 . The capacitor voltage v C1 is

vC 1 =

I0 (t − t 0 ) C1

(1)

• Stage 2 (t1 ≤ t ≤ t4 ): At t1 , the capacitor voltage reaches Vd , the diode D becomes forward biased. The capacitor voltage v C1 and the inductor current iLr are:

vC 1 = Vd + I 0 Z 0 sin ω 0 ( t − t1 )

(2)

i Lr = I 0 − I 0 cos ω o (t − t1 )

(3)

The half bridge dual converter requires that at least one of the two switches be on. In the above discussions, Q2 must turn off after Q1 turns on. The timing of this transition can generate three different modes of operation. The mode described above is referred to as the first discontinuous mode. This description is based on the inductor current behaviour, which has a prolonged period of zero current. If I0 Z0 > Vd , the converter can operate in the following three modes: • Discontinuous mode 1 – Q1 turns on between t4 and t 5 and Q2 turns off after t 6 . • Discontinuous mode 2 – Q1 turns on between t4 and t 5 and Q2 turns off between t5 and t 6 . • Continuous – Q1 turns on between t 4 and t 5 and Q2 turns off after Q1 turns on but between t4 and t5 . The Q1 mosfet inverse diode is on when Q2 turns off.

vc1 vc2 V d+I0Z

vc1

vc2

Vd t0 t1 t2 t3 t 4 iLr 2I0 I2

The equivalent circuit for each stage after the turn off of Q1 is shown in Figure 4 (Q1 turns off when the inverse diode of Q2 stops conducting). The current and voltage waveforms are shown in Figure 5. In this case, an initial current of –I0 exists in the resonant inductor. iLr Vd

t5 t 6 t7 t8 t 9 t 10 t11 t12 t13 t (a) I0

L +L C 1 +r l vC1 −

I0 t0 t1 t 2 t 3 t4

Stage 1 iLr Vd

t5 t6 t7 t8 t9 t10 t11 t12 t 13 t

-I0

iQ1 3I0

I0

I0

L +L C1 +r l vC1 − Stage 2 iLr Vd

Lr+Ll + v C1 −

Lr+Ll C2 + + vC1 v C2 − −

Stage 3

Stage 4

I0

(b) Figure 4. Equivalent Circuit of Continuous Mode • Stage 1 (t0 ≤ t ≤ tA ): The Mosfet Q1 turns off and C1 rapidly charges under the influence of the current source and the initial inductor current. The capacitor voltage v C1 and the inductor current iLr are:

2I0 I0 t 0 t1 t2 t3 t 4 I0-I2

iLr Vd

t 5 t 6 t7 t8 t 9 t10 t11 t 12 t13 t

vc1 = 2 I 0Z 0 sin ω0 (t − t 0 ) − Vd (1 − cos ω 0 (t − t 0 ))

(c)

i Lr = Figure 3. Voltage and Current Waveforms in the Resonant Converter (a) Capacitor Voltage (b) Inductor Current (c) Mosfet Current

4. CONTINUOUS MODE OPERATION The full analysis of the resonant modes of the converter depends on two key variables, the timing of the turn off of Q2 and the load condition. For this paper the analysis is simplified when a fixed switching point is assumed. We have selected the case that Q2 turns off at t5 , the point when the inverse diode of Q1 stops conducting. The converter runs in the continuous mode if the load current is large enough for I0 Z0 to exceed Vd . In this paper we select parameters that match the experimental model, I0 Z0 = 1.2Vd .

(5)

Vd sin ω 0 ( t − t 0 ) Z0 + I 0 (1 − 2 cos ω 0 (t − t 0 )) (6)

This period ends when inductor current reaches zero. This point depends on the magnitude of I0 Z0 relative to Vd . At I0 Z0 = 1.2Vd , the inductor current reaches zero at ω0 tA = 40°. The corresponding capacitor voltage VCA = 1.3Vd . • Stage 2 (tA ≤ t ≤ tC ): In this period, current is established in the inductor in the positive direction. The reflected transformer voltage reverses. For issues related to space, this analysis assumes the reversal is instantaneous but parasitic capacitances slow the transition. This effect will be seen in the experimental results. As shown in Figure 5, drain-source capacitor voltage continuously rises. For the parameters selected, capacitor voltage and inductor current are:

v c1 = I 0 Z 0 sin ω 0 (t − t A ) + Vd + (VCA − Vd ) cos ω 0 (t − t A ) (7) i Lr =

VCA − Vd sin ω 0 (t − t A ) Z0

+ I 0 (1 − cos ω 0 (t − t A ))

(8)

The capacitor voltage peaks at 2.2Vd and returns to zero at ω0 tC = 259°. At this point the inductor current ILC = 1.6I0 .

In the resonant circuit, resonant capacitors are required to be connected across the mosfets drain and source. High frequency oscillations, at frequencies up to 50 MHz were observed during experimentation, due to the Equivalent Series Inductance (ESL) of the resonant capacitor as well as the stray inductance of the leads and tracks connecting the capacitors and the mosfets. Considering the size of the mosfets, physically small capacitors are preferred because they can be paralleled with the mosfets using shorter leads and tracks. Other solutions include paralleling several capacitors to achieve a low effective stray inductance.

• Stage 4 (t ≥ tD): Q2 turns off at tD and the above cycle repeats for Q2.

Moreover, under high frequency operation, the power loss related to diode reverse recovery could be significant. This converter presents favourable conditions for the diodes, including clamping of the diode voltage to the output level, a slow current reversal due the resonance conditions, and slow voltage reversal due to junction capacitances. However a short diode reverse recovery time is still essential for a high conversion effic iency. Ultra -fast diodes must be selected in the design to obtain a low diode reverse recovery loss. In the initial prototypes, thermal run away due to reverse recovery was observed.

5. DESIGN CONSIDERATIONS

6. EXPERIMENTAL RESULTS

One of the shortcomings of the resonant converters is a higher peak voltage or current value than the conventional hard switched converters for the same output power level, [5]. Mosfets with a higher voltage or current rating are required. However, mosfets with higher voltage or current rating tend to have higher Rdson and consequently higher conduction loss for the same current level. Mosfets with small Rdson must be carefully selected in this converter in order that the decrease in the switching loss would not be offset by the increase in the conduction loss in mosfets.

The converter in the experiment is designed with I0 Z0 = 1.2Vd , running in the continuous mode. In the actual converter, each mosfet is replaced with two parallel mosfets to reduce Rdson . Also, seven monolithic ceramic capacitors are used in parallel with the mosfet in each side. Monolithic ceramic capacitors are selected because of their small size. Another advantage is its low ESL, [7]. Some of the key components and values used in the converter are:

•

Stage 3 (tC ≤ t ≤ tD): The inductor current is

i Lr = I LC −

Vd (t − t C ) Lr + Ll

(9)

where Ll is the transformer leakage inductance. The inductor current linearly declines to I0 at tE , when Q2 turns off.

Skin effects are significant in this design. The penetration depth is given in [6] as

∆ = kf −1/ 2

(10)

where k = 65.8mmHz for copper conductor at 20°C. From Equation 10, penetration depth is 0.09mm at 500kHz, the transformer and inductor excitation frequency. Therefore Litz wire must be used to obtain a low copper loss of the transformer and the resonant inductor. 1/ 2

• Transformer – Core type Philips ETD29, ferrite grade Neosid F44, Litz wire, leakage inductance = 0.34uH; • Inductor L1 and L2 – Core type Siemens RM10, ferrite grade Siemens N48; • Resonant Inductor – Core type Philips ETD39 gapped, ferrite grade Philips 3C90, Litz wire, 4.5uH; • Resonant Capacitor – Ceramic, C = 1.5nF, V = 250V; • Mosfet – Intersil RFP40N10, VDS = 100V, RDS(on) = 0.04O, ID = 40.0A; • Diode – ST STTA106U, IF = 1A, VRRM = 600V, VFM = 1.5V, t rr = 20ns; • I0 = 2.35A; • Vd = 41V.

vc1 vc2

vc1

significant improvements can be made with the magnetic components by substituting better ferrite grades. This was simply an issue of availability in small quantities of appropriate cores.

vc2

VCA

t0

tA

tB

tC tD t E

t F tG

t

(a) iLr I LC I0

Ch1

1 >

Ch2

2 >

t0

tA

tB tC tD tE

t F tG

1) Ch 1: 2) Ch 2:

t

20 Volt 500 ns 50 Volt 500 ns

(a)

-I 0 -I LC (b) vLr VL0Lr /L

1>

-VL0Lr/L

t0

tA

tB

tC tD tE

tF t G

t 1) Ch 2:

1 Ampere 500 ns

(b)

(c) Figure 5. Current and Voltage Waveforms (a) Capacitor Voltage (b) Inductor Current (c) Inductor Voltage The experimental results in Figure 6 compare very favourably with the predicted results in Figure 5. However, the parasitic capacitance does affect the experimental results with regard to the transformer voltage reversal after tA . This transition is not instantaneous, and the change in inductor current slope is less severe than the analytical solution suggests. The analysis could be extended to include this type of effect, [8]. Table 1 compares some key waveform parameters. The total power loss measured by calorimetry method is 9.9W. In the experiment, the input power is 96W and the efficiency is 89.7%. Table 2 shows the power loss breakdown in the converter, [9]. It is believed that

1 >

1) Math:

50 Volt 500 ns

(c)

Figure 6. Experimental Waveforms (a) Mosfet Drain Voltage and Gate Waveform (b) Inductor Current (c) Inductor Voltage

7. OPERATIONAL ISSUES

The resonant converter presented in this paper can be categorised to Half Wave Zero Voltage Switching (HW-ZVS) QRC. The voltage across the mosfet drain and source cannot swing to negative values due to the anti-paralleled diode within the mosfet. The disadvantage of this design is that the voltage conversion ratio depends much on the load condition. By series connecting a diode with the mosfet, the converter can run in the Full Wave (FW) mode and the output voltage will be insensitive to the load variations. However, for FW-ZVS, mosfets turn on at nonzero voltage and the energy stored in the parallel capacitor will dissipate in the mosfet.

capacitance. It is expected that the converter will be tolerant of winding capacitance and will in fact allow the placement of small capacitors across the output rectifiers to assist in reducing reverse recovery losses. While the experimental work conducted thus far has established that the converter can maintain good conversion efficiencies at higher frequencies, much more work can be done with regard to the implementation especially in regard to magnetic components.

9. REFERENCES Parameter VC1 ( t A ) (V) VLr(t A ) (V) VC1 (peak) (V) ILr(t C) (A) VLr(t C) (V)

Calculated 53.3 88.0 90.2 3.76 -38.1

Experimental 60.0 110.0 90.0 3.40 -38.0

Table 1. Waveform Parameters Component Transformer Inductor (L1, L2 ) Resonant Inductor Mosfet Resonant Capacitor Diode Total

Estimated Power Loss (W) 3.3 1.2 2.8 0.4 1.3 0.7 9.7

Table 2. Power Loss Breakdown The ZVS region can be increased at the expense of Mosfet voltage rating. One option for maintaining ZVS at reduced load is variable frequency operation.

8. CONCLUSIONS AND FUTURE WORK This paper studies a ZVS half bridge dual converter suitable for photovoltaic applications. It is shown that different resonant modes exist for different timing arrangements and load conditions. Analytic solutions are presented for these modes and experimental results were obtained for the continuous mode operation. The new converter presents a range of avenues for new research. Further work is required to fully characterise the operational modes, especially with regards to control, the maintenance of resonant operation over a wide range of load conditions and the inclusion of the effects of parasitic winding

[1] R. Severns, “Circuit Reinvention in Power Electronics and Identification of Prior Work”, IEEE Trans. Power Electronics, Vol. 16, No. 1, pp. 1-7, Jan., 2001. [2] N. Mohan, T. M. Undeland and W. P. Robbins, Power Electronics, Converters, Applications, and Design, New York: John Wiley & Sons, Inc., 1995, pp. 249-291. [3] Q. Li, P. Wolfs, S. Senini, “The Application of the Half Bridge Dual Converter to Photovoltaic Applications”, Proc. of Australasian Universities Power Engineering Conference, 2000, pp. 156161. [4] S. Freeland and R. D. Middlebrook, “A Unified Analysis of Converters with Resonant Switches,” Proc. IEEE PESC Conf. Rec. 1987, pp. 20-30. [5] K. Shenai, “Made-to-order Power,” Spectrum, July 2000, pp. 50-55.

IEEE

[6] E. C. Snelling, Soft Ferrites, Properties and Applications. London: Butterworths, 1988, pp. 317-330. [7] S. Guinta, “Capacitance and Capacitors”, http://www.analog.com/publications/magazines/D ialogue/archives/30-2/ask.html [8] G. D. Demetriades, P. Ranstad, C. Sadarangari, “Three Elements Resonant Converter: The LCC Topology by using MATLAB”, Proc. IEEE PESC Conf. Rec. 2000, pp. 1077-1083. [9] H. L. Chan, K. W. E. Cheng and D. Sutanto, “Superconducting Self-Resonant Air-Cored Transformer”, Proc. IEEE PESC Conf. Rec. 2000, pp. 314-319.

INTRODUCTION

In the design of the pulse-width-modulated DC-DC converters, a high power packing density and a high power conversion efficiency are extremely desirable. In order to obtain a high power packing density, engineers prefer increasing the switching frequency to minimise the size of the magnetic components in the converter. However, significant switching loss can occur due to high voltage and high current overlaps during the switching period. The advantage of high switching frequency can easily be cancelled out by the low conversion efficiency. Resonant switching techniques have been used in high frequency DC-DC converters for more than fifty years, [1]. Theoretically, resonant converters have no switching loss and are more suitable for high frequency operations. The switches in resonant converters turn on and off under zero current and/or zero voltage and there is no switching loss. According to the underlying operation principles of the resonant converters, there are three main approaches, [2]: • Load-Resonant Converter (LRC), it includes a resonant tank leading to oscillating load voltage and current. • Quasi-Resonant Converter (QRC), its resonant network shapes the current or voltage waveform of the main switch. Each switching period has resonant and non-resonant segments and is suitable for the operation in the low megahertz range. • Multi-Resonant Converter (MRC), resonant operation is applied to both the main switch and output rectifier diodes. It is more suitable for very high frequency operation.

Resonant conversion approaches can also be characterised by the use of a zero-voltage or zerocurrent switching condition. A zero-voltage switching (ZVS) quasi-resonant half bridge dual converter, that can actively utilise the drain-source capacitance and the transformer leakage inductance, is introduced in this paper. The authors believe that this is the first resonant version of the half bridge dual converter. During the development of this converter it became clear that a range of operational modes exist. A theoretical discussion on different possible resonance conditions is presented. To verify the theoretical discussion, a resonant half bridge dual converter was designed and constructed. It is used to demonstrate the existence of one of three possible resonant operating modes. Also, operational issues for different load conditions will be discussed.

2.

RESONANT CONVERTER

Half bridge dual converters are well suited to low voltage, high current inputs. They have been proposed by the authors as attractive candidates for photovoltaic module integrated power conditioning applications, where a relatively low module voltage must be boosted to a level, typically 360Vdc, suitable for a grid interconnected inverter, [3]. In the hard-switched implementations, an important barrier to operating efficiency and high frequency operation are losses associated with parasitic circuit elements especially primary-secondary leakage inductance, transformer capacitance and mosfet drain-source capacitance. Figure 1 shows a zero-voltage switching (ZVS) topology that actively exploits the converter parasitic components. As with other ZVS converters the mosfets turn on and off when the capacitor voltage is zero and no switching loss exists, [4].

where L1

1 Lr C1

ω0 =

L2 D2 D1 Lr

E

R C1

frequency and

Z0 =

D3 D4

C2 Q2

Q1

3.

V

is the angular resonance

Lr C1

is the characteristic

impedance. vC1 reaches its peak of Vd + I0 Z0 and iLr is

t 2 = t1 +

π π . And then at t 3 = t 1 + , vC1 2ω 0 ω0

Figure 1. ZVS Half Bridge Dual Converter

I0 at

RESONANCE CONDITIONS

is Vd and iLr reaches its peak of 2I0 . In order for the capacitor voltage vC1 to reach zero at t4 , I0 Z0 must be greater than Vd . At t 4 , v C1 is zero and iLr is I2 .

An equivalent resonant circuit that can be used to analyse the switching behaviour of Q1 is shown in Figure 2. The voltage and current waveforms are shown in Figure 3. The diode D and the voltage source Vd , correspond to secondary side diodes and output filter capacitor voltage as reflected to the primary side. These components present load components to resonant currents. An initial analysis assumes at t0 that Q1 and Q2 are conducting, L1 carries a constant current I0 , the current in the resonant inductor ILr0 = 0 and the voltage across the resonant capacitor VC10 = 0. i Lr i Q1

C1

I0 Q1

D Q1

+ vC1 −

Lr

D Vd

• Stage 3 (t4 ≤ t ≤ t6 ): At t4 Q1 (or the inverse body diode) turns on and the inductor current iLr is

i Lr = I 2 −

Vd (t − t4 ) Lr

(4)

iL linearly discharges to zero at t6 . The current in Q1 would be the difference between I0 and the inductor current. In the period from t4 to t5 the inverse mosfet diode conducts as the remaining current in the inductor is greater than I0 . For this condition it is required that I0 Z0 > Vd . The mosfet must be gated on during period t5 to t6 to maintain a zero drain source voltage. In a practical implementation, turn on between t4 and t5 is easily achieved and places the mosfet into the on state when required. • Stage 4 (t6 ≤ t ≤ t7 ): After t6 , iLr stays at zero until Q2 turns off at t 7 .

Figure 2. Equivalent Resonant Circuit • Stage 1 (t0 ≤ t ≤ t1 ): Q1 is turned off at time t0 . The capacitor voltage v C1 is

vC 1 =

I0 (t − t 0 ) C1

(1)

• Stage 2 (t1 ≤ t ≤ t4 ): At t1 , the capacitor voltage reaches Vd , the diode D becomes forward biased. The capacitor voltage v C1 and the inductor current iLr are:

vC 1 = Vd + I 0 Z 0 sin ω 0 ( t − t1 )

(2)

i Lr = I 0 − I 0 cos ω o (t − t1 )

(3)

The half bridge dual converter requires that at least one of the two switches be on. In the above discussions, Q2 must turn off after Q1 turns on. The timing of this transition can generate three different modes of operation. The mode described above is referred to as the first discontinuous mode. This description is based on the inductor current behaviour, which has a prolonged period of zero current. If I0 Z0 > Vd , the converter can operate in the following three modes: • Discontinuous mode 1 – Q1 turns on between t4 and t 5 and Q2 turns off after t 6 . • Discontinuous mode 2 – Q1 turns on between t4 and t 5 and Q2 turns off between t5 and t 6 . • Continuous – Q1 turns on between t 4 and t 5 and Q2 turns off after Q1 turns on but between t4 and t5 . The Q1 mosfet inverse diode is on when Q2 turns off.

vc1 vc2 V d+I0Z

vc1

vc2

Vd t0 t1 t2 t3 t 4 iLr 2I0 I2

The equivalent circuit for each stage after the turn off of Q1 is shown in Figure 4 (Q1 turns off when the inverse diode of Q2 stops conducting). The current and voltage waveforms are shown in Figure 5. In this case, an initial current of –I0 exists in the resonant inductor. iLr Vd

t5 t 6 t7 t8 t 9 t 10 t11 t12 t13 t (a) I0

L +L C 1 +r l vC1 −

I0 t0 t1 t 2 t 3 t4

Stage 1 iLr Vd

t5 t6 t7 t8 t9 t10 t11 t12 t 13 t

-I0

iQ1 3I0

I0

I0

L +L C1 +r l vC1 − Stage 2 iLr Vd

Lr+Ll + v C1 −

Lr+Ll C2 + + vC1 v C2 − −

Stage 3

Stage 4

I0

(b) Figure 4. Equivalent Circuit of Continuous Mode • Stage 1 (t0 ≤ t ≤ tA ): The Mosfet Q1 turns off and C1 rapidly charges under the influence of the current source and the initial inductor current. The capacitor voltage v C1 and the inductor current iLr are:

2I0 I0 t 0 t1 t2 t3 t 4 I0-I2

iLr Vd

t 5 t 6 t7 t8 t 9 t10 t11 t 12 t13 t

vc1 = 2 I 0Z 0 sin ω0 (t − t 0 ) − Vd (1 − cos ω 0 (t − t 0 ))

(c)

i Lr = Figure 3. Voltage and Current Waveforms in the Resonant Converter (a) Capacitor Voltage (b) Inductor Current (c) Mosfet Current

4. CONTINUOUS MODE OPERATION The full analysis of the resonant modes of the converter depends on two key variables, the timing of the turn off of Q2 and the load condition. For this paper the analysis is simplified when a fixed switching point is assumed. We have selected the case that Q2 turns off at t5 , the point when the inverse diode of Q1 stops conducting. The converter runs in the continuous mode if the load current is large enough for I0 Z0 to exceed Vd . In this paper we select parameters that match the experimental model, I0 Z0 = 1.2Vd .

(5)

Vd sin ω 0 ( t − t 0 ) Z0 + I 0 (1 − 2 cos ω 0 (t − t 0 )) (6)

This period ends when inductor current reaches zero. This point depends on the magnitude of I0 Z0 relative to Vd . At I0 Z0 = 1.2Vd , the inductor current reaches zero at ω0 tA = 40°. The corresponding capacitor voltage VCA = 1.3Vd . • Stage 2 (tA ≤ t ≤ tC ): In this period, current is established in the inductor in the positive direction. The reflected transformer voltage reverses. For issues related to space, this analysis assumes the reversal is instantaneous but parasitic capacitances slow the transition. This effect will be seen in the experimental results. As shown in Figure 5, drain-source capacitor voltage continuously rises. For the parameters selected, capacitor voltage and inductor current are:

v c1 = I 0 Z 0 sin ω 0 (t − t A ) + Vd + (VCA − Vd ) cos ω 0 (t − t A ) (7) i Lr =

VCA − Vd sin ω 0 (t − t A ) Z0

+ I 0 (1 − cos ω 0 (t − t A ))

(8)

The capacitor voltage peaks at 2.2Vd and returns to zero at ω0 tC = 259°. At this point the inductor current ILC = 1.6I0 .

In the resonant circuit, resonant capacitors are required to be connected across the mosfets drain and source. High frequency oscillations, at frequencies up to 50 MHz were observed during experimentation, due to the Equivalent Series Inductance (ESL) of the resonant capacitor as well as the stray inductance of the leads and tracks connecting the capacitors and the mosfets. Considering the size of the mosfets, physically small capacitors are preferred because they can be paralleled with the mosfets using shorter leads and tracks. Other solutions include paralleling several capacitors to achieve a low effective stray inductance.

• Stage 4 (t ≥ tD): Q2 turns off at tD and the above cycle repeats for Q2.

Moreover, under high frequency operation, the power loss related to diode reverse recovery could be significant. This converter presents favourable conditions for the diodes, including clamping of the diode voltage to the output level, a slow current reversal due the resonance conditions, and slow voltage reversal due to junction capacitances. However a short diode reverse recovery time is still essential for a high conversion effic iency. Ultra -fast diodes must be selected in the design to obtain a low diode reverse recovery loss. In the initial prototypes, thermal run away due to reverse recovery was observed.

5. DESIGN CONSIDERATIONS

6. EXPERIMENTAL RESULTS

One of the shortcomings of the resonant converters is a higher peak voltage or current value than the conventional hard switched converters for the same output power level, [5]. Mosfets with a higher voltage or current rating are required. However, mosfets with higher voltage or current rating tend to have higher Rdson and consequently higher conduction loss for the same current level. Mosfets with small Rdson must be carefully selected in this converter in order that the decrease in the switching loss would not be offset by the increase in the conduction loss in mosfets.

The converter in the experiment is designed with I0 Z0 = 1.2Vd , running in the continuous mode. In the actual converter, each mosfet is replaced with two parallel mosfets to reduce Rdson . Also, seven monolithic ceramic capacitors are used in parallel with the mosfet in each side. Monolithic ceramic capacitors are selected because of their small size. Another advantage is its low ESL, [7]. Some of the key components and values used in the converter are:

•

Stage 3 (tC ≤ t ≤ tD): The inductor current is

i Lr = I LC −

Vd (t − t C ) Lr + Ll

(9)

where Ll is the transformer leakage inductance. The inductor current linearly declines to I0 at tE , when Q2 turns off.

Skin effects are significant in this design. The penetration depth is given in [6] as

∆ = kf −1/ 2

(10)

where k = 65.8mmHz for copper conductor at 20°C. From Equation 10, penetration depth is 0.09mm at 500kHz, the transformer and inductor excitation frequency. Therefore Litz wire must be used to obtain a low copper loss of the transformer and the resonant inductor. 1/ 2

• Transformer – Core type Philips ETD29, ferrite grade Neosid F44, Litz wire, leakage inductance = 0.34uH; • Inductor L1 and L2 – Core type Siemens RM10, ferrite grade Siemens N48; • Resonant Inductor – Core type Philips ETD39 gapped, ferrite grade Philips 3C90, Litz wire, 4.5uH; • Resonant Capacitor – Ceramic, C = 1.5nF, V = 250V; • Mosfet – Intersil RFP40N10, VDS = 100V, RDS(on) = 0.04O, ID = 40.0A; • Diode – ST STTA106U, IF = 1A, VRRM = 600V, VFM = 1.5V, t rr = 20ns; • I0 = 2.35A; • Vd = 41V.

vc1 vc2

vc1

significant improvements can be made with the magnetic components by substituting better ferrite grades. This was simply an issue of availability in small quantities of appropriate cores.

vc2

VCA

t0

tA

tB

tC tD t E

t F tG

t

(a) iLr I LC I0

Ch1

1 >

Ch2

2 >

t0

tA

tB tC tD tE

t F tG

1) Ch 1: 2) Ch 2:

t

20 Volt 500 ns 50 Volt 500 ns

(a)

-I 0 -I LC (b) vLr VL0Lr /L

1>

-VL0Lr/L

t0

tA

tB

tC tD tE

tF t G

t 1) Ch 2:

1 Ampere 500 ns

(b)

(c) Figure 5. Current and Voltage Waveforms (a) Capacitor Voltage (b) Inductor Current (c) Inductor Voltage The experimental results in Figure 6 compare very favourably with the predicted results in Figure 5. However, the parasitic capacitance does affect the experimental results with regard to the transformer voltage reversal after tA . This transition is not instantaneous, and the change in inductor current slope is less severe than the analytical solution suggests. The analysis could be extended to include this type of effect, [8]. Table 1 compares some key waveform parameters. The total power loss measured by calorimetry method is 9.9W. In the experiment, the input power is 96W and the efficiency is 89.7%. Table 2 shows the power loss breakdown in the converter, [9]. It is believed that

1 >

1) Math:

50 Volt 500 ns

(c)

Figure 6. Experimental Waveforms (a) Mosfet Drain Voltage and Gate Waveform (b) Inductor Current (c) Inductor Voltage

7. OPERATIONAL ISSUES

The resonant converter presented in this paper can be categorised to Half Wave Zero Voltage Switching (HW-ZVS) QRC. The voltage across the mosfet drain and source cannot swing to negative values due to the anti-paralleled diode within the mosfet. The disadvantage of this design is that the voltage conversion ratio depends much on the load condition. By series connecting a diode with the mosfet, the converter can run in the Full Wave (FW) mode and the output voltage will be insensitive to the load variations. However, for FW-ZVS, mosfets turn on at nonzero voltage and the energy stored in the parallel capacitor will dissipate in the mosfet.

capacitance. It is expected that the converter will be tolerant of winding capacitance and will in fact allow the placement of small capacitors across the output rectifiers to assist in reducing reverse recovery losses. While the experimental work conducted thus far has established that the converter can maintain good conversion efficiencies at higher frequencies, much more work can be done with regard to the implementation especially in regard to magnetic components.

9. REFERENCES Parameter VC1 ( t A ) (V) VLr(t A ) (V) VC1 (peak) (V) ILr(t C) (A) VLr(t C) (V)

Calculated 53.3 88.0 90.2 3.76 -38.1

Experimental 60.0 110.0 90.0 3.40 -38.0

Table 1. Waveform Parameters Component Transformer Inductor (L1, L2 ) Resonant Inductor Mosfet Resonant Capacitor Diode Total

Estimated Power Loss (W) 3.3 1.2 2.8 0.4 1.3 0.7 9.7

Table 2. Power Loss Breakdown The ZVS region can be increased at the expense of Mosfet voltage rating. One option for maintaining ZVS at reduced load is variable frequency operation.

8. CONCLUSIONS AND FUTURE WORK This paper studies a ZVS half bridge dual converter suitable for photovoltaic applications. It is shown that different resonant modes exist for different timing arrangements and load conditions. Analytic solutions are presented for these modes and experimental results were obtained for the continuous mode operation. The new converter presents a range of avenues for new research. Further work is required to fully characterise the operational modes, especially with regards to control, the maintenance of resonant operation over a wide range of load conditions and the inclusion of the effects of parasitic winding

[1] R. Severns, “Circuit Reinvention in Power Electronics and Identification of Prior Work”, IEEE Trans. Power Electronics, Vol. 16, No. 1, pp. 1-7, Jan., 2001. [2] N. Mohan, T. M. Undeland and W. P. Robbins, Power Electronics, Converters, Applications, and Design, New York: John Wiley & Sons, Inc., 1995, pp. 249-291. [3] Q. Li, P. Wolfs, S. Senini, “The Application of the Half Bridge Dual Converter to Photovoltaic Applications”, Proc. of Australasian Universities Power Engineering Conference, 2000, pp. 156161. [4] S. Freeland and R. D. Middlebrook, “A Unified Analysis of Converters with Resonant Switches,” Proc. IEEE PESC Conf. Rec. 1987, pp. 20-30. [5] K. Shenai, “Made-to-order Power,” Spectrum, July 2000, pp. 50-55.

IEEE

[6] E. C. Snelling, Soft Ferrites, Properties and Applications. London: Butterworths, 1988, pp. 317-330. [7] S. Guinta, “Capacitance and Capacitors”, http://www.analog.com/publications/magazines/D ialogue/archives/30-2/ask.html [8] G. D. Demetriades, P. Ranstad, C. Sadarangari, “Three Elements Resonant Converter: The LCC Topology by using MATLAB”, Proc. IEEE PESC Conf. Rec. 2000, pp. 1077-1083. [9] H. L. Chan, K. W. E. Cheng and D. Sutanto, “Superconducting Self-Resonant Air-Cored Transformer”, Proc. IEEE PESC Conf. Rec. 2000, pp. 314-319.