# Non-isolated high step-up DC–DC converter adopting auxiliary capacitor and coupled inductor

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## Abstract

For grid-connected power system based on photovoltaic (PV) source and fuel cells, high step-up and high-efficiency DC–DC converters are needed, due to the bus voltage of the grid-connected inverter is much higher than the output voltage of PV and fuel cells. In this paper, a novel high step-up converter is proposed. An auxiliary capacitor is introduced into the boost converter, which serves as a voltage source. It is in series with the input voltage source with the same voltage polarities. Thus, the input voltage is increased equivalently and the voltage gain is increased accordingly. To reduce the voltage stresses of the switch and the diode, multiple output capacitors are introduced. The voltage of each output capacitor is degraded leading to the reduced voltage stress. To replenish energy for the multiple output capacitors, a coupled inductor is adopted. Based on this, high step-up converter adopting auxiliary capacitor and coupled inductor is derived. The operating principles and voltage gain of the proposed converters are analyzed in this paper. In the end, experiment results are given to verify the theoretical analysis.

## Keywords

High voltage gain High efficiency Non-isolated Photovoltaic (PV) Fuel cell## 1 Introduction

Since it takes centuries for the traditional fossil energy to be replenished, it will be exhausted with the growing demand for energy of human society. Thus the energy crisis is increasingly serious. Meanwhile, the excessive usage of the traditional fossil energy has polluted the environment and resulted in greenhouse effect on a global scale [1]. Therefore, it is becoming more and more important to optimize the energy consumption structure and to utilize clean and renewable energy. Solar energy and hydrogen energy are two promising renewable energy, and have extensive application prospect. As the utilization methods of the two new energy, photovoltaic (PV) and fuel cells power generations have been applied on a large scale [2, 3, 4, 5, 6, 7], such as photovoltaic power station and electric vehicle.

In recent years, the grid-connected power generation based on PV source for residential application has become globally popular. Usually, an interface unit is necessary, as the output voltage of PV source is relatively too low for the line voltage. If the line voltage is 220 V, the input voltage needed by the grid-connected inverter would approach 380 V. But the output voltage of PV source generally varies from 25 to 45 V. To boost the output voltage of PV source, one possible solution to is to make series-connected PV arrays. But the total output power of PV arrays will be degraded due to module mismatch or partial shading [8]. Another promising solution is to utilize a high step-up DC–DC converter to match the low output voltage of PV source and high input voltage of the inverter. Then every PV source can realize the function of maximum power point tracking. For the isolated DC–DC converters, the voltage gain can be increased by adjusting the turns ratio of the transformer. But the energy stored in the leakage inductor is difficult to be transferred to the output. Thus, for the application without galvanic isolation requirement, non-isolated high step-up DC–DC converters is preferred.

The boost converter is wildly used for voltage step-up. However, its duty cycle would be too large when the input voltage is much smaller than the output. And for the actual power switch and diode, a certain delay between turn-on and turn-off state will probably result that the power switch is turned on before being cut off completely and the diode is cut off before conducting. Thus, the reliability is degraded. When the duty cycle approaches unity, a large pulse current will conduct through the diode in a short time, which leads to large the current stress of the diode and severe reverse recovery problem. This will greatly affect the efficiency and brings about a serious electromagnetic interference problem [9, 10, 11, 12]. By cascading another boost converter, a high voltage gain can be easily obtained. But the additional switch makes the control scheme more complex. And it may cause instability issue for cascaded systems.

The impedance source networks are widely used in the inverters [13, 14, 15, 16] to increase the voltage boost inversion ability. Likewise, the impedance source networks can also be used in high step-up DC–DC converters to achieve high voltage gain [17, 18, 19, 20]. The converters can operate with a much smaller duty cycle, which improves the reliability. By combining quasi-Z-source network and transformer, the voltage stress of the switch is reduced. But most of the converters adopt multiple power switches, and have a relatively complex control scheme. In [21], a single power switch was adopted to simplify the control design. However, the voltage stress of the switch is as high as the output voltage, which brings large switching loss.

Another method of increasing the voltage gain is to introduce a coupled inductor [22, 23, 24, 25, 26, 27, 28]. However, the current through the coupled inductor is discontinuous. It goes against the lifetime of PV and fuel cell when the coupled inductor is placed on the input side. Especially for the low input voltage application, the input current is very large. Thus, the continuous input current is preferred.

To overcome the respective disadvantages of quasi-Z-source network and coupled inductor, some isolated high step-up DC–DC converters combining quasi-Z-source network and coupled inductor are proposed in [29, 30]. However, due to the isolation, the energy stored in the leakage inductor of the primary winding is difficult to be transferred to the output. In this paper, a non-isolated high step-up DC–DC converter with single switch based on quasi-Z-source network and coupled inductor is proposed. The input current is continuous and the voltage stress of the switch is low. Besides, the energy stored in the leakage inductor can be absorbed by the output capacitor, which is beneficial for the efficiency. And single switch is used to simplify the control scheme. The operating principle and parameter calculation are given in this paper, and an experiment is conducted to verify the theoretical analysis. The experiment results indicate that the proposed converters can achieve a higher efficiency.

## 2 Derivation of high step-up DC–DC converters adopting auxiliary capacitor and coupled inductor

### 2.1 High step-up converter adopting auxiliary capacitor

*V*

_{g}is the input voltage,

*L*

_{1}is the boost inductor, Q is the switch. To increase the voltage gain of boost converter, an auxiliary voltage source

*V*

_{a}can be introduced to the input terminal and the voltage polarity is the same as

*V*

_{g}, as shown in Fig. 2. When Q is turned on,

*V*

_{g}is in series with

*V*

_{a}to charge

*L*

_{1}. When Q is turned off,

*V*

_{g}is in series with

*V*

_{a}and

*L*

_{1}to supply the load. And the output voltage is the sum of

*V*

_{g},

*V*

_{a}and the voltage of

*L*

_{1}. Obviously, the auxiliary voltage source increases the input voltage equivalently, and a high voltage gain is obtained.

*V*

_{a}in Fig. 2 can be implemented with a capacitor

*C*

_{a1}, which is defined as the auxiliary capacitor. To replenish energy for the auxiliary capacitor

*C*

_{a1}, the inductor

*L*

_{2}, and the diode D

_{1}is introduced as shown in Fig. 3a. Obviously, the larger the voltage of the auxiliary capacitor is, the higher the derived voltage gain will be. To obtain a higher voltage for

*C*

_{a1}, an additional auxiliary voltage source

*V*

_{a}can be added in the charging path of

*L*

_{2}, as shown in Fig. 3b. When Q

_{a}is turned on,

*V*

_{a}is in series with the input voltage source to charge

*L*

_{2}. When Q

_{a}is turned off,

*L*

_{2}replenishes energy for

*C*

_{a1}. If

*V*

_{a}is equal to the electric potential difference between nodes

*a*and

*b*, the electric potentials of the drain electrodes are identical and can be connected directly. In doing so, Q

_{a}can be removed to simplify the structure. Likewise, the auxiliary voltage source

*V*

_{a}can be implemented by a capacitor

*C*

_{a2}, as shown in Fig. 4. As seen,

*L*

_{1}can be used to replenish energy for

*C*

_{a2}. This topology has been proposed and analyzed in [19], which is called Z-source DC–DC converter.

*C*

_{a1}and

*V*

_{g}in Fig. 4 are constant, the voltage between nodes

*c*and

*d*is also constant and equals the voltage sum of

*C*

_{a1}and

*V*

_{g}. Thus, a capacitor can be added between nodes C and D to serve as a new input source of the boost inductor

*L*

_{1}. As the new capacitor charges

*L*

_{1}instead of the original one, the original auxiliary capacitor can be removed as shown in Fig. 5. This structure consisting of the capacitor and inductor is called quasi-Z-source network [13]. Its operating modes when the network is applied for DC–DC converter with single switch has not been analyzed in detail in [13].

Compared with the converter shown in Fig. 4, the voltage stress of *C* _{a1} in Fig. 5 is larger. But the input current of the converter in Fig. 5 is continuous, which is beneficial for improving the lifetime of PV and fuel cell.

As shown in Fig. 5, the voltage stresses of the switch and the diode are both as high as the output voltage which leads to a large conduction resistor of the switch and severe reverse recovery problem of the diode. Thus, the conduction loss and the switching loss are both large.

### 2.2 High step-up converter adopting auxiliary capacitor and coupled inductor

*C*

_{o1}is reduced, and the voltage stress of Q, D

_{1}and D

_{o1}are reduced as well. To replenish energy for

*C*

_{o2}, the inductor

*L*

_{1}in Fig. 5 is replaced by the coupled inductor

*L*

_{cp}, and the secondary winding of the coupled inductor is used to charge

*C*

_{o2}. In [31], the inductor of the boost converter is replaced by the coupled inductor, which leads to a discontinuous input current. On the contrary, the input current of the converter in Fig. 6b remains continuous, which is beneficial for the lifetime of PV and fuel cell.

As shown in Fig. 6b, the voltage doubling rectifier circuit is adopted to further increase the voltage of *C* _{o2} in order to reduce the voltage stresses of Q, D_{1} and D_{o1}. As a result, a switch with a lower conduction resistor can be selected, and the conduction loss and switching loss can be reduced.

## 3 Analysis of high step-up DC–DC converters adopting auxiliary capacitor and coupled inductor

### 3.1 Operating principle of CCM

*L*

_{1}and the magnetizing inductor

*L*

_{m}are both continuous, there exist four operating modes and the key waveforms are shown in Fig. 8, where

*i*

_{L1}is the current of

*L*

_{1},

*i*

_{Tr_s}is the current of the secondary winding of the coupled inductor,

*i*

_{Lm}and

*i*

_{Llk}are the currents of the magnetizing inductor and the leakage inductor of the coupled inductor respectively,

*i*

_{D1}and

*i*

_{Do1}are the currents of D

_{1}and D

_{o1}. The operating modes are shown in Fig. 9.

Mode 1 [*t* _{1} ~ *t* _{2}]: When Q is turned on, *V* _{g} is in series with *C* _{a2} to charge *L* _{1}, and *C* _{a1} charges the magnetizing inductor *L* _{m}. In this mode, the secondary winding of the coupled inductor charges *C* _{o3} through D_{o3}.

Mode 2 [*t* _{2} ~ *t* _{3}]: When Q is turned off, *L* _{1} and *L* _{m} charge *C* _{a1} and *C* _{a2} through D_{1} respectively, and the input voltage source is in series with *L* _{1} and *L* _{m} to charge *C* _{o1}. In this mode, *i* _{Lm} is smaller than *i* _{Llk}, where *i* _{Lm} and *i* _{Llk} are the currents of the leakage inductor and the magnetizing inductor, respectively. Thus, the current direction of the secondary winding remains and the secondary winding still charges *C* _{o3} through D_{o3}.

Mode 3 [*t* _{3} ~ *T* _{s}]: In this mode, *i* _{Lm} is larger than *i* _{Llk}, leading to the current direction of the secondary winding changed. And the secondary winding charges *C* _{o2} in series with *C* _{o3} through D_{o2}.

Mode 4 [*T* _{s} ~ *t* _{4}]: In this mode, since *i* _{Lm} is larger than *i* _{Llk}, the secondary winding still charges *C* _{o2} in series with *C* _{o3} through D_{o2}.

### 3.2 Operating principle of DCM

*L*

_{1}is discontinuous, the key waveforms and operating modes in DCM are shown as Figs. 10 and 11, respectively. There are five operating modes for DCM, in which Mode 1, Mode 2, and Mode 3 are the same with those in CCM. Here, only Mode 4 and Mode 5 are given in detail.

Mode 4 [*t* _{4} ~ *t* _{5}]: When *i* _{L1} = *i* _{Do1} − *i* _{Llk}, the current through D_{1} decreases to zero and is cut off.

Mode 5 [*t* _{5} ~ *T* _{s}]: The currents through *L* _{1} and *L* _{cp} are zero, and *C* _{o1} and *C* _{o2} are in series to supply the load.

### 3.3 Voltage gain of CCM

As the leakage inductor is much smaller compared with the magnetizing inductor, the duration of Modes 2 and 4 in Fig. 8 are relatively short. Thus, the leakage inductor is neglected here, to simplify the analysis.

*L*

_{1}, we have:

*V*

_{g}is the input voltage;

*D*is the duty cycle of the switch;

*T*

_{s}is the switching period;

*V*

_{a1}and

*V*

_{a2}are the average voltages of

*C*

_{a1}and

*C*

_{a2}, respectively.

*L*

_{m}, then we have:

*V*

_{Ca1},

*V*

_{Ca2}can be derived as:

*C*

_{o1}equals the voltage sum of

*C*

_{a1}and

*C*

_{a2}.

*C*

_{o3}can be expressed as:

*N*

_{sp}=

*N*

_{s}/

*N*

_{p};

*N*

_{s}is the secondary winding turns;

*N*

_{p}is the primary winding turns.

*C*

_{o2}is:

_{1}and D

_{o1}equal

*V*

_{Co1}, which are much smaller than the output voltage. And it is beneficial for improving the efficiency of the converter.

### 3.4 Voltage gain of DCM

To simplify the analysis, an assumption is made that the leakage inductor is neglected. Thus, Mode 2 and Mode 4 are neglected as well. Then only Mode 1, Mode 3 and Mode 5 need to be considered.

*L*

_{1}and

*L*

_{m}, we have:

*D*

_{r}

*T*

_{s}=

*t*

_{4}−

*t*

_{1}.

*L*

_{1}can be derived:

### 3.5 Comparison of high step-up converters

*N*

_{sp}is selected as 4. As seen, the proposed configuration in Fig. 6b has larger voltage gain than the other high step-up converters with the same duty cycle and reaches a considerable value although the duty cycle has not been close to 0.5. As shown in Fig. 6b, since the coupled inductor replaces

*L*

_{1}in Fig. 5 rather than

*L*

_{2}on the input side, the input current is continuous, which is beneficial for the lifetime of PV and fuel cell. As a consequence, the voltage stress of Q in the proposed converter is a little larger.

Comparison of high step-up converters

Parameter | This work | [31] | [32] | [33] | [34] | [35] |
---|---|---|---|---|---|---|

Voltage gain | \(\frac{{1 + N_{\text{sp}} }}{1 - 2D}\) | \(\frac{{1 + N_{\text{sp}} }}{1 - D}\) | \(\frac{{1 + N_{\text{sp}} + N_{\text{sp}} D}}{1 - D}\) | \(\frac{{2 + N_{\text{sp}} + N_{\text{sp}} D}}{1 - D}\) | \(\frac{{1 + 2N_{\text{sp}} - N_{\text{sp}} D}}{1 - D}\) | \(\frac{{1 + N_{\text{sp}} }}{{\left( {1 - D} \right)^{2} }}\) |

MOSFET | 1 | 2 | 1 | 1 | 2 | 1 |

Diode | 4 | 2 | 4 | 4 | 3 | 5 |

Voltage stress of MOSFET | \(\frac{{V_{\text{o}} }}{{1 + N_{\text{sp}} }}\) | \(\frac{{V_{\text{o}} }}{{1 + N_{\text{sp}} }}\) | \(\frac{{V_{\text{o}} }}{{1 + N_{\text{sp}} + N_{\text{sp}} D}}\) | \(\frac{{V_{\text{o}} }}{{2 + N_{\text{sp}} + N_{\text{sp}} D}}\) | \(\frac{{V_{\text{o}} }}{{1 + 2N_{\text{sp}} - N_{\text{sp}} D}}\) | \(\frac{{V_{\text{o}} }}{{1 + N_{\text{sp}} }}\) |

Input current | Continuous | Discontinuous | Discontinuous | Discontinuous | Discontinuous | Continuous |

Input current ripple | Small | Large | Large | Large | Large | Small |

Magnetic component | 2 | 1 | 1 | 1 | 1 | 2 |

Capacitor | 5 | 3 | 4 | 4 | 4 | 4 |

## 4 Experiment verification

- 1)
Input voltage

*V*_{g}: 25–45*V*_{dc}; - 2)
Output voltage

*V*_{o}: 380*V*_{dc}; - 3)
Switching frequency

*f*_{s}: 100 kHz; - 4)
Maximal output power

*P*_{o}: 300 W.

### 4.1 Parameter design

As the design progress of the converters in Figs. 5 and 6b are similar, the topology as shown in Fig. 6b is taken as an example to design the parameter.

- 1)
Design of coupled inductor

*L*_{cp}

As shown in Table 1, the voltage stress of the switch decreases with the increase of *N* _{sp.} However, higher *N* _{sp} would increase the current stress of the switch. Thus, a trade-off design should be considered between the voltage stress and current stress of the switch. Here, we prefer the voltage stress lower than 100 V, and the resultant *N* _{sp} is 4.

*I*

_{Ca1_avg},

*I*

_{Ca2_avg}, and

*I*

_{Co3_avg}are zero. Thus, the average current of

*L*

_{1}equals the average current of

*L*

_{m,}and we have:

*L*

_{m}is 30% of the maximum average current, then we have:

*V*

_{g}= 25 V, the right part of (24) reaches the maximum value. Then we have

*L*

_{m}= 50 μH.

- 2)
Design of inductor

*L*_{1}

*L*

_{1}can be expressed as:

*V*

_{g}= 25 V, the right part of (26) reaches the maximum value. Then we have

*L*

_{m}= 50 μH.

- 3)
Design of auxiliary capacitor

*C*_{a1}and*C*_{a2}

*C*

_{a1}and

*C*

_{a2}can be derived according to the voltage ripple Δ

*V*

_{Ca1}and Δ

*V*

_{Ca2}:

*C*

_{o2}and

*C*

_{o3}are zero, the average current through D

_{o3}equals to

*I*

_{o}. Then we have:

*C*

_{a1}= 24 μF,

*C*

_{a2}= 32 μF.

- 4)
Design of output capacitor

*C*_{o1},*C*_{o2}and*C*_{o3}

*C*

_{o1},

*C*

_{o2}is placed on the output side, the voltage ripples of

*C*

_{o1}and

*C*

_{o2}are limited to a smaller scale. If the voltage ripples of

*C*

_{o1}and

*C*

_{o2}are limited to 1% of the respective maximum average voltage, and the voltage ripple of

*C*

_{o3}is limited to 5% of the maximum average voltage, we have

*C*

_{o1}= 4 μF,

*C*

_{o2}= 3 μF,

*C*

_{o3}= 3 μF.

- 5)
Switch Q

*V*

_{o}/(

*N*

_{sp}+ 1). When Q is turned on, the current of the switch

*i*

_{Q}can be expressed as:

*V*

_{g}= 25 V, the RMS current of Q reaches its maximum value 19.8 A.

- 6)
Diode D

_{1}, D_{o1}, D_{o2}and D_{o3}

The voltage stresses of D_{1} and D_{o1} are *V* _{o}/(*N* _{sp} + 1), and the voltage stresses of D_{o2} and D_{o3} are *N* _{sp} *V* _{o}/(*N* _{sp} + 1).

_{o2}and D

_{o3}can be expressed as:

*v*

_{Ca1},

*v*

_{Ca2}and

*v*

_{Co1}are the instantaneous voltages of

*C*

_{a1},

*C*

_{a2}and

*C*

_{o1}, respectively.

_{1}and D

_{o1}can be expressed as:

_{1}, D

_{o1}, D

_{o2}and D

_{o3}can be calculated.

### 4.2 Experiment results

The main components used in the prototypes are listed in the following.

- 1)
Q: IPW65R045C7;

- 2)
D

_{1}: IDW20G65C5, D_{o}: C3D10060A; - 3)
*L*_{1}: 263 μH,*L*_{2}: 263 μH; - 4)
*C*_{a1}: 5.6 μF,*C*_{a2}: 6.8 μF,*C*_{f}: 220 μF.

- 1)
Q: IPP110N20N3G;

- 2)
D

_{1}: STPS20120C, D_{o1}: STPS10120C; - 3)
D

_{o2}: C3D10060A, D_{o3}: C3D10060A; - 4)
*L*_{1}: 50 μH,*L*_{m}: 50 μH,*N*_{sp}: 4; - 5)
*C*_{a1}: 24 μF,*C*_{a2}: 32 μF,*C*_{f}: 220 μF; - 6)
*C*_{o1}: 4 μF,*C*_{o2}: 3 μF,*C*_{o3}: 3 μF.

*C*

_{f}is used to realize the power decoupling if high step-up converter is cascaded with an inverter. And it is parallel with

*C*

_{o1}and

*C*

_{o2}in the high step-up converter adopting auxiliary capacitor and coupled inductor.

*v*

_{ds}is the drain-source voltage of the switch. As seen in Fig. 14, D

_{1}and D

_{o}conducts simultaneously. It can be explained as follows. Due to the forward recovery phenomenon of D

_{1}, the voltage sum of

*C*

_{a1},

*C*

_{a2}and the voltage drop of D

_{1}is larger than the output filter capacitor when the switch is turned off. The voltage difference will drop on ESR of the output filter capacitor and cause a large current through D

_{o}. As shown in Fig. 14, at the instant of turning off the switch,

*v*

_{ds}is slightly large, and there is a large current through D

_{o}. Thus, the current supplied by

*L*

_{1}to replenish energy for

*C*

_{a2}is small, and

*i*

_{D1}is small. With the voltage drop of D

_{1}reducing gradually, the difference between

*v*

_{ds}and the voltage of

*C*

_{f}decreases, resulting that

*i*

_{Do}decreases and

*i*

_{D1}increases. As

*C*

_{a1}and

*C*

_{a2}are much smaller than

*C*

_{f}, the voltage ripples of

*C*

_{a1}and

*C*

_{a2}are larger. Thus, with the voltages of the auxiliary capacitors increasing, the difference between

*v*

_{ds}and the voltage of

*C*

_{f}increases, leading to

*i*

_{Do}increasing and

*i*

_{D1}decreasing.

*i*

_{cp_p}is the current of the primary winding,

*i*

_{Do3}is the current of D

_{o3},

*v*

_{D1}and

*v*

_{Do1}are the voltages of D

_{1}and D

_{o1}. According to the theoretical analysis,

*i*

_{Do3}should rise up from zero when the switch is turned on. However, in the real case, there exist reverse recovery problem for D

_{o2}at the instant of turning on the switch. During the time interval of the reverse recovery, the voltage of the secondary winding is clamped by

*C*

_{o2}and

*C*

_{o3}. The voltage is reflected to the primary side by electro-magnetic induction and in series with

*C*

_{a1}to charge the leakage inductor which leads to the current of the leakage inductor rising up rapidly. After the reverse recovery of D

_{o2}is over, the current of the leakage inductor is larger than that of the magnetizing inductor. Thus,

*i*

_{Do3}rises up from a positive value. The voltage stresses of the switch, D

_{1}and D

_{o1}shown in Fig. 16 are much smaller than the output voltage which will reduce the power loss and improve the efficiency.

*V*

_{g}= 36 V,

*P*

_{o}= 300 W) is shown in Fig. 18, where

*v*

_{o}is the output voltage, and

*i*

_{L1}is the current of

*L*

_{1}. As seen, the overshoot of the output voltage is less than 30 V, which is 7.9% of the steady-state value.

_{o}in the basic boost converter is extremely short, the current stress is large and the reverse recovery problem is severe which leads to a large switching loss of the switch. Thus, the efficiency of the basic boost converter is lower than that of high step-up converter adopting auxiliary capacitor at heavy load as shown in Fig. 19. When the coupled inductor is adopted, the efficiency is further improved. Due to the voltage stresses of the switch, D

_{1}and D

_{o1}decreasing, the switching loss can be reduced effectively and the efficiency is superior to that of the cascaded boost converter over a wide load range.

*r*

_{Q_sw}= (

*P*

_{Q_on}+

*P*

_{Q_off})/

*P*

_{in},

*r*

_{Q_con}=

*P*

_{Q_con}/

*P*

_{in},

*r*

_{fe}= (

*P*

_{L1_fe}+

*P*

_{Lcp_fe})/

*P*

_{in},

*r*

_{cu}= (

*P*

_{L1_cu}+

*P*

_{Lcp_cu})/

*P*

_{in},

*r*

_{D}= (

*P*

_{D1}+

*P*

_{Do1}+

*P*

_{Do2}+

*P*

_{Do3})/

*P*

_{in}. As seen,

*r*

_{Q_sw}and

*r*

_{fe}decrease with the increase of the output power, while

*r*

_{Q_con}and

*r*

_{cu}increase with the increase of the output power. Thus, the efficiency increases at light load and decreases at heavy load. And the present of the maximum efficiency depends on the parasitic parameter of the components.

The experiment results indicate that the proposed converters can achieve a higher efficiency and good dynamic performance as well.

## 5 Conclusion

A novel high step-up DC–DC converter adopting auxiliary capacitor and coupled inductor is proposed in this paper. The input current is continuous, and the voltage stress of the power switch is low, which reduces the switching loss. Thus, the efficiency of the converter is improved. The operating mode of the proposed topology is analyzed and an experiment is conducted. The results indicate that the converters proposed in this paper can operate steadily and the performance is good.

## Notes

### Acknowledgements

This work was supported by Lite-On Technology Corporation.

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