# An Inductor-Based and Capacitor-Free Bipolar Pulse Converter with Overvoltage Protection

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Converter Circuit Topology and Overvoltage Protection

#### 2.1. The Circuit Topology and Working Process

_{d}, a power inductor L, a freewheeling diode D and five semiconductor switches Q

_{1}~Q

_{5}. The output load is equivalent to a resistor R

_{L}.

_{d}, and discharging stage, in which the inductor L discharges to the load R

_{L}and generates bipolar pulses. The sequence diagram of the proposed converter and current passing through L and R

_{L}are shown in Figure 2. In order to simplify the diagram, only two pairs of bipolar pulses are shown in this figure. U

_{Q}

_{1}~U

_{Q}

_{5}are the driving signals of switches Q

_{1}~Q

_{5}, respectively. Switch is ON when the driving signal is high. I

_{L}and I

_{RL}are the current passing through L and R

_{L}, respectively.

- (1)
- The switches are ideal MOSFETs except for the constant on-resistance.
- (2)
- The freewheeling diode is ideal except for the constant threshold voltage.
- (3)
- The power inductor is ideal except for the constant ESR.

- (1)
- Charging stage: (t
_{0}− t_{1})

_{L}.

_{1}~Q

_{4}is R

_{DS}

_{(on)}, where R

_{DS}

_{(on)}is the on-resistance of the MOSFETs. Therefore, the equivalent circuit resistance is ${R}_{total}=2{R}_{DS(on)}+{R}_{L(ESR)}$, where R

_{L}

_{(ESR)}is the ESR of L. The differential equation that describes the inductor current can be expressed as:

_{L0}is the initial current and i

_{Lt}is the final current of the charging stage.

_{L}(t) is compared with a reference current I

_{c}. As the inductor current increases during the charging stage, switch Q

_{5}will be turned off when i

_{L}(t) = I

_{c}. In this way, the charging stage is over and the converter switches into discharging stage.

- (2)
- Discharging stage: (t
_{1}− t_{5})

_{5}is OFF and the freewheeling diode D is ON. Q

_{1}~Q

_{4}form a full bridge. Power inductor L generates bipolar pulses on R

_{L}through the full bridge and D. In this case, the equivalent circuit resistance is ${R}_{total}=2{R}_{DS(on)}+{R}_{L(ESR)}+{R}_{D}+{R}_{L}$, where ${R}_{D}={V}_{th}/{i}_{L}$ is the equivalent on-state resistance of D and Vth is the threshold voltage. When ${R}_{L}\gg 2{R}_{DS(on)}+{R}_{L(ESR)}+{R}_{D}$, R

_{total}can be approximated to R

_{L.}The inductor current i

_{L}(t) is:

_{discharge}is the time of L discharging to R

_{L}.

_{discharge}is short enough, $\Delta {i}_{L}\ll {I}_{c}$. Therefore, this converter can be considered as a constant current source approximately.

- (a)
- Positive pulse: (t
_{1}− t_{2})

_{1}, Q

_{2}and Q

_{3}are turned off while Q

_{1}and Q

_{4}keep ON. The inductor current passes through R

_{L}from node a to node b, generating a positive pulse on R

_{L}. The load current i

_{RL}(t) is:

- (b)
- Deadtime: (t
_{2}− t_{3}) and (t_{4}− t_{5})

_{L}. Therefore, the consumption of energy stored by inductor can be ignored and inductor current remains constant approximately during deadtime.

- (c)
- Negative pulse: (t
_{3}− t_{4})

_{1}, Q

_{1}and Q

_{4}are turned off while Q

_{2}and Q

_{3}keep ON. The inductor current passes through R

_{L}from node b to node a, generating a negative pulse on R

_{L}. The load current i

_{RL}(t) is:

_{L}changes in the process of converter working, the duty cycle will change to obtain a constant inductor peak current. That is to say, the value of the duty cycle is adaptive in different working conditions, which is determined for each cycle individually [28,29].

#### 2.2. Overvoltage Protection Scheme

_{1}and Q

_{4}are ON, so the voltage across their drain and source equals to Conduction Voltage Drop U

_{DS}

_{(on)}, which is very small. However, switch Q

_{2}and Q

_{3}are OFF. Therefore, they are in parallel with a turn-on switch and the load. The drain-source voltages are:

_{L}is too large, there will be a high voltage across the turn-off switches. When u

_{Q}

_{2}(t) = u

_{Q}

_{3}(t) > U

_{DSS}

_{(BR)}, Q

_{2}and Q

_{3}are very likely to be broken down, where U

_{DSS}

_{(BR)}is the drain-source breakdown voltage of the switch.

_{G}provides driving signals for Q. R

_{G}is the gate equivalent resistor and C

_{GS}is the equivalent stray capacitor between gate and source. A TVS D

_{Z}and a reverse series diode D

_{r}are connected between drain and gate. D

_{r}is used to prevent the case that the driving signal output by U

_{G}is coupled to drain and source.

_{DS}is the drain-source voltage and U

_{BR}is the breakdown voltage of D

_{Z}, D

_{Z}will be broken down. As Q is OFF and the output of U

_{G}is low at this moment, U

_{DG}equals to U

_{DS}approximately. Therefore, a current i

_{Z}will flow into gate, which can increase the gate potential and provide a driving signal for Q. Additionally, then Q will turn on and draw some of the inductor current. Hence, the load current i

_{RL}(t) will decrease, which results in the decrease in u

_{RL}(t). According to Formulas (8) and (9), the drain-source voltage will decrease as well.

_{BR}is the reference value and the drain-source voltage U

_{DS}is the controlled object. Module F is the forward transfer function, which can be considered as the effect of gate-source voltage U

_{GS}on i

_{RL}(t) and U

_{DS}. In this way, U

_{DS}will be rapidly stabilized and equal to U

_{BR}approximately, which realizes the active clamping process and overvoltage protection.

## 3. Results Simulation of the Converter and Overvoltage Protection

#### 3.1. Simulation of the Converter

_{L}increases linearly from 5.8 A to 10.0 A until i

_{L}= I

_{c}and the load current i

_{RL}is zero. The duration of the charging stage in this simulation is about 96.8 μs. The on-resistance R

_{DS}

_{(on)}of the MOSFETs can be obtained from the physical model, which is 190 mΩ. Therefore, according to Formula (4), the charging time can be calculated as about 94.2 μs, which agrees well with the simulation results. In the discharging stage, i

_{L}almost decreases linearly and bipolar pulses are generated on the load. The amplitude of i

_{RL}equals to i

_{L}. The simulation results can prove that the theoretical analyses in Section 2 are accurate and reliable.

_{3}is about 6.08 W. However, for an EV charger, it can hardly output power to the battery indeed, because the power flows from the battery to the inductor in the negative pulse. In this case, define the output power in the negative pulse as a negative value. Then, the average output power is only about 5.37 W, which can hardly output power to the battery indeed. In order to provide a considerable power flow to the battery, the width of the positive pulse must be much longer than that of the negative pulse. In this way, a simulation of Reflex charging mode based on this converter is realized and shown in Appendix A.

#### 3.2. Simulation of the Overvoltage Protection

_{Z}pass through TVS and provides a trigger signal to turn on Q

_{3}. Then, in Figure 6c Q

_{3}draws a current of about 4.0 A, which will return to the inductor. As a result, there will be only a current of about 6.0 A passing through the load, clamping the load voltage to 360 V. The response time of this overvoltage protection is only about 44 ns and there is no overvoltage spike on the load. With the decrease in i

_{L}, it cannot produce an overvoltage across the load anymore, as is shown in Figure 6b. In this condition, the TVS will not be broken down and all of the inductor current will flow into the load. These results agree well with the theoretical analyses in Section 2.2. However, the clamping voltage is higher than U

_{BR.}This is because the TVS is not an ideal device and the voltage across TVS will not remain constant but increase slightly with the increase in breakdown current. As a result, when the negative feedback process in Figure 4b reaches a steady state, the clamping voltage will be a little higher than U

_{BR}.

## 4. Experiments and Results

#### 4.1. Output under Normal Conditions

#### 4.2. Output When Overvoltage Protection Takes Effect

_{BR}and overvoltage protection does not take effect anymore. The waveforms fit well with the theoretical analyses in Section 2.2 and the simulation in Section 3.2. However, the clamping voltage is about 390 V, which is even higher than that in the simulation. This is because the parasitic parameters of the practical circuit result in a longer feedback time.

#### 4.3. Model and Calculation of the Power Loss on MOSFETs

_{1}~Q

_{4}are very likely to be overheated, which can damage them and limit the properties of the converter. The switching frequency of Q

_{5}is much lower, so its power loss is much smaller. In order to improve the reliability of the converter, this section will establish a power loss model of the switches Q

_{1}~Q

_{4}and calculate their power loss.

#### 4.3.1. Switching Loss

_{1}~Q

_{4}is the same in this converter. Take Q

_{3}as an example. In one cycle, Q

_{3}has two different working patterns. In the charging stage, Q

_{3}keeps ON. Additionally, in the discharging stage, Q

_{3}works at a high frequency. Therefore, the switching loss is mainly consumed in the discharging stage.

_{d}and drain-source voltage U

_{DS}of Q

_{3}are both nonzero. Switching loss is caused as a result. In order to simplify the calculation, suppose that I

_{d}and U

_{DS}vary linearly during the turn-on transient and turn-off transient. The waveform of I

_{d}and U

_{DS}in a bipolar pulse cycle is shown in Figure 10, including a positive pulse, a negative pulse and two deadtime periods.

_{L}is the inductor current.

_{1}~Q

_{4}are all ON. Therefore, it can be regarded that the inductor current will flow into the two bridge arms evenly. Consequently, I

_{d}in the deadtime period is

_{cross}= t

_{turnon}+ t

_{turnoff}, t

_{turnon}, and t

_{turnoff}are the time of turn-on and turn-off process, respectively.

_{sw}. According to Formula (6), the inductor current can be considered as varying linearly, so the decrease in inductor current between two adjacent bipolar pulses can be calculated as

_{L0}is the inductor current when the charging stage starts.

#### 4.3.2. Conduction Loss

_{3}is always ON. Additionally, in the discharging stage, Q

_{3}is ON in the deadtime and negative pulse. Conduction loss is caused in these cases:

- (1)
- Charging stage

_{1}~Q

_{4}are all ON in the charging stage, it can be regarded that the inductor current will flow into the two bridge arms evenly. The current of Q

_{3}is:

_{charge}is the charging duration and t

_{charge}can be calculated according to Formula (4). R

_{DS}

_{(on)}is the drain-source on-resistance of the MOSFET. According to Ref. [32], the on-resistance of the diode is mainly affected by the junction temperature, the variable of R

_{DS}

_{(on)}is ignorable when the heat dissipation is good.

- (2)
- Discharging stage

_{d}in deadtime is expressed as Formula (15). Taking the decrease in inductor current in the discharging stage into consideration, the total energy of conduction loss in the deadtime can be calculated as:

_{dead}is the deadtime.

_{1}, Q

_{4}are OFF and Q

_{2}, Q

_{3}are ON. Therefore, the current of Q

_{3}equals to inductor current. In this case, the energy of conduction loss can be calculated as:

_{1}~Q

_{4}can be calculated as:

_{charge}+ n(2t

_{pulse}+ 2t

_{dead}) is the time of a charging and discharging cycle.

_{1}~Q

_{4}) can be estimated according to the above formulas. The related electrical parameters and calculation results are listed in Table 4.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Parameter | Value |
---|---|

Power inductor | L = 1 mH, ESR = 50 mΩ |

Input dc voltage | U_{d} = 48 V |

Load impedance | R_{L} = 30 Ω |

Reference current | I_{c} = 10 A |

Positive pulse width | t_{p_pulse} = 5000 ns |

Negative pulse width | t_{n_pulse} = 400 ns |

deadtime | t_{dead} = 300 ns |

Number of bipolar pulses in discharge stage | n = 5 |

**Figure A1.**Simulation results of the Reflex charging mode converter: (

**a**) train of pulses; (

**b**) zoomed-view of the pulses train; (

**c**) output power on the load.

## Appendix B

**Figure A2.**Simulation results of the converter: (

**a**) input voltage with ripples; (

**b**) train of pulses; (

**c**) zoomed-view of the pulses train; (

**d**) input power of the DC source and output power on the load.

_{d}(t) = U

_{d}+ sin2πft, where U

_{d}= 48 V and f = 50 kHz. The output pulses are shown in Figure A2b,c, which is the same as that in the simulation in Section 3.1. The input and output power are shown in Figure A2d. As can be seen, the input power in the charging stage is not linear anymore because of the ripples. However, the inductor current is unaffected and the ripples of the input DC source are not coupled to the output.

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**Figure 3.**Simplified circuit of the converter in different stages: (

**a**) charging stage; (

**b**) positive pulse; (

**c**) deadtime; (

**d**) negative pulse.

**Figure 4.**The overvoltage protection scheme: (

**a**) topology of the overvoltage protection circuit; (

**b**) the control loop model.

**Figure 5.**Simulation results of the converter: (

**a**) train of pulses; (

**b**) zoomed-view of the pulses train; (

**c**) input power of the DC source and output power on the load; (

**d**) power loss of MOSFET Q

_{3}.

**Figure 6.**Simulation results of the overvoltage protection: (

**a**) current of inductor; (

**b**) current of load; (

**c**) current of MOSFET; (

**d**) current of TVS.

**Figure 8.**Experimental results of the converter under normal conditions: (

**a**) train of pulses; (

**b**) zoomed-view of the pulses train.

Parameter | Value |
---|---|

Power inductor | L = 1 mH, ESR = 50 mΩ |

Input dc voltage | U_{d} = 48 V |

Load impedance | R_{L} = 30 Ω |

Reference current | I_{c} = 10 A |

Pulse width | t_{pulse} = 800 ns |

deadtime | t_{dead} = 300 ns |

Number of bipolar pulses in discharge stage | n = 15 |

Parameter | Value |
---|---|

Power inductor | L = 1 mH, ESR = 50 mΩ |

Input dc voltage | U_{d} = 48 V |

Load impedance | R_{L} = 60 Ω |

Reference current | I_{c} = 10 A |

Pulse width | t_{pulse} = 800 ns |

deadtime | t_{dead} = 300 ns |

Breakdown voltage of TVS | U_{BR} = 350 V |

Number of bipolar pulses in discharge stage | n = 15 |

Parameter | Value |
---|---|

Power inductor | L = 1 mH, ESR = 50 mΩ |

Input dc voltage | U_{d} = 48 V |

Reference current | I_{c} = 10 A |

Pulse width | t_{pulse} = 800 ns |

deadtime | t_{dead} = 300 ns |

Number of bipolar pulses in discharge stage | n = 15 |

MOSFET Q_{1}~Q_{5} | SPP21N50C3 |

Drivers for Q_{1}~Q_{4} | IR2110STRPBF |

Driver for Q_{5} | TLP250H(F) |

TVS D_{Z} | 1.5KE350A |

Breakdown voltage of TVS D_{Z} | U_{BR} = 350 V |

Controller (FPGA) | EP1C3T100C8N |

Parameter | Value |
---|---|

Pulse width | t_{pulse} = 800 ns |

Time of turn-on process | t_{turnon} = 136 ns |

Time of turn-off process | t_{turnoff} = 112 ns |

Time of charging stage | t_{charge} = 123 μs |

Inductor current when the charging stage starts | I_{L0} = 5.10 A |

Energy of switching loss | E_{sw}_{(total)} = 545.27 μJ |

Energy of conduction loss | E_{con}_{(total)} = 503.47 μJ |

Average power loss of Q_{1}~Q_{4} | P_{loss} = 6.72 W |

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## Share and Cite

**MDPI and ACS Style**

Xu, J.; Yang, X.; Zhao, H.; Qiu, J.; Liu, K.
An Inductor-Based and Capacitor-Free Bipolar Pulse Converter with Overvoltage Protection. *World Electr. Veh. J.* **2022**, *13*, 91.
https://doi.org/10.3390/wevj13050091

**AMA Style**

Xu J, Yang X, Zhao H, Qiu J, Liu K.
An Inductor-Based and Capacitor-Free Bipolar Pulse Converter with Overvoltage Protection. *World Electric Vehicle Journal*. 2022; 13(5):91.
https://doi.org/10.3390/wevj13050091

**Chicago/Turabian Style**

Xu, Jianzhi, Xingjian Yang, Hui Zhao, Jian Qiu, and Kefu Liu.
2022. "An Inductor-Based and Capacitor-Free Bipolar Pulse Converter with Overvoltage Protection" *World Electric Vehicle Journal* 13, no. 5: 91.
https://doi.org/10.3390/wevj13050091