# An Inductive Isolation-Based 10 kV Modular Solid Boost-Marx Pulse Generator

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Topology and Operation Principle of Proposed Boost-Marx Pulse Generator

_{0}and δT is the discharge time of the pulse circuit when M

_{0}~M

_{n}is on. It is assumed that all semiconductor devices such as MOSFETs and diodes in the BMPG are ideal components. When they are turned on, the voltage between them is zero. The four operating modes in one cycle can be explained as follows:

#### 2.1. Mode 1 [0, t1]

_{0}in the circuit is turned on, and switches M

_{1}~M

_{n}are turned off. The duration of this mode is DT. The DC power supply U

_{dc}charges the inductor L through M

_{0}, D

_{2}, D

_{4}… D

_{2n}. At this time, the inductor voltage is equal to the input DC power supply voltage, and the charging current can be expressed by Equation (1):

#### 2.2. Mode 2 [t1, t2]

_{dc}and the inductor L charge the capacitors C

_{1}~C

_{n}through the diodes D

_{1}~D

_{n}. The charging equivalent circuit diagram is shown in Figure 4. All the capacitors in the circuit are connected in parallel, the value of the equivalent capacitor C

_{eq}is equal to the sum of all the energy storage capacitors, and its value is nC. The voltage value of the equivalent capacitor U

_{eq}is equal to the voltage of each capacitor. The equivalent current Ieq is the sum of each branch. Consequently, the expressions of the voltage and current of equivalent capacitor can be represented as:

#### 2.3. Mode 3 [t2, t3]

_{1}~C

_{n}are discharged in series through the switches M

_{1}~M

_{n}. At this time, the equivalent capacitance discharged in series is C/n. The output pulse voltage is estimated as (4). There is a short-term high voltage on the inductor, which can be calculated by Equation (5).

#### 2.4. Mode 4 [t3, t4]

_{1}~C

_{n}. In a working cycle, in the charging state, the current flowing through the equivalent capacitor is equal to the sum of the current flowing through C

_{1}~C

_{n}. In the capacitor pulse discharge mode, the equivalent capacitor’s total current is equal to the current of each capacitor branch, as shown in Figure 5 and Figure 6. There are two processes of capacitor charging. The charging voltages are represented by (7) and (9), respectively. The discharge mode can be equivalent to discharging the capacitor to the load. The capacitor voltage drop caused by this process can be represented by Formula (8). The three reach equilibrium in one cycle. Under normal circumstances, the pulse voltage can reach several kV, which is much larger than the voltage in the balanced state of the capacitor. The current, that is, the current value of the pulse output, can be approximated as (11).

## 3. Parameter Selection and Comparative Analysis

#### 3.1. Parameter Selection

_{d}. the value of the required capacitor can be calculated as:

#### 3.2. Comparative Analysis

## 4. Simulation Results

_{1}–M

_{12}are adjusted in different switching sequences. The delay time between each switch is 30 ns, which realizes the adjustable change of pulse rising time, falling time, or the above two.

_{0}and the discharge switches M

_{1}~M

_{12}in each mode, proving that their voltage levels are the same.

## 5. Experimental Results

_{0}~M

_{12}. Experiments have proved that, including the switch M

_{0}used for chopping, all switches have the same voltage level. This also shows that adding a chopper switch will not increase the voltage level of the Marx circuit switching device, which will be conducive to the expansion of topology modularity. Figure 11h,i are the voltage and current waveforms of the output pulse. Experiments show that BMPG can still ensure that the output pulse is a rectangular wave. The above experimental results are also in good agreement with the simulation results in the previous section. During the initial time of pulse output, the pulse voltage amplitude is a growing process, and the voltage amplitude increases from nU

_{dc}to βnU

_{dc}, as shown in Figure 12.

## 6. Conclusions

- (1)
- This article uses an inductive isolator on the basis of the traditional Marx circuit, and with the addition of only one solid-state switch to increase the gain of the output voltage pulse.
- (2)
- BMPG completes the isolation between the pulse generator and the DC power supply, reducing the voltage amplitude requirements of the DC power supply, and the entire system is modular and scalable.
- (3)
- The amplitude of the output pulse can be adjusted by varying the duty cycle D, and a new control method is proposed to make the adjustment more flexible. This provides a basis for the closed-loop control of the pulse power supply in the future.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**BMPG working mode schematic (

**a**) Inductor energy storage mode, (

**b**) Capacitor charge mode, (

**c**) Pulse discharge mode.

**Figure 8.**Simulation results of BMPG circuit (pulse frequency 10 kHz, amplitude 10 kV) (

**a**) Pulse waveforms with different pulse widths (

**b**) Pulse waveforms with different rising and falling time (

**c**) Inductor voltage waveform (

**d**) Inductor current waveform (

**e**) Capacitance Voltage waveform (

**f**) Switch M

_{1}~M

_{12}drain-source voltage (

**g**) Switch M

_{0}drain-source voltage (

**h**) Output pulse voltage waveform (

**i**) Output pulse current pulse.

**Figure 11.**Experiment results of BMPG circuit (pulse frequency 10 kHz, amplitude 10 kV) (

**a**) Pulse waveforms with different pulse widths (

**b**) Pulse waveforms with different rising and falling time (

**c**) Inductor voltage waveform (

**d**) Inductor current waveform (

**e**) Capacitance Voltage waveform (

**f**) Switch M

_{1}~M

_{12}drain-source voltage (

**g**) Switch M

_{0}drain-source voltage (

**h**) Output pulse voltage waveform (

**i**) Output pulse current pulse.

Reference | [15] | [16] | [17] | [21] | [23] | [25] | [27] | Proposed |
---|---|---|---|---|---|---|---|---|

Number of switches | 2n | n | n | n + 3m | n | 2n + 1 | n + 2 | n + 1 |

Number of diodes | n | 2n | 2n | n + m | n | n + 1 | 2n | 2n |

Number of capacitors | n | n | n | 2n + 2m | n | n + 1 | n | n |

Number of inductors | 1 | 1 | 0 | n | n | 0 | 1 | 1 |

Number of transforms | 0 | 0 | 0 | n | 0 | 0 | 0 | 0 |

Pulse voltage gain | n | n | n | $\frac{nN}{1-D}$ | Slight larger than n | ${2}^{\frac{n+2}{2}}-2$ | $n{I}_{L}\sqrt{\frac{L}{nC}}$ | $\frac{n}{1-D-(n+1)\delta}$ |

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

Input DC voltage | U_{dc} = 235 V |

Number of module | N = 12 |

Pulse period | T = 100 μs |

Voltage drop coefficient | α = 5% |

Duty cycle | D = 0.61 |

Storage capacitor | C = 1 μf |

Isolated inductor | L = 2.5 mH |

Load resistor | R = 400 Ω |

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

Input DC voltage | U_{dc} = 235 V |

Number of module | N = 12 |

Pulse period | T = 100 μs |

Voltage drop coefficient | α = 5% |

Duty cycle | D = 0.61 |

Storage capacitor | C = 1 μf |

Isolated inductor | L = 2.5 mH |

Load resistor | R = 400 Ω |

MOSFET part no | C2M0025120D |

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**MDPI and ACS Style**

Jin, Y.; Cheng, L. An Inductive Isolation-Based 10 kV Modular Solid Boost-Marx Pulse Generator. *Electronics* **2023**, *12*, 1586.
https://doi.org/10.3390/electronics12071586

**AMA Style**

Jin Y, Cheng L. An Inductive Isolation-Based 10 kV Modular Solid Boost-Marx Pulse Generator. *Electronics*. 2023; 12(7):1586.
https://doi.org/10.3390/electronics12071586

**Chicago/Turabian Style**

Jin, Yaobin, and Li Cheng. 2023. "An Inductive Isolation-Based 10 kV Modular Solid Boost-Marx Pulse Generator" *Electronics* 12, no. 7: 1586.
https://doi.org/10.3390/electronics12071586