Analysis of factors causing waveform oscillation in avalanche transistor-based Marx circuit
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摘要: 基于雪崩晶体管的Marx电路常用于产生高压纳秒脉冲，输出波形通常具有前沿时间百ps量级、指数型放电后沿、kV级输出电压等特征。然而这种电路结构的典型输出波形后沿通常存在振荡或畸变；Marx电路的储能电容较大时，波形前沿还会出现尖峰振荡；已有研究对此关注较少或将其归因于电路杂散参数、阻抗匹配的影响。从雪崩晶体管动态导通过程的角度进行了仿真分析，并对储能电容取值、Marx电路级数、充电电压等因素的影响开展了实验研究。结果表明，雪崩晶体管自身过压导通状态是引起波形振荡的关键因素；储能电容越大、Marx级数越低、充电电压越小，则振荡的现象越明显，振荡幅值甚至能够高于晶体管雪崩击穿形成的快前沿尖峰，此时快前沿尖峰即体现为波形前沿上的振荡。通过调整Marx电路储能电容大小、优化微带线结构等方式可改善输出波形振荡。Abstract: The avalanche transistor-based Marx circuit is often used to generate high-voltage nanosecond pulses, its output waveform usually has a rising time about hundreds of picoseconds, an exponential discharging falling edge, and an output voltage in kV-level. However, the typical output waveform falling edge of this circuit structure usually has oscillation or distortion. Meanwhile, as long as the main capacitance of Marx circuit is large enough, the spike oscillation would emerge in the rising edge of the output waveform. Previous studies have paid less attention to this or attributed it to the influence of circuit stray parameters and impedance matching. In this paper, the simulation analysis was carried out from the perspective of the dynamic switching process of the avalanche transistor, and the influences of the main capacitor, the number of Marx circuit stages and the charging voltage were studied experimentally. The results show that the operating state of the avalanche transistor in voltage ramp mode caused the waveform oscillation. The oscillation would be more obvious when the circuit has larger main capacitance, fewer Marx stages and lower charging voltage. Moreover, the amplitude of the pulse oscillation could even be higher than the fast front edge, at this time, the fast front edge could be regarded as the spike oscillation in the output waveform rising edge. The output waveform oscillation can be reduced by adjusting the main capacitance of Marx circuit and optimizing the structure of microstrip line.
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图 1 过压导通状态下雪崩晶体管集电极与发射极之间电压VCE的仿真结果
Figure 1. Simulation result of voltage between collector and emitter of the avalanche transistor in voltage ramp mode
图 3 储能电容取值不同的5级Marx电路输出波形
Figure 3. Output voltage waveforms of 5-stage Marx circuit under different main capacitance
图 4 储能电容取值不同的4级Marx电路输出波形
Figure 4. Output voltage waveforms of 4-stage Marx circuit under different main capacitance
图 5 储能电容取值不同的20级Marx电路输出波形(充电电压270 V)
Figure 5. Output voltage waveforms of 20-stage Marx circuit under different main capacitance (charging voltage: 270 V)
图 6 不同级数Marx电路的输出波形(储能电容1.0 nF，充电电压300 V)
Figure 6. Output voltage waveforms of Marx circuits under different stages (main capacitance: 1.0 nF, charging voltage: 300 V)
表 1 实测Marx电路中元器件选取类型及参数
Table 1. Package types and specific parameters of the Marx circuit in experiment
item package types specifications avalanche transistor surface mount SOT23 FMMT417 main capacitor surface mount 1808 /1812 18 pF～4.7 nF charging resistor surface mount 2512 10 kΩ trigger resistor surface mount 2512 750 Ω 
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表 2 储能电容取值不同的5级Marx电路输出波形参数
Table 2. Output characteristics of 5-stage Marx circuit under different main capacitance
main capacitance/pF charging voltage/V rising time/ps first peak amplitude/V amplitude/V width/ns 4700 270 338 323 963 44.34 4700 300 302 517 1090 42.86 1000 270 344 316 805 11.87 1000 300 293 518 937 11.37 100 270 392 245 359 3.13 100 300 271 436 457 2.77 56 270 392 242 242 2.51 56 300 266 426 426 2.10 33 270 394 196 196 1.03 33 300 280 368 368 1.38 18 270 627 91 91 2.15 18 300 325 260 260 0.74
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表 3 储能电容取值不同的4级与20级Marx电路输出波形参数
Table 3. Output characteristics of 4/20-stage Marx circuit under different main capacitance
stage main capacitance/pF charging voltage/V rising time/ps first peak amplitude/V amplitude/V width/ns 4 4700 270 516 202 799 55.44 4 4700 300 370 340 914 53.30 4 1000 270 470 208 687 13.83 4 1000 300 375 356 793 13.43 4 100 270 547 172 326 2.84 4 100 300 387 312 390 2.98 4 56 270 585 148 238 2.60 4 56 300 426 267 267 2.46 4 33 270 694 134 157 2.24 4 33 300 376 207 207 2.07 4 18 270 662 21 72 2.39 4 18 300 313 128 128 1.58 20 4700 270 275 2039 2765 15.36 20 1000 270 239 1883 1883 6.07
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表 4 不同级数Marx电路的输出波形参数(储能电容1.0 nF，充电电压300 V)
Table 4. Output characteristics of Marx circuits under different stages (main capacitance: 1.0 nF, charging voltage: 300 V)
stage rising time/ps amplitude/kV width/ns 10 257 1.50 6.79 15 262 2.00 5.77 20 286 2.42 5.99 25 309 2.60 4.89 30 309 2.89 4.42 35 306 3.27 3.80 40 319 3.40 3.45 45 326 3.56 3.46 50 320 3.65 3.21
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