准方波脉冲形成网络的理论分析与设计

王传伟; 李洪涛

doi:10.11884/HPLPB201830.170392

准方波脉冲形成网络的理论分析与设计

doi: 10.11884/HPLPB201830.170392

王传伟^{1, 2,},
李洪涛^1, ,

1.
中国工程物理研究院流体物理研究所, 脉冲功率科学与技术重点实验室, 四川绵阳 621900
2.
中国工程物理研究院研究生院, 北京 100088

基金项目:

国家自然科学基金项目 61504127

国家自然科学基金项目 U1530128

中国工程物理研究院院长基金项目 YZJJLX2016002

详细信息

作者简介:
王传伟(1983－)，男，博士研究生，副研究员，从事固态脉冲技术及测控技术研究；250705799@qq.com

通讯作者:
李洪涛(1968－)，男，研究员，从事脉冲功率技术研究；lihongtao-ifp@caep.cn

中图分类号: TN784
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出版历程
- 收稿日期: 2017-10-10
- 修回日期: 2017-11-26
- 刊出日期: 2018-03-15

Theoretical analysis and design of the trapezoidal pulse forming network

Wang Chuanwei^{1, 2
,},
Li Hongtao^{1
, ,}

1.
Key Laboratory of Pulsed Power, Institute of Fluid Physics, CAEP, P.O. Box 919-107, Mianyang 621900, China
2.
Graduate School of China Academy of Engineering Physics, Beijing 100088, China

摘要

摘要: 针对微波驱动源、固态调制器等对宽平顶脉冲源的应用需求，开展了基于脉冲形成网络输出准方波的理论研究与分析设计。首先采用Prony算法获得准方波波形的解析表达式，然后基于最佳一致逼近的优化控制思路，列出极点控制方程，采用数值方法求解非线性方程组，获得优化波形参数。在此基础上采用阻抗函数匹配的算法求解出脉冲形成网络的元件参数初始值，根据工程设计的实际情况舍弃部分参数并对个别参数进行优化后，获得最终的元器件参数。通过理论分析与数值模拟相结合的方法，系统地给出了获取长脉宽、低纹波准方波脉冲形成网络的设计方法以及设计准则。该方法可用于设计任意阶低纹波系数的准方波脉冲源，也可用于设计其他输出波形要求的脉冲源。
- 准方波 /
- 脉冲形成网络 /
- Prony算法 /
- 最佳一致逼近 /
- 阻抗匹配设计 /
- 低纹波
Abstract: For the application requirements of the high voltage pulse generator based on the pulse forming network(PFN) in the microwave driver and the solid-state modulator, the theory of the PFN with the trapezoidal pulse output was developed. First, the analytical expression of the trapezoidal pulse was obtained by the Prony algorithm. Secondly, the waveform parameters were optimized by using the best uniform approximation algorithm based on the equations of the optimal control with the maximum and minimum of the output wave, and solving these nonlinear equations with the Newton iteration method or other numerical methods. Then, the initial parameters of the PFN were worked out with the method of impedance matching. The final components parameters were obtained by rejecting some secondary parameters and adjusting a few of the main parameters. The method and criteria of the design for a PFN with the low ripple trapezoidal pulse output were proposed by theoretical analysis and numerical simulation. The results show that the proposed method can be used to design the PFN with any order and low ripple, and it can be used to design not only the pulse source with trapezoidal pulse output, but also the pulse sources with other pulse output.
- trapezoidal pulse /
- pulse forming network /
- Prony algorithm /
- best uniform approximation /
- impedance matching design /
- low ripple

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图 1 理想方波及Prony级数拟合准方波波形

Figure 1. Rectangular pulse and trapezoidal pulses fitted by Prony series

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图 2 最佳一致逼近优化波形

Figure 2. Waveforms obtained by best uniform approximation algorithm

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图 3 基于脉冲形成网络(PFN)的脉冲发生器电路模型

Figure 3. Circuit model of pulse generator based on pulse forming network(PFN)

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图 4 常用脉冲形成网络(PFN)电路构型

Figure 4. Circuits of commonly used PFN

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图 5 五级B型PFN仿真电路

Figure 5. Simulation circuit of 5-stage B-type PFN

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图 6 未优化电路元件参数时输出脉冲波形

Figure 6. Output pulses without optimization of element parameters

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图 7 优化电路元件参数后输出脉冲波形

Figure 7. Output pulses with optimization of element parameters

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表 1 Prony算法直接拟合所得复振幅和复频率

Table 1. Results of amplitudes and frequencies obtained by Prony algorithm

A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉	A₁₀
0.004 199 -0.014 816i	0.004 199 +0.014 816i	0.020 346 -0.033 943i	0.020 346 +0.033 943i	0.067 039 -0.070 089i	0.067 039 +0.070 089i	0.238 64 -0.221 1i	0.238 64 +0.221 1i	-0.330 22 -2.036 1i	-0.330 22 +2.036 1i

α₁	α₂	α₃	α₄	α₅	α₆	α₇	α₈	α₉	α₁₀
-0.051 922 +30.519i	-0.051 922 -30.519i	-0.217 84 +23.345i	-0.217 84 -23.345i	-0.537 27 +16.189i	-0.537 27 -16.189i	-1.125 6 +9.109 6i	-1.125 6 -9.109 6i	-2.226 3 +2.600 5i	-2.226 3 -2.600 5i

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表 2 最佳一致逼近优化所得复振幅

Table 2. Results of amplitudes obtained by best uniform approximation algorithm

ε	A₁	A₂	A₃	A₄	A₅	A₆	A₇	A₈	A₉	A₁₀
0.005	0.004 213 -0.008 190i	0.004 213 +0.008 190i	0.016 645 -0.020 462i	0.016 645 +0.020 462i	0.059 499 -0.051 987i	0.059 499 +0.051 987i	0.230 59 -0.196 64i	0.230 59 +0.196 64i	-0.310 95 -2.007 5i	-0.310 95 +2.007 5i
0.001	0.002 448 4 -0.003 337 2i	0.002 448 4 +0.003 337 2i	0.0130 59 -0.012 782i	0.013 059 +0.012 782i	0.053 507 -0.040 342i	0.053 507 +0.040 342i	0.224 76 -0.178 59i	0.224 76 +0.178 59i	-0.293 78 -1.984 5i	-0.293 78 +1.984 5i

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表 3 直接匹配求解出的五级B型脉冲形成网络参数(ε=0.001)

Table 3. Parameters of devices in 5- stage B-type PFN with ε=0.001

L₁	L₂	L₃	L₄	L₅	C₁	C₂	C₃	C₄	C₅
0.121 8	0.058 6	0.059 6	0.068 4	0.095 3	0.066 7	0.057 9	0.063 0	0.077 6	0.145 0

R₁	R₂	R₃	R₄	R₅	G₁	G₂	G₃	G₄	G₅
0.019 5	-0.007 4	0.000 6	0.000 6	-0.004 2	0.014 1	-0.001 9	0.001 1	-0.000 9	-0.012 4

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表 4 五级B型脉冲形成网络优化后参数

Table 4. Optimized parameters of devices in 5- stage B-type PFN

ε	L₁	L₂	L₃	L₄	L₅	C₁	C₂	C₃	C₄	C₅
0.005	0.102 4	0.056 2	0.061 4	0.070 9	0.098 6	0.059 3	0.058 8	0.065 8	0.081 1	0.151 4
0.001	0.126 7	0.058 6	0.059 6	0.068 4	0.095 3	0.066 7	0.057 9	0.063 0	0.077 6	0.145 0

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表 5 五级B型脉冲形成网络优化后输出脉冲波形特征参数

Table 5. Features of output pulses in simulation circuit of Fig. 5

ε(designed)	t_ri(10%~90%)	t_fi(90%~10%)	t_w1(10%~10%)	t_w2(100%~100%)	ε(simulated)
0.005	0.070	0.137	0.964	0.670	0.006 8
0.001	0.089	0.169	0.988	0.584	0.001 3

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