Simulation analysis of the equivalent circuit of a gyro-magnetic nonlinear transmission line
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摘要: 旋磁非线性传输线因其独特的小型化结构、实时频率调谐能力以及宽谱微波输出特性，在小型固态化高功率微波源方向展现出重要应用价值。通过理论推导获得GNLTL等效电路中的孤子解析表达式，通过电路仿真方法，构建旋磁非线性传输线的等效电路模型，系统研究关键电路参数对输出特性的影响机制。研究发现：非线性电感的饱和电流和初始电感对电路的非线性特性具有决定性影响。当饱和电流和初始电感取值较小时，输出脉冲出现前沿不完全陡化，且脉冲前沿加载有振荡波形；此时，若饱和电流和初始电感增大，输出脉冲的前沿陡化程度得到提升，即饱和电流和初始电感与电路的非线性正相关。此外，等效电路的非线性增强会导致输出频率的降低。饱和电流、饱和电感、初始电感以及每级电容与输出微波频率负相关。该研究可以为旋磁非线性传输线的设计分析提供参考。Abstract:
Background Owing to its unique miniaturized structure, real-time frequency tuning capability, and broad-spectrum microwave output characteristics, the gyromagnetic nonlinear transmission line (GNLTL) exhibits considerable application potential in the development of small-scale solid-state high-power microwave sources. This has driven the need for in-depth exploration of its circuit characteristics and parameter influences to optimize its performance.Purpose This study aims to derive the analytical expression of solitons in the GNLTL equivalent circuit, construct a reliable equivalent circuit model of GNLTL, and systematically clarify the influence mechanism of key circuit parameters on its output characteristics.Methods Firstly, the analytical expression of solitons in the GNLTL equivalent circuit was obtained through theoretical deduction. Secondly, an equivalent circuit model of GNLTL was established using circuit simulation methods. Finally, the influence mechanism of key circuit parameters on the output characteristics of GNLTL was systematically investigated based on the constructed model.Results The results show that the saturation current and initial inductance of the nonlinear inductor have a decisive effect on the nonlinear characteristics of the circuit: when these two parameters are small, the leading edge of the output pulse is not fully steepened and is accompanied by oscillating waveforms; increasing them improves the steepening degree of the pulse leading edge, indicating a positive correlation between these two parameters and circuit nonlinearity. Additionally, enhanced nonlinearity of the equivalent circuit leads to a decrease in output frequency; saturation current, saturation inductance, initial inductance, and capacitance per stage all show a negative correlation with the output microwave frequency.Conclusions The findings of this study clarify the relationship between key circuit parameters and the nonlinear characteristics as well as output frequency of GNLTL, thereby providing theoretical and simulation references for the design and performance analysis of gyromagnetic nonlinear transmission lines. -
图 2 仿真输出波形与实验波形对比以及仿真输出频率分布
Figure 2. Comparison of simulation output waveform and experimental waveform and simulation output frequency distribution
图 3 饱和电流对非线性电感随电流变化的曲线的影响
Figure 3. Effect of saturation current on the curve of nonlinear inductance with current variation
图 4 饱和电流分别设置为15A以及45A时，对比不同输入脉冲幅值GNLTL的输出波形
Figure 4. When the saturation current is set to 15A and 45A, respectively, the output waveforms of GNLTL with different input pulse amplitudes are compared
图 5 输入梯形脉冲的幅值和饱和电流对GNLTL等效电路输出波形频率的影响
Figure 5. The influence of the amplitude and saturation current of the input trapezoidal pulse on the modulation depth and frequency of the output waveform of the GNLTL equivalent circuit
图 6 饱和电感对GNLTL等效电路输出波形的影响
Figure 6. Effect of saturation inductance on the output waveform of GNLTL equivalent circuits
图 7 初始电感对GNLTL等效电路输出波形的影响
Figure 7. Effect of initial inductance on the output waveform of GNLTL equivalent circuits
图 8 初始电感对GNLTL等效电路输出波形频率的影响
Figure 8. The effect of the initial inductance on the modulation depth and frequency of the output waveform of the GNLTL equivalent circuit
图 9 非线性电路的单级电容对GNLTL等效电路输出的影响
Figure 9. The effect of a single-stage capacitance of a nonlinear circuit on the output of a GNLTL equivalent circuit
图 10 输入梯形脉冲的上升沿对GNLTL等效电路输出波形的影响
Figure 10. Effect of the rising edge of the input trapezoidal pulse on the output waveform of the GNLTL equivalent circuit
图 11 当输入梯形脉冲上升沿为7 ns和10 ns时，不同饱和电流条件下GNLTL等效电路的输出对比
Figure 11. When the rising edge of the input trapezoidal pulse is 7 ns and 10 ns, the output of the GNLTL equivalent circuit under different saturation current conditions is compared
表 1 相关参数
Table 1. relevant parameter
parameter $ \;{ \mu _{r0}} $ $ \;{ \mu _{rs}} $ $ {\varepsilon _d} $ $ {\varepsilon _r} $ $ {d_{in}} $/mm $ {d_f} $/mm $ {d_{out}} $/mm $ {L_t} $/m $ {f_0} $/GHz value 116 4.4 1 14 10 16 32 0.8 1 
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表 2 GNLTL等效电路参数
Table 2. GNLTL equivalent circuit parameters
parameter $ {L_{n0}} $/nH $ {L_{ns}} $/nH $ {C_n} $/pf n value 465 23 3 $20 \leqslant $
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表 3 各参数对模型影响
Table 3. Influence of each parameter on the model
parameter $ {I_s} $ $ {L_{ns}} $ $ {L_{n0}} $ $ {C_n} $ nolinear positive positive − − output frequency negative negative negative negative
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