Numerical simulation study on electromagnetic coupling characteristics of apertures based on FDTD method
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摘要: 针对电磁脉冲通过孔缝耦合进入电子设备腔体引发的干扰和损坏问题，基于时域有限差分法建立了理想导体矩形腔体的数值模型，系统分析了电磁脉冲的耦合特性。重点考察了不同入射角度和连续脉冲激励下腔体内的电磁场分布规律，采用时频联合分析方法揭示了孔缝耦合的共振机制。结果表明：孔缝耦合会导致特定频率下电场显著增强，其峰值可达入射场的数倍；正入射时腔体内共振效应最为明显，而斜入射条件下不同电场分量因边界条件限制呈现差异化响应；连续脉冲作用会引发电场能量累积，但其增长幅度受腔体驻波效应制约。此外，研究发现腔体共振频率与其结构尺寸密切相关，验证了孔缝耦合的频率选择特性，为电子设备在强电磁环境中的防护设计提供了理论依据和技术参考。Abstract:
Background Electromagnetic pulses (EMPs) can couple into electronic equipment cavities through apertures, causing severe interference and potential damage. Understanding the coupling characteristics and resonance mechanisms is critical for improving electromagnetic protection design.Purpose This study aims to investigate the coupling effects of EMPs on rectangular cavities with apertures, focusing on field distribution, resonance behavior, and the impact of incidence conditions.Methods A numerical model of a perfectly conducting rectangular cavity was established using the Finite-Difference Time-Domain (FDTD) method. The study analyzed electromagnetic field distributions inside the cavity under varying incidence angles and continuous pulse excitations. A time-frequency joint analysis method was applied to reveal the resonance mechanisms of aperture coupling.Results The results show that aperture coupling produces significant electric field enhancement at specific frequencies, with peak amplitudes several times larger than the incident field. Normal incidence yields the strongest resonant effects, while oblique incidence leads to different responses in electric field components due to boundary constraints. Continuous pulse excitation results in electric field energy accumulation, though limited by standing-wave effects. The resonant frequencies were found to be strongly dependent on cavity dimensions, confirming the frequency-selective characteristics of aperture coupling.Conclusions This research establishes the theoretical basis for understanding EMP aperture coupling and provides technical references for designing protection measures in high-intensity electromagnetic environments.-
Key words:
- FDTD /
- electromagnetic pulse /
- aperture coupling /
- resonance effect /
- incidence angle
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图 3 电磁脉冲入射腔体示意图
Figure 3. Schematic diagram of electromagnetic pulse incident on a cavity
图 6 狭缝中心与腔体中心功率密度
Figure 6. Power density at the center of the slit and the center of the cavity
图 7 狭缝中心与腔体中心频域图
Figure 7. Frequency domain diagram at the center of the slit and the center of the cavity
图 8 腔体中心与狭缝中心取样电场时域图
Figure 8. Time domain diagram of the sampled electric field at the center of the cavity and the center of the slit
图 9 腔体中心电场频域图
Figure 9. Frequency domain diagram of the electric field at the center of the cavity
图 10 平面波正入射和斜入射腔体中心频域图和耦合系数
Figure 10. Frequency domain diagram and coupling coefficient at the center of the cavity under normal and oblique incidence of plane waves
图 12 不同数量脉冲群激励下腔体中心时域图
Figure 12. Time domain diagram at the center of the cavity under excitation by pulse groups of different quantities
图 13 不同间隔脉冲群激励下腔体中心时域图
Figure 13. Time domain diagram at the center of the cavity under excitation by pulse groups with different intervals
表 1 不同时间段电场与功率密度峰值
Table 1. Peak values of electric field and power density at different time periods
time period/ns peak value of the electric field Ez component/(V·m−1) peak value of power density/(W·m−2) center of the slit center of the cavity center of the slit center of the cavity 0～50 3.7375 0.4344 3.0241 ×10−41.4830 ×10−650～100 0.0260 0.0429 5.0991 ×10−85.8427 ×10−8100～150 0.0082 0.0246 7.9147 ×10−91.8574 ×10−8150～200 0.0063 0.0181 3.4811 ×10−91.0960 ×10−8200～250 0.0050 0.0144 2.1121 ×10−96.1948 ×10−9250～300 0.0039 0.0112 1.5757 ×10−93.8135 ×10−9300～350 0.0031 0.0090 1.0266 ×10−92.2787 ×10−9
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表 2 腔体中心与狭缝中心时域图峰值
Table 2. Peak values of time domain diagrams at the center of the cavity and the center of the slit
sampling point Ex/(V·m−1) Ey/(V·m−1) Ez/(V·m−1) center of the slit 0.0478 0.5585 2.9415 center of the cavity 0.0043 0.0074 0.3114
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表 3 腔体中心电场第一个共振峰频率与谐振腔低次模频率
Table 3. First resonance peak frequency of the electric field at the center of the cavity and the lower mode frequencies of the resonant cavity
Ex/TE011/GHz) Ey/TE101/GHz) Ez/TE110/GHz) first resonance peak frequency 1.8010 1.6771 1.1793 resonant frequency of the cavity 1.8028 1.6771 1.2500
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表 4 不同数量脉冲激励下腔体中心电场峰值
Table 4. Peak values of the electric field at the center of the cavity under excitation by different numbers of pulses
number of incident
pulsespulse
duration/nspeak value of
Ex/(V·m−1)peak value of
Ey/(V·m−1)peak value of
Ez/(V·m−1)peak value of power
density/(W·m−2)10 51 16.1543 14.1553 573.4260 72.6571 20 102 30.3846 15.9893 573.4340 72.6292 80 410 65.0853 19.7964 561.0220 68.3825 160 820 84.8765 28.9687 573.4880 72.6366 320 1639 80.9581 41.0330 573.4640 72.7335 640 3279 85.4996 52.3679 576.6630 72.6639
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表 5 不同间隔脉冲群激励下腔体中心电场峰值
Table 5. Peak values of the electric field at the center of the cavity under excitation by pulse groups with different intervals
pulse
interval/nspulse
duration/nspeak value of
Ex/(V·m−1)peak value of
Ey/(V·m−1)peak value of
Ez/(V·m−1)peak value of power
density/(W·m−2)14.6363 7318 12.8499 87.0833 518.7520 85.3471 36.5908 7318 6.3700 17.4389 377.0730 34.8544 73.1817 7318 5.6504 37.6508 331.4450 33.2875
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