考虑异面孔缝电磁耦合的腔体屏蔽效能快速计算方法

doi:10.19595/j.cnki.1000-6753.tces.251359

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Abstract With the trend towards high frequency and high power density power electronics, electro-magnetic interference from switching devices has become a critical factor affecting system reliability. Metallic enclosures with apertures are widely used to mitigate this interference, so accurate evaluation of their shielding effectiveness and internal resonance is essential. For cavities with multiple apertures, however, existing analytical approaches usually treat the apertures on different faces independently. The internal field at an observation point is obtained by superposing fields transmitted through each aperture, while electromagnetic coupling among apertures and the propagation of these coupled fields inside the cavity are neglected. As a result, some resonance points and local field enhancements cannot be predicted, causing resonant points and local field enhancements cannot be predicted, leading to an incomplete assessment of shielding performance.
This paper develops an improved analytical method by incorporating electromagnetic coupling at the apertures. The method expresses the total electric field at an internal observation point as the vector superposition of the field produced by the incident wave directly exciting each aperture and the additional field generated by electromagnetic coupling and its propagation inside the cavity. The simplicity of field superposition is retained while capturing the interaction between apertures on different surfaces. The derivation is based on Bethe's small-aperture coupling theory and dyadic Green's functions. Each aperture is represented by an equivalent electric dipole and magnetic dipole at its center coordinates. For a given incident plane wave, the equivalent dipole moments associated with the directly transmitted field are obtained, and analytical expressions from the dyadic Green's functions of the rectangular cavity are used to calculate the internal electric field at the observation point. When coupling is ignored, the internal field is given by the superposition of the fields arising from the plane-wave components incident on each surface. In the improved formulation, Bethe's theory and the mirror theory are applied to determine additional equivalent dipoles associated with the coupled fields. The fields radiated by these coupling dipoles are again evaluated using the dyadic Green's functions and then vectorially added to the independently superposed field, thereby accounting for the effect of aperture coupling on the internal field distribution and the positions of resonance points.
The algorithm applies to cavities with multiple apertures under arbitrary plane-wave incidence, for arbitrary aperture locations and internal observation points over a wide frequency range, provided that the apertures satisfy the assumptions of the small-aperture model. The formulation yields the frequency-dependent shielding effectiveness and the associated resonance characteristics. Numerical results are compared with CST full-wave simulations for various cavity configurations, aperture arrangements, incidence conditions, and observation points. The results show that the method can accurately and efficiently evaluate shielding effectiveness and resonance points for cavities with multiple apertures. The approach can be used to assess the shielding performance of enclosures in high-frequency, high-power-density power electronic systems and to examine the influence of cavity geometry, aperture parameters, and observation locations on internal field distributions and resonance.

Key words： Electromagnetic coupling shielding effectiveness small aperture coupling dyadic Green's function cavity with apertures in multiple sides

Received: 03 August 2025

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	Huang Haihong
	Liao Heqi

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Huang Haihong,Liao Heqi. A Fast Calculation Method for Cavity Shielding Effectiveness Considering Electromagnetic Coupling of Apertures on Different Surfaces[J]. Transactions of China Electrotechnical Society, 2026, 41(16): 5375-5387.

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[1] 王凌云, 刘宏伟, 袁建强, 等. 高压快速光控脉冲晶闸管的设计与实现[J]. 电工技术学报, 2024, 39(23): 7566-7576.
Wang Lingyun, Liu Hongwei, Yuan Jianqiang, et al.Design and implementation of high-voltage high-speed optically controlled pulses thyristor[J]. Trans-actions of China Electrotechnical Society, 2024, 39(23): 7566-7576.
[2] Ma Zaojun, Pei Yunqing, Wang Laili, et al.An accurate analytical model of SiC MOSFETs for switching speed and switching loss calculation in high-voltage pulsed power supplies[J]. IEEE Trans-actions on Power Electronics, 2022, 38(3): 3281-3297.
[3] 郑翔, 杭丽君, 曾庆威, 等. SiC MOSFET新型负压关断串扰抑制驱动电路[J]. 中国电机工程学报, 2023, 43(20): 8038-8047.
Zheng Xiang, Hang Lijun, Zeng Qingwei, et al.A novel crosstalk suppression driving circuit for SiC MOSFET based on negative voltage level shift[J]. Proceedings of the CSEE, 2023, 43(20): 8038-8047.
[4] 徐浩东, 罗嗣勇, 毕闯, 等. 基于SiC MOSFET同步Buck DC-DC 变换器的宽频混合EMI滤波器设计[J]. 电工技术学报, 2024, 39(10): 3060-3069.
Xu Haodong, Luo Siyong, BiChuang, et al. Design of broadband hybrid EMI filter in synchronous buck DC-DC converter with SiC MOSFETs[J]. Trans-actions of China Electrotechnical Society, 2024, 39(10): 3060-3069.
[5] 惠琦, 任小永, 陈乾宏. 采用环形变压器的小功率隔离型DC-DC变换器共模电磁干扰噪声建模与抑制[J]. 电工技术学报, 2024, 39(22): 7126-7138.
Hui Qi, Ren Xiaoyong, Chen Qianhong.Common-mode electromagnetic interference noise modeling and suppressionfor low-power isolated power con-verter using toroidal transformer[J]. Transactions of China Electrotechnical Society, 2024, 39(22): 7126-7138.
[6] 杨磊, 何为, 贺玉成, 等. 开放式超低场移动磁共振系统的电磁干扰抑制方法[J]. 电工技术学报, 2024, 39(15): 4708-4717.
Yang Lei, He Wei, He Yucheng, et al.Electro-magnetic interference suppression method for an unshielded portableultra-low field magnetic resonance imaging scanner[J]. Transactions of China Electro-technical Society, 2024, 39(15): 4708-4717.
[7] 王华清, 黄道春, 双明镜, 等. 基于一体化电磁骚扰传导模型的开关柜微机保护装置电磁干扰滤波器设计[J]. 电工技术学报, 2024, 39(11): 3280-3290.
Wang Huaqing, Huang Daochun, Shuang Mingjing, et al.Design of EMI filter for microcomputer protection device of switchgear based on integrated electro-magnetic disturbance conduction model[J]. Trans-actions of China Electrotechnical Society, 2024, 39(11): 3280-3290.
[8] Yin Dongmei, Yu Nan, Sun Chengcheng, et al.Nume-rical analysis of the in-bore magnetic shielding of the series-enhanced electromagnetic railgun[J]. IEEE Transactions on Plasma Science, 2024, 52(9): 4705-4716.
[9] Kalantari M, Sadeghi S H H. An efficient surface integral equation-method of moments for analysis of electromagnetic shielding effectiveness of a per-forated isotropic and lossy enclosure[J]. IEEE Transactions on Electromagnetic Compatibility, 2024, 67(1): 99-107.
[10] Jia Zhenglang, Zhang Huanhuan, Zhao Lei, et al.Time-domain shielding effectiveness analysis based on DGTD method accelerated by local time-stepping and parallel techniques[J]. IEEE Transactions on Electromagnetic Compatibility, 2023, 65(3): 900-911.
[11] Bethe H A.Theory of diffraction by small holes[J]. Physical review, 1944, 66(7-8): 163-182.
[12] 白婉欣, 李天乐, 郭安琪, 等. 平面波照射下无限大导体板上周期孔阵屏蔽效能的解析研究[J]. 物理学报, 2019, 68(10): 89-97.
Bai Wanxin, Li Tianle, Guo Anqi, et al.Analytical theory on electromagnetic shielding effectiveness of infinite conductor plate with periodic aperture array under plane wave illumination[J]. Acta Physica Sinica, 2019, 68(10): 89-97.
[13] 张晗, 李常贤, 胡小龙. 快速预测干扰下斜开孔腔体屏蔽效能的模型[J]. 微波学报, 2023, 39(3): 73-79.
Zhang Han, Li Changxian, Hu Xiaolo.A model for quickly predicting the shielding effectiveness of an enclosure with an oblique aperture under inter-ference[J]. Journal of Microwaves, 2023, 39(3): 73-79.
[14] Nie Baolin, Liu Qingsong, Du Pingan.An improved thickness correction method of analytical for-mulations for shielding effectiveness prediction[J]. IEEE Transactions on Electromagnetic Compatibility, 2016, 58(3): 907-910.
[15] 张岩, 田铮, 刘尚合, 等. 内置介质板开孔腔体电磁屏蔽效能拓扑模型[J]. 微波学报, 2024, 40(2): 58-65.
Zhang Yan, Tian Zheng, Liu Shanghe, et al.Topological model of electromagnetic shielding effectiveness of cavity with built-in dielectric plate[J]. Journal of Microwaves, 2024, 40(2): 58-65.
[16] Xiao Pei, Du Pingan, Ren Dan, et al.A hybrid method for calculating the coupling to PCB inside a nested shielding enclosure based on electromagnetic topo-logy[J]. IEEE Transactions on Electromagnetic Compatibility, 2016, 58(6): 1701-1709.
[17] Wang Zian, Jiang Lijun, Mao Junfa, et al.Numerical Green's function-based method for modeling radiated emission from PCBs in shielding enclosures[J]. IEEE Transactions on Microwave Theory and Techniques, 2021, 69(12): 5250-5258.
[18] Wang Zian, Mao Junfa, Jiang Lijun, et al.Locali-zation and identification of EMI sources in shielding enclosures based on a two-step source reconstruction method[J]. IEEE Transactions on Electromagnetic Compatibility, 2023, 65(4): 972-981.
[19] Robinson M P, Benson T M, Christopoulos C, et al.Analytical formulation for the shielding effectiveness of enclosures with apertures[J]. IEEE Transactions on Electromagnetic Compatibility, 1998, 40(3): 240-248.
[20] Shim J, Kam D G, Kwon J H, et al.Circuital modeling and measurement of shielding effectiveness against oblique incident plane wave on apertures in multiple sides of rectangular enclosure[J]. IEEE Transactions on Electromagnetic Compatibility, 2010, 52(3): 566-577.
[21] 胡溥宇, 赵昱, 杨锦鹏, 等. 任意平面波辐照下开孔矩形腔体屏蔽效能快速计算方法[J]. 电工技术学报, 2018, 33(15): 3651-3660.
Hu Puyu, Zhao Yu, Yang Jinpeng.A fast approach for calculating the shielding effectiveness of rectangular enclosures with apertures under oblique plane wave illuminations[J]. Transactions of China Electro-technical Society, 2018, 33(15): 3651-3660.
[22] Kalantarnia A, Keshtkar A, Ghorbani A.Investigation of parameters affecting the level of perforated conductive enclosure protection against HEMP radiation using FDDM[J]. IEEE Transactions on Plasma Science, 2020, 48(6): 2115-2124.
[23] Xiao Zhifei, Wang Zian, Jiang Lijun, et al.Modeling wideband radiated emissions from PCBs in shielding enclosures based on single-plane phaselessnear-field scanning[J]. IEEE Transactions on Electromagnetic Compatibility, 2024, 66(3): 907-916.
[24] Harrington R F, Mautz J R.Characteristic modes for aperture problems[J]. IEEE Transactions on Micro-wave Theory and Techniques, 1985, 33(6): 500-505.
[25] Solin J R.Formula for the field excited in a rectangular cavity with an electrically large aperture[J]. IEEE Transactions on Electromagnetic Compatibility, 2012, 54(1): 188-192.
[26] Solin J R.Formula for the field excited in a rectangular cavity with a small aperture[J]. IEEE Transactions on Electromagnetic Compatibility, 2010, 53(1): 82-90.
[27] Li L W, Kooi P S, Leong M S, et al.On the eigenfunction expansion of electromagnetic dyadic Green's functions in rectangular cavities and waveguides[J]. IEEE Transactions on Mmicrowave Theory and Techniques, 2002, 43(3): 700-702.
[28] Shen Shicheng, Wang Yang, Xing Peishuai, et al.Prediction of shielding effectiveness at arbitrary observation points in rectangular cavities based on the BLT equation and field strength relationships[J]. IEEE Transactions on Electromagnetic Compatibility, 2025, 67(4): 1152-1161.
[29] 公延飞, 陈星彤, 高超飞, 等. 一种快速预测有损腔体屏蔽效能和谐振模式的解析模型[J]. 电工技术学报, 2021, 36(8): 1569-1578.
Gong Yanfei, Chen Xingtong, Gao Chaofei, et al.An analytical model for the fast prediction of the shielding effectiveness and resonances of a lossy enclosure[J]. Transactions of China Electrotechnical Society, 2021, 36(8): 1569-1578.