Statistical analysis on electromagnetic emission characteristics of phased array antenna
-
摘要: 相控阵天线波束指向高度动态变化，其电磁发射特性呈现出显著的统计规律，分析和测试所需的资源巨大。采用多项式混沌展开（PCE）探究二维平面相控阵天线发射特性的统计特性，根据方向图乘积定理等确定代表相控阵天线电磁发射特性的目标函数，利用PCE建立目标函数的等效代理模型。从理想点源构成的相控阵天线着手，分别考虑了主波束指向服从均匀分布和正态分布两种典型情况，通过计算机仿真模拟得到等效代理模型的概率密度函数和累积分布函数，并使用传统的蒙特卡罗方法结果作为参照来评估PCE方法的有效性和可靠性，最后对小型偶极子相控阵天线的波束指向服从两种典型分布的情况进行讨论。仿真对比结果表明，PCE方法在保证结果准确度的同时可以大大减少采样样本点数目，大幅提升相控阵天线电磁发射特性分析和测试的效率。Abstract: The beam direction of the phased array antenna changes dynamically. Its electromagnetic emission characteristics show significant statistical laws, and the resources required for analysis and testing are numerous. In this paper, polynomial chaos expansion (PCE) is used to explore the statistical characteristics of the two-dimensional planar phased array antenna’s emission. The objective function of the phased array antenna is determined according to the pattern product theorem, and PCE is used to establish an equivalent surrogate model of the array’s emission characteristics. The paper starts from the phased array antenna composed of ideal point sources, and considers two typical cases that the main beam direction obeys the uniform distribution and the normal distribution. The statistical characteristics of the equivalent surrogate model are obtained by computer simulation. The results of the traditional Monte Carlo (MC) method are used as a reference to evaluate the effectiveness and reliability of the PCE method. At the end of the paper, the situation that the beam direction of the dipole phased array antenna obeys two typical distributions is briefly discussed. The comparison of simulation results shows that the PCE method can greatly reduce the sampling numbers of calculation while ensuring the accuracy of the results, and significantly improve the efficiency of analysis and testing.
-
图 3
${\rm{U}}( - 5^\circ ,5^\circ )$ 阵因子统计特性（PCE阶数$ P = 4 $ ）Figure 3.
$ {\rm{U}}( - 5^\circ ,5^\circ ) $ statistical characteristics of array factor ($ P = 4 $ )
图 4
$ {\rm{U}}( - 10^\circ ,10^\circ ) $ 阵因子统计特性（PCE阶数$ P = 6 $ ）Figure 4.
$ {\rm{U}}( - 10^\circ ,10^\circ ) $ statistical characteristics of array factor ($ P = 6 $ )
图 5
$ {\rm{U}}( - 30^\circ ,30^\circ ) $ 阵因子统计特性（PCE阶数$ P = 13 $ ）Figure 5.
$ {\rm{U}}( - 30^\circ ,30^\circ ) $ statistical characteristics of array factor ($ P = 13 $ )
图 6
$ {\rm{U}}( - 45^\circ ,45^\circ ) $ 阵因子统计特性（PCE阶数$ P = 20 $ ）Figure 6.
$ {\rm{U}}( - 45^\circ ,45^\circ ) $ statistical characteristics of array factor ($ P = 20 $ )
图 7
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ 观察点$ (0^\circ ,0^\circ ) $ 处阵因子统计特性（PCE阶数$ P = 8 $ ）Figure 7.
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ statistical characteristics of array factor at$ (0^\circ ,0^\circ ) $ observation point ($ P = 8 $ )
图 8
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ 观察点$ (90^\circ ,90^\circ ) $ 处阵因子统计特性（PCE阶数$ P = 8 $ ）Figure 8.
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ statistical characteristics of array factor at$ (90^\circ ,90^\circ ) $ observation point ($ P = 8 $ )
图 9
${\rm{N}}(90^\circ ,{0.1^\circ}^2)$ 观察点$ (0^\circ ,0^\circ ) $ 处阵因子统计特性（PCE阶数$ P = 14 $ ）Figure 9.
${\rm{N}}(90^\circ ,{0.1^\circ}^2)$ statistical characteristics of array factor at$ (0^\circ ,0^\circ ) $ observation point ($ P = 14 $ )
图 10
${\rm{N}}(90^\circ ,{0.1^\circ}^2)$ 观察点$ (90^\circ ,90^\circ ) $ 处阵因子统计特性（PCE阶数$ P = 14 $ ）Figure 10.
${\rm{N}}(90^\circ ,{0.1^\circ}^2)$ statistical characteristics of array factor at$ (90^\circ ,90^\circ ) $ observation point ($ P = 14 $ )
图 12
$ {\rm{U}}( - 5^\circ ,5^\circ ) $ 电场统计特性（PCE阶数$ P = 4 $ ）Figure 12.
$ {\rm{U}}( - 5^\circ ,5^\circ ) $ statistical characteristics of E field ($ P = 4 $ )
图 13
$ {\rm{U}}( - 10^\circ ,10^\circ ) $ 电场统计特性（PCE阶数$ P = 6 $ ）Figure 13.
$ {\rm{U}}( - 10^\circ ,10^\circ ) $ statistical characteristics of E field ($ P = 6 $ )
图 14
$ {\rm{U}}( - 30^\circ ,30^\circ ) $ 电场统计特性（PCE阶数$ P = 13 $ ）Figure 14.
$ {\rm{U}}( - 30^\circ ,30^\circ ) $ statistical characteristics of E field ($ P = 13 $ )
图 15
${\rm{ U}}( - 45^\circ ,45^\circ ) $ 电场统计特性（PCE阶数$ P = 20 $ ）Figure 15.
$ {\rm{U}}( - 45^\circ ,45^\circ ) $ statistical characteristics of E field ($ P = 20 $ )
图 16
${\rm{N}}(90^\circ ,{0.02^\circ}^2)$ 观察点$(100 \;{\rm{m}},45^\circ ,45^\circ )$ 处电场统计特性（PCE阶数$ P = 9 $ ）Figure 16.
${\rm{N}}(90^\circ ,{0.02^\circ}^2)$ statistical characteristics of E field at$(100 \;{\rm{m}},45^\circ ,45^\circ )$ observation point ($ P = 9 $ )
图 17
${\rm{N}}(90^\circ ,{0.02^\circ}^2)$ 观察点$ (100\;{\rm{m}},90^\circ ,90^\circ ) $ 处电场统计特性（PCE阶数$ P = 9 $ ）Figure 17.
${\rm{N}}(90^\circ ,{0.02^\circ}^2)$ statistical characteristics of E field at$ (100\;{\rm{m}},90^\circ ,90^\circ ) $ observation point ($ P = 9 $ )
图 18
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ 观察点$ (100\;{\rm{m}},45^\circ ,45^\circ ) $ 处电场统计特性（PCE阶数$ P = 20 $ ）Figure 18.
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ statistical characteristics of E field at$ (100\;{\rm{m}},45^\circ ,45^\circ ) $ observation point ($ P = 20 $ )
图 19
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ 观察点$ (100\;{\rm{m}},90^\circ ,90^\circ ) $ 处电场统计特性（PCE阶数$ P = 20 $ ）Figure 19.
${\rm{N}}(90^\circ ,{0.05^\circ}^2)$ statistical characteristics of E field at$ (100\;{\rm{m}},90^\circ ,90^\circ ) $ observation point ($ P = 20 $ )表 1 均匀分布的对比结果
Table 1. Comparison results of uniform distribution
distribution order of PCE sampling number of PCE sampling number of MC $ {\rm{U}}(-5{\text{°}}, 5{\text{°}}) $ 4 25 100 000 $ {\rm{U}}(-10{\text{°}},10{\text{°}}) $ 6 49 100 000 $ {\rm{U}}(-30{\text{°}},30{\text{°}}) $ 13 196 100 000 $ {\rm{U}}(-45{\text{°}},45{\text{°}}) $ 20 441 100 000 
下载: 导出CSV
表 2 正态分布的对比结果（阵因子）
Table 2. Comparison results of normal distribution（Array Factor）
distribution order of PCE sampling number of PCE sampling number of MC ${\rm{N} }(90{\text{°} },{0.05{\text{°} } }^{2})$ 8 81 100 000 ${\rm{N} }(90{\text{°} },{0.1{\text{°} }}^{2})$ 14 225 100 000
下载: 导出CSV
表 3 正态分布的对比结果(电场)
Table 3. Comparison results of normal distribution (E field)
distribution order of PCE sampling number of PCE sampling number of MC ${\rm{N} }(90^\circ,{0.02^\circ}^2)$ 9 100 100 000 ${\rm{N} }(90^\circ,{0.05^\circ}^2)$ 20 441 100 000
下载: 导出CSV
-
[1] 张盼. 相控阵雷达识别方法与高效实现研究[D]. 成都: 电子科技大学, 2018Zhang Pan. Research on operation mode classification methods with fast implement of electronic-scan phased array radar[D]. Chengdu: University of Electronic Science and Technology of China, 2018 [2] Stutzman W L. Antenna theory and design[M]. 2nd ed. New York: J. Wiley, 1998. [3] 胡昌海, 王任, 陈传升, 等. 平面相控阵超大角度扫描的阵因子分析[J]. 物理学报, 2021, 70:098401. (Hu Changhai, Wang Ren, Chen Chuansheng, et al. Array factor analysis for untra-wide-angle scanning performance of planar phased arrays[J]. Acta Physica Sinica, 2021, 70: 098401 [4] Hansen R C. Phased array antennas[M]. New York: Wiley, 1998. [5] 张光义. 相控阵雷达原理[M]. 北京: 国防工业出版社, 2009Zhang Guangyi. Principles of phased array radar[M]. Beijing: National Defense Industry Press, 2009 [6] 陈绪元. 舰载多功能相控阵雷达概述[J]. 现代雷达, 2000, 22(1):20-24. (Chen Xuyuan. Summarization of the shipborne multi-function phased array radars[J]. Modern Radar, 2000, 22(1): 20-24 doi: 10.3969/j.issn.1004-7859.2000.01.004 [7] 张昀. 国外海军先进射频集成系统分析[J]. 电讯技术, 2009, 49(6):77-80. (Zhang Yun. Analysis of foreign naval advanced RF integrated systems[J]. Telecommunication Engineering, 2009, 49(6): 77-80 doi: 10.3969/j.issn.1001-893x.2009.06.019 [8] 吴楠, 宋东安, 郑生全. 舰船射频综合系统的电磁兼容分析[J]. 舰船科学技术, 2007, 29(6):101-103. (Wu Nan, Song Dongan, Zheng Shengquan. Brief discussing the EMC of the naval vessel's RF integration system[J]. Ship Science and Technology, 2007, 29(6): 101-103 [9] 王侃, 朱瑞平. 相控阵天线的电磁环境分析[J]. 电子学报, 2012, 40(3):571-574. (Wang Kan, Zhu Ruiping. Analysis of electromagnetic environment of phased array[J]. Acta Electronica Sinica, 2012, 40(3): 571-574 [10] 赵勋旺, 张玉, 梁昌洪. 舰载多天线系统电磁兼容性分析[J]. 电波科学学报, 2008, 23(2):252-256,283. (Zhao Xunwang, Zhang Yu, Liang Changhong. Fast EMC analysis of multiple shipborne antennas system[J]. Chinese Journal of Radio Science, 2008, 23(2): 252-256,283 doi: 10.3969/j.issn.1005-0388.2008.02.011 [11] 赵勋旺, 梁昌洪, 张玉. 机载多天线系统电磁兼容性研究[J]. 计算物理, 2008, 25(5):597-601. (Zhao Xunwang, Liang Changhong, Zhang Yu. EMC characteristics of multiple airborne antennas[J]. Chinese Journal of Computational Physics, 2008, 25(5): 597-601 doi: 10.3969/j.issn.1001-246X.2008.05.012 [12] 董宁, 谢彦召. 考虑参数不确定性的高空电磁脉冲E1分量环境计算及分析[J]. 强激光与粒子束, 2019, 31:070002. (Dong Ning, Xie Yanzhao. Early-time high-altitude electromagnetic pulse simulation and analysis considering parameter uncertainty[J]. High Power Laser and Particle Beams, 2019, 31: 070002 doi: 10.11884/HPLPB201931.190140 [13] 董宁, 孙颖力, 王宗扬, 等. 基于QMU的高空电磁脉冲下电气电子设备易损性评估方法[J]. 强激光与粒子束, 2021, 33:123011. (Dong Ning, Sun Yingli, Wang Zongyang, et al. Threat assessment method of electrical equipment under high-altitude electromagnetic pulse based on quantification of margins and uncertainties method[J]. High Power Laser and Particle Beams, 2021, 33: 123011 doi: 10.11884/HPLPB202133.210386 [14] 邓莉亭, 钟龙权, 刘强, 等. 多导体传输线串扰实验不确定度的预测[J]. 强激光与粒子束, 2021, 33:083002. (Deng Liting, Zhong Longquan, Liu Qiang, et al. Uncertainty prediction of crosstalk measurement for multi-conductor transmission lines[J]. High Power Laser and Particle Beams, 2021, 33: 083002 [15] 刘莹. 复杂电磁工程问题分析的几个关键技术[D]. 西安: 西安电子科技大学, 2016Liu Ying. Several key technologies of the analysis of complex electromagnetic engineering problems[D]. Xi’an: Xidian University, 2016 [16] 朱陆陆. 蒙特卡洛方法及应用[D]. 武汉: 华中师范大学, 2014Zhu Lulu. The Monte Carlo method and application[D]. Wuhan: Central China Normal University, 2014 [17] Su Donglin, Tian Bo, Zhao Zihua, et al. Emission characteristics measurement of phased array transmitter based on ultra-wideband dual polarized Vivaldi array[C]//Proceedings of 2017 IEEE Microwaves, Radar and Remote Sensing Symposium. Kiev: IEEE, 2017: 219-223. [18] Telford J K. A brief introduction to design of experiments[J]. Johns Hopkins APL Technical Digest, 2007, 27(3): 224-232. [19] Wen Zhongkui, Wu Qi, Yildiz Ö F, et al. Design of experiments for analyzing the efficiency of a multi-coil wireless power transfer system using polynomial chaos expansion[C]//Proceedings of 2019 Joint International Symposium on Electromagnetic Compatibility, Sapporo and Asia-Pacific International Symposium on Electromagnetic Compatibility. Sapporo: IEEE, 2019: 499-502. [20] Tomy G J K, Vinoy K J. A fast polynomial chaos expansion for uncertainty quantification in stochastic electromagnetic problems[J]. IEEE Antennas and Wireless Propagation Letters, 2019, 18(10): 2120-2124. doi: 10.1109/LAWP.2019.2938323 [21] Boeykens F, Rogier H, Vallozzi L. An efficient technique based on polynomial chaos to model the uncertainty in the resonance frequency of textile antennas due to bending[J]. IEEE Transactions on Antennas and Propagation, 2014, 62(3): 1253-1260. doi: 10.1109/TAP.2013.2294021 [22] 谭立容, 张照锋, 袁迎春, 等. 电磁波与天线仿真及实践[M]. 西安: 西安电子科技大学出版社, 2016Tan Lirong, Zhang Zhaofeng, Yuan Yingchun, et al. Simulation and practice of electromagnetic wave and antenna[M]. Xi’an: Xidian University Press, 2016 [23] 泽尔金, 索科洛夫. 天线综合法[M]. 陈祥禄, 倪湘, 译. 北京: 宇航出版社, 1986Зелкин Е Г, Соколов В Г. Методы синтеза антенн[M]. Chen Xianglu, Ni Xiang, trans. Beijing: Yuhang Publishing House, 1986 [24] Eldred M. Recent advances in non-intrusive polynomial chaos and stochastic collocation methods for uncertainty analysis and design[C]//Proceedings of the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. Palm Springs: AIAA, 2009: 2274. [25] Wiener N. The homogeneous chaos[J]. American Journal of Mathematics, 1938, 60(4): 897-936. doi: 10.2307/2371268 [26] Xiu Dongbi, Karniadakis G E. The Wiener-Askey polynomial chaos for stochastic differential equations[J]. SIAM Journal on Scientific Computing, 2002, 24(2): 619-644. doi: 10.1137/S1064827501387826 [27] 谢启苗. 基于多项式混沌展开的人员疏散时间不确定性研究[D]. 合肥: 中国科学技术大学, 2014Xie Qimiao. Study on uncertainty of occupant evacuation time in fire safety design[D]. Hefei: University of Science and Technology of China, 2014 [28] 王天皓. 汽车电磁兼容中线束串扰及其统计特性研究[D]. 长春: 吉林大学, 2016Wang Tianhao. Research on automotive wiring harness crosstalk and its statistical characteristics in automotive EMC[D]. Changchun: Jilin University, 2016 [29] 塞吉·N·马卡洛夫. 通信天线建模与MATLAB仿真分析[M]. 许献国, 译. 北京: 北京邮电大学出版社, 2006Makarov S N. Antenna and EM modeling with MATLAB[M]. Xu Xianguo, trans. Beijing: Beijing University of Posts and Telecommunications Press, 2006 -
点击查看大图
计量
- 文章访问数: 792
- HTML全文浏览量: 386
- PDF下载量: 60
- 被引次数: 0
