﻿ 一种快速测试线缆终端共模阻抗的方法<sup>*</sup>
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A method for quick measurement of terminal common-mode impedance of cables
LIU Hongyi, CHEN Yao, SU Donglin
School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2017-10-13; Accepted: 2017-11-17; Published online: 2018-01-24 13:20
Foundation item: National Natural Science Foundation of China (61601016, 61427803)
Corresponding author. SU Donglin, E-mail: SDL@buaa.edu.cn
Abstract: The cables connecting avionics equipment are important coupling path for electromagnetic interference. When modeling a cable, the terminal common-mode impedance of the cable is a crucial input parameter. Because the quantity of cables in avionics system is very large, it is beneficial for quickly modeling cables' coupling through improving the test efficiency of cable terminal common-mode impedance. Therefore, a method to quickly test the terminal common-mode impedances of cables is proposed. First, according to the theory of multi-conductor transmission line, the multi-core cable can be equivalent to a single conductor when the common-mode current is analyzed. In addition, a cable bundle can be equivalent to a multi-conductor transmission line, and a vector network analyzer and a current probe can be used to measure the voltage reflection coefficients at two optional positions of each cable. Then, based on the established model of multi-conductor transmission line, the terminal impedance equations are constructed. Finally, the numerical iterative algorithm is used to solve the equations, and the terminal common-mode impedance of each cable is extracted. Compared with the existing methods, the testing efficiency and accuracy are improved.
Keywords: electromagnetic compatibility (EMC)     multi-conductor transmission line     common-mode     avionics equipment     cable     terminal impedance     measurement

1 多条平行线缆的等效方法

 图 1 连接2个终端的3条线缆 Fig. 1 Three cables connecting two terminals
1.1 单根多芯线缆与单导体的等效

 (1)
 图 2 多芯线缆及其等效导体横截面结构尺寸 Fig. 2 Cross section structure of a cable bundle and its equivalent conductor.

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

1.2 平行多芯线缆与平行双导体的等效

 (8)

 (9)

 (10)

 (11)

lBe, 1Be, 2hB1hB2代入式(2)，即可求得两等效导体间的距离dij。对于图 1所示的系统，采用上述方法计算得到如图 3所示的等效多导体传输线。可得各等效导体半径re=0.000 35 m，等效导体间距d12= d21=0.01 m，d13=0.02 m，等效导体距地平面高度h1=h2=h3=0.025 m。可将求得的等效导体的参数代入式(1)求出该多导体传输线单位长度电感阵L对角线元素，将等效导体的参数代入式(2)求出L的非对角线元素，进而求得特征阻抗阵图 3中的zia(f)和zib(f)分别为各导体左端和右端在频率为f时的阻抗。在本文中，将各等效导体的左端坐标设为xia=0，右端坐标设为xib=2 m。

 图 3 与3条线缆等效的多导体传输线 Fig. 3 Equivalent multi-conductor transmission line of three cables
2 获取电流注入点处的输入阻抗阵

 图 4 测量导体i在xisL处的电压反射系数 Fig. 4 Measuring voltage reflection coefficient at xisL of conductor i

 图 5 测量导体电压反射系数的等效电路 Fig. 5 Equivalent circuit for measuring voltage reflection coefficient of a conductor

 (12)

α可由电流探头校准方法得到[14-15]

 (13)

 图 6 本文所用电流探头的电压变换比曲线 Fig. 6 Voltage conversion ratio curve of current probe used in this paper

 (14)

 (15)

m个频率上对3根导体分别应用式(14)、式(15)，可得到在XsL=[x1sL, x2sL, x3sL]TXsR=[x1sR, x2sR, x3sR]T处的输入阻抗阵:

 (16)
 (17)

3 计算等效多导体传输线终端阻抗

 (18)
 (19)
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 图 7 导体与地平面间的4个输入阻抗 Fig. 7 Four input impedances between conductor and ground

 (22)
 (23)
 (24)
 (25)

 (26)
 (27)
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 (29)

XsL处的输入阻抗阵Zin(f, XsL)及在XsR处的输入阻抗阵Zin(f, XsR)满足式(30)、式(31)：

 (30)
 (31)

 (32)
 (33)

4 实验结果

 图 8 由本文方法和直接测量得到的|z1a|、|z2a|、|z3a|、|z1b|、|z2b|和|z3b| Fig. 8 |z1a|, |z2a|, |z3a|, |z1b|, |z2b| and |z3b| achieved with proposed method and direct measurement
5 结论

1) 本文根据传输线理论证明，在计算线缆终端共模阻抗时，可将其等效为一根单导体；而对于相邻的平行线缆，可将其等效为多导体传输线。

2) 用矢量网络分析仪和电流探头快速获取线缆的电压反射系数后，能够同时计算出各条线缆终端的等效共模阻抗。而且，本文方法在测试电压反射系数过程中，电流探头与线缆通过空间电磁耦合，因而不会破坏被测系统的完整性。

3) 本文方法得到的结果与采用阻抗分析仪直接测量结果的相对误差只在少数频点上接近10%。考虑到电磁兼容试验的不确定度很少低于3 dB的实际，因而本文方法的测量精度能够满足线缆耦合的建模需求。

4) 本文方法适用于大体上平直的线缆束。对于弯曲线缆束，应用本方法会引入较大误差。对于弯曲线缆束终端共模阻抗的获取，需要在后续的研究加以解决。

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#### 文章信息

LIU Hongyi, CHEN Yao, SU Donglin

A method for quick measurement of terminal common-mode impedance of cables

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(8): 1643-1650
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0626