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CN109782069B - Method for measuring mutual impedance between antennas - Google Patents

Method for measuring mutual impedance between antennas Download PDF

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CN109782069B
CN109782069B CN201910145332.1A CN201910145332A CN109782069B CN 109782069 B CN109782069 B CN 109782069B CN 201910145332 A CN201910145332 A CN 201910145332A CN 109782069 B CN109782069 B CN 109782069B
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antenna
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field strength
spherical harmonic
electric field
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CN109782069A (en
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袁浩波
刘宏伟
贾建生
董欣欣
周虹光
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Xidian University
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Abstract

本发明公开了一种测量天线间互阻抗的方法，属于天线测量技术领域，通过获得第二天线在第二球面上的第二电场强度和第二磁场强度；根据正向球谐变换确定第一天线的第一球谐波展开系数和第二球谐波展开系数，其中，n、m均为整数；根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度和第一磁场强度；根据所述第一电场强度、第一磁场强度、第二电场强度和第二磁场强度，计算所述第一天线与所述第二天线之间的互阻抗值Z21。达到了快速、准确、稳定的分析任意两副天线间的互阻抗，具有通用性的技术效果。

Figure 201910145332

The invention discloses a method for measuring mutual impedance between antennas, belonging to the technical field of antenna measurement. The second electric field intensity and the second magnetic field intensity of the second antenna on the second spherical surface are obtained; The first spherical harmonic expansion coefficient and the second spherical harmonic expansion coefficient of the antenna, where n and m are both integers; according to the first spherical harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and using The FFT interpolation method calculates the first electric field strength and the first magnetic field strength of the first antenna on the second spherical surface; according to the first electric field strength, the first magnetic field strength, the second electric field strength and the second magnetic field strength, calculate the The mutual impedance value Z 21 between the first antenna and the second antenna. It achieves fast, accurate and stable analysis of the mutual impedance between any two antennas, and has the technical effect of universality.

Figure 201910145332

Description

一种测量天线间互阻抗的方法A method for measuring mutual impedance between antennas

技术领域technical field

本发明涉及天线测量技术领域，特别涉及一种测量天线间互阻抗的方法。The invention relates to the technical field of antenna measurement, in particular to a method for measuring mutual impedance between antennas.

背景技术Background technique

两天线之间的互耦具有重要的工程意义。有效地测量天线间的互耦属于天线系统的设计、故障排除，以及电磁兼容性设计的基本手段。一般可以用隔离度、耦合系数、互阻抗等参数描述互耦的大小。这些参数之间可以用简单的公式互相转化，只要得到其中一种就可以准确的描述两天线之间耦合的大小。The mutual coupling between two antennas has important engineering significance. Effectively measuring the mutual coupling between antennas belongs to the basic means of antenna system design, troubleshooting, and electromagnetic compatibility design. Generally, parameters such as isolation, coupling coefficient, and mutual impedance can be used to describe the size of mutual coupling. These parameters can be converted to each other with simple formulas, and as long as one of them is obtained, the size of the coupling between the two antennas can be accurately described.

目前，计算互耦合的经典方法由Yaghjian提出。首先将反应表面S取为处于两天线之间的无限大平面，然后用平面近场测量方法得到两种天线在S上的切向电场，并将其展开为平面波谱，最后将波谱带入反应积分得到两天线之间的耦合系数。由于平面波谱中的衰减谱分量对积分的贡献很小，可以忽略。剩下的波谱与天线的远场成线性关系，因此将远场带入反应积分即可算出耦合系数。该方法的缺点是忽略衰减谱在很多情况下会引入较大的误差，使得测量结果不准确。现有的另一种方法是采用近场而不是远场来计算反应积分。这种方法一般采用球面作为反应面，并采用球谐变换展开天线的近区电磁场。其理论依据是Hansen在1988年给出的一套两天线间耦合的传输公式。该公式是严格准确的，不带有任何近似。但是涉及到球谐波的平移和旋转计算。这两种计算都极其复杂且不稳定。特别是当球谐波的阶数很高时，平移计算在数值上根本不能实现。所以现有基于球谐变换的算法都只能应用于小天线的耦合分析，不可能分析较大尺寸的天线耦合。At present, the classical method for calculating mutual coupling is proposed by Yaghjian. First, the reaction surface S is taken as an infinite plane between the two antennas, and then the tangential electric field of the two antennas on S is obtained by the plane near-field measurement method, and it is expanded into a plane wave spectrum, and finally the wave spectrum is brought into the reaction Integrate to get the coupling coefficient between the two antennas. Since the contribution of the decay spectral components in the plane wave spectrum to the integral is small, it can be ignored. The remaining spectrum is linear with the far field of the antenna, so the coupling coefficient can be calculated by taking the far field into the reaction integral. The disadvantage of this method is that ignoring the attenuation spectrum will introduce large errors in many cases, making the measurement results inaccurate. Another existing method is to use the near field instead of the far field to calculate the reaction integral. This method generally uses a spherical surface as the reaction surface, and uses spherical harmonic transformation to expand the near-region electromagnetic field of the antenna. Its theoretical basis is a set of transmission formulas for coupling between two antennas given by Hansen in 1988. The formula is strictly accurate without any approximations. But it involves translation and rotation calculations of spherical harmonics. Both calculations are extremely complex and unstable. Especially when the order of spherical harmonics is very high, the translation calculation is simply not possible numerically. Therefore, the existing algorithms based on spherical harmonic transformation can only be applied to the coupling analysis of small antennas, and it is impossible to analyze the coupling of larger antennas.

发明内容SUMMARY OF THE INVENTION

本发明提供了一种测量天线间互阻抗的方法，用以解决现有技术中基于球谐变换的算法都只能应用于小天线的耦合分析，不能分析较大尺寸的天线耦合的技术问题，达到了快速、准确、稳定的分析任意两副天线间的互阻抗，具有通用性的技术效果。The invention provides a method for measuring mutual impedance between antennas, which is used to solve the technical problem that the algorithms based on spherical harmonic transformation in the prior art can only be applied to the coupling analysis of small antennas, but cannot analyze the coupling of larger-sized antennas. It achieves fast, accurate and stable analysis of the mutual impedance between any two antennas, and has the technical effect of universality.

本发明提供了一种测量天线间互阻抗的方法，包括：获得第二天线在第二球面上的第二电场强度

Figure BDA0001979823500000021
和第二磁场强度
Figure BDA0001979823500000022
根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，n、m均为整数；根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度
Figure BDA0001979823500000023
和第一磁场强度
Figure BDA0001979823500000024
根据所述第一电场强度
Figure BDA0001979823500000025
第一磁场强度
Figure BDA0001979823500000026
第二电场强度
Figure BDA0001979823500000027
和第二磁场强度
Figure BDA0001979823500000028
计算所述第一天线与所述第二天线之间的互阻抗值Z21。The present invention provides a method for measuring mutual impedance between antennas, comprising: obtaining a second electric field intensity of a second antenna on a second spherical surface
Figure BDA0001979823500000021
and the second magnetic field strength
Figure BDA0001979823500000022
Determine the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation, where n and m are both integers; harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and use the FFT interpolation method to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA0001979823500000023
and the first magnetic field strength
Figure BDA0001979823500000024
According to the first electric field strength
Figure BDA0001979823500000025
first magnetic field strength
Figure BDA0001979823500000026
second electric field strength
Figure BDA0001979823500000027
and the second magnetic field strength
Figure BDA0001979823500000028
Calculate the mutual impedance value Z 21 between the first antenna and the second antenna.

优选地，所述根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，具体为：Preferably, the determining of the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation is specifically:

所述第一电场强度

Figure BDA0001979823500000029
为
Figure BDA00019798235000000210
the first electric field strength
Figure BDA0001979823500000029
for
Figure BDA00019798235000000210

所述第一磁场强度

Figure BDA00019798235000000211
为
Figure BDA00019798235000000212
the first magnetic field strength
Figure BDA00019798235000000211
for
Figure BDA00019798235000000212

其中，π为圆周率，N为球谐波截断阶数，n、m均为整数，

Figure BDA00019798235000000213
为第一矢量球谐波函数，
Figure BDA00019798235000000214
为第二矢量球谐波函数；Among them, π is the pi ratio, N is the spherical harmonic truncation order, and n and m are both integers.
Figure BDA00019798235000000213
is the first vector spherical harmonic function,
Figure BDA00019798235000000214
is the second vector spherical harmonic function;

Figure BDA00019798235000000215
Figure BDA00019798235000000215

Figure BDA0001979823500000031
Figure BDA0001979823500000031

其中，

Figure BDA0001979823500000032
j为虚数的符号，
Figure BDA0001979823500000033
为空间点的球坐标，
Figure BDA0001979823500000034
和
Figure BDA0001979823500000035
为球坐标系的单位矢量，
Figure BDA0001979823500000036
为连带的勒让德函数，Zn(kr)为球贝塞尔函数，且
Figure BDA0001979823500000037
exp为指数函数；in,
Figure BDA0001979823500000032
j is the sign of the imaginary number,
Figure BDA0001979823500000033
is the spherical coordinate of the point in space,
Figure BDA0001979823500000034
and
Figure BDA0001979823500000035
is the unit vector of the spherical coordinate system,
Figure BDA0001979823500000036
is the associated Legendre function, Z n (kr) is the spherical Bessel function, and
Figure BDA0001979823500000037
exp is an exponential function;

获得所述第一天线在第二球面上的半径rmin和预设点处的球面半径r0，其中r0＞rmin；obtaining the radius r min of the first antenna on the second spherical surface and the spherical radius r 0 at the preset point, where r 0 >r min ;

获得所述第一天线在所述预设点处的切向电场

Figure BDA0001979823500000038
Obtain the tangential electric field of the first antenna at the preset point
Figure BDA0001979823500000038

根据所述切向电场计算所述第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，The first spherical harmonic expansion coefficient an ,m and the second spherical harmonic expansion coefficient b n,m are calculated according to the tangential electric field, wherein,

Figure BDA0001979823500000039
Figure BDA0001979823500000039

Figure BDA00019798235000000310
Figure BDA00019798235000000310

优选地，采样点的间距角度Δα满足奈奎斯特采样定理Δα≤λ/(2r0)。Preferably, the spacing angle Δα of the sampling points satisfies the Nyquist sampling theorem Δα≤λ/(2r 0 ).

优选地，所述采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度

Figure BDA00019798235000000311
具体为：采用FFT加速对
Figure BDA00019798235000000312
方向上的傅里叶级数进行求和，其中，求和公式为
Figure BDA00019798235000000313
其中，
Figure BDA00019798235000000314
Figure BDA00019798235000000315
Preferably, the FFT interpolation method is used to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA00019798235000000311
Specifically: using FFT to accelerate
Figure BDA00019798235000000312
The Fourier series in the direction are summed, where the summation formula is
Figure BDA00019798235000000313
in,
Figure BDA00019798235000000314
Figure BDA00019798235000000315

优选地，所述计算所述公式(10)，具体为：在θ方向上，对所述预设点θ0处的球面进行剖分，并获得多个圆环；对于每一个与θ0对应的圆环，当m和n不同时，计算所有的

Figure BDA00019798235000000316
将预设点θ0处的圆环在
Figure BDA00019798235000000317
方向上进行均匀剖分，使得每段圆弧长度小于0.5λ；计算获得所述公式(10)的值。Preferably, the calculation of the formula (10) is specifically: in the θ direction, the spherical surface at the preset point θ 0 is divided, and a plurality of rings are obtained; for each one corresponding to θ 0 The torus of , when m and n are different, calculate all
Figure BDA00019798235000000316
Place the ring at the preset point θ 0 at
Figure BDA00019798235000000317
Perform uniform division in the direction, so that the length of each arc is less than 0.5λ; the value of the formula (10) is obtained by calculation.

优选地，所述计算获得所述公式(10)的值之后，还包括：对圆环上所有均匀分布的点，采用FFT加速方法计算每一个点处对应的近场值；获得多个所述圆环的近场值，并根据多个所述圆环的近场值获得所述第二球面上所有离散点的场值。Preferably, after the calculation obtains the value of the formula (10), the method further includes: for all uniformly distributed points on the ring, using the FFT acceleration method to calculate the corresponding near field value at each point; The near field value of the ring is obtained, and the field values of all discrete points on the second sphere are obtained according to the near field values of the plurality of rings.

优选地，还包括：所述第一天线与所述第二天线之间的互阻抗值Z21为Preferably, it also includes: the mutual impedance value Z 21 between the first antenna and the second antenna is

Figure BDA0001979823500000041
其中，S为包围所述第二天线的反应面，I11为激励所述第一天线的电流值，I21为激励所述第二天线的电流值
Figure BDA0001979823500000041
Wherein, S is the reaction surface surrounding the second antenna, I 11 is the current value that excites the first antenna, and I 21 is the current value that excites the second antenna

本发明实施例中的上述一个或多个技术方案，至少具有如下一种或多种技术效果：The above-mentioned one or more technical solutions in the embodiments of the present invention have at least one or more of the following technical effects:

本发明实施例提供的一种测量天线间互阻抗的方法，通过获得第二天线在第二球面上的第二电场强度

Figure BDA0001979823500000042
和第二磁场强度
Figure BDA0001979823500000043
根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，n、m均为整数；根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度
Figure BDA0001979823500000044
和第一磁场强度
Figure BDA0001979823500000045
根据所述第一电场强度
Figure BDA0001979823500000046
第一磁场强度
Figure BDA0001979823500000047
第二电场强度
Figure BDA0001979823500000048
和第二磁场强度
Figure BDA0001979823500000049
计算所述第一天线与所述第二天线之间的互阻抗值Z21。从而解决了现有技术中基于球谐变换的算法都只能应用于小天线的耦合分析，不能分析较大尺寸的天线耦合的技术问题，达到了快速、准确、稳定的分析任意两副天线间的互阻抗，具有通用性的技术效果。An embodiment of the present invention provides a method for measuring mutual impedance between antennas, by obtaining the second electric field strength of the second antenna on the second spherical surface
Figure BDA0001979823500000042
and the second magnetic field strength
Figure BDA0001979823500000043
Determine the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation, where n and m are both integers; harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and use the FFT interpolation method to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA0001979823500000044
and the first magnetic field strength
Figure BDA0001979823500000045
According to the first electric field strength
Figure BDA0001979823500000046
first magnetic field strength
Figure BDA0001979823500000047
second electric field strength
Figure BDA0001979823500000048
and the second magnetic field strength
Figure BDA0001979823500000049
Calculate the mutual impedance value Z 21 between the first antenna and the second antenna. This solves the technical problem that the algorithms based on spherical harmonic transformation in the prior art can only be applied to the coupling analysis of small antennas, but cannot analyze the coupling of larger-sized antennas, and achieves a fast, accurate and stable analysis between any two antennas. The mutual impedance has a general technical effect.

上述说明仅是本发明技术方案的概述，为了能够更清楚了解本发明的技术手段，而可依照说明书的内容予以实施，并且为了让本发明的上述和其它目的、特征和优点能够更明显易懂，以下特举本发明的具体实施方式。The above description is only an overview of the technical solutions of the present invention, in order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand , the following specific embodiments of the present invention are given.

附图说明Description of drawings

图1为本发明实施例中一种测量天线间互阻抗的方法的流程示意图；1 is a schematic flowchart of a method for measuring mutual impedance between antennas in an embodiment of the present invention;

图2为本发明实施例中第一天线与第二天线之间的作用场示意图；2 is a schematic diagram of an action field between a first antenna and a second antenna in an embodiment of the present invention;

图3为本发明实施例中第一天线与第二天线之间最小球面和测量球面的示意图；3 is a schematic diagram of a minimum spherical surface and a measurement spherical surface between a first antenna and a second antenna in an embodiment of the present invention;

图4为本发明实施例中对反应球面剖分的示意图；Fig. 4 is the schematic diagram of dissecting reaction sphere in the embodiment of the present invention;

图5为图4中对圆环在

Figure BDA0001979823500000051
方向剖分的示意图；Figure 5 shows the pair of rings in Figure 4
Figure BDA0001979823500000051
Schematic diagram of the direction division;

图6为本发明实施例中反应球面中离散点的示意图；6 is a schematic diagram of discrete points in a reaction sphere in an embodiment of the present invention;

图7为本发明实施例中两个平面天线阵列的泰勒阵示意图；7 is a schematic diagram of a Taylor array of two planar antenna arrays in an embodiment of the present invention;

图8为图7中泰勒阵3d方向图；Figure 8 is a 3d pattern of the Taylor array in Figure 7;

图9为图7中的天线阵列在不同倾斜角度下的互阻抗图；Fig. 9 is the mutual impedance diagram of the antenna array in Fig. 7 under different tilt angles;

图10为图7中的天线阵列在不同倾斜角度下的另一互阻抗图。FIG. 10 is another transimpedance diagram of the antenna array in FIG. 7 under different tilt angles.

具体实施方式Detailed ways

本发明实施例提供了一种测量天线间互阻抗的方法，用以解决现有技术中基于球谐变换的算法都只能应用于小天线的耦合分析，不能分析较大尺寸的天线耦合的技术问题。The embodiment of the present invention provides a method for measuring mutual impedance between antennas, which is used to solve the problem that the algorithms based on spherical harmonic transformation in the prior art can only be applied to the coupling analysis of small antennas, but cannot analyze the coupling of larger-sized antennas. question.

本发明实施例中的技术方案，总体思路如下：The technical scheme in the embodiment of the present invention, the general idea is as follows:

本发明实施例提供的一种测量天线间互阻抗的方法，通过获得第二天线在第二球面上的第二电场强度

Figure BDA0001979823500000052
和第二磁场强度
Figure BDA0001979823500000053
根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，n、m均为整数；根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度
Figure BDA0001979823500000054
和第一磁场强度
Figure BDA0001979823500000061
根据所述第一电场强度
Figure BDA0001979823500000062
第一磁场强度
Figure BDA0001979823500000063
第二电场强度
Figure BDA0001979823500000064
和第二磁场强度
Figure BDA0001979823500000065
计算所述第一天线与所述第二天线之间的互阻抗值Z21。达到了快速、准确、稳定的分析任意两副天线间的互阻抗，具有通用性的技术效果。An embodiment of the present invention provides a method for measuring mutual impedance between antennas, by obtaining the second electric field strength of the second antenna on the second spherical surface
Figure BDA0001979823500000052
and the second magnetic field strength
Figure BDA0001979823500000053
Determine the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation, where n and m are both integers; harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and use the FFT interpolation method to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA0001979823500000054
and the first magnetic field strength
Figure BDA0001979823500000061
According to the first electric field strength
Figure BDA0001979823500000062
first magnetic field strength
Figure BDA0001979823500000063
second electric field strength
Figure BDA0001979823500000064
and the second magnetic field strength
Figure BDA0001979823500000065
Calculate the mutual impedance value Z 21 between the first antenna and the second antenna. It achieves fast, accurate and stable analysis of the mutual impedance between any two antennas, and has the technical effect of universality.

为使本发明实施例的目的、技术方案和优点更加清楚，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments These are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

实施例Example

图1为本发明实施例中一种测量天线间互阻抗的方法，如图1所示，所述方法包括：FIG. 1 is a method for measuring mutual impedance between antennas in an embodiment of the present invention. As shown in FIG. 1 , the method includes:

步骤1：获得第二天线在第二球面上的第二电场强度

Figure BDA0001979823500000066
和第二磁场强度
Figure BDA0001979823500000067
Step 1: Obtain the second electric field strength of the second antenna on the second spherical surface
Figure BDA0001979823500000066
and the second magnetic field strength
Figure BDA0001979823500000067

步骤2：根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，n、m均为整数。Step 2: Determine the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation, where n and m are both integers.

进一步的，所述根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，具体为：Further, determining the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation is specifically:

所述第一电场强度

Figure BDA0001979823500000068
为
Figure BDA0001979823500000069
the first electric field strength
Figure BDA0001979823500000068
for
Figure BDA0001979823500000069

所述第一磁场强度

Figure BDA00019798235000000610
为
Figure BDA00019798235000000611
the first magnetic field strength
Figure BDA00019798235000000610
for
Figure BDA00019798235000000611

其中，π为圆周率，N为球谐波截断阶数，n、m均为整数，

Figure BDA00019798235000000612
为第一矢量球谐波函数，
Figure BDA00019798235000000613
为第二矢量球谐波函数；Among them, π is the pi ratio, N is the spherical harmonic truncation order, and n and m are both integers.
Figure BDA00019798235000000612
is the first vector spherical harmonic function,
Figure BDA00019798235000000613
is the second vector spherical harmonic function;

Figure BDA0001979823500000071
Figure BDA0001979823500000071

Figure BDA0001979823500000072
Figure BDA0001979823500000072

其中，

Figure BDA0001979823500000073
j为虚数的符号，
Figure BDA0001979823500000074
为空间点的球坐标，
Figure BDA0001979823500000075
和
Figure BDA0001979823500000076
为球坐标系的单位矢量，
Figure BDA0001979823500000077
为连带的勒让德函数，Zn(kr)为球贝塞尔函数，且
Figure BDA0001979823500000078
exp为指数函数；in,
Figure BDA0001979823500000073
j is the sign of the imaginary number,
Figure BDA0001979823500000074
is the spherical coordinate of the point in space,
Figure BDA0001979823500000075
and
Figure BDA0001979823500000076
is the unit vector of the spherical coordinate system,
Figure BDA0001979823500000077
is the associated Legendre function, Z n (kr) is the spherical Bessel function, and
Figure BDA0001979823500000078
exp is an exponential function;

获得所述第一天线在第二球面上的半径rmin和预设点处的球面半径r0，其中r0＞rmin；obtaining the radius r min of the first antenna on the second spherical surface and the spherical radius r0 at the preset point, where r 0 >r min ;

获得所述第一天线在所述预设点处的切向电场

Figure BDA0001979823500000079
Obtain the tangential electric field of the first antenna at the preset point
Figure BDA0001979823500000079

根据所述切向电场计算所述第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，The first spherical harmonic expansion coefficient an ,m and the second spherical harmonic expansion coefficient b n,m are calculated according to the tangential electric field, wherein,

Figure BDA00019798235000000710
Figure BDA00019798235000000710

Figure BDA00019798235000000711
Figure BDA00019798235000000711

进一步的，采样点的间距角度Δα满足奈奎斯特采样定理Δα≤λ/(2r0)。Further, the spacing angle Δα of the sampling points satisfies the Nyquist sampling theorem Δα≤λ/(2r 0 ).

具体而言，如图2所示，两副天线之间互阻抗计算的理论依据是如下的互易定理：

Figure BDA00019798235000000712
其中S为包围天线2的反应面。
Figure BDA00019798235000000713
为所述第二天线不工作而所述第一天线工作时(以电流I11激励所述第一天线)，在空间中产生的电场强度和磁场强度。
Figure BDA00019798235000000714
是假定所述第一天线不存在，而所述第二天线工作时(以电流I21激励所述第二天线)，在空间中产生的场。这两种场的准确值难以得到，一般将其近似成所述第二天线不存在时，所述第一天线辐射的电磁场强度。
Figure BDA0001979823500000081
是假定所述第一天线不存在，而所述第二天线工作时在空间中产生的场。因此，所述第一球面即为包围所述第一天线的球面，所述第二球面即为包围所述第二天线的球面。由于
Figure BDA0001979823500000082
和
Figure BDA0001979823500000083
属于根本不相关的物理量，因此上述公式(1)中的积分量没有实际的物理意义，称为反应积分，进一步的，其中的第二电场强度
Figure BDA0001979823500000084
和第二磁场强度
Figure BDA0001979823500000085
可在实际工作中通过测量直接获得。天线的辐射特性可以通过测量得到，也就是天线的近区电场强度和磁场强度。Specifically, as shown in Figure 2, the theoretical basis for calculating the mutual impedance between two antennas is the following reciprocity theorem:
Figure BDA00019798235000000712
where S is the reaction surface surrounding the antenna 2 .
Figure BDA00019798235000000713
Electric and magnetic field strengths generated in space when the second antenna is inactive and the first antenna is in operation (exciting the first antenna with current I 11 ).
Figure BDA00019798235000000714
is the field generated in space assuming that the first antenna does not exist and the second antenna is operating (exciting the second antenna with current I 21 ). Accurate values of these two fields are difficult to obtain, and they are generally approximated as the intensity of the electromagnetic field radiated by the first antenna when the second antenna does not exist.
Figure BDA0001979823500000081
is the field generated in space when the second antenna is in operation, assuming that the first antenna does not exist. Therefore, the first spherical surface is a spherical surface surrounding the first antenna, and the second spherical surface is a spherical surface surrounding the second antenna. because
Figure BDA0001979823500000082
and
Figure BDA0001979823500000083
belongs to a physical quantity that is not related at all, so the integral quantity in the above formula (1) has no actual physical meaning, which is called the reaction integral. Further, the second electric field strength in
Figure BDA0001979823500000084
and the second magnetic field strength
Figure BDA0001979823500000085
It can be directly obtained by measurement in actual work. The radiation characteristics of the antenna can be obtained by measurement, that is, the strength of the electric field and the strength of the magnetic field in the near area of the antenna.

进一步的，球谐变换是近场天线测量中的一种较为成熟的算法。无源空间内的任意时谐电磁场都可以用球谐波展开。

Figure BDA0001979823500000086
Figure BDA0001979823500000087
其中，其中，π为圆周率，N为球谐波截断阶数，n、m均为整数，
Figure BDA0001979823500000088
为第一矢量球谐波函数，
Figure BDA0001979823500000089
为第二矢量球谐波函数；an,m和bn,m为展开系数，矢量球谐波如下:
Figure BDA00019798235000000810
Figure BDA00019798235000000811
Figure BDA00019798235000000812
其中，其中，
Figure BDA00019798235000000813
j为虚数的符号，
Figure BDA00019798235000000814
为空间某一点的球坐标，
Figure BDA00019798235000000815
和
Figure BDA00019798235000000816
为球坐标系的单位矢量，
Figure BDA00019798235000000817
为连带的勒让德函数，Zn(kr)为球贝塞尔函数，且定义
Figure BDA00019798235000000818
exp为指数函数；。Further, spherical harmonic transformation is a relatively mature algorithm in near-field antenna measurement. Any time-harmonic electromagnetic field in passive space can be expanded by spherical harmonics.
Figure BDA0001979823500000086
Figure BDA0001979823500000087
Among them, π is the pi, N is the spherical harmonic truncation order, n and m are integers,
Figure BDA0001979823500000088
is the first vector spherical harmonic function,
Figure BDA0001979823500000089
is the second vector spherical harmonic function; a n,m and b n,m are expansion coefficients, and the vector spherical harmonics are as follows:
Figure BDA00019798235000000810
Figure BDA00019798235000000811
Figure BDA00019798235000000812
of which,
Figure BDA00019798235000000813
j is the sign of the imaginary number,
Figure BDA00019798235000000814
is the spherical coordinate of a point in space,
Figure BDA00019798235000000815
and
Figure BDA00019798235000000816
is the unit vector of the spherical coordinate system,
Figure BDA00019798235000000817
is the associated Legendre function, Z n (kr) is the spherical Bessel function, and defines
Figure BDA00019798235000000818
exp is an exponential function; .

进一步的，如图3所示，给出了一副发射天线，包围该天线的最小球面半径为rmin。假设测量球面的半径为r0(r0＞rmin)，测得的切向电场为

Figure BDA00019798235000000819
注意测量时，采样点的间距角度Δα必须满足奈奎斯特采样定理Δα≤λ/(2r0)。然后(2)中的未知系数可以用下面的积分来计算。Further, as shown in Fig. 3, a pair of transmitting antennas is given, and the minimum spherical radius surrounding the antenna is rmin . Assuming that the radius of the measuring sphere is r 0 (r 0 >r min ), the measured tangential electric field is
Figure BDA00019798235000000819
Note that during measurement, the spacing angle Δα of the sampling points must satisfy the Nyquist sampling theorem Δα≤λ/(2r 0 ). Then the unknown coefficients in (2) can be calculated by the following integral.

Figure BDA0001979823500000091
Figure BDA0001979823500000091

Figure BDA0001979823500000092
Figure BDA0001979823500000092

上述二重积分包括内层积分和外层积分。内层积分是关于

Figure BDA0001979823500000093
的傅里叶积分，可以通过快速傅里叶变换(FFT)求出。外层积分通常用高斯求积法计算。考虑到天线的近场，由(6)和(7)求出球面谐波系数称为正向球谐变换，其计算复杂度为O(N3)。相反，在已知天线的球面谐波系数的情况下，利用(2)计算近场称为反向球谐变换。如果场点均匀分布在包围天线本身的球面上，则(2)中的级数求和项可以通过FFT加速，使得计算复杂度为O(N3)。The above double integral includes inner integral and outer integral. Inner Integral is about
Figure BDA0001979823500000093
The Fourier integral of , can be obtained by the Fast Fourier Transform (FFT). The outer integral is usually computed using the Gaussian quadrature method. Considering the near field of the antenna, the spherical harmonic coefficient obtained from (6) and (7) is called forward spherical harmonic transformation, and its computational complexity is O(N 3 ). Conversely, using (2) to calculate the near field is called the inverse spherical harmonic transform when the spherical harmonic coefficients of the antenna are known. If the field points are uniformly distributed on the sphere surrounding the antenna itself, the series summation term in (2) can be accelerated by FFT, making the computational complexity O(N 3 ).

步骤3：根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度

Figure BDA0001979823500000094
和第一磁场强度
Figure BDA0001979823500000095
Step 3: According to the first spherical harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and adopt the FFT interpolation method to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA0001979823500000094
and the first magnetic field strength
Figure BDA0001979823500000095

步骤4：根据所述第一电场强度

Figure BDA0001979823500000096
第一磁场强度
Figure BDA0001979823500000097
第二电场强度
Figure BDA0001979823500000098
和第二磁场强度
Figure BDA0001979823500000099
计算所述第一天线与所述第二天线之间的互阻抗值Z21。Step 4: According to the first electric field strength
Figure BDA0001979823500000096
first magnetic field strength
Figure BDA0001979823500000097
second electric field strength
Figure BDA0001979823500000098
and the second magnetic field strength
Figure BDA0001979823500000099
Calculate the mutual impedance value Z 21 between the first antenna and the second antenna.

进一步的，所述采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度

Figure BDA00019798235000000910
具体为：Further, the FFT interpolation method is used to calculate the first electric field intensity of the first antenna on the second spherical surface
Figure BDA00019798235000000910
Specifically:

采用FFT加速对

Figure BDA00019798235000000911
方向上的傅里叶级数进行求和，其中，求和公式为
Figure BDA00019798235000000912
其中，
Figure BDA00019798235000000913
Using FFT to speed up the pair
Figure BDA00019798235000000911
The Fourier series in the direction are summed, where the summation formula is
Figure BDA00019798235000000912
in,
Figure BDA00019798235000000913

进一步的，所述计算所述公式(10)，具体为：Further, the formula (10) of the calculation is specifically:

在θ方向上，对所述预设点θ0处的球面进行剖分，并获得多个圆环；In the θ direction, the spherical surface at the preset point θ 0 is divided, and a plurality of rings are obtained;

对于每一个与θ0对应的圆环，当m和n不同时，计算所有的

Figure BDA00019798235000000914
For each ring corresponding to θ 0 , when m and n are different, compute all
Figure BDA00019798235000000914

将预设点θ0处的圆环在

Figure BDA00019798235000000915
方向上进行均匀剖分，使得每段圆弧长度小于0.5λ；Place the ring at the preset point θ 0 at
Figure BDA00019798235000000915
Divide evenly in the direction, so that the length of each arc is less than 0.5λ;

计算获得所述公式(10)的值。The calculation obtains the value of the formula (10).

进一步的，所述计算获得所述公式(10)的值之后，还包括：Further, after the calculation obtains the value of the formula (10), it also includes:

对圆环上所有均匀分布的点，采用FFT加速方法计算每一个点处对应的近场值。For all uniformly distributed points on the ring, the FFT acceleration method is used to calculate the corresponding near field value at each point.

获得多个所述圆环的近场值，并根据多个所述圆环的近场值获得所述第二球面上所有离散点的场值。A plurality of near-field values of the rings are obtained, and field values of all discrete points on the second sphere are obtained according to the near-field values of the plurality of rings.

进一步的，还包括：所述第一天线与所述第二天线之间的互阻抗值Z21为

Figure BDA0001979823500000101
其中，S为包围所述第二天线的反应面，I11为激励所述第一天线的电流值，I21为激励所述第二天线的电流值。Further, it also includes: the mutual impedance value Z 21 between the first antenna and the second antenna is
Figure BDA0001979823500000101
Wherein, S is the reaction surface surrounding the second antenna, I 11 is the current value that excites the first antenna, and I 21 is the current value that excites the second antenna.

具体而言，用FFT/插值方法计算所述第一天线在第二球面上的第一电场强度

Figure BDA0001979823500000102
和第一磁场强度
Figure BDA0001979823500000103
但是直接计算的计算过程非常复杂且计算量很大，因为其计算复杂度为O(N4)，导致速度非常慢。因此，为了简单起见，可以将电场强度的每个分量简写成：Specifically, the FFT/interpolation method is used to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA0001979823500000102
and the first magnetic field strength
Figure BDA0001979823500000103
However, the calculation process of direct calculation is very complicated and the amount of calculation is very large, because its calculation complexity is O(N 4 ), resulting in a very slow speed. Therefore, for simplicity, each component of the electric field strength can be abbreviated as:

Figure BDA0001979823500000104
Figure BDA0001979823500000104

其中求和式的每一项都是一个常数、一个贝塞尔函数、一个连带勒让德函数和一个指数函数的成绩。如图3所示，观察点在一个偏心球面上，因此坐标r依赖于

Figure BDA0001979823500000105
和θ。为了对
Figure BDA0001979823500000106
方向上的傅里叶级数求和采用FFT加速，可改变求和的次序。Each term of the summation formula is the result of a constant, a Bessel function, an associated Legendre function, and an exponential function. As shown in Figure 3, the observation point is on an eccentric sphere, so the coordinate r depends on
Figure BDA0001979823500000105
and θ. in order to
Figure BDA0001979823500000106
The Fourier series summation in the direction is accelerated by FFT, and the order of summation can be changed.

Figure BDA0001979823500000107
Figure BDA0001979823500000107

其中，

Figure BDA0001979823500000108
in,
Figure BDA0001979823500000108

显然，如果场点在

Figure BDA0001979823500000109
方向均匀分布，如图5所示，则公式(9)可以采用FFT加速。进而即可得到所述第一天线的近区电场。同样的方法，可以得到公式(3)中的近区磁场。最后带入互易定理(1)，就得到了互阻抗。Obviously, if the field point is
Figure BDA0001979823500000109
If the directions are uniformly distributed, as shown in Figure 5, the formula (9) can be accelerated by FFT. Then, the near-field electric field of the first antenna can be obtained. In the same way, the near-field magnetic field in formula (3) can be obtained. Finally, the reciprocity theorem (1) is brought in, and the mutual impedance is obtained.

进一步的，计算所述公式(9)具体包括：在θ方向上，用图4所示的一些平面对反应球面进行剖分，得到一系列的圆环；对于每个与θ0对应的圆环，计算m和n不同时，所有的

Figure BDA0001979823500000111
如图5所示，将圆环在
Figure BDA0001979823500000112
方向均匀剖分，使得每段圆弧长度小于0.5λ；用式(10)来计算
Figure BDA0001979823500000113
对圆上所有均匀分布的点，用式(9)通过FFT加速来计算其近场值；在计算了所有的圆之后，可以得到图6中所有离散点的场。Further, calculating the formula (9) specifically includes: in the θ direction, using some planes shown in FIG. 4 to divide the reaction sphere to obtain a series of rings; for each ring corresponding to θ 0 , when calculating m and n are different, all
Figure BDA0001979823500000111
As shown in Figure 5, place the ring on the
Figure BDA0001979823500000112
The direction is evenly divided, so that the length of each arc is less than 0.5λ; use formula (10) to calculate
Figure BDA0001979823500000113
For all the evenly distributed points on the circle, use formula (9) to calculate the near field value through FFT acceleration; after calculating all the circles, the field of all discrete points in Fig. 6 can be obtained.

进一步的，图7给出了工作在3.0Ghz的两个平面天线阵列。左边的30×30阵由四分之一波长偶极子组成，单元间距为0.5λ。根据泰勒分布将总输入功率分配到每个偶极子上。这里，每个天线在包围球面上的近场分布采用高阶矩量法仿真得出，然后带入本方法中得到两天线的互阻抗。同时，本方法计算的结果与高阶矩量法直接得到的互阻抗进行了对比。Further, Figure 7 shows two planar antenna arrays operating at 3.0Ghz. The 30 × 30 array on the left consists of quarter-wavelength dipoles with a cell spacing of 0.5λ. The total input power is distributed to each dipole according to the Taylor distribution. Here, the near-field distribution of each antenna on the surrounding sphere is simulated by the high-order moment method, and then brought into this method to obtain the mutual impedance of the two antennas. At the same time, the results calculated by this method are compared with the transimpedance directly obtained by the higher order method of moments.

图8给出了左边泰勒阵的方向图，其旁瓣电平为-35dB。右边的天线阵与左边的天线阵完全一样。但是右边的天线阵在y’z’平面绕着x’轴旋转了某个角度α。两个阵列的几何中心之间的距离是d＝15λ。在球谐变换中，包围每一个阵列的球面的半径为15λ，截断阶数为114。Figure 8 shows the pattern of the Taylor array on the left with a side lobe level of -35dB. The antenna array on the right is exactly the same as the antenna array on the left. But the antenna array on the right is rotated by an angle α around the x' axis in the y'z' plane. The distance between the geometric centers of the two arrays is d=15λ. In the spherical harmonic transformation, the radius of the sphere surrounding each array is 15λ, and the truncation order is 114.

从图9可以看出，该方法的结果与高阶矩量法的结果几乎完全一致。该方法的最大误差和最大相对误差分别为0.08Ω和0.43％。高阶矩量法所需要的计算时间和本方法所需要的计算时间分别为2242秒和152秒，也就是说后者比前者快15倍。As can be seen from Figure 9, the results of this method are almost identical to those of the higher order method of moments. The maximum error and maximum relative error of this method are 0.08Ω and 0.43%, respectively. The computation time required by the higher order method of moments and the computation time required by this method are 2242 seconds and 152 seconds, respectively, that is to say, the latter is 15 times faster than the former.

因此，本发明实施例提供的一种测量天线间互阻抗的方法，可以快速、准确、稳定的分析任意两副天线间的互阻抗，具有通用性。其计算复杂度与普通的球谐变换一样，为O(N3)。数值仿真表明，在分析两个大型天线阵的互阻抗时，该方法比计算电磁学中的矩量法快十倍以上，而相对误差不到1％。进一步达到了结果准确可靠，与高阶矩量法完全一致；速度比高阶矩量法快十几倍；比传统的测量方法快更多；天线的类型、大小或位置都不受限制，无论什么天线之间的耦合都可以快速测量分析的技术效果。Therefore, the method for measuring the mutual impedance between antennas provided by the embodiment of the present invention can quickly, accurately and stably analyze the mutual impedance between any two antennas, and has universality. Its computational complexity is the same as that of ordinary spherical harmonic transformation, which is O(N 3 ). Numerical simulations show that the method is more than ten times faster than the method of moments in computational electromagnetics when analyzing the mutual impedance of two large antenna arrays, with a relative error of less than 1%. Further, the results are accurate and reliable, which is completely consistent with the high-order moment method; the speed is more than ten times faster than the high-order moment method; much faster than the traditional measurement method; the type, size or position of the antenna is not limited, no matter what Any coupling between antennas can be quickly measured and analyzed for technical effects.

本发明实施例中的上述一个或多个技术方案，至少具有如下一种或多种技术效果：The above-mentioned one or more technical solutions in the embodiments of the present invention have at least one or more of the following technical effects:

本发明实施例提供的一种测量天线间互阻抗的方法，通过获得第二天线在第二球面上的第二电场强度

Figure BDA0001979823500000121
和第二磁场强度
Figure BDA0001979823500000122
根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，n、m均为整数；根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度
Figure BDA0001979823500000123
和第一磁场强度
Figure BDA0001979823500000124
根据所述第一电场强度
Figure BDA0001979823500000125
第一磁场强度
Figure BDA0001979823500000126
第二电场强度
Figure BDA0001979823500000127
和第二磁场强度
Figure BDA0001979823500000128
计算所述第一天线与所述第二天线之间的互阻抗值Z21。从而解决了现有技术中基于球谐变换的算法都只能应用于小天线的耦合分析，不能分析较大尺寸的天线耦合的技术问题，达到了快速、准确、稳定的分析任意两副天线间的互阻抗，具有通用性的技术效果。An embodiment of the present invention provides a method for measuring mutual impedance between antennas, by obtaining the second electric field strength of the second antenna on the second spherical surface
Figure BDA0001979823500000121
and the second magnetic field strength
Figure BDA0001979823500000122
Determine the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation, where n and m are both integers; harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and use the FFT interpolation method to calculate the first electric field strength of the first antenna on the second spherical surface
Figure BDA0001979823500000123
and the first magnetic field strength
Figure BDA0001979823500000124
According to the first electric field strength
Figure BDA0001979823500000125
first magnetic field strength
Figure BDA0001979823500000126
second electric field strength
Figure BDA0001979823500000127
and the second magnetic field strength
Figure BDA0001979823500000128
Calculate the mutual impedance value Z 21 between the first antenna and the second antenna. This solves the technical problem that the algorithms based on spherical harmonic transformation in the prior art can only be applied to the coupling analysis of small antennas, but cannot analyze the coupling of larger-sized antennas, and achieves a fast, accurate and stable analysis between any two antennas. The mutual impedance has a general technical effect.

尽管已描述了本发明的优选实施例，但本领域内的技术人员一旦得知了基本创造性概念，则可对这些实施例做出另外的变更和修改。所以，所附权利要求意欲解释为包括优选实施例以及落入本发明范围的所有变更和修改。Although the preferred embodiments of the present invention have been described, additional changes and modifications to these embodiments may occur to those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be construed to include the preferred embodiment and all changes and modifications that fall within the scope of the present invention.

显然，本领域的技术人员可以对本发明实施例进行各种改动和变型而不脱离本发明实施例的精神和范围。这样，倘若本发明实施例的这些修改和变型属于本发明权利要求及其等同技术的范围之内，则本发明也意图包含这些改动和变型在内。Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, provided that these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (3)

1.一种测量天线间互阻抗的方法，其特征在于，所述方法包括：1. A method for measuring mutual impedance between antennas, wherein the method comprises: 获得第二天线在第二球面上的第二电场强度
Figure FDA0002518749020000011
和第二磁场强度
Figure FDA0002518749020000012
Obtain the second electric field strength of the second antenna on the second spherical surface
Figure FDA0002518749020000011
and the second magnetic field strength
Figure FDA0002518749020000012
 根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，n、m均为整数；Determine the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation, where n and m are both integers; 根据所述第一球谐波展开系数和所述第二球谐波展开系数，并采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度
Figure FDA0002518749020000013
和第一磁场强度
Figure FDA0002518749020000014
According to the first spherical harmonic expansion coefficient and the second spherical harmonic expansion coefficient, and adopt the FFT interpolation method to calculate the first electric field strength of the first antenna on the second spherical surface
Figure FDA0002518749020000013
and the first magnetic field strength
Figure FDA0002518749020000014
 根据所述第一电场强度
Figure FDA0002518749020000015
第一磁场强度
Figure FDA0002518749020000016
第二电场强度
Figure FDA0002518749020000017
和第二磁场强度
Figure FDA0002518749020000018
计算所述第一天线与所述第二天线之间的互阻抗值Z21；According to the first electric field strength
Figure FDA0002518749020000015
first magnetic field strength
Figure FDA0002518749020000016
second electric field strength
Figure FDA0002518749020000017
and the second magnetic field strength
Figure FDA0002518749020000018
Calculate the mutual impedance value Z 21 between the first antenna and the second antenna; 其中，第二球面为包围所述第二天线的球面；Wherein, the second spherical surface is a spherical surface surrounding the second antenna; 所述根据正向球谐变换确定第一天线的第一球谐波展开系数an,m和第二球谐波展开系数bn,m，具体为：The determining of the first spherical harmonic expansion coefficient a n,m and the second spherical harmonic expansion coefficient b n,m of the first antenna according to the forward spherical harmonic transformation is specifically: 所述第一电场强度
Figure FDA0002518749020000019
为
Figure FDA00025187490200000110
the first electric field strength
Figure FDA0002518749020000019
for
Figure FDA00025187490200000110
 所述第一磁场强度
Figure FDA00025187490200000111
为
Figure FDA00025187490200000112
the first magnetic field strength
Figure FDA00025187490200000111
for
Figure FDA00025187490200000112
 其中，π为圆周率，N为球谐波截断阶数，n、m均为整数，
Figure FDA00025187490200000113
为第一矢量球谐波函数，
Figure FDA00025187490200000114
为第二矢量球谐波函数；Among them, π is the pi ratio, N is the spherical harmonic truncation order, and n and m are both integers.
Figure FDA00025187490200000113
is the first vector spherical harmonic function,
Figure FDA00025187490200000114
is the second vector spherical harmonic function;
Figure FDA00025187490200000115
Figure FDA00025187490200000115
Figure FDA00025187490200000116
Figure FDA00025187490200000116
 其中，
Figure FDA00025187490200000117
j为虚数的符号，
Figure FDA00025187490200000118
为空间点的球坐标，
Figure FDA00025187490200000119
和
Figure FDA00025187490200000120
为球坐标系的单位矢量，
Figure FDA00025187490200000121
为连带的勒让德函数，Zn(kr)为球贝塞尔函数，且
Figure FDA0002518749020000021
exp为指数函数；in,
Figure FDA00025187490200000117
j is the sign of the imaginary number,
Figure FDA00025187490200000118
is the spherical coordinate of the point in space,
Figure FDA00025187490200000119
and
Figure FDA00025187490200000120
is the unit vector of the spherical coordinate system,
Figure FDA00025187490200000121
is the associated Legendre function, Z n (kr) is the spherical Bessel function, and
Figure FDA0002518749020000021
exp is an exponential function; 获得所述第一天线在第二球面上的半径rmin和预设点处的球面半径r0，其中r0＞rmin；obtaining the radius r min of the first antenna on the second spherical surface and the spherical radius r 0 at the preset point, where r 0 >r min ; 获得所述第一天线在所述预设点处的切向电场
Figure FDA0002518749020000022
其中，Eθ为球坐标系中所述预设点处θ方向电场强度；
Figure FDA0002518749020000023
为球坐标系中所述预设点处
Figure FDA0002518749020000024
方向电场强度；Obtain the tangential electric field of the first antenna at the preset point
Figure FDA0002518749020000022
Wherein, E θ is the electric field intensity in the θ direction at the preset point in the spherical coordinate system;
Figure FDA0002518749020000023
is the preset point in the spherical coordinate system
Figure FDA0002518749020000024
directional electric field strength; 根据所述切向电场计算所述第一球谐波展开系数an,m和第二球谐波展开系数bn,m，其中，The first spherical harmonic expansion coefficient an ,m and the second spherical harmonic expansion coefficient b n,m are calculated according to the tangential electric field, wherein,
Figure FDA0002518749020000025
Figure FDA0002518749020000025
Figure FDA0002518749020000026
Figure FDA0002518749020000026
 所述采用FFT插值方法计算所述第一天线在第二球面上的第一电场强度
Figure FDA0002518749020000027
具体为：The FFT interpolation method is used to calculate the first electric field intensity of the first antenna on the second spherical surface
Figure FDA0002518749020000027
Specifically: 采用FFT加速对
Figure FDA0002518749020000028
方向上的傅里叶级数进行求和，其中，求和公式为
Figure FDA0002518749020000029
其中，
Figure FDA00025187490200000210
Using FFT to speed up the pair
Figure FDA0002518749020000028
The Fourier series in the direction are summed, where the summation formula is
Figure FDA0002518749020000029
in,
Figure FDA00025187490200000210
 所述方法还包括：The method also includes: 所述第一天线与所述第二天线之间的互阻抗值Z21为The mutual impedance value Z 21 between the first antenna and the second antenna is
Figure FDA00025187490200000211
Figure FDA00025187490200000211
 其中，S为包围所述第二天线的反应面，I11为激励所述第一天线的电流值，I21为激励所述第二天线的电流值。Wherein, S is the reaction surface surrounding the second antenna, I 11 is the current value that excites the first antenna, and I 21 is the current value that excites the second antenna. 2.如权利要求1所述的测量天线间互阻抗的方法，其特征在于，所述计算所述公式(10)，具体为：2. The method for measuring mutual impedance between antennas according to claim 1, wherein the calculating the formula (10) is specifically: 在θ方向上，对所述预设点θ0处的球面进行剖分，并获得多个圆环；In the θ direction, the spherical surface at the preset point θ 0 is divided, and a plurality of rings are obtained; 对于每一个与θ0对应的圆环，当m和n不同时，计算所有的
Figure FDA0002518749020000032
For each ring corresponding to θ 0 , when m and n are different, compute all
Figure FDA0002518749020000032
 将预设点θ0处的圆环在
Figure FDA0002518749020000031
方向上进行均匀剖分，使得每段圆弧长度小于0.5λ，所述λ为波长；Place the ring at the preset point θ 0 at
Figure FDA0002518749020000031
Divide evenly in the direction, so that the length of each arc is less than 0.5λ, and the λ is the wavelength; 计算获得所述公式(10)的值。The calculation obtains the value of the formula (10). 3.如权利要求2所述的测量天线间互阻抗的方法，其特征在于，所述计算获得所述公式(10)的值之后，还包括：3. The method for measuring mutual impedance between antennas according to claim 2, wherein after the calculation obtains the value of the formula (10), the method further comprises: 对圆环上所有均匀分布的点，采用FFT加速方法计算每一个点处对应的近场值；For all uniformly distributed points on the ring, the FFT acceleration method is used to calculate the corresponding near field value at each point; 获得多个所述圆环的近场值，并根据多个所述圆环的近场值获得所述第二球面上所有离散点的场值。A plurality of near-field values of the rings are obtained, and field values of all discrete points on the second sphere are obtained according to the near-field values of the plurality of rings.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9053268B1 (en) * 2007-12-19 2015-06-09 The United States Of America As Represented By The Secretary Of The Navy Analytic antenna design for a dipole antenna
CN106771672A (en) * 2017-02-21 2017-05-31 北京邮电大学 The method and device of Far-Field antennas measurement system is carried out based on cubic spline interpolation

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9053268B1 (en) * 2007-12-19 2015-06-09 The United States Of America As Represented By The Secretary Of The Navy Analytic antenna design for a dipole antenna
CN106771672A (en) * 2017-02-21 2017-05-31 北京邮电大学 The method and device of Far-Field antennas measurement system is carried out based on cubic spline interpolation

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
三维空间多天线相关性及互耦影响研究;薛翠薇等;《电波科学学报》;20170228;第32卷(第1期);51-55 *
基于球谐函数天线间相互影响快速分析方法;关闯等;《电波科学学报》;20161231;第31卷(第6期);1166-1169 *

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