﻿ 水下磁感应通信阵列天线磁场仿真与特性研究
 舰船科学技术  2001, Vol. 44 Issue (6): 106-113    DOI: 10.3404/j.issn.1672-7649.2022.06.022 PDF

Research on magnetic-field simulation and characteristics of underwater magnetic induction communication array antenna
WANG Yi-ming, XIE Xu
Department of Electronic Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: The magnetic induction intensity at a fixed point in the space changes accordingly when geometric dimensions, spatial position and excitation mode of the coils start to change. In this paper, the magnetic induction intensity distribution of the single coil, double-coil array and four-coil array was simulated and analyzed one by one according to different spatial positions and excitation modes. The research results are as follows: The positive superposition effect of magnetic induction intensity in space is the best when the current of array antenna is in the same direction; With the increase of coil spacing: the peak value of magnetic induction intensity norm of double-coil and four-coil is 35% and 82% higher than that of single coil with the same power respectively; The optimal receiving position is divided into a number equal to the quantity of array coils; With the increasing axial distance of the receiver: the peak value of magnetic induction intensity norm of double-coil and four-coil is larger than that of single coil with the same power, and the coverage area of higher value is larger than that of single coil; When the axial distance is 10 m, the peak value of magnetic induction intensity norm of double-coil and four-coil is 1.37 times and 1.94 times of that of single coil with the same power respectively; The best receiver positions are finally closed to one at the origin.
Key words: magnetic induction communication     spatial positions     excitation mode     array antenna     magnetic induction intensity distribution
0 引　言

1 数学模型

1.1 单线圈

 ${\boldsymbol{B}} = \frac{{{\mu _0}NIS}}{{4\text{π} {r^3}}}(2\cos \theta {{\boldsymbol{e}}_r} + \sin\theta {{\boldsymbol{e}}_\theta })，$ (1)

 图 1 载流线圈在空间中P点产生的辐射 Fig. 1 Radiation generated by current-carrying coil at point P

 ${\boldsymbol{B}} = \frac{{{\mu _0}N{I_1}S}}{{4\text{π} {r^5}}}[3xz{{\boldsymbol{e}}_x} + 3yz{{\boldsymbol{e}}_y} + (2{z^2} - {x^2} - {y^2}){{\boldsymbol{e}}_z}]。$ (2)

1.2 双线圈阵列

 ${{\boldsymbol B}_{{\text{two}}}} = {{\boldsymbol{B}}_{{\text{T1}}}} + {{\boldsymbol{B}}_{{\text{T2}}}} ，$ (3)

 $\begin{split} {{\boldsymbol{B}}_{{\boldsymbol{T1}}}} = &\frac{{{\mu _0}N{I_2}S}}{{4\text{π} {{\left[ {{x^2} + {{(y - d)}^2} + {z^2}} \right]}^{\frac{5}{2}}}}}\{ 3xz{{\boldsymbol{e}}_x} + 3(y - d)z{{\boldsymbol{e}}_y} +\\ & [2{z^2} - {x^2} - {(y - d)^2}]{{\boldsymbol{e}}_z}\}，\end{split}$ (4)
 $\begin{split} {{\boldsymbol{B}}_{{\text{T2}}}} =& \frac{{{\mu _0}N{I_2}S}}{{4\text{π} {{\left[ {{x^2} + {{(y{\text{ + }}d)}^2} + {z^2}} \right]}^{\frac{5}{2}}}}}\{ 3xz{{\boldsymbol{e}}_x} + 3(y{\text{ + }}d)z{{\boldsymbol{e}}_y} + \\ & [2{z^2} - {x^2} - {(y{\text{ + }}d)^2}]{{\boldsymbol{e}}_z}\} 。\end{split}$ (5)
 图 2 双线圈阵列模型 Fig. 2 Double-coil array model
1.3 四线圈阵列

 图 3 四线圈阵列模型 Fig. 3 Four-coil array model
 ${{\boldsymbol{B}}_{{\text{four}}}} = {{\boldsymbol{B}}_{{\boldsymbol{T1}}}} + {{\boldsymbol{B}}_{{\boldsymbol{T2}}}}{\text{ + }}{{\boldsymbol{B}}_{{\boldsymbol{T3}}}} + {{\boldsymbol{B}}_{{\boldsymbol{T4}}}}，$ (6)

 $\begin{split} {{\boldsymbol{B}}_{{\text{T3}}}} =& \frac{{{\mu _0}N{I_3}S}}{{4\text{π} {{\left[ {{{(x - d)}^2} + {y^2} + {z^2}} \right]}^{\frac{5}{2}}}}}\{ 3(x - d)z{{\boldsymbol{e}}_x} + 3yz{{\boldsymbol{e}}_y} + \\ & [2{z^2} - {(x - d)^2} - {y^2}]{{\boldsymbol{e}}_z}\} ，\end{split}$ (9)
 $\begin{split} {{\boldsymbol{B}}_{{\text{T4}}}} =& \frac{{{\mu _0}N{I_3}S}}{{4\text{π} {{\left[ {{{(x{\text{ + }}d)}^2} + {y^2} + {z^2}} \right]}^{\frac{5}{2}}}}}\{ 3(x{\text{ + }}d)z{{\boldsymbol{e}}_x} + 3yz{{\boldsymbol{e}}_y} + \\ & [2{z^2} - {(x{\text{ + }}d)^2} - {y^2}]{{\boldsymbol{e}}_z}\} 。\end{split}$ (10)
2 建模与仿真

2.1 单线圈模型

z=2.0 m的XOY平面内，对于不同大小的激励电流I，单线圈|B| 的分布如图4所示。随着电流的减小，单线圈的|B| 在逐渐线性减小，较高值的覆盖面积也越来越小，|B| 的峰值（记为|B| max）具体大小及所在位置如表1所示。

 图 4 单线圈磁感应强度模的分布 Fig. 4 Distribution of the single coil

2.2 双线圈模型

2.2.1 双线圈电流同向

1）轴向距离一定时，改变线圈间隔

z=2.0 m的XOY平面内，对于不同的线圈间隔d，双线圈|B| 的分布如图5所示，图中|B| max具体大小及所在位置如表2所示。从d=0.8 m开始，峰值点由原点处的单个分裂为Y轴上对称的2个。

 图 5 z=2.0 m时双线圈磁感应强度模的分布 Fig. 5 Distribution of magnetic induction intensity norm of the double-coil array when z=2.0 m

2）线圈间隔一定时，改变轴向距离

 图 6 d=1.0 m时双线圈磁感应强度模的分布 Fig. 6 Distribution of magnetic induction intensity norm of the double-coil array when d=1.0 m

2.2.2 双线圈电流反向

1）轴向距离一定时，改变线圈间隔

z=2.0 m的XOY平面内，对于不同的线圈间隔d，双线圈|B| 的分布如图7所示，图中|B| max具体大小及所在位置如表4所示。随着d的变化，始终处于Y轴上对称两峰值点的状态。

 图 7 z=2.0 m时双线圈磁感应强度模的分布 Fig. 7 Distribution of magnetic induction intensity norm of the double-coil array when z=2.0 m

2）线圈间隔一定时，改变轴向距离

 图 8 d=1.0 m时双线圈磁感应强度模的分布 Fig. 8 Distribution of magnetic induction intensity norm of the double-coil array when d=1.0 m

2.3 四线圈模型

2.3.1 四线圈电流同向

1）轴向距离一定时，改变线圈间隔

z=2.0 m的XOY平面内，对于不同的线圈间隔d，四线圈|B| 的分布如图9所示，图中|B| max具体大小及所在位置如表6所示。从d=1.1 m开始，峰值点由原点处的单个分裂为XY轴上对称的4个。

2）线圈间隔一定时，改变轴向距离

 图 9 z=2.0 m时四线圈磁感应强度模的分布 Fig. 9 Distribution of magnetic induction intensity norm of the four-coil array when z=2.0 m

 图 10 d=1.0 m时四线圈磁感应强度模的分布 Fig. 10 Distribution of magnetic induction intensity norm of the four-coil array when d=1.0 m

2.3.2 负半轴线圈电流反向

1）轴向距离一定时，改变线圈间隔

z=2 m的XOY平面内，对于不同的线圈间隔d，四线圈|B| 的分布如图11所示，图中|B| max具体大小及所在位置如表8所示。随着d的增加，峰值点首先由一、三象限的2个合拢为原点处的一个，之后又继续分裂成二、四象限的2个，最终分裂为XY轴上对称的4个。

 图 11 z=2.0 m时四线圈磁感应强度模的分布 Fig. 11 Distribution of magnetic induction intensity norm of the four-coil array when z=2.0 m

2）线圈间隔一定时，改变轴向距离

 图 12 d=1.0 m时四线圈磁感应强度模的分布 Fig. 12 Distribution of magnetic induction intensity norm of the four-coil array when d=1.0 m

2.3.3 X轴线圈电流反向

1）轴向距离一定时，改变线圈间隔

z=2.0 m的XOY平面内，对于不同的线圈间隔d，四线圈|B| 的分布图13所示，图中|B| max具体大小及所在位置如表10所示。随着d的增加，一直处于XY轴上对称的４个峰值点的状态，而(0,0,2)处的B值始终为0。

 图 13 z=2.0 m时四线圈磁感应强度模的分布 Fig. 13 Distribution of magnetic induction intensity norm of the four-coil array when z=2.0 m

（2）线圈间隔一定时，改变轴向距离

 图 14 d=1.0 m时四线圈磁感应强度模的分布 Fig. 14 Distribution of magnetic induction intensity norm of the four-coil array when d=1.0 m

3 结果与分析 3.1 双线圈

z=2.0 m的XOY平面内，当线圈间隔 $d \leqslant 1.4\;{\text{m}}$ 时，同向激励的磁感应强度模|B| max比较高；随着d的继续增大，反向激励|B| max超过同向激励；在d=4.0 m之后，同向、反向2种激励方式对|B| max的大小影响不大，最终均收敛于相同条件下激励电流I= $1/\sqrt 2$ A的单线圈|B| 的峰值，即 $3.471 \times$ ${10^{ - 7}}$ T，如图15所示。

 图 15 z=2.0 m时各阵列天线磁感应强度模峰值的趋势 Fig. 15 Trend of peak value of each array antenna magnetic induction intensity norm when z=2.0 m

 图 16 d=1.0 m时各阵列天线磁感应强度模峰值的趋势 Fig. 16 Trend of peak value of each array antenna magnetic induction intensity norm when d=1.0 m
3.2 四线圈

z=2.0 m的XOY平面内，当线圈间隔d<2 m时，同向激励|B| max较高；随着d的继续增大，负半轴、X轴线圈反向激励方式|B| max超过同向激励；在d=6.0 m之后，同向、反向激励方式对|B| max的影响不大，最终3种激励方式|B| max均收敛于相同条件下激励电流I=0.5 A的单线圈|B| max，即 $2.45437 \times {10^{ - 7}}$ T（见图15）。

3.3 不同阵列天线的特性分析

4 结　语

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