﻿ 舰载大型相控阵天线的MOM仿真计算方法
 舰船科学技术  2023, Vol. 45 Issue (22): 182-185    DOI: 10.3404/j.issn.1672-7649.2023.22.034 PDF

Research on MOM simulation calculation method of shipborne large phased array antenna
WANG Zhi-xia, DONG Yan-ru, LU Jiong-yao, YANG Sen
Shanxi Vocational University of Engineering Science and Technology, Jinzhong 030619, China
Abstract: Shipborne large phased array antenna is an important communication and radar equipment, its performance directly affects the ship's communication and reconnaissance capabilities. In order to accurately evaluate the performance of this antenna, electromagnetic simulation calculation is needed. In this paper, the working principle of large-scale phased array radar is introduced, the target detection model of phased array radar is established, and a simulation calculation method of shipborne large-scale phased array antenna based on the method of moment (MOM) is proposed. The MOM method is used to calculate the radiation characteristics of the antenna. The results show that the method can effectively evaluate the performance of shipborne large phased array antennas, and provide an important reference for antenna design and optimization.
Key words: phased array radar     MOM simulation by moment method     simulation     array antenna
0 引　言

1）高速扫描

2）高分辨率

3）多目标跟踪

1 舰载大型相控阵雷达系统及信号特性研究

1）时延扫描

 $T = L\sin \frac{{{\theta _B}}}{c} \text{，}$

2）频率扫描

3）相位扫描

 图 1 舰船相控阵雷达系统的功能原理图 Fig. 1 Functional schematic diagram of ship phased array radar syste

 ${s_t}(t) = {a_t}(t)\exp \left( {j2{\text π} {f_t}t + j{\text π} \gamma {t^2}} \right) \text{。}$

 ${a_t}(t) = \sqrt {\frac{{{P_t}{L_t}}}{{4{\text π} }}} \sum\limits_{i = 0}^{N - 1} {{rect} } \left( {\frac{{t - i{T_r}}}{{{T_p}}}} \right),0 \leqslant t < N \text{。}$

 ${\rm{rect}}(t) = \left\{ {\begin{array}{*{20}{l}} {1,}{t \in (0,1)} \text{，}\\ {0,}{{\text{else }}} \text{。} \end{array}} \right.$

 $X(t) = {S_r}(t) + N(t) + C(t) + J(t) \text{。}$

 ${S_r}(t,r) = {\sigma _k}(t){a_t}\left( {t - {\tau _k}} \right)\exp \left[ {j{\text π} \gamma {{\left( {t - {\tau _k}} \right)}^2}} \right] \text{。}$

 图 2 舰船相控阵雷达系统的调频信号与幅频特性 Fig. 2 Frequency modulation signal and amplitude-frequency characteristics of ship phased array radar system

2 舰载相控阵雷达天线的目标探测建模分析

 图 3 相控阵雷达天线的目标探测坐标系 Fig. 3 Target detection coordinate system of phased array radar antenna

 $\left\{ {\begin{array}{*{20}{l}} {\cos {\alpha _x} = \cos {\theta _0}\sin {\varphi _0}}\text{，} \\ {\cos {\alpha _y} = \sin {\theta _0}} \text{。} \end{array}} \right.$

 $F\left( {{\theta _0},{\varphi _0}} \right) = \left( {\cos {\theta _0}\sin {\varphi _0},\sin {\theta _0}} \right) \text{，}$

 $\left( {i{d_x},j{d_y}} \right) \text{，} i = 1,2,...,N \text{，} j = 1,2,...,M \text{。}$

 ${\boldsymbol{K}} = \left[ {\begin{array}{*{20}{c}} {}&0 \\ {{d_y}}&{{d_x}} \\ {}&{{d_y}} \\ \begin{gathered} 0 \\ 0 \\ \end{gathered} &\begin{gathered} 0 \\ 1 \\ \end{gathered} \\ {(N - 1){d_x}}&{(M - 1){d_y}} \end{array}} \right] \text{。}$

 ${\delta _K}\left( {{\theta _0},{\varphi _0}} \right) = \exp \left[ {j\frac{{2{\text π} }}{\lambda }K \cdot {K^{\text{T}}}\left( {{\theta _0},{\varphi _0}} \right)} \right] \text{。}$

3 舰载大型相控阵天线的MOM仿真计算 3.1 相控阵雷达天线的MOM仿真算法原理

MOM仿真算法可以用于分析和设计各种类型的相控阵雷达天线，包括线性阵列、平面阵列、圆形阵列等。它可以提供准确的电磁场分布和辐射散射特性，对于优化天线结构和性能具有重要的指导作用。

 图 4 舰载相控阵雷达的天线分布示意图 Fig. 4 Antenna distribution diagram of shipborne phased array radar

MOM仿真算法的关键步骤包括：

1）离散化。将天线结构离散化为有限数量的电流元素。每个电流元素代表天线上的一个小电流段，可以是线性电流、面电流或体电流。

2）电流分布计算。根据天线结构和辐射场的要求，确定电流元素的分布方式。可以根据天线的几何形状、驱动方式和辐射方向等因素来确定电流元素的位置、大小和相位。

3）边界条件施加。根据Maxwell方程组和边界条件，建立电流元素之间的相互作用关系。边界条件可以是电流元素之间的电流连续性、电压连续性或电场连续性等。

4）矩阵方程建立。根据电流元素之间的相互作用关系，建立矩阵方程。矩阵方程描述了电流元素之间的耦合关系，可以通过求解矩阵方程得到电流元素的分布和电磁场的分布[4]

5）求解矩阵方程。通过数值方法，如LU分解、迭代法或快速多极子算法等，求解矩阵方程。求解矩阵方程可以得到电流元素的分布和电磁场的分布。

6）辐射和散射特性。根据电流元素的分布和电磁场的分布，计算天线的辐射和散射特性。可以计算天线的辐射图案、增益、波束宽度、散射截面等。

MOM仿真算法的流程如图5所示。

 图 5 MOM仿真算法流程图 Fig. 5 Flow chart of MOM simulation algorithm
3.2 船舶相控阵雷达天线的MOM仿真计算

 ${\vec I_i}(\vec r) = \sum\limits_{n = 1}^N {{I_n}} {\vec J_n}\left( {{{\vec r}_n}} \right) \text{。}$

 ${Z_{mn}} = {\vec w_n}\left( {{{\vec r}_n}} \right) \cdot L\left[ {{{\vec J}_n}\left( {{{\vec r}_n}} \right)} \right] \text{。}$

 $\begin{gathered} \sum\limits_{n = 1}^N {{I_n} \cdot } {{\vec w}_n}\left( {{{\vec r}_n}} \right) \cdot L\left[ {{{\vec J}_n}\left( {{{\vec r}_n}} \right)} \right] = \left[ K \right] \text{，} \\ \left[ {{Z_{mn}}} \right]\left[ {{I_n}} \right] = \left[ {{V_m}} \right] \text{。} \\ \end{gathered}$

 图 6 基于MOM仿真算法的相控阵天线磁场强度仿真结果 Fig. 6 Simulation results of magnetic field intensity of phased array antenna based on MOM simulation algorithm

4 结　语

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