共形天线及阵列的分析和综合研究
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摘要
共形天线由于其独有的优点在现代雷达中得到广泛地应用：首先，与其载体表面共形，对载体本身的空气动力学性能影响不大；其次，在保证天线性能的条件下，采用共形天线可以简化天线安装；而且目前普遍采用的平面相控阵列天线还存在很多问题，如：①波束扫描范围窄；②天线单元之间的互耦效应与扫描角相关等。共形天线阵可以采用圆形、球形阵列等形式，可有效地避免上述缺点，它们可以在扫描过程中基本保持天线的波束形状和增益，同时使互耦维持在一定水平上。
本论文就基于复杂载体上共形微带天线单元及阵列进行分析和综合研究，对现阶段共形天线研究中的重点、难点以及一些前沿问题进行了较为深入地探讨。围绕共形微带天线的精确分析方法、共形微带天线单元及阵列的优化方法等，论文系统而深入地研究了以下几个方面的内容：
第一、基于体面线积分方程(VSWIE)的共形微带天线精确分析。
本文采用体、面、线及线面结合的四种基函数结合的VSWIE方程，精确计算任意形状、有限大介质和地板、探针馈电的共形微带天线辐射和阻抗特性。四种不同的基函数分别代表介质体内的体位移电流、金属表面的面电流、馈电探针上的线电流以及探针同天线结合处的电流。利用矩量法(MOM)建立线性方程组，通过求解这个线性方程组，得到各个基函数上的电流值，从而很容易地计算出天线的辐射和阻抗特性。
第二、基于VSWIE的共形微带天线阵列精确分析。
由于介质部分采用体剖分，其未知量大，直接采用MOM很难处理相关的阵列问题，所以有必要使用快速算法加速计算。因此，本文采用多层快速多极子(MLFMA)方法提高计算效率，减小了计算机的资源消耗。同时，针对电大载体上的微带共形天线及阵列的数值计算问题，本文还将物理光学法(PO)同VSWIE结合，在微带天线阵列区使用VSWIE方法，在金属载体区使用PO，大大提高了算法在实际问题中的应用范围。
第三、适合共形的微带天线单元设计。
由于微带天线共形于载体之上，其介质厚度不宜过大，本章对共形微带天线的讨论均建立在单层薄介质材料之上。针对如何展宽微带天线带宽问题，文中详细介绍了采用MOM和遗传算法(GA)开发的宽频带微带天线设计工具，以及两款宽频带微带天线。同时，由于载体上可供天线的安装空间有限，本章还对微带天线中的可重构技术展开研究，提出了：①新型频率可重构天线；②新型方向图可重构天线：③新型宽带方向图可重构天线；④新型的极化可重构天线。
第四、空间映射技术(SM)在共形天线优化中的应用。
文中使用SM技术针对复杂载体上的共形天线进行优化。采用SM技术后，共形天线的整体优化时间降低了约一个数量级左右。由于粗模型选用平面微带天线，因此对不同载体上的同类型的共形微带天线优化能够使用相同的粗模型。同时在深入研究后，本文还总结出了如何合理选择响应函数以加快优化速度的方法。
第五、共形天线阵列的精确快速综合设计
现代天线设计及优化问题往往涉及天线的各个参数，需要优化的天线参数不只一个。经典的多目标优化方法中，通常把多个目标函数整合成单个目标，将多目标优化问题转变为单目标优化问题。然而当优化目标改变时，其优化过程必须重启，同时存在多个目标函数之间量纲不同、难以统一，加权值的分配带有较强的主观性等缺点。因此本章对多目标优化算法进行了研究，在多目标优化算法的研究中，针对非支配遗传-Ⅱ(NSGA-Ⅱ)算法的不足之处，文中进行了三点改进，从而提出了一种改进的非支配遗传算法(INSGA-Ⅱ)。通过数值实验证明，改进算法提高了收敛速度和种群多样性，使种群收敛更加均匀，同时应用它来优化共形天线阵列，取得了很好的结果。
Conformal antennas have been widely used in modern radar systems with theirspecial advantages. First of all, because the antenna attaches with aircraft surface, itdoesn't affect the performance in aerodynamics. Then, with the same performance,conformal antennas can simplify the fixing, too. Plane phased antenna arrays have lotsof disadvantages such as narrow scanning angle and variable mutual couple related withthe scanning angle. However, the conformal antenna arrays such as circle array, spherearray, as a result of keeping the mutual couple balance, could avoid these defectsefficiently.
This paper focus on analysis and synthesis of conformal microstrip antennas andarrays, and also make a further research in conformal microstrip antennas analysis,conformal microstrip antennas and arrays synthesis for solving the important, difficultyand front problems in present study. Several problems are studied systematic by thenumbers and deeply, and the contents list as follows.
The first: accurate analysis of conformal microstrip antennas based on the volume,surface, wire integral equations (VSWIE).
This section uses the VSWIE equation which takes four basis functions includingvolume, surface, wire and wire-surface junction, to analyze the radiation and impedanceof probe feed conformal microstrip antennas on arbitrarily-shaped, finite-sized groundplanes and substrates. The dielectric slab, conducting patch, ground plane, and the probefeed are replaced by equivalent volume current, surface current, wire current, andwire-surface junction singularity current respectively, with the four different basisfunctions. The method of moments (MOM) is used to establish the linear equationfunctions and the currents can be calculated by solving these functions. Then, theantenna radiation patterns and impedance characteristics can be computed easily.However, meshing the dielectric slab with volume makes unknows too huge to solveantenna arrays by MOM directly.
The second: accurate analysis of conformal microstrip antenna arrays based on the VSWIE.
As mentioned above, without accelerated algorithms, it's difficult to directlyanalyze the conformal microstrip antennas with MOM, which produces too muchunknown quantities by using volume meshing in substrate part. Hence, the multi-layerfast multi-pole algorithm (MLFMA) is used to accelerate computing and reduceconsuming of computer resources in this paper. Simultaneously, we combinephysics-optical (PO) in which the microstrip antennas is solved using VSWIE and metalplatform is solved using PO
The third: design of conformal microstrip antennas.
Because the conformal microstrip antennas can't be too thick, in this section, theresearches of conformal antennas are based on single layer substrate. For broaden theoperating band, a tool is introduced by combining the MOM and genetic algorithm (GA)for broadband microstrip antenna design, and two kinds of antennas are designed by thismethod. For overcoming the limitation of fixed space on the aircraft platform,reconfigurable technique has been researched in this paper: (1) novel frequencyreconfigurable microstrip antenna; (2) novel pattern reconfigurable microstrip antenna;(3) novel broadband pattern reconfigurable microstrip antenna; (4) novel circularpolarization reconfigurable microstrip antenna.
The forth: application of space mapping(SM) technique in the optimization ofconformal antenna.
Conformal antennas based on complex carrier are designed with SM. The examplesdemonstrate that SM can reduce the overall design process by an order of magnitude (10times). A plane structure antenna is treated as a coarse model, then, the same coarsemodel is used to optimize the conformal microstrip antennas in different carriers.Simultaneously, we find that the convergence of this scheme is sensitive to the responsefunctions in the same problem. So, different response functions are studied foraccelerating convergence in this paper too.
The fifth: Synthesis of conformal antenna arrays
Synthesis of antenna arrays is a multi-objective problem. In the simplesingle-objective algorithm, the different objectives with different weights are combinedinto a single cost function, and the optimization process must be repeated when an objective goal changes. Moreover, the desired objective goals can't be achieved unlessall the weights are exactly chosen. In this section, the improved NSGA-Ⅱapproach withthree modifications, is put forward to improve the diversity and convergence in theoptimization of antenna array.
本论文就基于复杂载体上共形微带天线单元及阵列进行分析和综合研究，对现阶段共形天线研究中的重点、难点以及一些前沿问题进行了较为深入地探讨。围绕共形微带天线的精确分析方法、共形微带天线单元及阵列的优化方法等，论文系统而深入地研究了以下几个方面的内容：
第一、基于体面线积分方程(VSWIE)的共形微带天线精确分析。
本文采用体、面、线及线面结合的四种基函数结合的VSWIE方程，精确计算任意形状、有限大介质和地板、探针馈电的共形微带天线辐射和阻抗特性。四种不同的基函数分别代表介质体内的体位移电流、金属表面的面电流、馈电探针上的线电流以及探针同天线结合处的电流。利用矩量法(MOM)建立线性方程组，通过求解这个线性方程组，得到各个基函数上的电流值，从而很容易地计算出天线的辐射和阻抗特性。
第二、基于VSWIE的共形微带天线阵列精确分析。
由于介质部分采用体剖分，其未知量大，直接采用MOM很难处理相关的阵列问题，所以有必要使用快速算法加速计算。因此，本文采用多层快速多极子(MLFMA)方法提高计算效率，减小了计算机的资源消耗。同时，针对电大载体上的微带共形天线及阵列的数值计算问题，本文还将物理光学法(PO)同VSWIE结合，在微带天线阵列区使用VSWIE方法，在金属载体区使用PO，大大提高了算法在实际问题中的应用范围。
第三、适合共形的微带天线单元设计。
由于微带天线共形于载体之上，其介质厚度不宜过大，本章对共形微带天线的讨论均建立在单层薄介质材料之上。针对如何展宽微带天线带宽问题，文中详细介绍了采用MOM和遗传算法(GA)开发的宽频带微带天线设计工具，以及两款宽频带微带天线。同时，由于载体上可供天线的安装空间有限，本章还对微带天线中的可重构技术展开研究，提出了：①新型频率可重构天线；②新型方向图可重构天线：③新型宽带方向图可重构天线；④新型的极化可重构天线。
第四、空间映射技术(SM)在共形天线优化中的应用。
文中使用SM技术针对复杂载体上的共形天线进行优化。采用SM技术后，共形天线的整体优化时间降低了约一个数量级左右。由于粗模型选用平面微带天线，因此对不同载体上的同类型的共形微带天线优化能够使用相同的粗模型。同时在深入研究后，本文还总结出了如何合理选择响应函数以加快优化速度的方法。
第五、共形天线阵列的精确快速综合设计
现代天线设计及优化问题往往涉及天线的各个参数，需要优化的天线参数不只一个。经典的多目标优化方法中，通常把多个目标函数整合成单个目标，将多目标优化问题转变为单目标优化问题。然而当优化目标改变时，其优化过程必须重启，同时存在多个目标函数之间量纲不同、难以统一，加权值的分配带有较强的主观性等缺点。因此本章对多目标优化算法进行了研究，在多目标优化算法的研究中，针对非支配遗传-Ⅱ(NSGA-Ⅱ)算法的不足之处，文中进行了三点改进，从而提出了一种改进的非支配遗传算法(INSGA-Ⅱ)。通过数值实验证明，改进算法提高了收敛速度和种群多样性，使种群收敛更加均匀，同时应用它来优化共形天线阵列，取得了很好的结果。
Conformal antennas have been widely used in modern radar systems with theirspecial advantages. First of all, because the antenna attaches with aircraft surface, itdoesn't affect the performance in aerodynamics. Then, with the same performance,conformal antennas can simplify the fixing, too. Plane phased antenna arrays have lotsof disadvantages such as narrow scanning angle and variable mutual couple related withthe scanning angle. However, the conformal antenna arrays such as circle array, spherearray, as a result of keeping the mutual couple balance, could avoid these defectsefficiently.
This paper focus on analysis and synthesis of conformal microstrip antennas andarrays, and also make a further research in conformal microstrip antennas analysis,conformal microstrip antennas and arrays synthesis for solving the important, difficultyand front problems in present study. Several problems are studied systematic by thenumbers and deeply, and the contents list as follows.
The first: accurate analysis of conformal microstrip antennas based on the volume,surface, wire integral equations (VSWIE).
This section uses the VSWIE equation which takes four basis functions includingvolume, surface, wire and wire-surface junction, to analyze the radiation and impedanceof probe feed conformal microstrip antennas on arbitrarily-shaped, finite-sized groundplanes and substrates. The dielectric slab, conducting patch, ground plane, and the probefeed are replaced by equivalent volume current, surface current, wire current, andwire-surface junction singularity current respectively, with the four different basisfunctions. The method of moments (MOM) is used to establish the linear equationfunctions and the currents can be calculated by solving these functions. Then, theantenna radiation patterns and impedance characteristics can be computed easily.However, meshing the dielectric slab with volume makes unknows too huge to solveantenna arrays by MOM directly.
The second: accurate analysis of conformal microstrip antenna arrays based on the VSWIE.
As mentioned above, without accelerated algorithms, it's difficult to directlyanalyze the conformal microstrip antennas with MOM, which produces too muchunknown quantities by using volume meshing in substrate part. Hence, the multi-layerfast multi-pole algorithm (MLFMA) is used to accelerate computing and reduceconsuming of computer resources in this paper. Simultaneously, we combinephysics-optical (PO) in which the microstrip antennas is solved using VSWIE and metalplatform is solved using PO
The third: design of conformal microstrip antennas.
Because the conformal microstrip antennas can't be too thick, in this section, theresearches of conformal antennas are based on single layer substrate. For broaden theoperating band, a tool is introduced by combining the MOM and genetic algorithm (GA)for broadband microstrip antenna design, and two kinds of antennas are designed by thismethod. For overcoming the limitation of fixed space on the aircraft platform,reconfigurable technique has been researched in this paper: (1) novel frequencyreconfigurable microstrip antenna; (2) novel pattern reconfigurable microstrip antenna;(3) novel broadband pattern reconfigurable microstrip antenna; (4) novel circularpolarization reconfigurable microstrip antenna.
The forth: application of space mapping(SM) technique in the optimization ofconformal antenna.
Conformal antennas based on complex carrier are designed with SM. The examplesdemonstrate that SM can reduce the overall design process by an order of magnitude (10times). A plane structure antenna is treated as a coarse model, then, the same coarsemodel is used to optimize the conformal microstrip antennas in different carriers.Simultaneously, we find that the convergence of this scheme is sensitive to the responsefunctions in the same problem. So, different response functions are studied foraccelerating convergence in this paper too.
The fifth: Synthesis of conformal antenna arrays
Synthesis of antenna arrays is a multi-objective problem. In the simplesingle-objective algorithm, the different objectives with different weights are combinedinto a single cost function, and the optimization process must be repeated when an objective goal changes. Moreover, the desired objective goals can't be achieved unlessall the weights are exactly chosen. In this section, the improved NSGA-Ⅱapproach withthree modifications, is put forward to improve the diversity and convergence in theoptimization of antenna array.
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