基于卦型基元的高增益超材料微带天线拓扑优化

Topology Optimization of High-Gain Metamaterial Microstrip Antenna Based on Bagua Elements

针对超材料微带天线在拓扑优化中存在基元结构复杂导致加工高精度要求等问题,本文提出了一种极简设计理念——卦型基元;并基于卦型基元完成了超材料微带天线的拓扑优化设计,在保证天线高增益性能的同时,超材料结构构型简洁从而具有良好的可制备性。超材料结构由固定的圆弧基元和变化的卦型基元组成,其中卦型基元中每条卦线对应一个设计变量,每个设计变量的取值规则为1对应连续卦线、0对应断口卦线。继而以天线增益最大化为目标函数、工作频率24 GHz为约束建立超材料微带天线设计的拓扑优化模型;并基于遗传算法的求解策略分别研究了对称型和非对称型超材料微带天线算例。分析结果表明基于卦型基元的超材料微带天线增益均得以显著提高,且四重卦线基元结构具有更大的增益;超材料结构的对称性可以保证辐射方向为Z轴主方向;样品制备效果验证了卦型基元超材料微带天线的良好制备性;对拓扑优化设计的深入分析发现,相比方格子基元,卦型基元设计更具有高效性。最后从天线的表面波角度阐释了其高增益性能的机理。

For the problems of high-precision processing requirements from complex elements′ structure in the topology optimization of metamaterial microstrip antenna, this paper proposes a minimalist design concept: the Bagua element;and the topology optimization design of the metamaterial microstrip antenna is completed based on the Bagua elements, which not only ensures the high gain performance of the antenna, but also has a simple metamaterial structure and good manufacturability. The metamaterial structure is composed of invariable arc elements and changed Bagua elements, and each Bagua line in Bagua elements corresponds to one design variable, which value rules are as follows: 1 corresponds to the continuous Bagua line, and 0 corresponds to the broken Bagua line. Then taking maximization of the antenna gain as the design objective, setting the working frequency of 24 GHz as constraint, a topology optimization model for the design of metamaterial microstrip antennas is established;and based on the solution strategy of genetic algorithm, the symmetric and asymmetric metamaterial microstrip antennas are studied respectively. The results show that the gain of metamaterial microstrip antennas based on Bagua elements can be significantly improved, moreover the metamaterial antenna of Bagua element with four lines has greater gain;and the symmetry of the metamaterial structure can ensure that the Z axis is the main direction of radiation direction;the sample results verify the good preparation of the Bagua element metamaterial microstrip antenna;from the in-depth analysis of topology optimization design, it is found that the Bagua element design is more efficient, compared with the square lattice element. Finally, the mechanism of high-gain metamaterial microstrip antennas is explained from the perspective of the surface wave.