频率选择表面的小型化设计与优化技术研究
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摘要
频率选择表面（Frequency Selective Surface，FSS）是由相同的贴片或孔径单元按二维周期性排列构成的无限大平面结构，它对具有不同工作频率、极化状态和入射角度的电磁波具有频率选择特性，因而在电磁领域得到广泛应用。本文主要研究了实现频率选择表面单元尺寸减缩和剖面降低的方法，以及差分进化算法结合谱域法在频率选择表面优化设计中的应用。主要研究工作包括以下几个方面：
（1）从研究几种基本单元形式的频率选择表面的频率响应出发，分析了尺寸参数变化和阵列结构变化对FSS性能的影响；然后研究了多种基于曲折型单元和交指型单元的单屏孔径型FSS的传输特性，分析了尺寸参数变化对FSS谐振频率和带宽的影响；设计了一款基于交指六边形环单元的单屏孔径型FSS，该FSS的阵列周期小于λ/30（λ为真空波长），电磁波法向入射时-3dB相对带宽达到63.4%，入射角度在0~60°范围内变化时，谐振频率的偏移小于1%。
（2）对单元曲折和相邻单元交指这两种FSS单元尺寸减缩的方法从小型化程度、带宽和入射角度稳定性等方面进行了对比研究，并得出结论——交指型FSS的小型化程度更高，相对带宽更宽，对电磁波入射角度的稳定性更好；从孔径型FSS上等效磁流分布的角度给出了性能改善的物理解释；分别加工了单元形式为曲折型和交指型六边形环的双屏孔径型FSS的试验模型，并在微波暗室中对其传输系数进行了测试，测试结果验证了结论。
（3）以基于天线-滤波器-天线阵列的频率选择表面（AFA-FSS）的设计方法为基础，分别设计了具有二阶、三阶带通响应和具有传输零点的AFA-FSS，分析了尺寸参数的变化对传输特性的影响；以二阶AFA-FSS为基本模块进行直接级联，设计出了具有高滚降特性的低剖面频率选择表面。
（4）从分形FSS的设计与分析出发，将分形技术应用于AFA-FSS的设计中，从而对传统的AFA-FSS单元的横向尺寸实现了可观的减缩；分析了分形迭代阶数和分形迭代因子对FSS传输特性的影响；设计了一款基于二阶Minkowski分形贴片和十字分形缝隙的AFA-FSS，该分形AFA-FSS在通带内具有二阶频率响应，且剖面很低，单元周期相对于传统AFA-FSS有了较大改善；加工了二阶分形AFA-FSS的试验模型，利用波导测试系统测试了传输系数，测试结果与仿真结果的良好吻合验证了设计方法的有效性。
（5）实现了利用谱域法来分析具有多层介质加载的多屏频率选择表面的数值计算方法，其中FSS为无限大平面结构。首先根据Floquet定理，将无限大FSS的计算区域限定在一个FSS单元，利用傅里叶变换在谱域内建立电场（或磁场）积分方程；然后利用谱域导纳法计算出多层各向同性媒质的谱域格林函数，并将未知电流（或等效磁流）用屋顶基函数展开；利用伽略金矩量法求解该积分方程从而得到贴片上的表面电流分布；再根据表面电流分布来计算空间任意位置处的散射场，并最终计算出FSS的反射和透射系数。
（6）将差分进化算法与谱域法结合对频率选择表面的优化设计进行了研究。对单元形式为方环形的单屏贴片型FSS的尺寸参数进行优化，设计了一款单频段的带阻型FSS；对单元形式为双方环形的单屏贴片型FSS的尺寸参数进行优化，设计了一款三频段FSS；采用布尔差分进化算法对FSS单元形状进行优化，设计了一款具有任意单元形式的三频段FSS。
AFrequency Selective Surface (FSS) is basically composed of identical patch oraperture elements periodically arranged in two-dimension infinite array. The uniquespatial filtering characteristic of FSS to incident electromagnetic waves with differentpolarizations and angles of incidence activates its extensive use in electromagneticdomain. The study of this dissertation is concentrated on the realization of sizereduction and profile decrease for FSSs, and the application of Differential Evolutionin the optimization of FSSs. Investigations on the miniaturization and optimization ofFSSs have been carried out, and the main contributions of this thesis can besummarized as follows:
(1) Started with the investigations on several FSSs with basic shapes, the effectsof parameters variations and changes of array configuration on the performances ofthese FSSs are analyzed. The transmission performances of some single-screenaperture FSSs with convoluted and interdigitated elements are studied, and theeffects of parameters variations on the resonant frequency and bandwidth of theseFSSs are also analyzed, with an emphasis on the number of convolution orinterdigitation. Asingle-screen aperture FSS with interdigitated haxagnal unit cells isdesigned, with its periodicity smaller than λ/30(where λ represents the wavelength infree space at resonance), a fractional bandwidth of63.4%for-3dB bandwidth atnormal incidence, and a shift of frequency less than1%for the incident angleranging from0to60degrees.
(2) Comparision study has been carried out between two approaches of sizereduction of FSSs, i.e. element convolution and interdigitation, with respet to theextent of miniaturization and bandwidth. A conclusion has been drawn that theinterdigitated FSSs possess inherently the higher extent of miniaturization and widerbandwidth compared with the convoluted ones, and the physical interpretation ofimprovement has been presented from the viewpoint of equivalent magnetic currentswithin the slots. Prototypes of double-layered aperture FSSs with convoluted andinterdigitated hexagonal loops were fabricated. The transmission coefficients weretested in microwave chamber, and the measured results manifested the conclusionaforementioned.
(3) Based on the design method of FSS composed of antenna-filter-antennaarrays (AFA-FSS), three AFA-FSSs have been designed, which exhibit transmission response of the second-order, the third-order and the third-order with transmission azero. Effects of parameter variation on the transmission reponse have beenconsidered. The AFA-FSS of the second order is selected as the building block todesign high-order AFA-FSSs with high roll-off characterisitic and low profile bydirectly cascading the modules.
(4) The fractal technique is introduced into the design of AFA-FSS so as toachieve size reduction for the conventional AFA-FSS. The influences of iterationorder and iteration factors on the transmission performance are investigated. AfractalAFA-FSS of second order is designed, which adopts the Minkowski island andfractal cross as the patches and coupling slot, respectively. This proposed AFA-FSSexhibits a considerable size reduction and yields a two-pole frequency response inthe pass-band, while keeping a low profile. A prototype of second-order AFA-FSS isfabricated and measured using waveguide testing system, and the well agreementbetween measured and simulated results validate the effectness of design approach.
(5) The spectral domain approach (SDA), which can be used for the analysis ofinfinite sigle-layered and multi-layered FSSs based on multi-layered isotropic media,is deduced. On the basis of Floquet theorem, the calculation region is restrictedwithin only one unit cell, and then the Fourier transformation is adopted to build theelectric (or magnetic) field integral equation (EFIE or MFIE) in the spectral domain.The EFIE (or MFIE) is solved by using the method of moments so that the unkownelecreic current on the pathes (or the fictious magnetic current within the apertures)can be computed, where the spectral dyadic Green’s function is obtained by means ofthe spectral domain immitance approach and the unkown electric (or magnetic)current is as the combination of the roof-top basis function. The omputed electric (ormagnetic) current yields the scattering fields in space and finally leads to thecalculation of transmission or reflection coefficients.
(6) The differential evolution (DE) algorithm is combined with the SDA tooptimize FSSs’ performance. A sigle-layered band-stop FSS with sinlge square loopelement is designed by optimizing the geometry parameters via DE and SDA. Asingle-layered tri-band FSS with doube square loops is further designed by means ofDE optimization. At last, the Boolean DE coupled with SDA is utilized to synthesizea tri-band FSS with unit cell of arbitrary shape.
（1）从研究几种基本单元形式的频率选择表面的频率响应出发，分析了尺寸参数变化和阵列结构变化对FSS性能的影响；然后研究了多种基于曲折型单元和交指型单元的单屏孔径型FSS的传输特性，分析了尺寸参数变化对FSS谐振频率和带宽的影响；设计了一款基于交指六边形环单元的单屏孔径型FSS，该FSS的阵列周期小于λ/30（λ为真空波长），电磁波法向入射时-3dB相对带宽达到63.4%，入射角度在0~60°范围内变化时，谐振频率的偏移小于1%。
（2）对单元曲折和相邻单元交指这两种FSS单元尺寸减缩的方法从小型化程度、带宽和入射角度稳定性等方面进行了对比研究，并得出结论——交指型FSS的小型化程度更高，相对带宽更宽，对电磁波入射角度的稳定性更好；从孔径型FSS上等效磁流分布的角度给出了性能改善的物理解释；分别加工了单元形式为曲折型和交指型六边形环的双屏孔径型FSS的试验模型，并在微波暗室中对其传输系数进行了测试，测试结果验证了结论。
（3）以基于天线-滤波器-天线阵列的频率选择表面（AFA-FSS）的设计方法为基础，分别设计了具有二阶、三阶带通响应和具有传输零点的AFA-FSS，分析了尺寸参数的变化对传输特性的影响；以二阶AFA-FSS为基本模块进行直接级联，设计出了具有高滚降特性的低剖面频率选择表面。
（4）从分形FSS的设计与分析出发，将分形技术应用于AFA-FSS的设计中，从而对传统的AFA-FSS单元的横向尺寸实现了可观的减缩；分析了分形迭代阶数和分形迭代因子对FSS传输特性的影响；设计了一款基于二阶Minkowski分形贴片和十字分形缝隙的AFA-FSS，该分形AFA-FSS在通带内具有二阶频率响应，且剖面很低，单元周期相对于传统AFA-FSS有了较大改善；加工了二阶分形AFA-FSS的试验模型，利用波导测试系统测试了传输系数，测试结果与仿真结果的良好吻合验证了设计方法的有效性。
（5）实现了利用谱域法来分析具有多层介质加载的多屏频率选择表面的数值计算方法，其中FSS为无限大平面结构。首先根据Floquet定理，将无限大FSS的计算区域限定在一个FSS单元，利用傅里叶变换在谱域内建立电场（或磁场）积分方程；然后利用谱域导纳法计算出多层各向同性媒质的谱域格林函数，并将未知电流（或等效磁流）用屋顶基函数展开；利用伽略金矩量法求解该积分方程从而得到贴片上的表面电流分布；再根据表面电流分布来计算空间任意位置处的散射场，并最终计算出FSS的反射和透射系数。
（6）将差分进化算法与谱域法结合对频率选择表面的优化设计进行了研究。对单元形式为方环形的单屏贴片型FSS的尺寸参数进行优化，设计了一款单频段的带阻型FSS；对单元形式为双方环形的单屏贴片型FSS的尺寸参数进行优化，设计了一款三频段FSS；采用布尔差分进化算法对FSS单元形状进行优化，设计了一款具有任意单元形式的三频段FSS。
AFrequency Selective Surface (FSS) is basically composed of identical patch oraperture elements periodically arranged in two-dimension infinite array. The uniquespatial filtering characteristic of FSS to incident electromagnetic waves with differentpolarizations and angles of incidence activates its extensive use in electromagneticdomain. The study of this dissertation is concentrated on the realization of sizereduction and profile decrease for FSSs, and the application of Differential Evolutionin the optimization of FSSs. Investigations on the miniaturization and optimization ofFSSs have been carried out, and the main contributions of this thesis can besummarized as follows:
(1) Started with the investigations on several FSSs with basic shapes, the effectsof parameters variations and changes of array configuration on the performances ofthese FSSs are analyzed. The transmission performances of some single-screenaperture FSSs with convoluted and interdigitated elements are studied, and theeffects of parameters variations on the resonant frequency and bandwidth of theseFSSs are also analyzed, with an emphasis on the number of convolution orinterdigitation. Asingle-screen aperture FSS with interdigitated haxagnal unit cells isdesigned, with its periodicity smaller than λ/30(where λ represents the wavelength infree space at resonance), a fractional bandwidth of63.4%for-3dB bandwidth atnormal incidence, and a shift of frequency less than1%for the incident angleranging from0to60degrees.
(2) Comparision study has been carried out between two approaches of sizereduction of FSSs, i.e. element convolution and interdigitation, with respet to theextent of miniaturization and bandwidth. A conclusion has been drawn that theinterdigitated FSSs possess inherently the higher extent of miniaturization and widerbandwidth compared with the convoluted ones, and the physical interpretation ofimprovement has been presented from the viewpoint of equivalent magnetic currentswithin the slots. Prototypes of double-layered aperture FSSs with convoluted andinterdigitated hexagonal loops were fabricated. The transmission coefficients weretested in microwave chamber, and the measured results manifested the conclusionaforementioned.
(3) Based on the design method of FSS composed of antenna-filter-antennaarrays (AFA-FSS), three AFA-FSSs have been designed, which exhibit transmission response of the second-order, the third-order and the third-order with transmission azero. Effects of parameter variation on the transmission reponse have beenconsidered. The AFA-FSS of the second order is selected as the building block todesign high-order AFA-FSSs with high roll-off characterisitic and low profile bydirectly cascading the modules.
(4) The fractal technique is introduced into the design of AFA-FSS so as toachieve size reduction for the conventional AFA-FSS. The influences of iterationorder and iteration factors on the transmission performance are investigated. AfractalAFA-FSS of second order is designed, which adopts the Minkowski island andfractal cross as the patches and coupling slot, respectively. This proposed AFA-FSSexhibits a considerable size reduction and yields a two-pole frequency response inthe pass-band, while keeping a low profile. A prototype of second-order AFA-FSS isfabricated and measured using waveguide testing system, and the well agreementbetween measured and simulated results validate the effectness of design approach.
(5) The spectral domain approach (SDA), which can be used for the analysis ofinfinite sigle-layered and multi-layered FSSs based on multi-layered isotropic media,is deduced. On the basis of Floquet theorem, the calculation region is restrictedwithin only one unit cell, and then the Fourier transformation is adopted to build theelectric (or magnetic) field integral equation (EFIE or MFIE) in the spectral domain.The EFIE (or MFIE) is solved by using the method of moments so that the unkownelecreic current on the pathes (or the fictious magnetic current within the apertures)can be computed, where the spectral dyadic Green’s function is obtained by means ofthe spectral domain immitance approach and the unkown electric (or magnetic)current is as the combination of the roof-top basis function. The omputed electric (ormagnetic) current yields the scattering fields in space and finally leads to thecalculation of transmission or reflection coefficients.
(6) The differential evolution (DE) algorithm is combined with the SDA tooptimize FSSs’ performance. A sigle-layered band-stop FSS with sinlge square loopelement is designed by optimizing the geometry parameters via DE and SDA. Asingle-layered tri-band FSS with doube square loops is further designed by means ofDE optimization. At last, the Boolean DE coupled with SDA is utilized to synthesizea tri-band FSS with unit cell of arbitrary shape.
引文
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