Design of unsymmetrical slot antenna based on ANN for RFID tag
应用于天线的高介电常数聚合物基覆铜板
应用于天线的高介电常数聚合物基覆铜板Pape r Code:A-041颜善银苏民社殷卫峰广东生益科技股份有限公司摘要近年来，由于无线通信的快速发展，使无线通信成为生活的必需。
天线负责电路与空气中电磁能量的转换，为通信系统中不可或缺的基本设备。
随着电子产品轻、薄、短、小的发展趋势，电子产品中元器件的设计也要朝此趋势发展。
当前业界对于天线设计的重点在于小型化、结构简单化及多频或宽带。
采用陶瓷作为基板制作小型化天线已经是众所周知，然而，陶瓷的不足之处是它易碎，并且有较高的制作成本，因为它必须使用烧结的方法来制备。
高介电常数聚合物基覆铜板由于具有易加工、低温成型、低成本和优异的机械性能，已经引起了人们的广泛关注。
本文对高介电常数聚合物基覆铜板的设计与制作进行了简要概述。
关键词高介电常数；覆铜板；天线中图分类号：TN41文献标识码：A文章编号：1009-0096（2012）增刊-0044-05High dielectric constant polymer based copperclad laminate for antenna applicationY AN Shan-y in SU M in-she Y IN W ei-fengAbst rac t Due to the rapid development of wireless communication technology in recent years,wireless communication has become an essential part of modern life.The antenna is used for electromagnetic energy conversion between the circuit and the air,and is an indispensable piece of basic equipment for communication systems.With the trend of electronic products becoming light,thin,short,and small,the components for electronic products must also consider this trend in design.Current antenna design is focusing on miniaturization,structure simpli cation,and multi-band or broadband.An antenna employing ceramics as a substrate has also been known as the small-sized antenna.However,the ceramics is disadvantageous in that it can be easily broken and has a high manufacturing cost since it has to be fabricated using sintering.High dielectric constant polymer based copper clad laminate have drawn much attention due to their easy fabrication,low temperature process,low cost and excellent mechanical properties.The design and fabrication of high dielectric constant polymer based copper clad laminate were reviewed in this paper.Key wo rd s High Diele ctric Consta nt;Coppe r Clad La minate;A ntenna1前言无线通信技术是通过电磁波的辐射来完成。
一种新颖的超宽带平面等角螺旋天线的设计
2013年第06期，第46卷 通 信 技 术 Vol.46，No.06,2013 总第258期 Communications Technology No.258,Totally一种新颖的超宽带平面等角螺旋天线的设计罗 旺（电子科技大学 物理电子学院，四川 成都 611731）【摘 要】分析了平面螺旋天线的研究方法，并设计了工作于2～12 GHz的新颖的超宽带平面等角螺旋天线，由天线的宽带特性指标和平衡结构特性，天线两臂的辐射部分设计了一种带环状贴片的天线辐射结构，使圆极化轴比带内小于3 dB，天线馈电部分设计了一种阻抗为指数渐变和梯形渐变相结合的双线形式微带线宽带巴伦，并可采用50 Ω同轴探针馈电，使带内反射系数小于-10 dB。
测试结果表明，馈电的微带巴伦和天线带环状的结构形式都表现出良好的宽频带和圆极化特性。
【关键词】宽带巴伦；平面等角螺旋天线；圆极化轴比；反射系数【中图分类号】TN822 【文献标识码】A 【文章编号】1002-0802(2013)06-0012-03 Design of A Novel Ultra-wideband Planar Equiangular Spiral AntennaLUO Wang(College of Physical Electronics, ESTUC, Sichuan Chengdu 611731, China)【Abstract】The planar spiral antenna research methods are analyzed, and the planar equiangular spiral antenna working in 2～12 GHz novel ultra-wideband is designed. For the balanced structure and broadband characteristics of the antenna, a belt-ring stickers antenna radiating structure for the antenna radiation part is designed, so that the circular polarization axis is less than 3dB than the band, while a two-form microstrip line broadband balun combining the impedance index gradient and trapezoidal grodient is designed for the antenna feed part, and 50Ω coaxial probe feed may also be adopted, so that the reflection coefficient could be less than -10dB band. The measurement results indicate that both the antenna and the balun exhibit good circular polarization and broad-band property.【Key words】broadband balun; planar equiangular spiral antenna; circular polarization axial ratio; reflection coefficient0 引言平面螺旋天线是一种比较常见的超宽带天线，它本身属于非频变天线系列。
A NOVEL WIDEBAND ANTENNA DESIGN USING U-SLOT
A NOVEL WIDEBAND ANTENNA DESIGN USING U-SLOTChai Wenwen;Zhang Xiaojuan【期刊名称】《电子科学学刊（英文版）》【年(卷),期】2008(025)002【摘要】U-slot patch antennas with ∏-shaped feed slot are studied, and numerical results based on the FDTD method are presented. The effects of varying physical parameters are investigated with a goal of understanding the coupling among different resonators. It is found that the U-slot patch antenna can be designed to attain 50% impedance bandwidth as well as 30-40% gain bandwidth. By altering the sizes of U-slot and feed slot, the wideband characteristic can be changed into a dual-frequency characteristic.【总页数】5页(P192-196)【关键词】微带天线;宽带天线;双频天线; U型槽进纸槽【作者】Chai Wenwen;Zhang Xiaojuan【作者单位】Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China;Graduate University of Chinese Academy of Sciences, Beijing 100039, China;Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China【正文语种】中文【中图分类】TN822.8因版权原因，仅展示原文概要，查看原文内容请购买。
新型舰载超短波宽带平面天线
新型舰载超短波宽带平面天线李晓林;李韩;熊烨;陈永良;陈聪【摘要】A novel shipborne V/UHF broadband plane antenna is designed. The planar unsymmetrical dipoles are used for the antenna. The elliptical-fitting structure is adopted for upper radiator, and the exponentially graded ladder structure for lower radiator. The antenna input impedance and radiation pattern are calculated with finite differential time domain （FDTD） method. Within a bandwidth of 13.3 ： 1, the voltage standing wave ratio（VSWR） is less than 2.9, the pattern distortion factor in horizontal plane is less than 3. 8dB, and the antenna height is only 0.326λmax. The theoretical values are compared with experimental results and both fit well.%设计出一种新型舰载超短波宽带天线，该天线采用平面非对称偶极子形式，上辐射面为椭圆拟合结构，下辐射面为指数渐变梯形结构。
采用时域有限差分法（FDTD）计算了天线的输入阻抗和辐射方向图。
在13．3：1的频带内，天线的电压驻波比小于2．9，水平面方向图失真度小于3．8dB，而天线高度仅为0．326λmax．理论值与实验结果进行了比较，两者吻合较好【期刊名称】《电波科学学报》【年(卷),期】2011(026)003【总页数】5页(P539-543)【关键词】宽频带;超短波;平面天线;FDTD【作者】李晓林;李韩;熊烨;陈永良;陈聪【作者单位】中国船舶重工集团公司第七二二研究所,湖北武汉430079;中国船舶重工集团公司第七二二研究所,湖北武汉430079;中国船舶重工集团公司第七二二研究所,湖北武汉430079;中国船舶重工集团公司第七二二研究所,湖北武汉430079;中国船舶重工集团公司第七二二研究所,湖北武汉430079【正文语种】中文【中图分类】TN822.21．引言舰船隐身技术的发展，催生出集成化上层结构设计新思路。
基于动态超表面天线的雷达通信一体化设计
doi:10.3969/j.issn.1003-3114.2023.05.021引用格式:高克,张海洋,王保云.基于动态超表面天线的雷达通信一体化设计[J].无线电通信技术,2023,49(5):946-952.[GAO Ke,ZHANG Haiyang,WANG Baoyun.Beamforming Design for Dual-functional Radar-communication Systems with Dynamic Metasurface Antennas[J].Radio Communications Technology,2023,49(5):946-952.]基于动态超表面天线的雷达通信一体化设计高㊀克,张海洋,王保云(南京邮电大学通信与信息工程学院,江苏南京210003)摘㊀要:雷达通信一体化(Dual-Functional Radar-Communication,DFRC)利用相同的硬件平台㊁频谱资源同时实现雷达感知和无线通信双功能,是当前无线通信领域研究的热点技术㊂针对动态超表面天线(Dynamic Metasurface Antenna,DMA)辅助的雷达通信一体化系统,研究了最优波束成形设计问题㊂最优波束成形设计是一个非凸优化问题,很难直接求解㊂设计全数字天线架构下的最优波束,将动态超表面天线雷达波束设计转换为拟合最优编码矩阵问题㊂转换后的波束设计问题仍为非凸,为此将其分解为两个子问题交替最小化,其中两个子问题分别采用黎曼共轭梯度和半正定松弛算法求解㊂数值仿真表明,满足通信质量约束的情况下,动态超表面天线架构的DFRC 雷达波束性能接近于无频谱共享时的纯雷达波束性能㊂关键词:雷达通信一体化;动态超表面天线;交替最小化;黎曼共轭梯度;半正定松弛中图分类号:TN929.5㊀㊀㊀文献标志码:A㊀㊀㊀开放科学(资源服务)标识码(OSID):文章编号:1003-3114(2023)05-0946-07Beamforming Design for Dual-functional Radar-communicationSystems with Dynamic Metasurface AntennasGAO Ke,ZHANG Haiyang,WANG Baoyun(Communication and Information Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210003,China)Abstract :Dual-Functional Radar-Communication (DFRC)uses same hardware platform and spectrum re-sources to realize dualfunctions of radar detection and wireless communication simultaneously,which is a hot topic in the field of wireless communications.Forthe Dynamic Metasurface Antennas (DMA)-assisted DFRC system,an optimal beamforming design problem is studied.The optimalbeamforming design is a non-convex optimization problem that is difficult to solve directly.In this paper,an optimal beam with a digitalantenna architecture is designed first,and then the dynamic metamaterial antenna radar beam design is converted into a fitting optimalcoding matrix problem.Though the resulting design problem is still non-convex.it can be decom-posed into two sub-problems and then been solved alternately.In particular,the two sub-problems are solved by riemannian conjugate gradient and semidefinite relaxation algo-rithms,respectively.Finally,numerical results show that the performance of our proposed beamforming design for DMA-assisted DFRC system is close to that of the radar only beamforming without communication requirement.Keywords :DFRC;DMA;alternate minimization;riemannian conjugate gradient;semidefinite relaxation收稿日期:2023-05-050 引言随着5G 时代的到来,无线设备数量和种类均呈现出了爆发性增长,全球通信产业对无线频谱的需求日益迫切㊂有很多场景需要感知与通信联合设计,例如:自动驾驶㊁智慧城市和智能家居等[1]㊂与此同时,随着无线通信速率需求的不断提高,载波频率被推向了传统上分配给雷达系统的毫米波频率频段[2]㊂未来后5G 及6G 时代,为提高频谱效率以及降低雷达与通信系统之间的电磁干扰问题,雷达通信一体化(Dual-Functional Radar-Communication,DFRC)系统成为了一个有前途的热门研究领域㊂在雷达通信一体化系统中,雷达与通信系统之间共享相同的硬件平台和频谱资源,同时实现通信和雷达感知的双功能㊂在雷达通信一体化系统中,由于雷达和通信具有不同的需求且共享相同的资源,因此需要精心设计传输波束以平衡二者的性能㊂为了在保证通信用户服务质量的同时提高雷达的性能,文献[3]研究了发射波束成形优化设计㊂针对全数字天线架构,文献[4]考虑波束之间的相互干扰因素,设计了性能更优的雷达波束㊂考虑到全数字天线功耗大㊁成本高的问题,目前对雷达通信一体化系统研究比较广泛的是基于相移器的混合波束天线架构[5-10],其中文献[5-6]研究了设计模拟和数字预编码矩阵,使其与最优通信预编码矩阵和最优雷达波束预编码矩阵之间误差的加权总和最小;文献[7-8]研究主要集中在雷达波束与理想波束差距小于一定阈值作为约束条件,最大化用户通信质量;文献[9-10]研究了在保证用户通信质量前提下,最优化雷达波束性能,其雷达的波束性能直接由雷达接收机的信干扰加噪声比(Signal to Interference plus Noise Ratio, SINR)决定㊂智能超表面是当前无线通信领域的另外一个研究热点,其可用于增强无线通信盲区覆盖㊁物理层辅助安全通信㊁大规模D2D(Device-to-Device)通信㊁物联网中无线携能通信以及室内覆盖等领域[11]㊂然而,智能超表面除了用来做被动的反射外,还可以用来实现低功耗的主动收发天线㊂动态超表面天线(Dynamic Metasurface Antennas,DMA)是一种典型的基于超表面天线的收发天线㊂在基于DMA的收发器中,每个超表面天线单元是由低功耗的超表面组成,且每个天线单元的幅频特性可以动态实时调控[12]㊂DMA天线架构可以被视为混合模拟数字天线架构,即它不需要额外的专用模拟相移器网络,仅利用自身的信号处理功能便可实现模拟预编码[13]㊂此外,DMA可以包含大量可调谐的超表面天线元件,并且其天线单元之间的距离可以是亚波长,DMA需要的物理面积可以更小,有助于设备的小型化[14]㊂1㊀系统模型和问题描述1.1㊀系统模型雷达通信一体化系统场景示意图如图1所示,一个雷达通信一体化基站拥有N T根天线,为K个单天线用户提供通信服务并探测区域内目标㊂基站使用的动态超表面天线架构,其由数字预编码矩阵㊁L T条射频链路和模拟预编码矩阵组成㊂图1㊀雷达通信一体化系统场景示意图Fig.1㊀Schematic diagram of DFRC基带信号表示为sɪKˑ1,s i~(0,1),iɪ{1, 2, ,K}为第i个用户接收到的信息符号㊂发射信号可以表示为:y=UF DMA F BB s,(1)式中:F DMAɪN TˑL T为DMA天线模拟预编码矩阵, F BBɪN DMAˑK为数字预编码矩阵,DMA微带内的信号传播公式为:u i,j=e-ρi,j(αi+jβi),∀i,j,其中αi为波导衰减系数,βi为波数,ρi,j表示第i微带中第l个单元的位置,其中U((i-1)L+l,(i-1)L+l)=u i,l,L为每条微带上单元的个数[13]㊂功率约束条件为 UF DMA F BB 2FɤP max,P max为基带最大分配功率㊂F DMA矩阵满足以下形式[15]:F DMA=t10 00t2 0︙︙︙00 t L Téëêêêêêùûúúúúú,(2)式中:t iɪN TN DMAˑ1,非零相q i,l=j+e jφi,l2,{φi,lɪ[0,2π]}ɪF DMA,∀i,l㊂雷达在θ角方向的传输功率波束图可以表示为:P(θ;R)=a H(θ)Ra(θ),(3)式中:RɪN TˑN T为传输波束的协方差矩阵,R= UF DMA F BB ss H F H BB F H DMA U-H=UF DMA F BB F H BB F H DMA U H㊂对于N个天线单元的均匀线性天线阵列,其导向矢量为:a(θ)=1N[1,e j2πλdsin(θ), ,e j2πλd(N-1)sin(θ)]T,(4)式中:λ为信号波长,d=λ/2为天线单元间距㊂雷达在θ1和θ2两角之间的波束互相关可以表示为:P c(θ1,θ2;R)=a H(θ1)Ra T(θ2)㊂(5)由式(3)和式(5)可以看出,雷达的传输功率波束图和波束互相关都是由传输波束的协方差矩阵R决定㊂通过波束方向误差和波束互相关两部分的加权和组成一个损失函数,用损失函数评估雷达性能㊂第一部分可以用接收到的波束与理想波束之间的均方差来评估:L r,1(R,α)=1LðL l=1|αd(θl)-P(θl;R)|2,(6)式中:α为比例因子,d(θl)为θl方向理想接收波束㊂第二部分用波束互相关均方差来评估:L r,2(R)=2P2-PðP-1p=1㊀ðP q=p+1|P c(θ-p,θ-q);R|2㊂(7)㊀㊀将以上两部分加权和后,雷达波束图的损失函数表示为:L r(R,α)=L r,1(R,α)+ωL r,2(R)㊂(8)在本文雷达通信一体化系统中,假设通信用户是单天线的,则第k个用户接收信号为:y k=h H k UF DMA F BB,k s k+ðK iʂk h H k UF DMA F BB,i s i+n k,(9)式中:h kɪN Tˑ1为基站与第k个用户之间的下行通道,n k~(0,σ2k)为第k个用户加性高斯白噪声(Additive White Gaussian Noise,AWGN)㊂第k个用户接收信号的SINR可以表示为:γk=|h H k UF DMA F BB,k|2σ2k+ðK iʂk|h H k UF DMA F BB,i|2㊂(10)1.2㊀问题描述雷达通信一体化系统需要权衡通信和雷达之间的性能㊂基于动态超表面天线的雷达通信一体化系统,在保证每个通信用户的SINR高于给定阈值前提下的式(10),使雷达传输波束的性能达到最优的式(8)㊂另外,加上预编码矩阵有功率限制和模拟预编码矩阵相位限制的式(2),雷达通信一体化系统传输波束成形设计问题可以表示为:㊀min FBB,F DMA L r(R,α)㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀s.t.㊀ UF DMA F BB 2FɤP max,F DMA(i,l)=j+e jφi,l2,φi,lɪ[0,2π],|h H k UF DMA F BB,k|2σ2k+ðK iʂk|h H k UF DMA F BB,i|2ȡΓ,(11)式中:Γ为给定用户的SINR阈值㊂式(11)涉及到数字预编码矩阵和模拟预编码矩阵的联合设计,并且问题本身也是非凸的,很难求解㊂当天线架构为全数字天线架构时,该问题对应的问题容易求解,并且在用户SINR满足一定阈值时,其最优预编码矩阵获得的波束与理想波束十分相似㊂因此可以先求出全数字天线最优预编码矩阵,然后将动态超表面天线的模拟预编码矩阵和数字预编码矩阵拟合全数字天线的最优预编码矩阵,由此得到动态超表面天线的模拟与数字最优预编码矩阵㊂2㊀雷达通信一体化波束成形设计2.1㊀基于全数字天线架构先设计基于全数字天线架构的雷达通信一体化系统预编码矩阵W,使其在满足功率约束和用户SINR高于一定阈值前提下,雷达波束性能达到最优㊂其问题表示为:㊀㊀㊀min R L r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP max|h H k w k|2σ2k+ðK iʂk|h H k w i|2ȡΓ,(12)式中:w i为W的第i列,W=(w1,w2 ,w K)㊂将第三个约束化简后的问题为:min R,RkL r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP maxRkɪS+M,rank(R k)=1,k=1,2, ,K(1-Γ-1)h H k R k h kȡh H k Rh k+σ2k,(13)式中:R k=w k w H k,R=ðK k=1R k㊂由于其中的约束条件rank(R k)=1,k=1,2, , K是非凸的,可以先将其松弛掉,松弛后的问题是凸问题:min R,RkL r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP maxRkɪS+M,k=1,2, ,K(1-Γ-1)h H k R k h kȡh H k Rh k+σ2kW=(w1,w2, ,w K),R k=w k w H k㊂(14)可以用Matlab中CVX工具箱求得最优解:R^, R^k,k=1,2, ,K㊂如果式(14)全局最优解满足R^kɪS+M,k=1,2, ,K 秩为1,那么求解式(13)中使用的松弛就是紧的,即松弛后问题的解也是原非凸问题的解㊂定理1㊀式(13)存在最优解R ~,R ~k ,k =1,2, ,K ,满足rank(R ~k )=1,k =1,2, ,K ㊂证明㊀R ^,R ^i ,i =1,2, ,K 为式(14)的全局最优解,将R ^,R ^i,i =1,2, ,K 做以下变换:R ~=R ^,w ~i =(h H i R ^i h i )-1/2R ^i h i ,R ~i =w ~i w ~H i ,R ~,R ~i ,i =1,2, ,K 为半正定矩阵且秩为一㊂因为R ~=R^,并且式(13)和式(14)的最终问题是相同的,所以R ~是式(13)全局最优解㊂现在只要证明R ~,R ~i ,i =1,2, ,K 为式(13)的可行解,则R ~,R ~i ,i =1,2, ,K 为式(13)的全局最优解㊂由于h H kR ~k h k =h H kw ~k w ~H k h k =h H k R ^k h k ,将其带入到(1-Γ-1)h H k R ~k h k=(1-Γ-1)h H k R ^k h k ȡh H k R ^k h k +σ2k =h H k R ~k h k +σ2k 满足式(13)的限制条件㊂所以R ~,R ~i ,i =1,2, ,K 为原问题的全局最优解㊂由定理1可知将式(14)最优解做以下变换:R ~=R ^,w ~k =(h H k R ^k h k )-1/2R ^k h k ,R ~k=w ~k w ~H k ,R ~k ɪS +M ,k=1,2, ,K 且秩为1,并且R ~仍为原问题的解㊂由此可以求解得到全数字天线最优预编码矩阵的列向量w k ,全数字天线架构的最优预编码矩阵W 也就可以求出㊂2.2㊀基于动态超表面天线架构在上节求解得到了全数字天线最优预编码矩阵,本节设计动态超表面天线架构预编码矩阵,使雷达通信一体化系统在满足功率约束㊁模拟预编码矩阵相位约束和通信用户信干扰加噪声比高于一定阈值前提下,最优拟合全数字天线预编码矩阵,其问题表示为:min F BB ,F DMAUF DMA F BB -W ~2Fs.t.㊀ UF DMA F BB 2F ɤP maxq i ,l =j +ej φi ,l2,φi ,l ɪ[0,2π]}{ɪF DMA ,∀i ,l|h H kUF DMA F BB,k|2σ2k+ðKi ʂk|h H kUF DMA F BB,i|2ȡΓ㊂(15)由于此问题不是凸问题,故将问题分解成设计两个子问题相互迭代来求解,两个子问题分别设计数字和模拟预编码矩阵㊂然而,数字和模拟预编码矩阵的设计问题都是非凸问题㊂为此,本文分别采用半正定松弛(Semidefinite Relaxation,SDR )技术[16-17]和黎曼共轭梯度(Riemannian Conjugate Gra-dient,RCG)算法[18]分别设计最优数字和模拟预编码矩阵㊂2.2.1设计模拟预编码矩阵当固定数字预编码矩阵F BB 设计最优模拟预编码矩阵时,限制条件只有模拟预编码矩阵的相位限制㊂其问题为:min FDMAUF DMA F BB -W ~2Fs.t.㊀q i ,l =j +ej φi ,l2,φi ,l ɪ[0,2π]}{ɪF DMA ,∀i ,l ㊂(16)由于问题是矩阵形式,不方便求解,所以将矩阵向量化:min FDMAUF DMA F BB -W ~2F =min F DMA(F T BB U )vec(F DMA )-w 2F ,式中:w =vec(W ~)㊂因为vec(F DMA )中的元素除了相位限制元素,其他为零元素㊂由于零元素的具体位置是已知的,所以可以先将零元素剔除掉㊂令q 为vec(F DMA )去除零元素后的向量,A 为(F T BB U )去除掉与vec(F DMA )零元素相对应的列向量㊂此时的问题转换为:㊀min F DMA(F T BB U )vec(F DMA )-w 2F =min q(Aq -w )H (Aq -w )=min qq H A H Aq -2q H A H w +w H w ㊂(17)由于模拟预编码矩阵的非零元素q i ,l 可以描述为圆心点为0,12e j π2(),半径为12的复平面圆上:q i ,l -12e j π2=12,定义向量b 为:b k =2q k -e j π2,所以q =12b +e j π21(),|b k |=1㊂最终可以将问题转换为关于向量b 的问题:min bq H A H Aq -2q H A H w +w H w =min b 14b +e j π21()H A H A b +e j π21()-b +e j π21()H A H w +w H w s.t.㊀|b k |=1ɪb ,(18)这时搜索空间为N T 个复数圆上,是一个N T的黎曼子流形,可以通过RCG 求得最优解b opt ㊂其中该问题的黎曼梯度为Δf (bt +1k)=AH㊃12A b t +1k +e j π21()-w ()㊂由于F DMA 非零位置是已知的,所以将最优解bopt扩展成矩阵形式,可以得到最优模拟预编码矩阵F opt DMA ㊂2.2.2设计模拟预编码矩阵当固定模拟预编码矩阵F DMA 时,限制条件为预编码矩阵功率约束和通信SINR 阈值约束,其问题为:㊀㊀㊀㊀min F BBUF DMA F BB -W ~ 2F㊀㊀㊀㊀s.t.㊀ UF DMA F BB 2FɤP maxh H k UF DMA F BB,k2σ2k+ðKi ʂk|h H kUF DMA F BB,i |2ȡΓ㊂(19)由于式(19)中第二个限制条件F BB 是按列展开的,所以将问题中的矩阵F BB 和W ~也按列展开:ðKk =1UF DMA F BB,k-W ~k 2F =ðK k =1F H BB,k F H DMA U H UF DMA F BB,k -2F H BB,k F H DMA U H W ~k +W ~Hk W ~k ㊂(20)展开后的问题并不容易求解,引入辅助变量t 2=1,可以化解成二次约束二次规划问题(Quadrati-cally Constrained Quadratic Programs,QCQP):v -k =F BB,kt(),Q k =F H DMA U H UF DMA ,-F H DMA U HW ~k ㊀㊀-W ~H k UF DMA ,W ~H k W ~k(),F H BB,k F H DMA U H U F DMA F BB,k -2F H BB,k F H DMA U H W ~k +W ~H k W ~k=v -H k Q v -k ㊂但此时,由于式(20)中第二个限制条件是非凸的,所以该问题也是非凸的㊂引用SDR 技术将问题进行化简,令V k =v -k v -H k ,rank(V k )=1,可以将问题简化为SDR 的标准形式:min V k ðKk =1tr(Q k V k )s.t.㊀ðKk =1trF H DMA U HUF DMA ,00,()V k ()ɤP max ,∀k ,trH k ,00,0()V k ()Γ-ðKi ʂktrH k ,00,()V i ()ȡσ2k ,tr0K ∗K ,00,1()V k ()=1,V k ȡ0,rank(V k )=1,H k =F H DMA U H h k h Hk UF DMA ㊂(21)由于约束项rank(V k )=1是非凸的,先将其松弛掉,之后的问题是凸问题,可以用Matlab 中CVX 工具箱求最优解V opt k ㊂如果该问题可解或有界,则ðKk =1[rank(V opt k )]ɤK +1,又因为每个用户的SINR 阈值限制,最优解满足:rank (V opt k )ȡ1,所以其最优解满足rank(V opt k )=1㊂由此证得rank(V k )=1的松弛是紧的,V opt k是原问题的最优解㊂F opt BB,k 是V optk的最大特征向量乘以最大特征值的平方根,因此,可以得到最优数字预编码矩阵F opt BB ㊂3 仿真分析本节采用数值仿真验证DMA 雷达通信一体化设计算法的性能,并且与全数字天线架构㊁基于相移器的混合波束天线架构和理想雷达波束进行对比㊂考虑雷达通信一体化基站的天线为均匀线性天线阵列,总发射功率为1W 和天线数量为24,其为用户提供通信服务并探测区域内目标㊂在探测区域内设置了方向为-40㊁0ʎ和40ʎ的3个理想目标,其波束表达式为:d (θ)=1,θ0-Δ2ɤθɤθ0+Δ20,㊀㊀otherwise{,(22)式中:Δ为理想波束的宽度,设置为2ʎ㊂当系统设计的DMA 射频链路为12个,信噪比设置为20dB 时,不同天线架构随角度变化的波速比较如图2所示㊂不同天线架构在满足用户需求前提下,使雷达波束达到最优的仿真,图中K =0㊁FD㊁DMA 和BP 线分别为理想目标波束㊁全数字天线架构波束㊁DMA 天线架构波束和基于相移器架构波束㊂可以看出,全数字天线的雷达波束图基本与理想的波束重合,DMA 天线架构和基于相移器架构也很好地还原了最优波束图,并且从中很容易查找出在-40ʎ㊁0ʎ和40ʎ方向有目标,因为这3个方向的波束峰值明显高于其他方向㊂图3是在4个通信用户SINR 的阈值从6dB 调整到14dB,不同天线架构随角度变化的波束比较㊂图2与图3对比可知,在通信用户阈值提高的情况下,DMA 架构和基于相移器的混合架构的目标雷达波束图峰值有明显的变差㊂图4是在6个通信用户信SINR 的阈值为6dB 情况下,不同天线架构随角度变化的波束比较㊂图2与图4对比可知,服务通信用户增加,目标雷达波束图峰值会变差㊂图5是在4个通信用户信SINR 的阈值为6dB,功率约束调整为2W 情况下,不同天线架构随角度变化的波束比较㊂图2与图5对比可知,增加发射功率,图5中目标雷达波束图峰值接近图2中目标峰值的2倍㊂图2㊀不同天线架构随角度变化的波束比较Fig.2㊀Comparison of beams varying by angle fordifferent antennaarchitectures图3㊀调整用户SINR 后的波束比较Fig.3㊀Beam comparison after adjusting theuser sSINR图4㊀调整用户个数后的波束比较Fig.4㊀Beam comparison after adjusting the number ofusers图5㊀调整功率约束后的波束比较Fig.5㊀Beam comparison after adjusting power constraints图6展示了基于DMA 的雷达一体化系统在不同发射功率情况下,用户SINR 阈值约束和雷达波束性能之间的权衡㊂可以看出,在发射功率一定时,随着用户SINR 阈值的增加,DMA 天线预编码矩阵与全数字天线预编码矩阵之间的均方差也在增加,并且发射功率为2W 时的均方差明显大于功率为1W 的设计㊂这是因为当通信质量要求增加时,为满足用户质量需要消耗更多的功率,而生成雷达波束的功率会变少,雷达波束性能也会变差㊂因此,降低通信质量要求,可以提高雷达波束性能㊂图6㊀用户SINR 阈值与雷达波束均方差之间关系Fig.6㊀Relationship between the user s SINR threshold andthe mean square deviation of the radarbeam4 结束语本文研究了基于动态超表面天线的雷达通信一体化系统,设计了相应的最优波束成形策略㊂采用了数字预编码矩阵与模拟预编码矩阵设计联合交替优化设计,分别应用半正定松弛和黎曼共轭梯度算法求解㊂数值仿真结果表明,所提算法设计的动态超表面天线架构的雷达通信一体化系统,在满足通信用户性能的前提下,其雷达性能接近理想雷达波束㊂动态超表面天线架构与基于相移器的混合波束天线架构整体性能相似,其雷达通信一体化系统中雷达与通信性能之间存在负相关,雷达性能随着通信性能的提高而降低㊂参考文献[1]㊀刘凡,袁伟杰,原进宏,等.雷达通信频谱共享及一体化:综述与展望[J].雷达学报,2020,10(3):467-484. [2]㊀ZHENG L,LOPS M,ELDAR Y C,et al.Radar and Com-munication Coexistence:An Overview:A Review of RecentMethods[J].IEEE Signal Processing Magazine,2019,36(5):85-99.[3]㊀CHU J,LIU R,LIU Y,et al.AN-aided Secure Beamform-ing Design for Dual-functional Radar-communication Sys-tems[C]ʊ2021IEEE/CIC International Conference onCommunications in China(ICCC Workshops).Xiamen:IEEE,2021:54-59.[4]㊀LIU X,HUANG T,SHLEZINGER N,et al.Joint TransmitBeamforming for Multiuser MIMO Communications andMIMO Radar[J].IEEE Transactions on Signal Process-ing,2020,68:3929-3944.[5]㊀KAUSHIK A,MASOUROS C,LIU F.Hardware EfficientJoint Radar-communications with Hybrid Precoding andRF Chain Optimization[C]ʊICC2021-IEEE InternationalConference on Communications.Montreal:IEEE,2021:1-6.[6]㊀LIU F,MASOUROS C.Hybrid Beamforming with Sub-arrayed MIMO Radar:Enabling Joint Sensing and Commu-nication at mmWave Band[C]ʊICASSP2019-2019IEEE International Conference on Acoustics,Speech andSignal Processing(ICASSP).Brighton:IEEE,2019:7770-7774.[7]㊀CHENG Z,LIAO B,HE Z.Hybrid Transceiver Design forDual-functional Radar-communication System[C]ʊ2020IEEE11th Sensor Array and Multichannel Signal Process-ing Workshop(SAM).Hangzhou:IEEE,2020:1-5. [8]㊀CHENG Z,HE Z,LIAO B.Hybrid Beamforming for Multi-carrier Dual-function Radar-communication System[J].IEEE Transactions on Cognitive Communications and Net-working,2021,7(3):1002-1015.[9]㊀CHEN C Y,VAIDYANATHAN P.MIMO Radar Wave-form Optimization with Prior Information of the ExtendedTarget and Clutter[J].IEEE Transactions on Signal Pro-cessing,2009,57(9):3533-3544.[10]DAI Y,HAN K,WEI G,et al.Hybrid Beamforming forDFRC System Based on SINR Performance Metric[C]ʊ2021IEEE/CIC International Conference on Communicationsin China(ICCC Workshops).Xiamen,IEEE,2021:82-87.[11]LAN G,IMANI M F,DEL HOUGNE P,et al.WirelessSensing Using Dynamic Metasurface Antennas:Challengesand Opportunities[J].IEEE Communications Magazine,2020,58(6):66-71.[12]SMITH D R,YURDUSEVEN O,MANCERA L P,et al.Analysis of a Waveguide-fed Metasurface Antenna[J].Physical Review Applied,2017,8(5):054048. [13]ZHANG H,SHLEZINGER N,GUIDI F,et al.Beam Focu-sing for Near-field Multiuser MIMO Communications[J].IEEE Transactions on Wireless Communications,2022,21(9):7476-7490.[14]SHLEZINGER N,ALEXANDROPOULOS G C,IMANI M F,et al.Dynamic Metasurface Antennas for6G ExtremeMassive MIMO Communications[J].IEEE WirelessCommunications,2021,28(2):106-113. [15]SHLEZINGER N,DICKER O,ELDAR Y C,et al.Dynam-ic Metasurface Antennas for Uplink Massive MIMO Sys-tems[J].IEEE Transactions on Communications,2019,67(10):6829-6843.[16]LUO Z Q,MA W K,SO A M C,et al.Semidefinite Relax-ation of Quadratic Optimization Problems[J].IEEE Sig-nal Processing Magazine,2010,27(3):20-34. [17]ZHANG S.Quadratic Maximization and Semidefinite Re-lax-ation[J].Mathematical Programming,2000,87:453-465.[18]YU X,SHEN J C,ZHANG J,et al.Alternating Minimiza-tion Algorithms for Hybrid Precoding in Millimeter WaveMIMO Systems[J].IEEE Journal of Selected Topics inSignal Processing,2016,10(3):485-500.作者简介:㊀㊀高㊀克㊀男,(1994 ),硕士研究生㊂主要研究方向:雷达通信信号处理㊂张海洋㊀男,(1987 ),博士研究生㊂主要研究方向:无线通信信号处理㊁面向6G近场无线通信㊂王保云㊀男,(1967 ),博士,教授㊂主要研究方向:香农信息论㊁无线通信中的博弈与协作㊁无线通信中的信号处理技术㊁视频信息的分析与理解㊂。
基于单脊波导的缝隙阵列天线研究
基于单脊波导的缝隙阵列天线研究任宇辉;高宝建;伍捍东;周旭冉【摘要】采用理论分析和电磁仿真相结合的方法,详细分析了单脊波导中电磁场和表面电流的分布特点,并结合计算机辅助设计的方法,实现了一款工作于C波段单脊波导脊边双缝阵列天线.这种新型天线通过在单脊波导的脊边上成对开设倾斜缝隙来实现.仿真实验表明:本设计中天线的交叉极化降低到-50.26 dB,而天线的横截面尺寸仅为同频段标准矩形波导的47％.【期刊名称】《电波科学学报》【年(卷),期】2014(029)002【总页数】6页(P391-396)【关键词】缝隙天线;单脊波导;交叉极化;计算机辅助设计【作者】任宇辉;高宝建;伍捍东;周旭冉【作者单位】西北大学信息科学与技术学院,陕西西安710069;西北大学信息科学与技术学院,陕西西安710069;西安恒达微波技术开发公司,陕西西安710100;西北大学信息科学与技术学院,陕西西安710069【正文语种】中文【中图分类】TN928引言波导缝隙阵列天线具有口面场分布容易控制、口径效率高、性能稳定、结构简单、强度好、安装方便等优点，且容易实现窄波束、低副瓣乃至超低副瓣，所以此类天线己经成为现代雷达和通信系统的首选［1－2］.尤其是波导窄边缝隙阵列天线，已广泛应用于多种雷达系统.但是近年来，随着电子对抗技术的发展，我们必须不断降低天线的旁瓣电平，从而提高雷达的抗干扰能力.这就要求天线不仅要有较宽的带宽，而且要有较低的交叉极化电平.否则，强烈的交叉极化分量将使主极化分量的低旁瓣特性失去意义.比如在合成口径雷达系统中，较高的交叉极化辐射会使数据的后处理算法产生较大误差，出现成像模糊等问题.因此，传统的波导窄边缝隙阵列天线就不能满足需求了，因为倾斜的缝隙不可避免地产生较大的交叉极化分量.传统波导缝隙天线的另一个不足之处就是它的尺寸较大，标准矩形波导的宽度对应设计频率大约为0.7λ0（λ0 为自由空间波长），这对诸如机载雷达等空间非常有限的应用场合来说就不太适用了.为了最大程度地减小交叉极化辐射，学者们提出了一些方法［3－4］.但是这些方法都需要在天线阵列中引入扼流槽等新的装置，这不仅会使天线的结构变得复杂，而且会影响到主极化场的辐射.本设计中，我们采用理论分析和电磁仿真相结合的方法，详细分析了单脊波导中的电磁场和表面电流的分布.并且设计了一种小型化、超低交叉极化辐射的新型波导缝隙行波天线.如图1所示，这种新型结构通过在单脊波导的脊边上成对开设倾斜缝隙来实现.因为缝隙角度的交替倾斜，在x方向上相邻缝隙的交叉极化辐射将相互抑制，而且单脊波导的截面尺寸要比矩形波导小，所以可以实现天线的小型化. 图1 单脊波导脊边双缝天线目前，利用脊波导来实现波导缝隙天线也有一些成果问世.文献［5］介绍了用单脊波导馈电的缝隙阵列天线设计方法，其采用的缝隙形式是在单脊波导非脊宽边开并联纵缝.文献［6］通过在双脊波导窄边上开缝，设计了工作于5GHz的波导缝隙天线，大大降低了交叉极化辐射.本文则创新性的在单脊波导的脊边上开缝来设计行波天线.1 单脊波导的基本特性如图2所示，单脊波导是矩形波导的变形，它的截面呈“凹”形.而由于脊的存在，单脊波导边界条件比较复杂，故用一般的“场”的方法来求解其内部的电磁场分布将非常困难.因此在这里，我们将通过理论分析和电磁仿真相结合的方法，来认识单脊波导中的电磁场和表面电流的分布.图2 单脊波导基本参数1.1 单脊波导中的电磁场分布在文献［7］中，W.J.Getsinger提出了一种在截止频率上求解单脊波导场分布的方法.他把单脊波导的左横截面分成了Ⅰ和Ⅱ两个区域（图2），并假设在脊下边的区域即Ⅰ区传输横电磁波（Transverse Electrical Magnetic Wave，TEM）.而在非脊区域即Ⅱ区，根据横向谐振条件，认为既有TEM波，又有沿横向传输的高次横磁波（Transverse Magnetic Wave，TM波）.然后在Ⅰ区和Ⅱ区的交界面上进行电场匹配，确定TE10模的幅值系数，从而得到主模TE10模在整个单脊波导中的场分布：为了更加直观地理解以上分析，对单脊波导中电场和磁场的分布进行仿真，结果如图3、4所示.从表达式（1）、（2）出发，再结合图3和图4，我们可以分析出以下结论：1）在区域Ⅱ中，电磁场分布比较复杂，除了Ey、Hx和Hz分量，还产生了Ex和Hy分量.而在区域Ⅰ中仅有Ey、Hx和Hz分量.2）如图3（a）所示，不论是在哪个区域，电场都没有纵向分量（Ez＝0），只有横向分量，所以单脊波导中传输的是TE波.3）但是在脊的两边，随着y的增大，Ex分量逐渐减小而Ey分量则越来越大.在y ＝b处，Ex几乎为零（图3（b））.4）对于磁场，在0＜y＜d的非脊区域，具有Hx、Hy和Hz三个分量.此时，y越小，Hy分量就越弱.所以，此时可以近似认为非脊区域的磁场和矩形波导中的磁场分布相似（图4（a））.5）在d＜y＜b的加脊区域，由公式（1）可知，越靠近y＝b的脊边，Hy越小.而此区域中由于脊的存在，客观上阻隔了x方向的磁场，所以我们认为在两个脊边附近，磁场只有Hz分量（图4（b））.综上所述，我们可以认为单脊波导的场是由多个模式的场叠加而成，但其主模仍是TE10模.1.2 单脊波导中的管壁电流根据1.1节的分析，我们知道在单脊波导两个脊边（y＝b）附近，可以近似认为磁场只存在Hz分量.所以，可以求出单脊波导两个脊边上的电流：此处Js为管壁电流面密度，n为波导壁法向单位矢量，ay、az表示直角坐标系中y和z轴方向的单位矢量.可见，单脊波导脊边上的管壁电流近似只有沿x方向的横向分量，其分布如图5所示.据此，我们发现单脊波导脊边和矩形波导窄边上的管壁电流分布类似.因此，我们可以采用和在矩形波导窄边上开倾斜缝隙一样的思路［3，8－9］，在单脊波导的脊边上开缝来辐射电磁波.图3 单脊波导中的电场分布图4 单脊波导中的磁场分布图5 波导管壁电流分布2 单脊波导脊边缝隙天线的设计方法2.1 设计基本步骤在文献［9］中，我们详细分析了波导窄边缝隙天线的计算机辅助设计方法.这里我们将采取相似的方法来设计单脊波导双缝天线：1）设计单脊波导因为单脊波导经常和矩形波导一起使用，所以参数a和b是确定的.为了保证波导中的单模传输，一般要满足由此，可以确定参数s.此外，文献［10-11］介绍了单脊波导传输特性的相关计算方法.据此，我们可以得到截止波长λc，然后再求得参数d.2）确定缝隙间距单脊波导双缝天线在z方向上的缝间距dz和波束倾角θ之间满足一般地，当dz＜λg/2时，波束指向馈电端；当dz＞λg/2时，波束指向负载端；而当dz＝λg2时，波束指向阵列的法向.此外还可以根据缝隙间距和天线总体长度来确定缝隙数目.3）天线综合与分析结合文献［9］，我们总结出如下步骤：第一步，天线阵综合.采用泰勒（Taylor）分布综合实现天线要求的口面分布，即确定缝隙的激励幅度分布，进而可求得单脊波导双缝天线阵列中各个缝隙的电导值，称之为缝隙电导分布.第二步，提取缝隙电导函数，即确定缝隙电导和尺寸之间的关系.计算考虑互耦的缝隙电导函数是设计这类天线的一个主要难点，通常有两种方法：一种是数值计算的方法［12－13］，但是因为单脊波导边界条件较为复杂，计算难度很大，所以目前很少用于工程实践，另外一种是实验法；通过加工大量试验件来测量缝隙的参数［3］，目前应用中使用较多，但其最大的不足之处就是设计工作量和误差太大.所以，我们采取计算机辅助设计的方法得到缝隙电导函数.2.2 缝隙电导函数的计算机辅助设计法这里我们采用复传输系数法，将天线阵列看作微波网络，通过其散射参数，得到缝隙的平均导纳所以，若获取缝隙的复传输系数，便可以由式（6）求得出缝隙g和b，这就是考虑互耦情况下缝隙的导纳.而若缝隙处于谐振状态，则b＝0，由式（6）可知φ≈0. 采用计算机辅助设计的方法，步骤如下：1）选用N个尺寸完全相同的缝隙，在软件中建模，各个缝隙间距、宽度与实际相同.2）仿真计算S21参数，不断调整缝的深度，使得各个缝隙在设计频率上达到谐振状态（b＝0）.根据式（6）式可得到N个缝隙的谐振电导值，进而求取平均值得到单个缝隙的谐振电导值.3）每隔1°改变缝隙倾角，重复以上步骤.经过大量仿真，得到不同缝隙谐振时的倾角和深度.4）最后根据得到的数据，绘制曲线或图表，以备使用.这组曲线就反映了缝隙尺寸和等效电导值之间的关系——缝隙电导函数.2.3 C波段单脊波导双缝天线设计作为实例，我们设计了一个工作在C波段（5.45～5.65GHz）的单脊波导脊边行波缝隙阵列天线.要求：方位面波束倾角为5±0.5°；方位面旁瓣电平小于－25dB.采用上述方法，我们首先设计单脊波导尺寸，最终选定a＝28.27mm，b＝17.46mm，s＝10.65 mm，d＝6.75mm，波导壁厚t＝1mm.其次，根据波导尺寸求得波导波长，进而由公式（4）求出缝隙间距dz＝28.26mm，缝隙总数为39.再次，设计等旁瓣数＝5，旁瓣电平LSL＝－30 dB的Taylor线源，进而求得缝隙电导分布.最后，采用计算机辅助设计的方法求得缝隙电导函数.图6（a）表示不同缝隙倾角对应的缝隙电导值，其纵轴表示缝隙电导对波导特性导纳的归一化值.而图6（b）表示不同倾角缝隙切入脊边的深度，其纵轴表示缝隙切入深度对中心频率波长的归一化值.根据所求电导分布，再结合图6查表、插值得到各个缝隙的尺寸参数.然后，在仿真软件CST中建立模型仿真并优化，结果见图7和图8.图6 缝隙电导函数分布曲线图7为天线中心频率的方位面方向图，其中实线表示主极化分量，虚线表示交叉极化.由图可见天线增益为21.9dB，旁瓣电平为－26.3dB，波束宽度等于3.1°.而文献［9］中采用BJ58标准波导设计的同频率窄边缝隙天线，其增益为19.4dB，旁瓣电平为－24.3dB.此外，采用本设计天线交叉极化电平达到－50.26dB.而文献［9］中的相同指标为－38.74 dB.显然本设计能很好地抑制交叉极化辐射.图7中的零度方向表示天线阵面的法向，可见天线波束倾角为5.3°.图8为天线回波损耗仿真曲线，因为天线为行波阵列，所以其在较宽的频带范围内，回波损耗小于－26dB.此外，本课题中设计的单脊波导其横截面尺寸为387mm2，这仅为BJ58标准波导横截面的47%左右，显然本设计可以大大减小天线的尺寸.3 结论图7 天线方位面方向图为了克服传统波导窄边缝隙天线交叉极化辐射强，且尺寸较大的缺点，本文首先研究和分析了单脊波导中电磁场和管壁电流的分布规律，然后设计出一种工作于C 波段的新型单脊波导脊边双缝天线.和传统波导窄边缝隙天线相比，本设计能有效减小交叉极化辐射和天线尺寸.另外，文中将传统电磁理论和现代电磁软件结合，提出了基于计算机辅助设计来提取缝隙电导函数的方法，从而提高了工作效率，节约了设计成本.图8 天线回波损耗仿真曲线参考文献［1］MILLOUX R J.Phased array antenna handbook［M］.London：Artech House Antennas and Propagation Library，2005：272-275.［2］VOLAKIS J L.Antenna Engineering Handbook［M］.New York：McGraw-Hill，2007：199-206.［3］钟顺时.波导窄边缝隙阵天线的设计［J］.西北电讯工程学院学报，1976（1）：165-183.［4］张祖稷.雷达天线技术［M］.北京：电子工业出版社，2005：177-199. ［5］MORADIAN M， KHALAJ-AMIRHOSSEINI M，TAYARAN M.Design of planar slotted array antenna fed by single ridge waveguide［J］.International Journal of RF and Microwave Computer-aided Engineering，2010，20（6）：593-602.［6］MALLAHZADEH A R，NEZHAD S M A.Untilted slot array antenna at the narrow wall of the waveguide using double-ridge［J］.International Journal of RF and Microwave Computer-Aided Engineering，2010，20（6）：699-710.［7］GETSINGER W J.Ridged waveguide field description and applicationto directional couplers［J］.IRE Trans Microwave Theory Tech，1962，MTT-10：41-50.［8］李建瀛，梁昌洪.波导窄边纵缝的理论分析及频扫缝阵［J］.西安电子科技大学学报，1998，25（5）：689-692.LI Jianying，LIANG Changhong.Theoretical analysis of the longitudial slotin the narrow wall of a rectangular waveguide and frequency scan array ［J］.Journal of XiDian University，1998，25（5）：689-692.（in Chinese）［9］任宇辉，高宝建，伍捍东，等.基于CST的波导窄边缝隙天线的分析与设计［J］.西北大学学报，2010，40（5）：798-801.REN Yuhui，GAO Baojian，WU Handong，et al.A-nalysis and design of the slotted antenna in the narrow wall of a rectangular waveguide based CST ［J］.Journal of Northwest University，2010，40（5）：798-801.（in Chinese）［10］张晓娟，宋文淼.非对称单脊波导的特性计算［J］.电波科学学报，2007，22（5）：825-828.ZHANG Xiaojuan，SONG Wenmiao.Characteristic calculation of unsymmetrical ridged waveguide［J］.Chinese Journal of Radio Science，2007，22（5）：825-828.（in Chinese）［11］鲁加国，吴双桂，陈嗣乔.非对称单脊波导裂缝阵天线分析［J］.电波科学学报，1998，13（4）：388-392.LU Jiaguo，WU Shuanggui，CHEN Siqiao.Analysis for slot array antennas fed by asymmetric single-ridge waveguide［J］.Chinese Journal of RadioScience，1998，13（4）：388-392.（in Chinese）［12］王宏建，刘世华，郝齐焱，等.星载Ku波段波导缝隙天线的缝隙特性分析［J］.电波科学学报，2012，27（6）：1225-1231.WANG Hongjian，LIU Shihua，HAO Qiyan，et al.Slots characterization of space-borne waveguide slots array antenna in Ku band［J］.Chinese Journal of Radio Science，2012，27（6）：1225-1231.（in Chinese）［13］ELLIOTT R S，KURTZ L A.The design of small slot arrays［J］.IEEE Trans Antennas Propag，1978，AP-26：214-219.。
手性metamaterials的非对称传输特性-研究
A dual band microstrip-fed slot antenna
0:55 20:65 to0:65 20:75 meets the three design goals:(1) The radiation pattern is dipole-like with positive gain in the x0y plane,(2)the antenna structure above the ground plane is smaller than one-tenth of a wavelength,and(3)the010dB impedance bandwidth is more than10%.If the ground plane is smaller than0:55 20:65 , the impedance matching becomes poor and the impedance bandwidth is reduced.If the ground plane is larger than0:65 20:75 ,the main beam is steered toward =45 ,violating thefirst design goal.In this work,the ground plane size of0:55 20:65 gives a broad band in reflection coefficient and a dipole-like radiation pattern.V.C ONCLUSIONSA small antenna with broad bandwidth has been designed and mea-sured.Its dimension is about0:1 20:1 20:098 and is mounted on a horizontal ground plane size of0:55 20:65 at the center fre-quency of1.495GHz,its fractional bandwidth is10.8%with VSWR of less than2,its radiation pattern in the x0y plane is nearly omnidi-rectional.The ground plane size is optimized to meet the three design goals:Dipole-like radiation pattern with positive gain in the x0y plane, smaller than =10of structure size above ground,and more than10% of impedance bandwidth.The measured radiation efficiency exceeds 65%over the whole band.The broadband performance is achieved by proximity coupling between the dual-meander folded loop and the disk-loaded monopole.R EFERENCES[1]J.S.McLean,“A re-examination of the fundamental limits on the radi-ation Q of electrically small antenna,”IEEE Trans.Antennas Propag.,vol.44,no.5,pp.672–676,May1996.[2]H.D.Foltz,J.S.Mclean,and G.Crook,“Disk-loaded monopoles withparallel strip elements,”IEEE Trans.Antennas Propag.,vol.46,no.12,pp.1894–1896,Dec.1998.[3]W.Dou and W.Y.M.Chia,“Compact monopole antenna forGSM/DCS operation of mobile handsets,”Electron.Lett.,vol.39,no.22,Oct.30,2003.[4]I.F.Chen and C.M.Chiang,“Multi-folded tapered monopole antennafor wideband mobile handset applications,”Electron.Lett.,vol.40,no.10,May13,2004.[5]N.Behdad and K.Sarabandi,“Bandwith enhancement and further sizereduction of a class of miniaturized slot antennas,”IEEE Trans.An-tennas Propag.,vol.22,no.8,pp.1928–1935,Aug.2004.[6]R.Azadegan and K.Sarabandi,“A novel approach for miniaturizationof slot antenna,”IEEE Trans.Antennas Propag.,vol.51,no.3,pp.421–429,Mar.2003.[7]J.Anguera,C.Puente,E.Martinez,and E.Rozan,“The fractal Hilbertmonopole:A two-dimensional wire,”Microwave Opt.Technol.Lett.,vol.36,no.2,pp.102–104,Jan.2003.[8]J.P.Gianvittorio and Y.Rahmat-Samii,“Fractal antennas:A novelantenna miniaturization technique,and applications,”IEEE AntennasPropag.Mag.,vol.44,no.1,pp.20–36,2002.[9]J.Anguera,C.Puente,C.Borja,and J.Soler,“Fractal-shaped antennas:A review,”Wiley Encycl.RF Microwave Eng.,vol.2,pp.1620–1635,2005.[10]W.Dou and W.Y.M.Chia,“Small broadband stacked planarmonopole,”Microw.Opt.Technol.Lett.,vol.27,no.4,pp.288–289,Nov.2000.[11]T.-H.Chang and J.-F.Kiang,“Broadband dielectric resonator antennawith metal coating,”IEEE Trans.Antennas Propag.,vol.55,no.5,pp.1254–1259,May2007.[12]J.W.Jung,H.J.Lee,and Y.S.Lim,“Broadbandflexible meander lineantenna with vertical lines,”Microw.Opt.Technol.Lett.,vol.49,no.8,pp.1984–1987,Aug.2007.[13]M.Ali,S.S.Stuchly,and K.Caputa,“A wideband dual meander sleeveantenna,”J.Electromagn.Waves Appl.,vol.10,no.9,pp.1223–1236,1996.[14]H.D.Chen,“Compact broadband microstrip-line-fed sleeve monopoleantenna for DTV application and ground plane effect,”IEEE AntennasWireless Propag.Lett.,vol.7,pp.497–500,2008.[15]M.Ali,G.J.Hayes,H.S.Hwang,and R.A.Sadler,“Design of amultiband internal antenna for third generation mobile phone hand-sets,”IEEE Trans.Antennas Propag.,vol.51,no.7,pp.1452–1461,July2003.[16]C.M.Kruesi,R.J.Vyas,and M.M.Tentzeris,“Design and devel-opment of a novel3-D cubic antenna for wireless sensor networks(WSNs)and RFID applications,”IEEE Trans.Antennas Propag.,vol.57,no.10,pp.3293–3299,Oct.2009.[17]F.Qureshi,M.A.Antoniades,and G.V.Eleftheriades,“A compactand low-profile metamaterial ring antenna with vertical polarization,”IEEE Antennas Wireless Propag.Lett.,vol.4,pp.333–336,2005.[18]S.Risco,J.Anguera,A.Andujar,A.Perez,and C.Puente,“Coupledmonopole antenna design for multiband handset devices,”Microw.Opt.Technol.Lett.,vol.52,no.2,pp.359–364,Feb.2010.[19]A.Erentok and R.W.Ziolkowski,“Metamaterial-inspired efficientelectrically small antennas,”IEEE Trans.Antennas Propag.,vol.56,no.3,pp.691–707,Mar.2008.[20]K.Noguchi,M.Mizusawa,T.Yamaguchi,Y.Okumura,and S.Bet-sudan,“Increasing the bandwidth of a small meander-line antenna con-sisting of two strips,”mun.Jpn,Part.2,vol.83,no.10,pp.35–43,2000.A Dual Band Microstrip-Fed Slot AntennaMahmoud N.Mahmoud and Reyhan Baktur Abstract—A simple new design method to achieve a dual band mi-crostrip-fed slot antenna is presented.It is shown that when two slot antennas are placed in series,the spacing between the two antennas can be adjusted to achieve an effective secondary resonance.The new resonance is found to be due to the mutual coupling between the two slot antennas. An approximate circuit model for the dual band antenna is presented to explain the dual band mechanism and to provide a design guideline.The model is validated with a prototype antenna that operates at4.22GHz and5.26GHz,which are commonly used as the downlink and uplink in satellite communications.Measured results show good return loss at both frequencies,and radiation patterns agree well with the simulations.The proposed antenna has a simple geometry can be easily produced using printed circuit board techniques for applications where compactness and multiband operation are of interest.Index Terms—Microstrip,multifrequency antennas,mutual coupling, slot antennas.I.I NTRODUCTIONSlot antennas have appealing features such as low profile,low cost, and ease of integration on planar or non-planar surfaces[1].An ex-ample application is integrating slot antennas with solar panels of small satellites to save surface real estate[1],[3].While slot antennas are valuable for space applications and self-powered ground sensors[4], most designs are limited to single frequency operation.This commu-nication presents a very simple design where one can achieve a dual band antenna by utilizing coupling between two adjacent slots. Manuscript received May11,2010;revised August23,2010;accepted Oc-tober07,2010.Date of publication March07,2011;date of current version May 04,2011The authors are with the Electrical and Computer Engineering Department, Utah State University,Logan,UT84341USA(e-mail:reyhan.baktur@usu. edu).Color versions of one or more of thefigures in this communication are avail-able online at .Digital Object Identifier10.1109/TAP.2011.21230650018-926X/$26.00©2011IEEEA slot antenna,when not backed by a cavity,radiates to both sides of the ground plane and can be a good substitute for a dipole antenna [5].In applications such as solar panel integration,it is important to limit the radiation to only the front side of the slot by utilizing a cavity backing[6]–[8].The cavity can be loaded with dielectrics to improve antenna performance,such as enhancing the impedance bandwidth. Due to the conformal nature and versatility in choosing the cavity ge-ometry and material,cavity backed antennas have found popularity in both single element implementations and array configurations[9]–[12]. When there is more than one slot element,it is necessary to study the coupling between elements.It has been found that cavity backed slot antennas have small mutual coupling[9].Further studies have been re-ported to compute the coupling using numerical techniques[10]and analytical methods[11].Although there is abundant literature on cavity backed slot antennas and their coupling,most studies have focused on studying the slot el-ements in parallel alignments.When the slots are placed in series,the spacing between the elements is usually large enough(e.g.,at least a half wavelength)for one to ignore the resonance due to coupling.But when two series slot antennas are placed close to each other,we found that one can achieve two resonances.This suggests a dual band an-tenna design.The design principle is simple and can be conveniently implemented using printed circuit board techniques.This communica-tion presents the design method,analysis using an equivalent circuit modal,and a prototyped dual band antenna.The antenna is studied using Ansoft’s HFSS,and measured results agree well with the simu-lations,validating the dual band antenna design that can be potentially implemented on solar panels as communication links or sensor nodes.II.D UAL B AND A NTENNA A NALYSISThe configuration of the proposed dual band cavity backed slot an-tenna is shown in Fig.1.The antenna and the feed lines are com-posed of two circuit board substrates(Fig.1(a)).Two radiating slots are etched on the top layer,which is a copper layer,of thefirst substrate (Fig.1(b)).The feed lines are printed on the top layer of the second substrate(Fig.1(c)).The bottom layer of the second substrate is the ground plane.The two substrates are then assembled together with an-tennas on the topmost layer and the feed lines sandwiched between the two substrates(Fig.1(a)).Also,the antenna elements are designed and assembled to be orthogonal to the feed lines(Fig.1(a)).It should be noted that one does not have to choose the same substrates to etch antennas and to print feed lines.Depending on applications and prac-tical demands,the excitation method can be simple probe feed[13], coplanar waveguide(CPW)feed[14],or microstrip line feed[5],[15]. This communication demonstrates the microstrip line feed due to its simplicity and ease in matching the lines to the slot antenna by ad-justing the position and length of the feed lines.After assembling the two substrates,the four side-walls of the substrates and the top plane (i.e.,slot antenna and the metal plane)are shorted to the ground plane with either conductive pastes or conductive tapes.When prototyping the antenna,it was necessary to cut a rectangular notch on the top sub-strate in order to solder a SMA connector(Fig.1).The existence of the notch affects the resonance frequency and impedance matching,and we have included it in the full wave simulation.The feed design is a50 microstrip line divided into two100 lines to excite the two slot elements that resonate at the same frequency (Fig.1).We found that when the two elements are placed close,a new resonance appears due to the strong coupling between the two slots. The explanation for the second resonance is that the coupling between the two slots acts as if there were an equivalent slot antenna that is longer than the individual slot but shorter than the total length of the two slotelements.Fig.1.The proposed dual band slot antenna.(a)An illustration of the antenna geometry,(b)top layer of the fabricated antenna,(c)middle layer,i.e.,the mi-crostrip feed lines,of the fabricatedantenna.Fig.2.Illustration of the location of feed lines and the two slot antennas.In order to analyze the mechanism of the dual band resonance and provide some insight for designing effective antennas for both frequen-cies,an approximate circuit model to study the input impedance of the slot antenna is established.The important parameters of the slot geom-etry are marked in Fig.2,where L e1and L e2are critical for matching the impedance of the two slots,and the spacing between the two slots (d in Fig.2)has been seen to affect the impedance of the equivalent slot.The approximate model is presented in Fig.3.It is derived by mod-ifying Syahkal’s circuit model for a single slot antenna fed by a mi-crostrip line[16].Each slot is modeled as two short-circuited slot lines in parallel with a radiation conductance G r that represents the radiated power from the slot[16].The parameters L e1and L e2(Fig.2)corre-spond to the length of the two short-circuited slot lines,and are marked on Fig.3for ease of reading.The characteristic impedance of the slot line is Z cs,and L1,L2are inductance of the microstrip feed line andFig.3.Approximate circuit model of the dual band slotantenna.Fig.4.Circuit model of the equivalent slot antenna that is due to the coupling of the two original slot antennas.slot line,respectively.The mutual inductance M 1represents the cou-pling between the microstrip line and slot line.The mutual inductance M 2represents the coupling between two se-ries slots.Because of the coupling,there appears an equivalent slot that radiates at a frequency lower than the two slots.The circuit model for the equivalent slot is presented in Fig.4.The length of the equiv-alent slot is L eq total ,and is expected to be between (L e1+L e2)and 2(L e1+L e2).The coupling between the two slots appears as an added impedance Z couple to the slot line (Fig.4).It is straightforward to ex-pect that changing the spacing d (Fig.3)between the two slots will change M 2,and accordingly change Z couple ,which is the dominant factor for the input impedance of the equivalent slot.The other fac-tors (characteristic impedance Z cs ,radiation conductance G er,and the length L eqtotal of the equivalent slot line)do not vary much with respect to d .Therefore,after matching the impedance of the two slots,one can adjust the spacing between the two slots to achieve a reasonable return loss for the equivalent slot antenna.Two methods can be employed to validate the model shown in Figs.3–4.One can determine the values of Z cs ,L 1,L 2,M 1,M 2following Syahkal [16],then compute the input impedance of the equivalent slot,and finally compare the computed S 11value of the equivalent slot at the input port (i.e.,the SMA connector)with experi-ments.Or,using the model as guidelines,one can perform a parametric study using simulation software,and then validate the design withmeasurements.We chose the second approach in this communication since there are several well tested antenna design software tools.Ansoft’s HFSS is used to perform the simulations for two series slot antennas on substrates with different thicknesses and relative permit-tivity,and different ground plane sizes.It is found that after matching two identical series slots to a resonant frequency f 1,a secondary res-onance f 2(f 2<f 1)appears when the spacing d (Fig.2)between the two slots is less than 0.20wavelength.This resonance is generally weak with an S 11higher than 03dB and we need to continue to move two slots closer to achieve a reasonable S 11at f 2.It is observed that changing the spacing only changes the level of the resonance,and does not have much effect on f 2.It is also observed that the spacing affects the resonance at f 1too,and one has to adjust the matching microstrip lines to achieve a good S 11at f 1.Same as the case for f 2,the spacing between two slots does not affect the location of f 1.These observations are consistent for different substrates and ground plane sizes,and they are also consistent with the model in Figs.3and 4.When the dimen-sion of the slots is fixed,the input impedance of the equivalent slot is mainly determined by Z couple (Fig.4),which is affected by the mu-tual inductance M 2(Fig.3).It is also seen from Fig.3that M 2affects the input impedances of two series slots,and therefore the spacing be-tween them will affect S 11value at f 1.The ratio of f 1=f 2is found to be close to 1.3,the fluctuation is less than 10%for different substrates and ground planes.In other words,the ratio between the length of the equivalent slot and one of the series slots is about 1.3.We studied three substrates (air,teflon,and RO 4003c)with the same thickness of 3.38mm.The ratio of f 1=f 2for the three substrates is found to be 1.41,1.32,and 1.27,respectively.Increasing the thickness of the substrate seemed to increase f 1,but the increase is found to be less than 10%for most commonly used substrates.III.P ROTOTYPE AND M EASUREMENT R ESULTSUsing the approximate model and observations from HFSS studies in Section II as guidelines,we designed and fabricated a dual band slot antenna prototype.The substrates used are Rogers’high frequency laminates RO 4003c (thickness =0:831mm ,permittivity =3:38)and the two slots are designed and matched to operate at 5.26GHz.The equivalent slot operates at 4.22GHz.The spacing between the two slots and the position of the microstrip feed line are adjusted to be d =0:5mm and L e1=1:5mm to achieve good S 11values at both frequencies.The antennas and the feeding microstrip lines were fabricated using a LPKF circuit board milling machine,and the ground plane or the size of the substrate was chosen to be 1002100mm 2.The two slots on the upper plane have the same width of 1mm and the same length of 25mm.After assembling the two substrates,the four side-walls were shorted with conductive copper tape.It is known that reducing the size of the ground plane results in reduction in the resonant frequency and gain of a slot antenna.We found that the resonance and gain stabilize for both bands when the ground plane reaches 323in-air wavelength 2.The ground plane of the prototyped antenna is less than 222wavelength 2,which means we lose about 1dB gain for each band.But this size is chosen because the antenna is for integration on a cube satellite which has a solar panel of 1002100mm 2.The simulated and measured results of frequency response are plotted in Fig.5.The S -parameters were measured using a vector net-work analyzer (Agilent 8510C).The agreements between simulation and measurements are good for both frequencies.The slight shift in the frequency is likely due to the fabrication accuracy when milling the two slots and cutting the rectangular notch for soldering the SMA connector (Fig.1),and the possibility of having some air between two substrates when they were assembled.The normalized radiation patterns for both bands were measured using a far-field range in an anechoic chamber.The simulated E -plane,parisons between the simulated and measured Sparameter.Fig.6.Simulated and measured radiation patterns of the antenna at 5.26GHz.(a)Simulated E and H plane patterns.(b)Measured co-and cross-polarization E and H plane patterns.H -plane patterns for 5.2GHz antennas were plotted in Fig.6(a).The measured co-and cross-polarization patterns at 5.2GHz were plotted in Fig.6(b).The agreement between E -plane patterns is good and the cross-polarization level is than 020dB in the principal plane.The mea-surement facility is not ideal for measuring H -plane patters,and it is reasonable to expect some distortion on the H -plane pattern from the measurement.Taking this into account,the agreement in overall shape in H -plane patterns is reasonably good.The radiation patterns for the band at 4.22GHz are plotted in Fig.7.Agreements between simula-tions and measurements are good,and the measured cross polarization level is less than 020dB in the principal plane.The cross polarization level was calculated using HFSS for the entire unit sphere and the max-imum was found to be in the principal plane.The notch for soldering the connector (Fig.1)was not found to have a visible effect on the cross-polarization level.The gain of the dual band antenna was mea-sured using a NSI 2000near-field scanner,and was found to be 3.5dB and 4.2dB for the lower and upper bands respectively.The result is rea-sonable considering the dielectric loss in the two layers ofsubstrates.Fig.7.Simulated and measured radiation patterns of the antenna at 4.22GHz.(a)Simulated E and H plane patterns.(b)Measured co-and cross-polarization E and H plane patterns.IV .D ISCUSSIONS AND C ONCLUSIONSA simple geometry to obtain a dual band cavity backed slot antenna is presented.The antenna was designed using two dielectric substrates and was fed by microstrip lines.The antenna can be easily designed to operate effectively at 4.22GHz and 5.26GHz,which are downlink and uplink frequencies for satellite communication at C band.The an-tenna can be integrated with solar panels to save surface real estate of small satellites,and to replace traditional deployed dipole antennas.When a higher gain is needed for communication links,the proposed antenna can be designed in array configurations to achieve the required gain.The dual band operation is achieved simply by utilizing the mu-tual coupling between two closely placed series slot antennas,and the design procedure is straightforward.In order to understand the mechanism of the dual band operation,an approximate circuit model was presented.The model was validated by parametric study from Ansoft’s HFSS and by a prototype antenna.It is found that when two slot antennas were placed within 0.15wavelength (i.e.,d 0:15wavelength ),there was a reasonably strong secondary resonance due to the coupling between the two antennas.The coupling results in an equivalent longer slot antenna that operates at a frequency about 1.25times lower than the original antenna resonance.The dual band resonance can be tuned by adjusting spacing between the two slots and by modifying the matching microstrip feed lines.When an optimum spacing d has been found to produce strong resonances for both bands,it is seen that varying d slightly does not severely affect S 11levels of two bands.For example,the frequency response in Fig.5is for when d =0:5mm .When d was changed to 0.4mm or 0.6mm,only a 2dB variation was observed in one of the two bands.One prototype antenna was fabricated on high frequency laminates and the measured results agree well with simulations.In this study,we shorted the side-walls of the substrates to obtain a cavity.When the walls were not shorted,we found that more resonances appear,and the front-to-back ratio in the antenna pattern was severely degraded.In the prototype,the walls were shorted with conductive copper tapes.The fabrication at Utah State University was performed using a cir-cuit milling machine,but the proposed antenna can be easily produced using printed circuit board techniques,and can be conveniently adapted to communication links where multiband operations are required.R EFERENCES[1]G.John,D.Kraus,and R.J.Marhefka,Antennas for All Applica-tions.New York:McGraw-Hill,2002.[2]S.Vaccaro,P.Torres,J.R.Mosig,A.Shah,J.-F.Ziircher,A.K.Skrivervik,F.Gardiol,P.de Maagt,and L.Gerlach,“Integrated solarpanel antennas,”Electron.Lett.,vol.36,no.5,pp.390–391,Mar.2000.[3]S.Vaccaro,C.Pereira,J.R.Mosig,and P.de Maagt,“In-flight exper-iment for combined planar antennas and solar cells(SOLANT),”IETMicrow.Antennas Propat.,vol.3,no.8,pp.1279–1287,2009.[4]T.Wu,R.L.Li,and M.M.Tentzeris,“A mechanically stable,low pro-file,omni-directional solar-cell integrated antenna for outdoor wirelesssensor nodes,”presented at the IEEE Antenna and Propag.Society Int.Symp.,Charleston,SC,Jun.2009.[5]Y.Yoshimura,“A microstrip slot antenna,”IEEE Trans.Microw.Theory Tech.,vol.MTT-20,pp.760–762,Nov.1972.[6]T.Adams,“Flush mounted rectangular cavity slot antennas–Theoryand design,”IEEE Trans.Antennas Propag.,vol.15,pp.342–351,May1967.[7]C.R.Cockrell,“The input admittance of the rectangular cavity-backedslot antenna,”IEEE Trans.Antennas Propag.,vol.24,no.3,pp.288–294,May1976.[8]A.Hadidi and M.Hamid,“Aperturefield and circuit parameters ofcavity-backed slot radiator,”IEE Proc.,vol.136,no.2,pp.139–146,Apr.1989.[9]H.G.Akhavan and D.Mirshekar-Syahkal,“Study of coupled slot an-tennas feed by microstrip lines,”in Proc.IEE10th Int.Conf.on An-tenna and Propagation,Apr.1997,pp.290–293.[10]T.Hikage and K.Itoh,“FDTD analysis of mutual coupling of cavitybacked slot antenna arrays,”IEICE Trans.Electron.,vol.E81-C,no.12,Dec.1998.[11]D.Pozar,“A reciprocity method of analysis for printed slot and slotcoupled microstrip antennas,”IEEE Trans.Antennas Propag.,vol.34,no.12,pp.1439–1446,Dec.1986.[12]S.Long,“Experimental study of the impedance of cavity-backed slotantennas,”IEEE Trans.Antennas Propag.,vol.23,pp.1–7,Jan.1975.[13]D.Sievenpiper,H.-P.Hsu,and R.M.Riley,“Low-profilecavity-backed crossed-slot antenna with a single-probe feed designedfor 2.34-GHz satellite radio applications,”IEEE Trans.AntennasPropag.,vol.47,no.1,pp.58–64,Jan.1999.[14]S.Sierra-Garcia and urin,“Study of a CPW inductively cou-pled slot antenna,”IEEE Trans.Antennas Propag.,vol.52,no.3,pp.873–879,Mar.2004.[15]B.Zheng and Z.Shen,“Effect of afinite ground plane on microstrip-fedcavity-backed slot antennas,”IEEE Trans.Antennas Propag.,vol.53,no.2,pp.862–865,Feb.2005.[16]H.G.Akhavan and D.Mirshekar-Syahkal,“Approximate model formicrostrip fed slot antennas,”Electron.Lett.,vol.30,no.23,pp.1902–1903,Nov.1994.A New Super Wideband Fractal Microstrip AntennaAbolfazl AzariAbstract—The commercial and military telecommunication systems re-quire ultrawideband antennas.The small physical size and multi-band ca-pability are very important in the design of ultrawideband antennas.Frac-tals have unique properties such as self-similarity and space-filling.The use of fractal geometry in antenna design provides a good method for achieving the desired miniaturization and multi-band properties.In this communi-cation,a multi-band and broad-band microstrip antenna based on a new fractal geometry is presented.The proposed design is an octagonal fractal microstrip patch antenna.The simulation and optimization are performed using CST Microwave Studio simulator.The results show that the proposed microstrip antenna can be used for10GHz–50GHz frequency range,i.e., it is a super wideband microstrip antenna with40GHz bandwidth.Radia-tion patterns and gains are also studied.Index Terms—Bandwidth,fractal microstrip antenna,fractals,ultra-wideband.I.I NTRODUCTIONModern communication systems require antennas with more band-width and smaller dimension.One of the main components of ultraw-ideband(UWB)communication systems is an UWB antenna.Custom-arily,wideband antennas need different antenna elements for different frequency bands.If antenna size is less than a quarter of wavelength, antenna will not be efficient.Fractal geometry is a very good solution to fabricate multi-band and low profile antennas.Applying fractals to antenna elements allows for smaller size,multi-band and broad-band properties.Thus,this is the cause of spread research on fractal antennas in recent years[1]–[4].Fractals have self-similar shapes and can be subdivided in parts such that each part is a reduced size copy of the whole.The self-similarity of fractals is the cause of multi-band and broad-band properties and their complicated shapes provides design of antennas with smaller size. Fractals have convoluted and jagged shapes such that these discontinu-ities increase bandwidth and the effective radiation of antennas.The space-filling property of fractals leads to curves which have long elec-trical length butfit into a compact physical volume.[5]–[9]. Several UWB antenna configurations based on fractal geometries have been investigated including Koch,Sierpinski,Minkowski,Hilbert, Cantor,and fractal tree antennas in recent years.The numerical simu-lation and experimental results of these antennas are available in liter-ature to date.In this communication,a fractal microstrip antenna is presented.This new fractal geometry is based on an iterative octagon.The huge band-width is the main advantage of this fractal antenna over conventional fractal antennas.The commercially available simulation software CST Microwave Studio has been used for the design and simulation of the proposed microstrip antenna.According to the results,this new fractal antenna is applicable in10GHz–50GHz frequency range and the gain of this fractal microstrip antenna is reasonable in entire bandwidth. Manuscript received February16,2010;revised September29,2010;ac-cepted January24,2011.Date of manuscript publication March17,2011;date of current version May04,2011.The author is with the Young Researchers Club,Islamic Azad University–Gonabad Branch,Iran(e-mail:azari@).Color versions of one or more of thefigures in this communication are avail-able online at .Digital Object Identifier10.1109/TAP.2011.21282940018-926X/$26.00©2011IEEE。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Design of unsymmetrical slot antenna based on ANN for RFID tagJuhong LU 1,3, Yongming ZHOU 2, Chunlong ZHENG2(1. Department of mechanical-electrical engineering, Li Shui Polytechnic College Lishui, 323000, P.R China 2.Department of electronic engineering Shaoguan University Shaoguan 512005, P.R China 3. The School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou China 310018)Abstract-To study the optimizing design of unsymmetrical slot antenna for RFID tag an attention is paid to optimize design of the unsymmetrical slot antenna based on ANN (Artificial Neural Networks) for UHF tag. The designing shortcoming of traditional method with one dimension geometrical parameter for tag antenna has avoided. The presented slot antenna has been matched with the testing chip of Philips Company. The design result is better consistent with that of IE3D simulation which is based on MOM (method of moment). A unsymmetrical slot antenna for tag has been fabricated and the reading distance has been measured with the compatible reader. The result of measurement shows that the unsymmetrical slot antenna can basically meet the needs of UHF tag.I.INTRODUCTIONRFID (radio frequency identification) uses RF signals to identify objects automatically. It becomes a rapidly developing automatic identification technology and its applications include electronic toll collection, asset identification, retail item management, access control, and vehicle security [1][2], etc. RFID system is a mini network of information. RFID system consists of radio frequency tags, readers and a host computer. A typical RFID tag consists of an antenna and an integrated circuit (chip). The chip is usually placed right at the terminals of the tag antenna. Tag antennas and chips have complex impedance. The imaginary part of chip impedance is usually negative and the value of imaginary part is usually much bigger than that of the real part. During RFID tag antenna design, the matching between antenna and chip is one of the important factors which determine the performance of RFID system. The fast match rule between antenna and its chip is always an important goal for researchers and designers. At present, there are some types of tag antennas [3][4][5][6]], such as dipole antenna, folded dipole antenna, inverse F-type antenna, fractal antenna, etc. They are the transfigurations of half wave dipole. Their lengths appear large (their length is about O / 2 ). It is not easy for tag antenna to match with chip, and their bandwidth is somewhat narrow for applications [7][8]. Their fabrication is relatively complex [9][10]. Therefore, those types are not suitable for RFID wide applications. Recent years, there are some reports of application design [11][12][13] on slot antenna for tags, and the matchingperformance between slot antenna and UHF tag is much better than that of traditional dipole antennas. To reach at the goal of designing the unsymmetrical slot antenna for UHF tag with high efficiency, this paper presents a design of the unsymmetrical slot antenna based on ANN (Artificial Neural Networks) of BP algorithm for UHF tag. The design course is of very concision and practical. The design result is better consistent with that of IE3D simulation which is based on MOM (method of moment). A unsymmetrical slot antenna for tag has been fabricated and the reading distance has been measured with the compatible reader. The result of measurement shows that the unsymmetrical slot antenna can basically meet the needs of UHF tag. This paper starts with a brief introduction of UHF tag antenna, and continues to build the model of the unsymmetrical slot antenna for tag with IE3D in part II. It then presents an optimizing design based on ANN and testing of the unsymmetrical slot antenna in part III, and finally reaches the conclusions in part V. II. MODELINGUnsymmetrical slot antenna is a slot antenna that its slot is straight towards one side of the antenna, and the powered source is at the side. Considering the attributes of slot antenna and demand of the size of slot antenna, at the same time for simple modeling, Figure 1 is the structure of our discussed slot antenna. The size of conductor plane is L×W, the height of the slot h, the bent length of the slot l. The distance from one side is 'l . Figure 1(a) and (b) are both look down and side view map respectively. keep L=50mm W 40mm 'l 9mm and the width of the slot is 2mm this paper will present the process of optimizing the slot antenna matched with the tag chip that its port impedance is 11.5-j422 Ohm based on ANN with BP algorithm. The purpose is the mult-parameter design of antenna performance and enhances the design the efficiency. We get the sample data of impedance of the slot antenna changing with the parameters of both l and h by IE3D which is based on MOM (method of moment). The sample data is shown at table 1. The sizes of both real and imaginary part of impedance along with l and h are at the frequency 915MHz. One l is corresponding to six h, and the total sample data is 36, which is basically contained in the range of geometry parameters.978-1-4244-5708-3/10/$26.00 ©2010 IEEE317ICMMT 2010 Proceedings(a)(b) Figure 1 structure of our discussed slot antennaneurons since there are two targets. We will use the Levenberg-Marquardt algorithm for training. The learning speed is set to be 0.05. The increment of the learning speed is set to be 1.05. The total times of epochs are set to be 1000. The error of train goal is set to be 10-6 We train the neural network with taking both real and imaginary part set of the proposed slot antenna’s impedance as the network’s inputs, and both l and h geometry parameters as the network’s outputs. Therefore, we can get the geometry parameters of both l and h from the well trained ANN that it reaches the set goal with a particular input set of any wanted antenna’s impedance. The trend curve of the trained ANN’s convergence is shown as figure 2. We can see in figure 2 that the trained ANN well reaches the previous set goal with 14 trained times and meets the need of the set error. It is shown that both convergence’s speed and training efficiency of the proposed ANN are very high. Now, The well trained ANN can lead to the expected outputs h=33.6mm l=6.7mm with the particular input of both real part equal to 11.5 Ohm and imaginary part equal to 422 Ohm for our designed unsymmetrical slot antenna. As a validation, we have a simulation with IE3D and reach the following result with the matched impedance 11.5+j422 Ohm as a reference. The simulation results are h=33.5mm l=6.8mm related electrical parameters are as follows:TABLE SAMPLE DATA OF UNSYMMETRICAL SLOT ANTENNA l /mm h /mm 30 31 32 33 34 35 30 31 32 33 34 35 30 31 32 33 34 35 Re /Ohm 5.9 6.6 7.8 9.3 9.5 12.6 6.6 7.8 8.9 9.8 10.0 13.6 7.0 8.6 9.5 11.7 11.5 15.9 Im /Ohm 285.1 298.7 319.7 339.6 342.8 385.9 298.6 319.8 336.5 345.7 348.4 397.7 304.3 329.3 341.7 506.9 368.0 423.8 l /mm h /mm 30 31 32 33 34 35 30 31 32 33 34 35 30 31 32 33 34 35 Re /Ohm 8.2 9.6 11.0 13.6 13.9 18.7 9.7 11.7 12.8 16.8 17.1 23.0 11.2 14.1 15.8 18.3 24.0 28.0 Im /Ohm 323.6 345.1 364.0 393.5 398.3 453.5 346.6 374.7 388.0 431.1 434.4 496.1 366.8 404.9 423.8 446.7 505.6 538.4364758Figure 2the curve of convergenceIII. DESIGN AND TEST A. Optimizing design To be simple and not lost universality, we use the threelayer artificial network based on back propagation algorithm to optimizing the slot antenna. The numbers of neuron in front two layers are 20. The network should have two outputThe impedance of the slot antenna is 15.03+j422.49 Ohm -10db bandwidth of impedance is 300MHz radiant efficiency is 70.87 direction coefficient is 1.65dbi, S11=48.5dB both curve of S11 and radiation pattern are shown as figure 3 and 4 respectively. The result shows that the design result with ANN is well consistent with that of simulation.318B. Fabrication and Test The port impedance of the unsymmetrical slot antenna matched with the testing chip of Philips’ Company is 11.5+j422 Ohm. The slot antenna is designed and fabricated on FR4 substrate based on the results analyzed above. The operating frequency of proposed antenna is 915 MHz, thewidth of slot 2.0 mm, the height h of slot 33.7mm and the length l of slot 6.6 mm. Figure 5 is the fabricated slot antenna. The measurement conditions are: the RF source frequency is 915MHz, attenuation on -10dbm, the modulation AM, the depth of modulation 100% and the source of modulation 1 KHz The proposed slot antenna which connects with the testing matching network shown as figure 6, and the testing matching network is conformed to the input network of circuit of the tag chip is receiving signal from the transmitting antenna directly connected with the RF source. Then the performance of the proposed slot antenna can be evaluated by measuring the output voltage of the matching network. The bigger the output voltage is, the better the performance of the antenna under the same measured condition is. The measured results are shown in table 2. Here, the distance is from the transmitting antenna to the measured unsymmetrical slot antenna. We can see that the performance of proposed antenna is better than that of paper [5].Figure 3S11 curveFigure 6 The sketch map of test matching networkdistance/cm Vpp/mV10.0 32.2TABLE The measured results 15.0 20.0 25.0 30.0 15.3 11.5 10.0 9.035.0 8.440.0 7.9Figure 4 Radiation patternIn addition, under the good receiving condition between the proposed tag antenna and the reader antenna, the measured read distance is 1.5 meters by the reader of MPR-3014 with its transmitting power of 4W and center frequency of 915MHz. According to the report of paper [14], the performance of proposed slot antenna reaches the basic requirement of application.IV. CONCLUSION To boost the efficiency of designing the tag antenna for RFID and improve the performance of mult-parameter optimizing design for UHF tag antenna, this paper presents a design of the unsymmetrical slot antenna for RFID tag with ANN based on BP algorithm. The presented slot antenna is matched with the testing chip of Philips Company. The optimized result is better consistent with that of IE3D simulation which is based on MOM (method of moment). TheFigure 5 The fabricated slot antenna319efficiency of design has greatly boosted up and this design method based on ANN has realized mult-parameter optimized design for UHF tag antenna. The designing shortcoming of traditional method with one dimension geometrical parameter for tag antenna has avoided. The optimizing design is of very concision and practical. The size of the proposed slot antenna is fit for UHF RFID tag. Finally, a slot antenna matched with the chip concerned is fabricated on FR4 substrate. Testing results and matching process show that the presented matching method has universality and reliability, and the proposed slot antenna meet the basic requirements of application. ACKNOWLEDGMENTS The author, Zhou Yongming, would give best wishes to my wife Li lin and my daughter Zhou yi for their self-giving assistance and support of this work. Thanks! REFERENCES[1]K. V. Seshagiri Rao, Pavel V. Nikitin, and Sander F. Lam. Antennadesign for UHF RFID tags: A review and a practical application [C]. IEEE Trans. On Antennas And Propagation. 2005, 53(12)3870-3876. [2] Bansal R. Coming soon to a Wal-Mart near you [J]. IEEE Antennas and Propagation Magazine , 2003,45(6):105–106. [3] Qing X M, YANG N. A folded dipole antenna for RFID [C]. Antennas and Propagation Society International Symposium, IEEE, 2004, 1: 97100.Lai X Z, Zhang X Y, Lai S L, et al. RFID tag antennas based on Hilbert fractal structure [J]. Journal of South China University of Technology : Natural Science Edition, 2006, 34(6):26-28. [5] Lai X Z, Zhang X Y, Lai S L. Resonant characteristics of the Meanderline dipole antenna [J]. Journal of Microwaves, 2006, 22(3):18-22. [6] Zhou Y M. A design of RFID tag antenna based on bowtie[C]// Proceedings of IET International Conference on Wireless Mobile and Multimedia Networks. Hangzhou, China: IEE, 2006:374-377. [7] Min Kyeong-Sik, Kim Jin-Woo, Park Chul-Keun, et al . A study of capacity change antenna for RFID tag depending on ground plane[C]//Proceedings of Asia-Pacific Microwave Conference. Suzhou, China: IEEE, 2005:4-7. [8] Saeed I Latif, Lotfollah Shafai, and Satish Kumar Sharma. Bandwidth enhancement and size reduction of microstrip slot antennas [J]. IEEE Transactions. on Antenna and Propagation, 2005,53(3) : 994-1003. [9] Azadegan R, Sarabandi K. Miniaturized folded-slot: an approach to increase the bandwidth and efficiency of miniaturized slot antennas[C]// Proc of IEEE Antennas and Propagation Society International Symposium, San Antonio: IEEE, 2002 :14–17. [10] Zhou Y M. Study on UHF tag antenna and signal denoise of RFID [D]. PhD. Thesis, South China University of Technology, Guangzhou, China, 2007: 52-56. [11] ZHOU Y M and LAI S L. Analysis and study on bent slot antenna for RFID tag [J]. Journal of Jinan university(Natural Science Edition), 2007, 28(1): 74-78. [12] Zhou Y M, Lai X Z and Lai S L. Design of dissymmetrical slot antenna for RFID Tag [J]. Journal of Microwaves, ( Weibo xuebao ), 2009, 25(3):39-42. [13] Zhou Y M, Lai X Z and Lai S L. Design of RFID tag antenna based on slot antenna[J]. Journal of South China University of Technology : Natural Science Edition, 2007,35(9):6-10. [14] Rao K V S. An overview of backscattered radio frequency identification system (RFID) [C]. Asia Pacific Microwave Conference, 1999,3: 746749.[4]320。