基于超材料的微带天线小型化研究
摘要
现代无线通信对器件小型化的要求越来越高,天线是通信系统的重要组成部分,所以天线的小型化设计也变得非常重要。如何使用更小的面积实现更低频率更好性能的微带天线已逐渐成为科研工作者与工程师们研究的重点和焦点。
超材料(Metamaterials)作为一类新型的人工电磁材料,目前已经成为实现微带天线小型化的重要技术与手段。通过在传统的媒质材料(ε>0,μ>0)中水平或者垂直嵌入某种几何结构的单元,便可以获得ε<0或者μ<0的超常材料,它具有天然媒质所不具备的奇特物理性质。
本文主要采用两种方法实现微带天线的小型化。一种是运用等效Smith结构,通过在传统微带半波贴片天线的地面水平加载各种不同形式的结构单元来实现微带天线的小型化。另一种是通过在介质基板中垂直填充某种结构单元构成复合材料,从而使得微带贴片天线的物理尺寸不主要取决于构成材料的本征性质,而取决于其中填充的人工结构,避免了微带天线物理尺寸与谐振频率的相互制约,实现了微带天线的小型化。
通过软件仿真可以知道,使用传统的半波贴片,在10GHz频率辐射,需要尺寸14.98mm×9.29mm。若采用第一种方法,在介质基板下水平加载四个SRR(开口谐振环)结构,使用同样的贴片,可使谐振频率降至8.9GHz；若加载六个SRR结构,可使频率降至8.5GHz。在同样尺寸下,谐振频率分别下降了11%与15%,从而实现了天线的小型化。通过进一步的研究,发现若水平加载四个SR(螺旋谐振环)结构,可使频率降至5.9GHz；若加载六个SR结构,则可降至5.8GHz。在同样的贴片下,谐振频率下降了约42%,小型化的效果更加良好。
若采用第二种方法,通过在传统介质中嵌入八个SR结构来实现负磁导率(u-negative)的超材料,可使谐振频率从2.45GHz降至434MHz,在低频段天线尺寸大幅减小,不仅实现了天线的小型化,还可以实现双频工作。
Modern wireless communication devices are required to be miniaturized, while antenna is an important part of communication system. Many scientists and engineers focus on how to achieve better performance at lower frequency on microstrip antennas in a small area.
As a composite or structured material that exhibits properties not found in naturally occurring materials or compounds, Metamaterial is an important approach to implement miniaturization of microstrip antenna.
In this thesis, two methods are used to implement miniaturization of microstrip antenna. Load different types of structural elements on traditional media substrate to achieve the miniaturization. After the traditional media substrate is filled with the Metamaterial, microstrip antenna's physical size primarily depends on constitutive parameters of Metamaterial. Therefore, the mutual constraints between the microstrip antenna's physical size and resonant frequency are avoided.
Numerical simulation shows that traditional microstrip antenna's physical size is 14.98mm by 9.29mm at lOGHz. While using the first method, if 4 SRR (Split-Ring Resonator) structure under patch is loaded, the resonant frequency is down to 8.9GHz; if 6 SRR structure is loaded, the resonant frequency is down to 8.5GHz. Compare to the same patch size, the resonant frequency decreases by 11% and 15%, so miniaturization of the microstrip antenna is achieved. Further studies have shown that if 4 SR (spiral resonator) structure in the same place is loaded, which allows the resonant frequency down to 5.9GHz; if 6 SR structure is loaded, the resonant frequency can be reduced to 5.8GHz. In the same patch, the resonant frequency decreases by about 42%. Effects on miniaturization become pronounced.
While using the second method, theμ-negative meta-materials is realized by filling substrate with 8 spiral resonators (SR), which can miniaturize the low frequency antenna, and the resonant frequency is from 2.45GHz down to 434MHz. Not only miniaturization of the microstrip antenna is achieved, but also dual-band work can be obtained.
超材料(Metamaterials)作为一类新型的人工电磁材料,目前已经成为实现微带天线小型化的重要技术与手段。通过在传统的媒质材料(ε>0,μ>0)中水平或者垂直嵌入某种几何结构的单元,便可以获得ε<0或者μ<0的超常材料,它具有天然媒质所不具备的奇特物理性质。
本文主要采用两种方法实现微带天线的小型化。一种是运用等效Smith结构,通过在传统微带半波贴片天线的地面水平加载各种不同形式的结构单元来实现微带天线的小型化。另一种是通过在介质基板中垂直填充某种结构单元构成复合材料,从而使得微带贴片天线的物理尺寸不主要取决于构成材料的本征性质,而取决于其中填充的人工结构,避免了微带天线物理尺寸与谐振频率的相互制约,实现了微带天线的小型化。
通过软件仿真可以知道,使用传统的半波贴片,在10GHz频率辐射,需要尺寸14.98mm×9.29mm。若采用第一种方法,在介质基板下水平加载四个SRR(开口谐振环)结构,使用同样的贴片,可使谐振频率降至8.9GHz；若加载六个SRR结构,可使频率降至8.5GHz。在同样尺寸下,谐振频率分别下降了11%与15%,从而实现了天线的小型化。通过进一步的研究,发现若水平加载四个SR(螺旋谐振环)结构,可使频率降至5.9GHz；若加载六个SR结构,则可降至5.8GHz。在同样的贴片下,谐振频率下降了约42%,小型化的效果更加良好。
若采用第二种方法,通过在传统介质中嵌入八个SR结构来实现负磁导率(u-negative)的超材料,可使谐振频率从2.45GHz降至434MHz,在低频段天线尺寸大幅减小,不仅实现了天线的小型化,还可以实现双频工作。
Modern wireless communication devices are required to be miniaturized, while antenna is an important part of communication system. Many scientists and engineers focus on how to achieve better performance at lower frequency on microstrip antennas in a small area.
As a composite or structured material that exhibits properties not found in naturally occurring materials or compounds, Metamaterial is an important approach to implement miniaturization of microstrip antenna.
In this thesis, two methods are used to implement miniaturization of microstrip antenna. Load different types of structural elements on traditional media substrate to achieve the miniaturization. After the traditional media substrate is filled with the Metamaterial, microstrip antenna's physical size primarily depends on constitutive parameters of Metamaterial. Therefore, the mutual constraints between the microstrip antenna's physical size and resonant frequency are avoided.
Numerical simulation shows that traditional microstrip antenna's physical size is 14.98mm by 9.29mm at lOGHz. While using the first method, if 4 SRR (Split-Ring Resonator) structure under patch is loaded, the resonant frequency is down to 8.9GHz; if 6 SRR structure is loaded, the resonant frequency is down to 8.5GHz. Compare to the same patch size, the resonant frequency decreases by 11% and 15%, so miniaturization of the microstrip antenna is achieved. Further studies have shown that if 4 SR (spiral resonator) structure in the same place is loaded, which allows the resonant frequency down to 5.9GHz; if 6 SR structure is loaded, the resonant frequency can be reduced to 5.8GHz. In the same patch, the resonant frequency decreases by about 42%. Effects on miniaturization become pronounced.
While using the second method, theμ-negative meta-materials is realized by filling substrate with 8 spiral resonators (SR), which can miniaturize the low frequency antenna, and the resonant frequency is from 2.45GHz down to 434MHz. Not only miniaturization of the microstrip antenna is achieved, but also dual-band work can be obtained.
引文
[1]V.G. Veselago, The electrodynamics of substrate with simultaneously negative ε and μ, Sov Phys Usp VOL.10, NO.4,1968:509-514.
[2]J. B. Pendry, A.J. Holden, D. J. Robbins, W. J. Stewart, Magnetism from Conductors and Enhanced Non-Linear Phenomena, IEEE Transactions on Microwave Theory and Techniques, VOL.47, Issue 11, Nov.1999 Page(s):2075-2084.
[3]D. R. Smith, D. C. Vier, Padilla Willie, Loop-Wire Medium for Investigating Plasmas at Microwave Frequencies, Applied Physics Letters, VOL.75,1999:1425-4127.
[4]R. A. Shelby, D. R. Smith, S. Schultz, Experimental Verification of a Negative-Index Refraction [J], Science, VOL.292,2001:77-79.
[5]Marco Caiazzo, Stefano Maci, Nader Engheta, A Metamaterial Surface for Compact Cavity Resonator, IEEE Antennas and Wireless Propagation Letters, VOL.3,2004: 261-264.
[6]Lubkowski, G., Damm, C., Bandlow, B., Schuhmann, R., Schussler, M., Weiland, T., Broadband Transmission Below the Cutoff Frequency of a Waveguide Loaded With Resonant Scatterer Arrays, Microwaves, Antennas & Propagation, IET, VOL.1, Issue 1, February 2007:165-169.
[7]Silvio Hrabar, Juraj Bartolic, Zvonimir Sipus, Waveguide Miniaturization Using Uniaxial Negative Permeability Metamaterial, IEEE Transactions on Antennas and Propagation, VOL.53, NO.1, January 2005:110-119.
[8]C. Caloz, T. Itoh., Application of The Transmission Line Theory of Left-Handed (LH) Materials to the Realization of a Microstrip LH Transmission Line, Proc. IEEE-MTT-S, 2002:412-415.
[9]A. Lai, T. Itoh, C. Caloz, Composite Right/Left-Handed Transmission Line Metamaterials, IEEE Microwave Magazine, VOL.5, NO.3,2004:34.
[10]Alexandre Dupuy, Ajay Gummalla, Maha Achour, Gregory Poilasne, Compact Single and Dual Band Zero-degree Metamaterial N-way Radial Power Combiner/Divider, Microwave Symposium Digest,2008 IEEE MTT-S International:659-662.
[11]J. Bonache, F. Martin, F. Falcone, J. Garcia, I. Gil, T. Lopetegi, M.A.G. Laso, R. Marques, F. Medina, M. Sorolla, Super Compact Split Ring Resonators CPW Band Pass Filtres, IEEE MTT International Microwave Symposium Digest, Fort Worth(TX), USA, June 2004:1483-1486.
[12]J. Garcia-Garcia, F. Martin, F. Falcone, J. Bonache, I. Gil, T. Lopetegi, M. A. G. Laso, M. Sorolla, and R. Marques, Spurious Passband Suppression in Microstrip Coupled Line Bandpass Filters by Means of Split Ring Resonators, IEEE Microw. Wireless Compon. Lett., VOL.14, NO.9, Sep.2004:416-418.
[13]F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M.Sorolla, "Effective Negative-"Stop-Band Microstrip Lines Based on Complementary Split Ring Resonators, IEEE Microw.Wireless Compon. Lett., VOL.14, Jun. 2004:280-282.
[14]Abid Ali, Zhirun Hu, Metamaterial Resonator Based Wave Propagation Notch for Ultrawideband Filter Applications, IEEE Antennas and Wireless Propagation Letters, VOL.7,2008:210-212.
[15]Hoang Van Nguyen, Christophe Caloz, Generalized Coupled-Mode Approach of Metamaterial Coupled-Line Couplers:Coupling Theory, Phenomenological Explanation, and Experimental Demonstration, IEEE Transactions on Microwave Theory and Techniques, VOL.55, NO.5, MAY 2007:1029-1039.
[16]高初,陈志宁,王蕴仪,杨宁,Qing Xian-ming,一种低通带波纹的EBG带阻滤波器,微波学报,第22卷第5期,2006年10月：63-66.
[17]Shi L, Lou D., The Design of a Photonic Bandgap Wideband Filter at 2.4GHz. 5th Vacuum Electon Sources Conf. Dig.,2004:358-360.
[18]夏祖学,一种EBG微带滤波器的设计,西南科技大学学报,第21卷第2期,2006年6月：36-39.
[19]赵建中,杨瑾屏,夏文勇,吴文,具有谐波抑制功能微带线EBG功分器的研究,南京理工大学学报,第31卷第4期,2007年8月：499-502.
[20]陈燕斌,朱守正,UC-EBG结构在微波抗流器中的应用研究,第11届中国微波能应用学术研讨会：6-9.
[21]Cyril Cheype, Cedric Serier, Marc Thevenot, Thierry Monediere, Alain Reineix, and Bernard Jecko, An Electromagnetic Bandgap Resonator Antenna, IEEE Transactions on Antennas and Propagation, VOL.50, NO.9, SEPTEMBER 2002:1285-1290.
[22]D. Pavlickovski, Rod B. Waterhouse, Shorted Microstrip Antenna on a Photonic Bandgap Substrate, IEEE Transactions on Antennas and Propagation, VOL.51, NO.9, SEPTEMBER 2003:2472-2475.
[23]Limaye, A.U.; Venkataraman, J.; Size reduction in microstrip antennas using left-handed materials realized by complementary split-ring resonators in ground plane, Antennas and Propagation Society International Symposium,2007 IEEE, 2007:1869-1872.
[24]Aparna U. Limaye, Jayanti Venkataraman, Size Reduction in Microstrip Antennas using Left-Handed Materials Realized by Complementary Split-Ring Resonators in Ground Plane, IEEE Antennas and Propagation International Symposium,2007:1869-1872.
[25]A. Ali, Z. Hu, Microstrip Patch Antenna Incorporating Negative Permittivity Metamaterial for Harmonic Suppression, Antennas and Propagation,2007. EuCAP 2007. The Second European Conference on11-16 Nov.2007:1-3.
[26]Yoonjae Lee, Tse, S.,Yang Hao; Parini, C.G., A compact microstrip antenna with improved bandwidth using Complementary Split-Ring Resonator (CSRR) loading, Antennas and Propagation Society International Symposium,2007 IEEE,_2007: 5431-5434.
[27]Qun Wu; Fan-Yi Meng; Fu Jiahui; Yang Guohui; Zhang kuang; Antennas and Microwave Passive Device Miniaturization Design and Ralization by Left-Handed Metamaterials, Microwave Conference,2008 China-Japan Joint,2008:381 -384.
[28]Ali, A.; Khan, M.A.; Zhirun Hu, Applying Negative Permittivity Media to Microstrip Patch Antennas for Harmonic Supression, Antennas and Propagation Conference,2007. LAPC 2007. Loughborough,2007:245-248
[29]Palandoken, M.; Grede, A.; Henke, H.; Broadband Microstrip Antenna with Left-Handed Metamaterials, Antennas and Propagation, IEEE Transactions on, 2009:331-338.
[30]Debasis Mishra, IG. Arun Kumar, D. R. Poddar, R. K. Mishra, Simulated Resonant Characteristics of Embedded Metamaterial Patch Antenna, Applied Electromagnetics Conference,2007. AEMC 2007. IEEE,19-20 Dec.2007:1-3.
[31]Cheng-Jung Lee, Kevin M. K. H. Leong, Tatsuo Itoh, Composite Right/Left-Handed Transmission Line Based Compact Resonant Antennas for RF Module Integration, IEEE Transactions on Antennas and Propagation, VOL.54, NO.8,AUG.2006:2283-2291.
[32]Sanada A, Murakami K, Awai I, Kubo H, Caloz C, Itoh T, A Plannar Zerothorder Resonator Antenna Using Left-handed Transmission Line [C],34th European Microwave Conference, Amsterdam, The Netherland,2004:1341-1344.
[33]Kyung Duk Jang, Jae Hee Kim, Dong Hyun Lee, Gi Ho Kim, Won Mo Seong, Wee Sang Park, A Small CRLH-TL Metamaterial Antenna with a Magneto-Dielectric Material, IEEE Antennas and Propagation Society International Symposium,2008. AP-S 2008.5-11 July 2008:1-4.
[34]Kevin Buell, Hossein Mosallaei, Kamal Sarabandi, A substrate for small patch Antennas Provding Tunable Miniaturization Factors, IEEE Transactions on Microwave Theory and Techniques, VOL.54, NO.1,January 2006:135-146.
[35]Kyung Duk Jang, Jae Hee Kim, Dong Hyun Lee, Gi Ho Kim, Won Mo Seong, Wee Sang Park, A Small CRLH-TL Metamaterial Antenna with a Magneto-dielectric Material, Antennas and Propagation Society International Symposium,2008. AP-S 2008. IEEE,5-11 July 2008:1-4.
[36]Bilotti, F.; Capolino, F.; Gonzalo, R.; Ozbay, E.; Romeu, J.; Schuchinsky, A.; Tretyakov, S.; Vardaxoglou, Y.; Development of micro-structured metamaterials for innovative antenna layouts, Microwave Conference,2007. European,2007: 504-507.
[37]Ortiz, N.; Falcone, F.; Sorolla, M.; Dual band patch antenna based on complementary rectangular split-ring resonators, Microwave Conference,2009. APMC 2009. Asia Pacific,2009:2762-2765.
[38]Meng Li; Mingzhi Lu; Tie Jun Cui; Novel miniaturized dual band antenna design using complementary metamaterial, Metamaterials,2008 International Workshop on,2008:374-376.
[39]Jackson J D.Classical Electrodynamics[M].New York:Wiley,1975
[40]Brown J.Artifcial dielectrics[J].Progress in Dielectrics.1960,2:195-225.
[41]Pendry J B,Holden A J,Stewart W J,et al.Extremely Low Frequency Plasmons in Metallic Mesostructures[J].Physical Review Letters.1996,76(25):4773-4776.
[42]Maslovsky S I,Tretyakov S A,Belov P A.Wire media with negative effective permittivity: a quasistatic model [J].Microwave and Optical Technology Letters.2002,35(1):47-51
[43]Thompson G H B.Unusual waveguide characteristics associated with the apparent negative permeability obtainable in ferrites[J].Nature.1955,175:1165-1166
[44]Filiberto Bilotti, Andrea Alu, Lucio Vegni, "Design of Miniaturized Metamaterial Patch Antennas With mue-Negative Loading", IEEE Transactions on Antennas and Propagation,VOL.56, NO.6, JUN.2008:1640-1647.
[45]Andrea Alu, Filiberto Bilotti, Nader Engheta, Lucio Vegni, "Subwavelength, Compact, Resonant Patch Antennas Loaded With Metamaterials", IEEE Transactions on Antennas and Propagation, VOL.55, NO.1, JAN.2007:13-25
[46]D. M. Pozar and D. H. Schaubert, Microstrip Antennas:The Analysis and Design of Microstrip Antennas and Arrays. New York:IEEE Press,1995
[47]Filiberto Bilotti, Alessandro Toscano, Lucio Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples", IEEE Transactions on Antennas and Propagation, VOL.55, NO.8, AUG 2007:2257-2267.
[2]J. B. Pendry, A.J. Holden, D. J. Robbins, W. J. Stewart, Magnetism from Conductors and Enhanced Non-Linear Phenomena, IEEE Transactions on Microwave Theory and Techniques, VOL.47, Issue 11, Nov.1999 Page(s):2075-2084.
[3]D. R. Smith, D. C. Vier, Padilla Willie, Loop-Wire Medium for Investigating Plasmas at Microwave Frequencies, Applied Physics Letters, VOL.75,1999:1425-4127.
[4]R. A. Shelby, D. R. Smith, S. Schultz, Experimental Verification of a Negative-Index Refraction [J], Science, VOL.292,2001:77-79.
[5]Marco Caiazzo, Stefano Maci, Nader Engheta, A Metamaterial Surface for Compact Cavity Resonator, IEEE Antennas and Wireless Propagation Letters, VOL.3,2004: 261-264.
[6]Lubkowski, G., Damm, C., Bandlow, B., Schuhmann, R., Schussler, M., Weiland, T., Broadband Transmission Below the Cutoff Frequency of a Waveguide Loaded With Resonant Scatterer Arrays, Microwaves, Antennas & Propagation, IET, VOL.1, Issue 1, February 2007:165-169.
[7]Silvio Hrabar, Juraj Bartolic, Zvonimir Sipus, Waveguide Miniaturization Using Uniaxial Negative Permeability Metamaterial, IEEE Transactions on Antennas and Propagation, VOL.53, NO.1, January 2005:110-119.
[8]C. Caloz, T. Itoh., Application of The Transmission Line Theory of Left-Handed (LH) Materials to the Realization of a Microstrip LH Transmission Line, Proc. IEEE-MTT-S, 2002:412-415.
[9]A. Lai, T. Itoh, C. Caloz, Composite Right/Left-Handed Transmission Line Metamaterials, IEEE Microwave Magazine, VOL.5, NO.3,2004:34.
[10]Alexandre Dupuy, Ajay Gummalla, Maha Achour, Gregory Poilasne, Compact Single and Dual Band Zero-degree Metamaterial N-way Radial Power Combiner/Divider, Microwave Symposium Digest,2008 IEEE MTT-S International:659-662.
[11]J. Bonache, F. Martin, F. Falcone, J. Garcia, I. Gil, T. Lopetegi, M.A.G. Laso, R. Marques, F. Medina, M. Sorolla, Super Compact Split Ring Resonators CPW Band Pass Filtres, IEEE MTT International Microwave Symposium Digest, Fort Worth(TX), USA, June 2004:1483-1486.
[12]J. Garcia-Garcia, F. Martin, F. Falcone, J. Bonache, I. Gil, T. Lopetegi, M. A. G. Laso, M. Sorolla, and R. Marques, Spurious Passband Suppression in Microstrip Coupled Line Bandpass Filters by Means of Split Ring Resonators, IEEE Microw. Wireless Compon. Lett., VOL.14, NO.9, Sep.2004:416-418.
[13]F. Falcone, T. Lopetegi, J. D. Baena, R. Marques, F. Martin, and M.Sorolla, "Effective Negative-"Stop-Band Microstrip Lines Based on Complementary Split Ring Resonators, IEEE Microw.Wireless Compon. Lett., VOL.14, Jun. 2004:280-282.
[14]Abid Ali, Zhirun Hu, Metamaterial Resonator Based Wave Propagation Notch for Ultrawideband Filter Applications, IEEE Antennas and Wireless Propagation Letters, VOL.7,2008:210-212.
[15]Hoang Van Nguyen, Christophe Caloz, Generalized Coupled-Mode Approach of Metamaterial Coupled-Line Couplers:Coupling Theory, Phenomenological Explanation, and Experimental Demonstration, IEEE Transactions on Microwave Theory and Techniques, VOL.55, NO.5, MAY 2007:1029-1039.
[16]高初,陈志宁,王蕴仪,杨宁,Qing Xian-ming,一种低通带波纹的EBG带阻滤波器,微波学报,第22卷第5期,2006年10月：63-66.
[17]Shi L, Lou D., The Design of a Photonic Bandgap Wideband Filter at 2.4GHz. 5th Vacuum Electon Sources Conf. Dig.,2004:358-360.
[18]夏祖学,一种EBG微带滤波器的设计,西南科技大学学报,第21卷第2期,2006年6月：36-39.
[19]赵建中,杨瑾屏,夏文勇,吴文,具有谐波抑制功能微带线EBG功分器的研究,南京理工大学学报,第31卷第4期,2007年8月：499-502.
[20]陈燕斌,朱守正,UC-EBG结构在微波抗流器中的应用研究,第11届中国微波能应用学术研讨会：6-9.
[21]Cyril Cheype, Cedric Serier, Marc Thevenot, Thierry Monediere, Alain Reineix, and Bernard Jecko, An Electromagnetic Bandgap Resonator Antenna, IEEE Transactions on Antennas and Propagation, VOL.50, NO.9, SEPTEMBER 2002:1285-1290.
[22]D. Pavlickovski, Rod B. Waterhouse, Shorted Microstrip Antenna on a Photonic Bandgap Substrate, IEEE Transactions on Antennas and Propagation, VOL.51, NO.9, SEPTEMBER 2003:2472-2475.
[23]Limaye, A.U.; Venkataraman, J.; Size reduction in microstrip antennas using left-handed materials realized by complementary split-ring resonators in ground plane, Antennas and Propagation Society International Symposium,2007 IEEE, 2007:1869-1872.
[24]Aparna U. Limaye, Jayanti Venkataraman, Size Reduction in Microstrip Antennas using Left-Handed Materials Realized by Complementary Split-Ring Resonators in Ground Plane, IEEE Antennas and Propagation International Symposium,2007:1869-1872.
[25]A. Ali, Z. Hu, Microstrip Patch Antenna Incorporating Negative Permittivity Metamaterial for Harmonic Suppression, Antennas and Propagation,2007. EuCAP 2007. The Second European Conference on11-16 Nov.2007:1-3.
[26]Yoonjae Lee, Tse, S.,Yang Hao; Parini, C.G., A compact microstrip antenna with improved bandwidth using Complementary Split-Ring Resonator (CSRR) loading, Antennas and Propagation Society International Symposium,2007 IEEE,_2007: 5431-5434.
[27]Qun Wu; Fan-Yi Meng; Fu Jiahui; Yang Guohui; Zhang kuang; Antennas and Microwave Passive Device Miniaturization Design and Ralization by Left-Handed Metamaterials, Microwave Conference,2008 China-Japan Joint,2008:381 -384.
[28]Ali, A.; Khan, M.A.; Zhirun Hu, Applying Negative Permittivity Media to Microstrip Patch Antennas for Harmonic Supression, Antennas and Propagation Conference,2007. LAPC 2007. Loughborough,2007:245-248
[29]Palandoken, M.; Grede, A.; Henke, H.; Broadband Microstrip Antenna with Left-Handed Metamaterials, Antennas and Propagation, IEEE Transactions on, 2009:331-338.
[30]Debasis Mishra, IG. Arun Kumar, D. R. Poddar, R. K. Mishra, Simulated Resonant Characteristics of Embedded Metamaterial Patch Antenna, Applied Electromagnetics Conference,2007. AEMC 2007. IEEE,19-20 Dec.2007:1-3.
[31]Cheng-Jung Lee, Kevin M. K. H. Leong, Tatsuo Itoh, Composite Right/Left-Handed Transmission Line Based Compact Resonant Antennas for RF Module Integration, IEEE Transactions on Antennas and Propagation, VOL.54, NO.8,AUG.2006:2283-2291.
[32]Sanada A, Murakami K, Awai I, Kubo H, Caloz C, Itoh T, A Plannar Zerothorder Resonator Antenna Using Left-handed Transmission Line [C],34th European Microwave Conference, Amsterdam, The Netherland,2004:1341-1344.
[33]Kyung Duk Jang, Jae Hee Kim, Dong Hyun Lee, Gi Ho Kim, Won Mo Seong, Wee Sang Park, A Small CRLH-TL Metamaterial Antenna with a Magneto-Dielectric Material, IEEE Antennas and Propagation Society International Symposium,2008. AP-S 2008.5-11 July 2008:1-4.
[34]Kevin Buell, Hossein Mosallaei, Kamal Sarabandi, A substrate for small patch Antennas Provding Tunable Miniaturization Factors, IEEE Transactions on Microwave Theory and Techniques, VOL.54, NO.1,January 2006:135-146.
[35]Kyung Duk Jang, Jae Hee Kim, Dong Hyun Lee, Gi Ho Kim, Won Mo Seong, Wee Sang Park, A Small CRLH-TL Metamaterial Antenna with a Magneto-dielectric Material, Antennas and Propagation Society International Symposium,2008. AP-S 2008. IEEE,5-11 July 2008:1-4.
[36]Bilotti, F.; Capolino, F.; Gonzalo, R.; Ozbay, E.; Romeu, J.; Schuchinsky, A.; Tretyakov, S.; Vardaxoglou, Y.; Development of micro-structured metamaterials for innovative antenna layouts, Microwave Conference,2007. European,2007: 504-507.
[37]Ortiz, N.; Falcone, F.; Sorolla, M.; Dual band patch antenna based on complementary rectangular split-ring resonators, Microwave Conference,2009. APMC 2009. Asia Pacific,2009:2762-2765.
[38]Meng Li; Mingzhi Lu; Tie Jun Cui; Novel miniaturized dual band antenna design using complementary metamaterial, Metamaterials,2008 International Workshop on,2008:374-376.
[39]Jackson J D.Classical Electrodynamics[M].New York:Wiley,1975
[40]Brown J.Artifcial dielectrics[J].Progress in Dielectrics.1960,2:195-225.
[41]Pendry J B,Holden A J,Stewart W J,et al.Extremely Low Frequency Plasmons in Metallic Mesostructures[J].Physical Review Letters.1996,76(25):4773-4776.
[42]Maslovsky S I,Tretyakov S A,Belov P A.Wire media with negative effective permittivity: a quasistatic model [J].Microwave and Optical Technology Letters.2002,35(1):47-51
[43]Thompson G H B.Unusual waveguide characteristics associated with the apparent negative permeability obtainable in ferrites[J].Nature.1955,175:1165-1166
[44]Filiberto Bilotti, Andrea Alu, Lucio Vegni, "Design of Miniaturized Metamaterial Patch Antennas With mue-Negative Loading", IEEE Transactions on Antennas and Propagation,VOL.56, NO.6, JUN.2008:1640-1647.
[45]Andrea Alu, Filiberto Bilotti, Nader Engheta, Lucio Vegni, "Subwavelength, Compact, Resonant Patch Antennas Loaded With Metamaterials", IEEE Transactions on Antennas and Propagation, VOL.55, NO.1, JAN.2007:13-25
[46]D. M. Pozar and D. H. Schaubert, Microstrip Antennas:The Analysis and Design of Microstrip Antennas and Arrays. New York:IEEE Press,1995
[47]Filiberto Bilotti, Alessandro Toscano, Lucio Vegni, "Design of Spiral and Multiple Split-Ring Resonators for the Realization of Miniaturized Metamaterial Samples", IEEE Transactions on Antennas and Propagation, VOL.55, NO.8, AUG 2007:2257-2267.