微波平面周期结构及其应用研究
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摘要
本文所研究的微波平面周期结构对象主要包括复合左/右手传输线（compositeright/left handed transmission line, CRLH TL）、电磁带隙（electromagnetic band-gap,EBG）结构以及零阶谐振器天线(zeroth-order resonator antenna, ZOR antenna)等。主要研究了这几种周期结构的理论、电磁特性、研究方法、仿真技术及工程应用。本文以CRLH理论为线索将所研究的这几种周期结构联系起来。具体研究内容包括：
1.概述各种微波平面周期结构的发展、电磁特性及研究进展，并讨论了它们之间的关系。这些周期结构包括：频率选择表面（Frequency Selective Surface，FSS）、软/硬表面（Soft/Hard Surface）、左手媒质（Left-handed Materials，LHM）、复合左/右手传输线（Composite Right/Left Handed Transmission Line，CRLH TL）、缺陷地结构（Defected Ground Structures，DGS）、光子晶体（Photonic Bandgap，PBG）与电磁带隙（Electromagnetic Band-gap，EBG）结构。
2.研究了复合左/右手传输线（CRLH TL）或说Metamaterial TL的理论、发展及应用。首先阐述了CRLH TL的几个概念，然后以简单而又清晰的方式介绍了普通复合左/右手传输线（C-CRLH TL）和对偶复合左/右手传输线（D-CRLH TL）的特性。然后提出并研究了混合C-CRLH和D-CRLH特性的新型复合左/右手传输线。应用该新传输线的独特性质设计了低通滤波器。该低通滤波器的3dB截止频率为2.38GHz，尺寸为16mm*16mm（0.13λg*0.13λg，λg为截止频率在自由空间中波长）。还应用复合左/右手传输线的概念设计小型、宽阻带的带通滤波器。该带通滤波器的3dB通带带宽为1.04-1.34GHz（即25.2%），尺寸为20mm*17mm，即0.080λg*0.068λg，λg为滤波器工作中频频率在自由空间中的波长。
3.研究了电磁带隙（EBG）结构。首先讨论普通蘑菇型电磁带隙（conventionalmushroom-type EBG, CMT-EBG）结构的工作机理及其与CRLH TL的关系。讨论了EBG结构的三种常用仿真技术；然后提出一种基于CRLH及ZOR理论的CMT-EBG结构带隙频率的新评估方法。这种方法是依据带隙频段可由两个零阶谐振频率fsh和fse界定的结论；推导了这种方法所需的边界条件，并设计了两个基于微带线的模型来计算带隙频率。研究发现所提出方法具有准确性好、建模简单和制作方便且可测试的特点。依据电磁系统对小型化、多频带的要求，设计紧凑多频的EBG结构。其中一个是基于CSRR（complementary split ring resonator）的EBG结构，其尺寸比CMT-EBG结构减少了28%。所提出的另一种结构（DAU-EBG）更紧凑，其尺寸比CMT-EBG结构减少了74.1%，并在x方向和y方向分别有三个和两个带隙频段。
4.研究EBG结构在UWB带阻天线上的应用。利用EBG结构与UWB天线的微带馈线耦合的方法设计和分析单阻带、双阻带及三阻带的UWB天线。研究发现基于这种方法设计的UWB带阻天线不但克服了阻带设计的两个主要问题：即高效多频设计和阻带宽度控制；而且EBG结构的引入对UWB天线通带的性能几乎没有影响。还通过群时延、波形变换、相关系数和波形展宽系数分析了这类UWB带阻天线的时域特性。研究发现所引入的EBG结构对天线时域特性的影响较小，所以这种阻带设计方法对于保持UWB天线的时域特性非常好。
5.提出一种新型的零阶谐振器：MZR-EZR零阶谐振器，并研究了其应用。首先介绍以CRLH TL电路推导零阶谐振器（ZOR），并得到ZOR的分类：零磁导率谐振器（mu-zero resonator, MZR）和零介电常数谐振器（epsilon-zero resonator, EZR）。然后提出一种以简单电路模型推导两种不同ZOR所需的边界条件的方法。根据EZR和MZR所需边界条件及场分布，设计一种混合MZR和EZR特点的新型零阶谐振器：MZR-EZR谐振器。研究发现这种谐振器用作天线时，耦合馈电的方式更好得到阻抗匹配，且这种天线可取得较大半功率波瓣宽度（Half-power beam width, HPBW）的定向辐射。还研究了用MZR-EZR谐振器作为寄生谐振器来增强微带天线的带宽，且将微带天线的带宽从2.2%增大到5.1%。最后，研究发现MZR-EZR谐振器有两个互相正交的极化波且它们之间的相位差固定为900。利用这些特点，通过巧妙排列四个MZR-EZR谐振器成一圆周，使得两种极化的波都为全向辐射,从而得到全向圆极化天线。通过该圆极化天线的场分布发现，该天线在一定相位时等效为电偶极子，而在相差900时等效为磁偶极子。这样就得到了全向低剖面的圆极化天线。
In this dissertation, microwave planar periodic structures are researched. Theyinclude: composite right/left handed transmission lines (CRLH TLs), electromagneticband-gap (EBG) structures and zeroth-order resonator (ZOR) antennas, etc. The theories,research methodology, simulation techniques and engineering applications of theperiodic structures are investigated. Besides, a clue to link the researched periodicstructures is the CRLH theory. Specific research contents include:
1. The development, electromagnetic characteristics and research progress ofdifferent kinds of microwave planar periodic structures are introduced, and theirrelations are discussed. These periodic structures include: frequency selective surface(FSS), soft/hard surface, left-handed material (LHM), composite right/left handedtransmission line (CRLH TL), defected ground structure (DGS), photonic band-gap(PBG) and electromagnetic band-gap (EBG) structure.
2. The theory, development and applications of CRLH TL (or metamaterial TL) arestudied. First, several concepts related to CRLH TL are stated follow by the simple andclear introductions of characteristics of conventional CRLH TL (C-CRLH TL) and dualCRLH TL (D-CRLH TL). Then, a new TL that composite C-CRLH and D-CRLHcharacteristics is proposed and investigated. The new TL is utilized to design low-passfilter (LPF). The proposed LPF has a3dB cut-off frequency at2.38GHz, and its size is16mm*16mm (0.13λg*0.13λg，and λgis the free space wavelength of the cut-offfrequency). The concept of CRLH TL is also used to design compact wide-stop-bandband-pass filter (BPF). The3dB band-width of the proposed BPF ranges from1.04-1.34GHz (25.2%bandwidth), and its size is20mm*17mm (0.080λg*0.068λg，and λgis the free space wavelength of the center frequency).
3. EBG structures are researched. First, the operational mechanism of conventionalmushroom-type EBG (CMT-EBG) structure and its relationship with CRLH TL isdiscussd. Three simulation techniques for EBG structures are discussed, then, a newsimulation approach for CMT-EBG structure's band-gap frequencies detection areproposed based on CRLH and ZOR theories. The new approach are proposed according to the conclusion that band-gap of CMT-EBG can be delimited by resonant frequenciesfshand fse. Boundary conditions for the new approach are deduced and two microstripline based models are designed to calculate the band-gap frequencies. Research foundthe proposed approach have the advantages of good accuracy, simple model, easyfabrication and measurement. According to electromagnetic system's requirements ofcompactness and multi-band, compact multi-band EBG structures are designed. OneEBG design is based on complementary split ring resonator (CSRR), and its size is28%smaller than the CMT-EBG structure. Another EBG design (DAU-EBG) is morecompact: its size is74.1%smaller than the CMT-EBG structure, and three and twoband-gaps are happened at x and y directions, respectively.
4. The applications of EBG structures on ultra-wideband (UWB) antennas fornotches design are investigated. The approach of utilizing EBG structures couple tomicrostrip feeding ling of UWB antennas for single, double and triple band-gaps arestudied. Research found the proposed UWB band-notched design approach can conquerthe two main problems of notch design: high-efficiency multi-notches design and notchwidth control. Besides, the introduction of EBG structures has little effect on UWBantennas' pass-band characteristics. Time domain characteristics of the UWBband-notched antennas are researched by group delay, waveform response, correlationcoefficient, and pulse width stretch ratio (SR). Research found the introduction of EBGstructure have very small effect on the antennas' time domain characteristics, therefore,the proposed notch design approach is good for maintain UWB antennas' time domaincharacteristics.
5. A new ZOR (the MZR-EZR resonator) is proposed, and its applications areinvestigated. First, conventional ZORs that deduced from CRLH TL are introduced, andthe classification of ZORs is derived: mu-zero resonator (MZR) and epsilon-zeroresonator (EZR). Then, an approach to deduce the boundary conditions of ZORs wasproposed by simple circuit model. According to the necessary boundary conditions andfields distributions of EZR and MZR, a new resonator, composite the characteristics ofMZR and EZR, is designed. The resonator is MZR-EZR resonator. Research foundcoupling feeding system would be a better way for impedance matching when theresonator used as antenna, and the antenna has a wide HPBW. The MZR-EZRresonators are also utilized as parasitic resonators to enhance microstrip antennas' bandwidth. Research found microstrip antennas' bandwidth can be increased from2.2%to5.1%. Research also found the proposed MZR-EZR resonator has two orthogonalpolarized fields, and the phase difference between the fields is fixed to be900. Thus,four MZR-EZR resonators are form in a circular way to make both the polarizationsradiate omni-directionally. From field distributions of the circular polarized antenna, itis found that the antenna acts like an electric dipole in certain phase, and acts like amagnetic dipole in a900phase difference. Then, a low-profile omni-directional circularpolarized antenna is obtained.
1.概述各种微波平面周期结构的发展、电磁特性及研究进展，并讨论了它们之间的关系。这些周期结构包括：频率选择表面（Frequency Selective Surface，FSS）、软/硬表面（Soft/Hard Surface）、左手媒质（Left-handed Materials，LHM）、复合左/右手传输线（Composite Right/Left Handed Transmission Line，CRLH TL）、缺陷地结构（Defected Ground Structures，DGS）、光子晶体（Photonic Bandgap，PBG）与电磁带隙（Electromagnetic Band-gap，EBG）结构。
2.研究了复合左/右手传输线（CRLH TL）或说Metamaterial TL的理论、发展及应用。首先阐述了CRLH TL的几个概念，然后以简单而又清晰的方式介绍了普通复合左/右手传输线（C-CRLH TL）和对偶复合左/右手传输线（D-CRLH TL）的特性。然后提出并研究了混合C-CRLH和D-CRLH特性的新型复合左/右手传输线。应用该新传输线的独特性质设计了低通滤波器。该低通滤波器的3dB截止频率为2.38GHz，尺寸为16mm*16mm（0.13λg*0.13λg，λg为截止频率在自由空间中波长）。还应用复合左/右手传输线的概念设计小型、宽阻带的带通滤波器。该带通滤波器的3dB通带带宽为1.04-1.34GHz（即25.2%），尺寸为20mm*17mm，即0.080λg*0.068λg，λg为滤波器工作中频频率在自由空间中的波长。
3.研究了电磁带隙（EBG）结构。首先讨论普通蘑菇型电磁带隙（conventionalmushroom-type EBG, CMT-EBG）结构的工作机理及其与CRLH TL的关系。讨论了EBG结构的三种常用仿真技术；然后提出一种基于CRLH及ZOR理论的CMT-EBG结构带隙频率的新评估方法。这种方法是依据带隙频段可由两个零阶谐振频率fsh和fse界定的结论；推导了这种方法所需的边界条件，并设计了两个基于微带线的模型来计算带隙频率。研究发现所提出方法具有准确性好、建模简单和制作方便且可测试的特点。依据电磁系统对小型化、多频带的要求，设计紧凑多频的EBG结构。其中一个是基于CSRR（complementary split ring resonator）的EBG结构，其尺寸比CMT-EBG结构减少了28%。所提出的另一种结构（DAU-EBG）更紧凑，其尺寸比CMT-EBG结构减少了74.1%，并在x方向和y方向分别有三个和两个带隙频段。
4.研究EBG结构在UWB带阻天线上的应用。利用EBG结构与UWB天线的微带馈线耦合的方法设计和分析单阻带、双阻带及三阻带的UWB天线。研究发现基于这种方法设计的UWB带阻天线不但克服了阻带设计的两个主要问题：即高效多频设计和阻带宽度控制；而且EBG结构的引入对UWB天线通带的性能几乎没有影响。还通过群时延、波形变换、相关系数和波形展宽系数分析了这类UWB带阻天线的时域特性。研究发现所引入的EBG结构对天线时域特性的影响较小，所以这种阻带设计方法对于保持UWB天线的时域特性非常好。
5.提出一种新型的零阶谐振器：MZR-EZR零阶谐振器，并研究了其应用。首先介绍以CRLH TL电路推导零阶谐振器（ZOR），并得到ZOR的分类：零磁导率谐振器（mu-zero resonator, MZR）和零介电常数谐振器（epsilon-zero resonator, EZR）。然后提出一种以简单电路模型推导两种不同ZOR所需的边界条件的方法。根据EZR和MZR所需边界条件及场分布，设计一种混合MZR和EZR特点的新型零阶谐振器：MZR-EZR谐振器。研究发现这种谐振器用作天线时，耦合馈电的方式更好得到阻抗匹配，且这种天线可取得较大半功率波瓣宽度（Half-power beam width, HPBW）的定向辐射。还研究了用MZR-EZR谐振器作为寄生谐振器来增强微带天线的带宽，且将微带天线的带宽从2.2%增大到5.1%。最后，研究发现MZR-EZR谐振器有两个互相正交的极化波且它们之间的相位差固定为900。利用这些特点，通过巧妙排列四个MZR-EZR谐振器成一圆周，使得两种极化的波都为全向辐射,从而得到全向圆极化天线。通过该圆极化天线的场分布发现，该天线在一定相位时等效为电偶极子，而在相差900时等效为磁偶极子。这样就得到了全向低剖面的圆极化天线。
In this dissertation, microwave planar periodic structures are researched. Theyinclude: composite right/left handed transmission lines (CRLH TLs), electromagneticband-gap (EBG) structures and zeroth-order resonator (ZOR) antennas, etc. The theories,research methodology, simulation techniques and engineering applications of theperiodic structures are investigated. Besides, a clue to link the researched periodicstructures is the CRLH theory. Specific research contents include:
1. The development, electromagnetic characteristics and research progress ofdifferent kinds of microwave planar periodic structures are introduced, and theirrelations are discussed. These periodic structures include: frequency selective surface(FSS), soft/hard surface, left-handed material (LHM), composite right/left handedtransmission line (CRLH TL), defected ground structure (DGS), photonic band-gap(PBG) and electromagnetic band-gap (EBG) structure.
2. The theory, development and applications of CRLH TL (or metamaterial TL) arestudied. First, several concepts related to CRLH TL are stated follow by the simple andclear introductions of characteristics of conventional CRLH TL (C-CRLH TL) and dualCRLH TL (D-CRLH TL). Then, a new TL that composite C-CRLH and D-CRLHcharacteristics is proposed and investigated. The new TL is utilized to design low-passfilter (LPF). The proposed LPF has a3dB cut-off frequency at2.38GHz, and its size is16mm*16mm (0.13λg*0.13λg，and λgis the free space wavelength of the cut-offfrequency). The concept of CRLH TL is also used to design compact wide-stop-bandband-pass filter (BPF). The3dB band-width of the proposed BPF ranges from1.04-1.34GHz (25.2%bandwidth), and its size is20mm*17mm (0.080λg*0.068λg，and λgis the free space wavelength of the center frequency).
3. EBG structures are researched. First, the operational mechanism of conventionalmushroom-type EBG (CMT-EBG) structure and its relationship with CRLH TL isdiscussd. Three simulation techniques for EBG structures are discussed, then, a newsimulation approach for CMT-EBG structure's band-gap frequencies detection areproposed based on CRLH and ZOR theories. The new approach are proposed according to the conclusion that band-gap of CMT-EBG can be delimited by resonant frequenciesfshand fse. Boundary conditions for the new approach are deduced and two microstripline based models are designed to calculate the band-gap frequencies. Research foundthe proposed approach have the advantages of good accuracy, simple model, easyfabrication and measurement. According to electromagnetic system's requirements ofcompactness and multi-band, compact multi-band EBG structures are designed. OneEBG design is based on complementary split ring resonator (CSRR), and its size is28%smaller than the CMT-EBG structure. Another EBG design (DAU-EBG) is morecompact: its size is74.1%smaller than the CMT-EBG structure, and three and twoband-gaps are happened at x and y directions, respectively.
4. The applications of EBG structures on ultra-wideband (UWB) antennas fornotches design are investigated. The approach of utilizing EBG structures couple tomicrostrip feeding ling of UWB antennas for single, double and triple band-gaps arestudied. Research found the proposed UWB band-notched design approach can conquerthe two main problems of notch design: high-efficiency multi-notches design and notchwidth control. Besides, the introduction of EBG structures has little effect on UWBantennas' pass-band characteristics. Time domain characteristics of the UWBband-notched antennas are researched by group delay, waveform response, correlationcoefficient, and pulse width stretch ratio (SR). Research found the introduction of EBGstructure have very small effect on the antennas' time domain characteristics, therefore,the proposed notch design approach is good for maintain UWB antennas' time domaincharacteristics.
5. A new ZOR (the MZR-EZR resonator) is proposed, and its applications areinvestigated. First, conventional ZORs that deduced from CRLH TL are introduced, andthe classification of ZORs is derived: mu-zero resonator (MZR) and epsilon-zeroresonator (EZR). Then, an approach to deduce the boundary conditions of ZORs wasproposed by simple circuit model. According to the necessary boundary conditions andfields distributions of EZR and MZR, a new resonator, composite the characteristics ofMZR and EZR, is designed. The resonator is MZR-EZR resonator. Research foundcoupling feeding system would be a better way for impedance matching when theresonator used as antenna, and the antenna has a wide HPBW. The MZR-EZRresonators are also utilized as parasitic resonators to enhance microstrip antennas' bandwidth. Research found microstrip antennas' bandwidth can be increased from2.2%to5.1%. Research also found the proposed MZR-EZR resonator has two orthogonalpolarized fields, and the phase difference between the fields is fixed to be900. Thus,four MZR-EZR resonators are form in a circular way to make both the polarizationsradiate omni-directionally. From field distributions of the circular polarized antenna, itis found that the antenna acts like an electric dipole in certain phase, and acts like amagnetic dipole in a900phase difference. Then, a low-profile omni-directional circularpolarized antenna is obtained.
引文
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