【学位授与の要件】中央大学学位規則第4条第1項【論文審査委員主査】白井　宏　（中央大学理工学部教授）【論文審査委員副査】趙　晋輝（中央大学理工学部教授）、小林　一哉（中央大学理工学部教授）、宇野　亨（東京農工大学工学部教授）博士（工学）中央大

BA HIEN CHU

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CHU, BA HIEN

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博士論文要旨 (2017年度)A Study on Metamaterial Transmission Lines for RF andMicrowave Applications中央大学大学院理工学研究科情報セキュリティ科学専攻Chu Ba Hien1. IntroductionMetamaterial is a terminology to describe a compos-ite material in form of effective medium with negativepermittivity ε and/or negative permeability µ. In 1998,thin wire structures (TWs) exhibit a negative value ofeffective permittivity which was first demonstrated byPendry [1]. In 1999, he presented split ring resonatorstructures (SRRs) with a negative value of effective per-meability [2]. Shelby and Smith verified a negative indexof refraction of negative ε and negative µ by constitut-ing TWs and SRRs in 2001 [3]. Later, a transmissionline approach for metamaterials was first introduced ap-proximately at the same time in June 2002 by threedifferent groups, Eleftheriades [4], Oliner [5], and Caloz[6]. The proposed structures consist simply of L-C ele-ments loaded-transmission line networks and are calledby left-handed transmission line (LH TL) or negative-refractive-index transmission line (NRI TL). In 2006,composite right/left-handed transmission line (CRLHTL) and dual composite right/left-handed transmissionline (D-CRLH L) are presented by Caloz [7, 8]. TheCRLH TL exhibits a LH band at low frequency, a RHband at high frequency, and is of pass-band while D-CRLH TL is in opposition. More recently, an extended-composite right/left-handed transmission line (E-CRLHTL) has been combined from CRLH and D-CRLH TLsto get more involved band structures [9]. This TL isalso known as a generalized negative refraction indextransmission line (NRI TL) [10].Metamaterials have been applied in a large numberof RF and microwave devices such as antennas, filters,power dividers, direction couplers, absorbers and mi-crowave lens. With the unique electromagnetic proper-ties, metamaterials seem to allow manufacturers to re-duce the size of these devices while maintaining goodperformance at a low cost.Therefore, in this thesis, a study on metamaterialtransmission lines is presented to bring new researchresults and applications for E-CRLH TL, the most re-cent metamaterial TL. This study also paves the way fornovel arbitrary dual-, tri- and quad-band RF and mi-crowave devices. In addition, there is a growing demandfor faster data transmission of ultra wide band (UWB)applications. Antipodal Vivaldi antenna is a candidatefor UWB applications. With resonant metamaterial ap-proach, the gain of the antipodal Vivaldi antenna is im-proved by using nearly zero-index metamaterial (ZIM)unit cell. Also, a new estimation method for low fre-quency end of antipodal Vivaldi antennas is presentedin this study.2. Metamaterial transmission lines2.1 Analysis and design of E-CRLH TLwith new closed-form solutionsFigure 1 shows the equivalent circuit of an E-CRLHTL unit cell [9, 10]. By applying the periodic boundaryconditions related with Bloch-Floquet theorem [11], thedispersion relation is obtained ascos(βd) = 1 + ZhYv, (1)where β is the propagation constant for the Bloch wavesand d is the length of the unit cell. An example ofthe dispersion diagram of the unbalanced E-CRLH TL(fC5 ̸= fC6 and fC7 ̸= fC8) is depicted in Fig. 2. Thebalanced E-CRLH TL is obtained when fC5 = fC6 andfC7 = fC8.C1dL1 C2L2C2L2L1 C1Zh ZhY vL3C3 L4C4Figure 1: Equivalent circuit of an E-CRLH TL unit cell[9, 10].0.0 0.5 1.0 1.5 2.0 2.5 3.0β d(radians)864210120Frequency [GHz]fC4fC3fC2fC1fC8fC7fC6fC5RHLHRHLHFigure 2: A typical dispersion diagram of E-CRLH TLin an unbalanced case [15].The Bloch impedance is a quantity to use for theimpedance matching. The Bloch impedance of the pro-posed metamaterial TL may be approximately calcu-lated by the expression [10, 12]:ZB =√2ZhYv. (2)Most microwave application design with the E-CRLHTL are based on the controllability of the dispersion di-agram, and the impedance matching consideration ofthe Bloch impedance. Therefore, it is important to findappropriate L–C elements to match the requirements.Previous studies for designing E-CRLH TL have pre-sented for balanced cases and have seldom mentionedabout unbalanced cases. Reference [13] presented a pos-sible solution for a balanced case to achieve a desiredphase at four specified frequencies. A balanced E-CRLHTL with arbitrary phase shifts at four arbitrary frequen-cies is reported in Ref. [14] by using the results of ho-mogeneous E-CRLH medium. Homogeneous E-CRLHmedium may be useful for idealization, but not for thecase of a practical E-CRLH TL lumped implementation,since the unit-cells would sometimes cascaded periodi-cally to build effectively the corresponding uniform TLstructure [9].In this study, a different approach is proposed to de-termine lumped elements of the equivalent circuit. Re-quired L-C elements of the E-CRLH unit cell are calcu-lated from the cut-off frequencies fC1∼fC8. Moreover,we complement a mix case (fC5 = fC6 and fC7 ̸= fC8),(fC5 ̸= fC6 and fC7 = fC8), and a special case for aconstant Bloch impedance. It shows a complete view ofE-CRLH TLs. While a proper method for deriving theparameters of the unbalanced and mixed E-CRLH TLs isnot yet reported, our closed-form solutions clearly haveeffectiveness for deriving these cases. By solving a set ofequations explicitly, one can design easily a desired dis-persion diagram and control Bloch impedance. To avoidcomplexity, References [9, 13, 14] have not characterizedS-parameters of the E-CRLH TL in the unbalanced case.In our study, S-parameters of a periodic E-CRLH unitcell network have been investigated carefully for unbal-anced, mixed, balanced and special cases. In addition,our method can be used for a desired phase character-istic, which is very useful for phase shift devices. Ourcalculated result covers the result of Ref. [13], in whichthe balanced case with some specified conditions is aspecial case in this study.In conclusion, unlikely the previous methods, ourmethod is in a general form and helpful for various cases.The numerical results has demonstrated the usefulnessof the method. Thus this study contributes to the the-ory and applications of the E-CRLH TLs, and its resultscan be applied to design dual-, tri- and quad-band RFand microwave devices [15].2.2 A compact metamaterial antennabased on asymmetric E-CRLH TLunit cell for multiband applicationsFor wireless communications, few antennas based onE-CRLH TL and NRI-TL were proposed up to now.Reference [16] presents a dual-band antenna based ona modified asymmetric NRI-TL unit cell. This antennahas a compact size, but exhibits a very low gain at theoperating frequencies. More recently, a multiband an-tenna based on one asymmetric E-CRLH unit cell is de-signed for quad-band [17]. However, the resonant fre-quencies are not analyzed yet.In this chapter, a compact quad-band antenna hasbeen designed from one E-CRLH unit cell for GSM810,WLAN 2.45/5.5 GHz and WiMAX 3.5 GHz bands [18].Asymmetric E-CRLH unit cell is chosen to design theantenna because of smaller configuration to comparewith symmetric E-CRLH unit cell. The resonant fre-quencies of the proposed antenna have been predictedtheoretically from L–C lumped elements and comparedwith simulated values. A photograph of the fabricatedantenna is shown in Fig. 3. Figure 4 presents the mea-sured return loss S11 of the antenna from 0.5 to 6 GHz.The measurements are executed by Agilent E8361A net-work analyzer in an anechoic chamber and comparedwith the corresponding HFSS simulated results. Ourquad-band antenna has an electrical size 0.15λ0×0.08λ0at the center frequency of the lowest band (GSM810)and its size is very small to compare with the previ-ous quad-band antennas which designed by conventionalmethods. Although Reference [17] has made from the E-Figure 3: Fabricated antenna0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0-35-30-25-20-15-10-505  S11 [dB]Frequency [GHz] Simulated MeasuredFigure 4: S11 characteristics of the fabricated antennaCRLH unit cell, our antenna can be designed by roughlyone half size. The gains of the proposed antenna are es-timated as 3.66 dBi at 5.5 GHz, 1.46 dBi at 3.5 GHz,−1.31 dBi at 2.45 GHz and −8.12 dBi at 0.81 GHz. Dueto the compact size, the gains of the antenna are quitelow at low frequencies. At the higher frequencies, thegains of the antenna are enhanced and comparable withthe previous quad-band antennas. In fact, the proposedantenna has a better gain at the low frequencies thanthe reported dual-band NRI-TL antenna (−17 dBi at0.9 GHz and −8 dBi at 2.4 GHz) in Ref. [16].In conclusion, the proposed antenna shows advantagesof small size, omnidirectional radiation characteristics,and easy fabrication of single copper layer on the lowcost of FR4 substrate. Basically, this antenna could bea candidate for multiband wireless communications.3. Resonant metamaterials3.1 Zero-index metamaterial (ZIM) unitcell for improving gain of antipodalVivaldi antennasThe antipodal type of Vivaldi antennas (AVAs) offersbroad bandwidth, minimal signal distortion, and highgain properties. However, the operation mechanism ofthe antipodal Vivaldi antenna is not well understood.Previously, antipodal Vivaldi antennas have been mainlydesigned by empirical methods without rigorous theoryor formulas. While the operational upper frequency endof the antipodal Vivaldi antenna is theoretically infin-ity, the low frequency end has not been predicted andexplained clearly. Therefore, the first objective of thisstudy is to get better insight on the operation of theantipodal Vivaldi antennas, and to develop an accurateestimation of the low frequency end of the operationalrange [19].Since the gain of the antipodal Vivaldi antenna is avery important parameter for UWB applications, many23 mm13579111915zxy5×5 mm2Figure 5: The configuration of the antipodal Vivaldiantenna with ZIM unit cell3 4 5 6 7 8 9 10 11-45-40-35-30-25-20-15-10-50  S11 [dB]Frequency [GHz] Antipodal Vivaldi antenna without ZIM unit cells  Antipodal Vivaldi antenna with ZIM unit cellsFigure 6: Simulated S-parameters for the antipodal Vi-valdi antenna without and with ZIM unit cells3 4 5 6 7 8 9 10 11024681012  Gain [dBi]Frequency [GHz] Antipodal Vivaldi antenna without ZIM unit cells  Antipodal Vivaldi antenna with ZIM unit cells Figure 7: Simulated gains for the antipodal Vivaldi an-tenna without and with ZIM unit cellsstudies have been carried out to enhance the gain of thisantenna. Some methods have been proposed such asmaking corrugated structure at the edges of the Vivaldiantenna, and adding a high permittivity dielectric or aparasitic elliptical patch as a director in the aperture ofthe Vivaldi antenna. However, these methods increasethe complexity and the cost for fabrication, and theyelongate the antenna length too much for some appli-cations. Hence, the second objective of this study is toenhance the gain of the antipodal Vivaldi antenna byusing resonant metamaterials. A symmetric zero-indexmetamaterial (ZIM) unit cell is proposed in this study.The ZIM unit cell has anisotropic metamaterial charac-teristics. When wave propagation is along y directionand the electric field polarization is in x direction, theunit cell exhibits positive permittivity and permeabilityas a normal material. When wave propagation is alongx direction and the electric field polarization is in y di-rection, the unit cell shows negative permittivity andhas nearly zero-refractive index at a certain frequencyrange.The ZIM unit cells are arranged to the aperture ofAVA as shown in Fig. 5. This arrangement makes astronger end-fire radiation in y direction because veryfew waves can propagate along x direction. The perfor-mance of the proposed configuration can be seen fromFigs. 6 and 7. Even the AVA adds the ZIM unit cells,the S11 is lower than −10 dB in entire frequencies ofUWB. It confirms that the proposed configuration hasa very good impedance matching. In general, the gainof the designed AVA has been improved roughly 2 dBfrom 3.0 to 7.5 GHz.References[1] J. B. Pendry, A. J. Holden, D. J. Robbins, and W.J. Stewart, “Low frequency plasmons in thin-wirestructures,” J. Phys. Condens. Matter, vol. 10, pp.4785–4809, 1998.[2] J. B. Pendry, A. J. Holden, D. J. Robbins,and W. J. Stewart, “Magnetism from conduc-tors and enhanced nonlinear phenomena,” IEEETrans. Microwave Theory Tech., vol. MTT-47, pp.2075−2084, Nov. 1999.[3] R. A. Shelby, D. R. Smith, and S. Schultz, “Exper-imental verification of a negative index of refrac-tion,” Science, vol. 292, pp. 77−79, Apr. 2001.[4] A. K. Iyer and G. V. Eleftheriades, “Nega-tive refractive index metamaterials supporting 2-D waves,” Proc. of IEEE-MTT International Mi-crowave Symposium Digest, vol. 2, pp. 412–415,June 2002.[5] A. A. Oliner, “A periodic-structure negative-refractive-index medium without resonant el-ements,” Proc. of URSI Digest, IEEE-AP-SUSNC/URSI National Radio Science Meeting, pp.41, June 2002.[6] C. Caloz and T. Itoh, “Application of the trans-mission line theory of left-handed (LH) materialsto the realization of a microstrip LH transmissionline,” Proc. of IEEE-AP-S USNC/URSI NationalRadio Science Meeting, vol. 2, pp. 412–415, June2002.[7] C. Caloz, and T. Itoh, Electromagnetic Metama-terials: Transmission Line Theory and MicrowaveApplications, John Wiley & Sons, 2006.[8] C. Caloz, “Dual composite right/left-handed (D-CRLH) transmission line metamaterial,” IEEE Mi-crowave and Wireless Components Letters, vol. 16,no. 11, 585–587, Nov. 2006.[9] A. Rennings, S. Otto, J. Mosig, C. Caloz and I.Wolff, “Extended composite right/left-handed (E-CRLH) metamaterial and its application as quad-band quarter-wavelength transmission line,” Proc.of Asia-Pacific Microwave Conference, pp. 1405–1408, Dec. 2006.[10] G. V. Eleftheriades, “A generalized negative-refractive-index transmission line (NRL-TL) meta-material for dual-band and quad-band applica-tions,” IEEE Microwave and Wireless ComponentLetters, vol. 17, no. 6, 415–417, June 2007.[11] D. M. Pozar, Microwave Engineering , John Wiley& Sons, 2012.[12] L. Peng, and C. I. Ruan, “Design, analysis andimplementation of novel metamaterial transmissionline with dual composite right/left-handed and con-ventional composite right/left-handed properties,”IET Microwaves, Antennas and Propagation, vol.6, no. 15, pp. 1687–1695, Oct. 2012.[13] G. V. Eleftheriades, “Design of generalisednegative-refractive-index transmission lines forquad-band applications,” IET Microwaves, Anten-nas and Propagation, vol. 4, no. 8, pp. 977–981,Aug. 2010.[14] M. Fozi, S. Nikmehr, M. V. Ghurt-Tappeh and M.Bemani, “Design of dual- and quad-band E-CRLH-TLs with arbitrary phase characteristics,” ProgressIn Electromagnetics Research M , vol. 35, pp. 141–149, Mar. 2014.[15] H. B. Chu, and H. Shirai, “Analysis and design ofE-CRLH TL characteristics with new closed-formsolutions,” Progress In Electromagnetics ResearchC, vol. 68, pp. 163–178, Oct. 2016.[16] M. A. Abdalla, and M. A. Fouad, “CPW dual-bandantenna based on asymmetric generalized metama-terial π NRI transmission line for ultra compact ap-plications,” Progress In Electromagnetics ResearchC , vol. 62, pp. 99–107, Feb. 2016.[17] X. Gao, T. J. Jackson, and P. Gardner, “Multibandopen-ended resonant antenna based on one ECRLHunit cell structure,” IEEE Antennas and WirelessPropagation Letters, vol. 16, pp. 1273–1276, May2017.[18] H. B. Chu, and H. Shirai, “Design of multiband an-tennas using asymmetric E-CRLH TL unit Cells,”Proc. of the 2017 IEEE International Symposiumon Antennas and Propagation and USNC-URSIRadio Science Meeting , pp. 2531–2532, San Diego,USA, July 2017.[19] H. B. Chu, H. Shirai, and D. N. Chien, “New Esti-mation Method for the Operational Low FrequencyEnd of Antipodal Vivaldi Antennas,” IEICE Trans-actions on Electronics, vol. E99-C, no. 8, pp. 947–955, Aug. 2016.

A Study on Metamaterial Transmission Lines for RF and Microwave Applications

中央大学博士（工学）application/pdf【学位授与の要件】中央大学学位規則第4条第1項
【論文審査委員主査】白井　宏　（中央大学理工学部教授）
【論文審査委員副査】趙　晋輝（中央大学理工学部教授）、小林　一哉（中央大学理工学部教授）、宇野　亨（東京農工大学工学部教授）doctoral thesi

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RFおよびマイクロ波応用のためのメタマテリアル伝送線路に関する研究

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Chuo University Academic Information Repository / 中央大学学術リポジトリ

Chuo University Academic Information Repository / 中央大学学術リポジトリ