C-OW2-B-1-041(수정).hwp
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1 ISSN (Print) / ISSN (Online) The Transactions of the Korean Institute of Electrical Engineers Vol. 62, No. 12, pp. 1706~1711, 단락개방간극링구조와인터디지틀선로의결합형소형초광대역여파기설계 Design of the Miniaturized Ultra-WideBand(UWB) Filter of the Shorted Open Gap Ring Structure combined with the interdigital Line 오승훈 * 김군태 * 강성인 * 이정혁 * 한준희 * 김형석 (Seunghun Oh Koon-Tae Kim Seong-In Kang Jeong-Hyeok Lee Jun-Hee Han Hyeong-Seok Kim) Abstract This paper presents the filter of a resonator comprising a shorted open gap ring(sogr) and interdigital lines. The proposed filter has the ultra wideband characteristic operating from 3 GHz to 10.5 GHz. In order to achieve the remarkable improvement in the size-reduction of the overall filter structure, only one cell of the SOGR with the inter-digital lines is adopted. It is shown that this filter has the size of 18mm 15mm using a metamaterial, the fractional bandwidth over 100%, the insertion loss much less than 1dB, an acceptable return loss performance in the results. Key Words : CRLH-TL(Composite Right and Left Handed-Transmission Line), Meta-material, UWB(Ultra WideBand) Filter, SOGR(Shorted Open Gap Ring) Structure, Interdigital line 1. 서론 2002년미합중국 FCC에서통신용주파수로 3.1~10.6 GHz 초광대역 (Ultra Wideband, UWB) 이일반에게허가됨에따라 UWB 통신용초고주파소자들에대한연구들이진행되어져왔다. 또한 UWB용통신에연관된연구활동중의하나인초광대역통과여파기에대한개발기술도국내및국외에서지속적으로발표되고있다 [1]-[3]. 기존 UWB 여파기의연구는주로다중모드 (multi mode) 공진기를마이크로스트립 (microstrip) 에적용하여 UWB 여파기를구현하는고전적인전자기공진방법을사용하였다 [1]-[2]. 기존연구된다중모드공진기는광대역특성을얻기위해저역통과여파기와고역통과여파기의혼합형구조를사용하였다. 혼합형구조는일정한전기적공진길이가요구되기때문에전체적인여파기의길이가증가하게된다. UWB 여파기의다른방법으로병렬의링 (Ring) 공진기와낮은특성임피던스를갖는관내파장길이의 0.25배길이의개방형마이크로스트립선로를결합한구조를갖는 UWB 여파기를제시하였다 [3]. 이것은병렬스터브를 10 이하의매우낮은임피던스로설계하기때문에마이크로스트립선로폭이커지게되된다. 이를개선하기위해 50의임피던스를갖는병렬스터브끝에가변콘덴서를연결하였다. 하지 Corresponding Author : School of Electrical and Electronics Eng., Chung-Ang University, Korea kimcaf2@cau.ac.kr * School of Electrical and Electronics Eng., Chung-Ang University, Korea Received : October 22, 2013; Accepted : November 12, 2013 만가변콘덴서로인해여파기제작이어려워진다. 위의여파기는 UWB 여파기로써동작할수는있으나, 여파기전체를초소형으로만드는데는적합하지않을수있다. 이를개선하기위해전기적공진길이에따른여파기의크기를소형화하기위한연구의필요성이대두된다. 기존여파기의크기에대한문제점등을해결하기위해, 본논문에서는전기적공진방법과는다른좌우수결합형전송선로 (Composite Right and Left Handed-Transmission Line, CRLH-TL) 의이론을적용하여소형의초광대역여파기와공진기를설계하는방법을제안한다. 이때, 여파기의소형화를위하여많은수의 CRLH-TL 단위구조를이용하는방식과는다르게 1단의 CRLH-TL을사용한공진기를설계한다 [4]-[7]. 하지만기존 π-형 CRLH-TL 구조는인터디지틀단자와폐쇄형스터브의단순결합형으로파장방향의직교축길이가길어지는단점이있다 [5]-[8]. 이러한현상을막기위해단락개방간극링 (Shorted Open Gap Ring, SOGR) 구조와인터디지틀선로와의커플링결합을통한 1단 π-형 CRLH-TL 공진기구조를적용한 UWB 여파기를제안한다. 2. 본론 2.1 CRLH-TL 회로및공진기설계메타재질은일반전자기이론에서언급된현상과는다른특이한현상을보인다. 메타재질은음의투자율과유전율을가지는인위적인구조또는매질이다. 특정주파수의전자기파가메타재질내에서진행할때, 음의위상상수와위상속도를가진다. 이러한현상으로메타재질내의파는기존의양의투자율과양의유전율을가지는일반매질과다르 1706
2 Trans. KIEE. Vol. 62, No. 12, DEC, 2013 게파의진행이이루어진다. 메타재질내에서파의진행이기존매질과달라지는현상은 Veselago에의해처음발견되었다 [4]. 이러한매질을전송선로관점에서현재는좌수전송선로 (Left-Handedness Transmission Line, LH-TL) 라명명되었다. 또한, 기존의양의투자율과양의유전율을가지는매질은우수전송선로 (Right-Handedness Transmission Line, RH-TL) 가되었다. RH-TL과 LH-TL을결합하면, 통과대역이기존의 RH-TL 만의구조와는다르게광대역의특성을가지게된다. 단점이있다. 따라서, 단일구조로도회로의특성이 T-형보다안정된 π-형회로를이용하여 CRLH-TL을설계한다 [4]. CRLH π-형회로설계변수식은식 (1) 과같다. (1) 이러한 1단의 π형 CRLH-TL을 UWB 공진기에적용한다. 우선 LH-TL의하한주파수와 RH-TL의상한주파수를 UWB인 3~10.5GHz대역에맞춘다. 그리고 CRLH-TL의균형조건을맞추기위해상 / 하한주파수에따른설계변수를결정한다. UWB 공진기는 CRLH-TL의균형조건에의한광대역매칭을위해, 중심주파수 f 0, 직렬공진주파수 f series, 병렬공진주파수 f shunt 는같게하여식 (1) 에맞게 L R, C R, L L, C L 를구하면된다. 그림 1 CRLH-TL 의주기적인회로모델 1 Periodic circuit model of CRLH-TL 그림 1은주기적인 CRLH-TL의회로배치구성도이다. 각각의단은두쌍의인덕터와커패시터로구성된다. 이때병렬커패시턴스와직렬인덕턴스 (C R, L R) 는 RH-TL을구성하고, 직렬커패시턴스와병렬인덕턴스 (C L, L L) 는 LH-TL 을구성한다. 여기서 RH-TL을구성하는공진소자와 LH-TL을구성하는공진소자사이에주파수대소관계에따라개방형혹은폐쇄형소자로간략화할수있다. 즉, 회로의하한저주파에서는 CRLH-TL이 LH-TL로동작되며, 반대로상한고주파에서는 RH-TL로동작하게된다. 따라서하한과상한주파수에따라 CRLH-TL이 RH-TL 혹은 LH-TL으로동작하도록소자값의대소구분을정확히해주어야한다 [4]. (a) (b) 그림 3 CRLH-TL 설계용구조 (a) 인터디지털선로 (b) 단락스터브 3 Components to design the CRLH-TL (a) Inter-digital line (b) Short Stub 그림 2 CRLH-TL의단일 π-형회로모델 2 Unit π-type circuit model of CRLH-TL 소형여파기의제작을위해그림 2와같이주기적인회로모델에서 π-형 CRLH-TL 단일회로를추출할수있다. T-형회로는다단의직렬구조설계로인해길이가길어지는 그림 3은 CRLH-TL 공진기설계를위한소자들이다. 공진기를그림 2의회로에맞게설계하기위해, 회로의소자값 L R, C L 은인터디지틀선로를사용하여얻을수가있다. 이는인터디지틀선로의자계결합과전계결합두가지를한번에취하는방법을선택한다. 또한병렬커패시턴스와병렬인덕턴스값은접지스터브를사용하여동시에추출한다. 이때접지스터브와인터디지틀선로는상호커플링을통하여결합하게된다. 이때, 결합한전체구조의길이를 CRLH-TL 조건 ( 전체구조 <<λ/4) 에맞춰야한다. 이러한조건하에메타재질구조의파장방향의길이는 4~5mm가되어야한다. 먼저, 하한주파수 f L 에따른 L L, C L 를얻어야한다. 소자값 C L 은인터디지틀라인의커패시턴스이다. CRLH-TL의조건에맞추어보았을때 C L 을얻을수있는인터디지털단의길이는 0~2mm의길이의제한이있다. 인터디지틀라인의핑거개수는핑거사이의간격까지고려하여 12~14개를선 단락개방간극링구조와인터디지틀선로의결합형소형초광대역여파기설계 1707
3 전기학회논문지 62 권 12 호 2013 년 12 월 정하였다. 이때인터디지틀결합선로의캐패시턴스공식에의거하여초기 C L 값을조정할수있다. 또한, L L 값은주어진 C L 값과하한주파수 f L 을기준으로하여접지스터브의길이와폭을조정하여하한주파수에맞는 L L 을얻어낸다. 그리고, 상한주파수 f R 에따른 L R, C R 를얻어야한다. C R 은인터디지틀의결합단및스터브선로의평판과접지면의커패시턴스값을말한다. 또한, L R 은인터디지틀선로의핑거개수에따른개방형스터브의인덕턱스값이라할수있다. 각각의 L R, C R, L L, C L 값을구하는식은식 (2)~(4) 와같다. 여기서식 (2) 는인터디지틀라인의커패시턴스, 식 (3) 은인터디지틀라인및스터브의인덕턴스, 식 (4) 는소자들의구조에따른병렬커패시턴스식이다. 식 (2) 의변수인 W는인터디지틀핑거의폭, S는핑거사이의간격이며식 (3) 의변수 W는스터브의폭이다 [9]. tan (2) 어진공진구조를보여주고있다. 서론에서언급되었던 CRLH-TL의횡축방향길이가길어지는단점 [5] 을개선하기위하여단락개방간극링구조와인터디지틀선로와의강한결합을통하여구조를개선할수있다. 단락개방간극링구조의아랫단부분은단락스터브역할과동시에간극으로인한커플링역할을같이수행하게된다. 또한, 단락개방간극링구조의윗단은급전부및스터브사이의직접적인전류경로를형성한다. 이는인터디지틀라인과단락개방간극링구조와의전체적인커플링을유도한다. 또한여파기전체에다중공진을유도한다. 즉. 단락개방간극링의윗단의다단임피던스변화공진설계로추가적인공진을유도할수있는집적구조라는장점이있다. 따라서추가적인임피던스매칭라인을및커플링을통하여 CRLH-TL의반사손실및여파기의반사손실및통과특성을개선할수있다. 그림 5는설계된 CRLH-TL공진기의전류흐름을보여준다. ln (3) ln (4) 표 1 CRLH-TL의회로소자값 Table 1 Component value of the circuit of CRLH-TL C L(pF) L L(nH) C R(pF) L R(nH) CRLH-TL 이론이적용된초소형공진기설계 그림 5 설계된 CRLH-TL 공진기의전류흐름도 5 Current flow of the designed CRLH-TL resonator 설계된공진기의크기는 4.35mm x 9.05mm로매우작으며, 관내파장 /10.3 의크기로축소할수있었다. 또한, 기존 CRLH-TL에비해파장방향직교축의길이가 1.44배감소되었다. 그림 4 기존 CRLH-TL 공진구조와제안된단락개방간극링구조와인터디지틀선로의커플링결합 CRLH-TL 공진구조 4 Existing resonator applied the CRLH-TL and proposed structure 그림 4는 2.1의설계이론에따라설계된두개의공진기를보여주고있다. 접지스터브와인터디지틀라인의단순결합으로이뤄진기존의 CRLH-TL공진기와새로운단락개방간극링구조와인터디지틀라인과의결합을통하여얻 2.3 CRLH-TL 공진기기반의 UWB 여파기설계앞서설계한 CRLH-TL 공진기를여파기에적용하기위하여공진기양옆단에급전부를연결하여 UWB 여파기를설계한다. 먼저, 공진기에연결되는급전부와단락개방간극링윗단의결합은앞선 2.2에서보였듯이추가적인공진을유도할수있는일종의다단임피던스라인으로생각할수있다 [10]. 그림 6. 7에서보듯급전부과단락개방간극링의윗단이결합된다단임피던스구조는 7.5GHz에서낮은반사손실특성을가지는것을확인할수있다. 1708
4 Trans. KIEE. Vol. 62, No. 12, DEC, 2013 그림 6 단락개방간극링의윗단과급전부가연결된다단임피던스구조 6 Stepped impedance line connected to the top of the SOGR 0 S-Parameter [db] Measured S 11 Measured S 21 Simulated S Simulated S Frequency [GHz] 그림 9 구현된 UWB 여파기의 S- 파라미터그래프 9 S-parameters of the realized UWB Filter -5 S-Parameter (db) S11 S Frequency (GHz) 그림 7 단락개방간극링의윗단과피드단이연결된다단임피던스구조의 S-파라미터 7 S-parameters of the stepped impedance line connected to the top of the SOGR 위에서다단임피던스구조를앞서제안된 CRLH-TL공진기와결합하여 UWB에서동작하는여파기를설계하였다. 이는 CRLH-TL과다단임피던스의병렬접합구조인데, 공진기구조가 UWB대역의중심주파수의파장길이보다매우작은길이이기때문에병렬접합이효과적으로적용이되었다. 설계및제작된여파기와삽입 / 반사손실특성도는그림 8, 9, 10에기술하였다. 그림 10 제작된 UWB 여파기 10 Manufactured UWB Filter 설계된여파기는 UWB 100% 이상의통과대역폭과 UWB 인 3~10.5GHz에서 1dB이하의삽입손실을가지며, 전체적인크기는 18mmx15mm의매우작은크기를가진다. 2.4 CRLH-TL 공진기적용 UWB 여파기의메타재질특성관찰 그림 11 제안된 UWB 여파기의분산특성도 11 Dispersion diagram of proposed UWB filter 그림 8 다단임피던스구조와제안된 CRLH-TL공진기가결합된 UWB 여파기의설계단면부 8 UWB Filter comprising the stepped impedance line combined with the proposed CRLH-TL resonator 그림 11은설계된공진구조에서얻어진분산특성도이다. 분산특성도는전자기시뮬레이션으로측정된데이터를근간으로 ABCD 네트워크파라미터를추출하여얻어내었다. 분산특성도를보면설계된여파기는중심주파수 5.9GHz 단락개방간극링구조와인터디지틀선로의결합형소형초광대역여파기설계 1709
5 전기학회논문지 62 권 12 호 2013 년 12 월 를기준으로중심주파수보다낮은주파수영역에서위상상수가음의값을가지는왼손진행법칙의선로 (LH-TL) 의특성을보인다. 그리고높은주파수영역에서는위상상수가양의값을가지는오른손진행법칙의선로 (RH-TL) 의특성을보이는것을알수있다. 또한왼손진행법칙의선로 (LH-TL) 와오른손진행법칙의선로 (RH-TL) 의정합과정에서생겨난중간경계지점에서위상상수가 0이된다. 그림 12-14의전자기시뮬레이션결과를기술하였다. 그림 12를살펴보면 LH영역의주파수에서는음의위상상수로파의움직임이진행파와반대방향으로움직이는것을살펴볼수있다. 그림 13에서는흡사진행파가정재파처럼움직이는것과같은현상을지켜볼수있는데, 이는왼손진행법칙의선로 (LH-TL) 와오른손진행법칙의선로 (RH-TL) 의정합과정에서생겨난 0차공진지점에서나타나는파의움직임이다. 그림 14에서는일반적인전자기파의움직임을볼수있다. 나는것이라할수있다. 이러한파의움직임의관찰을통하여실제 CRLH-TL이제대로동작하고있음을확인할수있다. 또한실제로여파 기에적용된공진기가단순한다중모드공진이아닌 CRLH-TL로써동작하게됨을확인할수있다. 그림 14 RH-영역에서의파의움직임 14 Motion of the traveling wave in the RH-region 3. 결론 그림 12 LH- 영역에서의진행파의움직임 12 Motion of the traveling wave in the LH-Region 본논문에서는제시된단락개방간극링 (SOGR) 구조와인터디지틀선로가결합된 CRLH-TL 공진특성을사용하여 UWB에서적용가능한소형여파기를제안하였다. 설계된 CRLH-TL공진기의크기는 4.35mm x 9.05mm로매우작으며, 관내파장 /10.3 의크기로축소할수있었다. 또한, 기존 CRLH-TL에비해파장방향직교축의길이가 1.44배감소되었다. 설계된 UWB여파기는 100% 이상의통과대역폭을가지며, 1dB이하의삽입손실과우수한반사손실특성을가진다. 또한, 설계된여파기의전체적인크기는 18mmx15mm로매우작은크기를가진다. 이는 UWB 시스템에서높은통신품질을보장할것으로기대되며, 여파기뿐만아니라집적회로혹은다양한 RF 소자의소형화에기여를할것으로전망된다. 감사의글본논문은 2012년도정부 ( 교육과학기술부 ) 의재원으로한국연구재단의기초연구사업지원을받아수행된연구임 (2012R1A1A ) References 그림 13 LH-영역과 RH-영역이합쳐지는지점에서파의움직임 13 Motion of the wave at the point where the LH-region added to the RH-region [1] H. Wang, L. Zhu and W. Menzel, Ultra-Wideband Bandpass Filter with Hybrid Microstrip/CPW Structure, IEEE Microwave And Wireless Component Letters, vol. 15, no. 12, pp , December [2] C.-L. Hsu, F.-C. Hsu, and J.-T. Kuo, Microstrip 1710
6 Trans. KIEE. Vol. 62, No. 12, DEC, 2013 Bandpass Filters for Ultra-Wideband(UWB) Wireless Communications, IEEE MTT-S Intl. Dig., pp , June [3] H. Ishida, and K. Araki, Design and Analysis of UWB Bandpass Filter with Ring Filter, IEEE MTT-S Intl. Dig., vol. 3, pp , June [4] Christophe Caloz, Tatsuo Itoh, Electromagnetic Metamaterials : Transmission Line Theory and Microwave Applicaions, WILEY-INTERSCIENCE, John-Wiley & Sons Inc., Hobokin, NJ [5] Sungtek Kahng, and Jeongho Ju, Design of the UWB BandPass Filter based on the 1 Cell of Microstrip CRLH-TL, International Conference Microwave and Millimeter Wave Technology, 2008, vol. 1, pp , April [6] J. Ju, S. Kahng, A compact UWB bandpass filter using a center-tapped composite right/left-handed transmission-line zeroth-order resonator Microwave and Optical Technology Letters, Volume 53, Issue 9, pages , September 2011 [7] S. Kahng and Dongjin Lim, A Center-Tapped CRLH ZOR UWB Bandpass Filter with Improved Stopband, Microwave Journal, vol. 55, no. 6, pp , June 2012 [8] Boram Lee, Sungtek Kahng Compact UWB Bandpass Filter as Cascaded Center-Tapped CRLH Transmission-Line ZORs for Improved Stopband Journal of Electrical Engineering & Technology, vol.8, no.2, pp , August 2013 [9] K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, Artech House, Inc., Norwood, MA [10] David M. Pozar, Microwave Engineering Third Edition, John Wiley & Sons, Inc., Wiley publishing company 저자소개 오승훈 ( 吳承勳 ) 2013년중앙대학교전자전기공학부졸업, 2013년 ~ 현재중앙대학교전자전기공학부석사과정 [ 주관심분야 ] 초고주파부품설계, 안테나설계 김군태 ( 金君泰 ) 2008년서경대학교정보통신공학과졸업, 2010년중앙대학교전자전기공학부공학석사 2012년중앙대학교전자전기공학부박사수료 [ 주관심분야 ] 초고주파부품설계, 안테나설계, 등가회로모델링, 최적화설계강성인 ( 姜星仁 ) 2003년창원대학교전기공학과졸업, 2010년중앙대학교미디어통신공학석사 2012년중앙대학교전자전기공학부박사과정 [ 주관심분야 ] RF, 무선통신, Radar, 무선충전이정혁 ( 李灯赫 ) 2010년동양미래대학교정보전자과졸업, 2013년중앙대학교전자전기공학부졸업, 2013년 ~ 현재중앙대학교전자전기공학부석사과정 [ 주관심분야 ] 최적화설계, FEM, MFC 한준희 ( 韓俊熙 ) 2013년중앙대학교전자전기공학부졸업, 2013년 ~ 현재중앙대학교전자전기공학부석사과정 [ 주관심분야 ] 초고주파부품설계, 안테나설계김형석 ( 金炯碩 ) 1985년서울대학교전기공학공학사, 1987년서울대학교전기공학공학석사, 1990년서울대학교전기공학공학박사, 1990~2002년순천향대학교정보기술공학부교수, 1997~1998년 R.P.I ECSE, USA 방문교수, 2002년~현재중앙대학교전자전기공학부교수 [ 주관심분야 ] 전자파수치해석, 무선통신부품해석및설계, 최적설계기법연구, 전력설비모니터링시스템, SoC 응용회로, EMI/EMC, RFID 응용기술 단락개방간극링구조와인터디지틀선로의결합형소형초광대역여파기설계 1711
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