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THE JOURNAL OF KOREAN INSTITUTE OF ELETROMAGNETI ENGINEERING AND SIENE. 16 Aug.; 7(8), 71 78. http://dx.doi.org/1.5515/kjkiees.16.7.8.71 ISSN 16-3133 (Print) ISSN 88-6X (Online) -FGPW Ultra-Wideand Microstrip-to-Finite Ground oplanar Waveguide Transition for Millimeter-Wave Systems 김영곤 김홍락 정배호 김강욱 Young-Gon Kim Hong-Rak Kim Bae-Ho Jung Kang Wook Kim* 요약 -FGPW.., EM 3.3 %. 9 4 GHz 1 db 1 db. Astract A new design for an ultra-wideand microstrip-to-fgpw(finite Ground oplanar Waveguide) transition is presented. The proposed transition provides the electric field and impedance matching etween adjacent transmission lines y ground shaping. The transition is designed on the analytical expressions of whole transitional structure. onformal mapping is applied to otain the characteristic impedance of FGPW with ottom aperture within 3.3 % accuracy as compared with the EM-simulation results. As design example, the faricated transition in ack-to-ack configuration provides insertion loss less than 1 db per transition and return loss etter than 1 db for frequencies from 9 GHz to over 4 GHz. Key words: onformal Mapping, Finite Ground oplanar Waveguide(FGPW), Klopfenstein Taper, Microstrip, Transition. 서론 PW(oplanar waveguide), [1].,., [1]. PW,, PW(FGPW) [] [4]. PW,, LIG / (Seeker & EO/IR R & D La, LIG Nex1) * (School of Electronics Engineering, Kyoungpook National University) Manuscript received April 7, 16 ; Revised June 4, 16 ; Accepted August 9, 16. (ID No. 1647-5) orresponding Author: Young-Gon Kim, Kang Wook Kim (e-mail: younggon.kim@lignex1.com, kang_kim@ee.knu.ac.kr) c opyright The Korean Institute of Electromagnetic Engineering and Science. All Rights Reserved. 71

THE JOURNAL OF KOREAN INSTITUTE OF ELETROMAGNETI ENGINEERING AND SIENE. vol. 7, no. 8, Aug. 16.., PW [].,,, FGPW-. - FGPW [] [4]. D 4 GHz []. W-and -FGPW [3], 36.6 GHz PW- [4].,., 1. (A-A') (B-B'). (B-B' -') FGPW(D-D')., A-A', B-B'. (B-B' -'). FGPW.,. -FGPW. B A MSL A B via D Transition B' A' D A B PW D' ' D. 마이크로스트립 -PW 전이구조해석 -PW Schwarz-hristoffel.,. w, g w. s. A' B' ' D' 그림 1. -FGPW, Fig. 1. Perspective view of microstrip-to-fgpw transition and top and ottom view. A' B' ' D' 그림. 3 Fig.. onfiguration of the transitional structure: the whole structure, divided structure for analysis. 7

-FGPW (w),. (g),. (w ),,. (s), (s). (w), (g), (w ), (h) (s). BPW(onductor Backed PW), 3D.. BPW. PE,, TEM. -1 영역 의해석 I 1(ε r =1) PW [5]. PW, 3 (magnetic wall) [5]. I ( 1 ) (1) (), K 1, k. O w/ w/+g w / A B ε 그림 3. I Fig. 3. onformal mapping tranformation for Region I. K( k) 1 = e K( k ') ( w g ) w w 1 - ( + / ) k =, k ' = 1- k ( w + g ) 1 - ( w / w ) 1 [6],[7]. 1 1+ k ln( ),.5 k 1 K ( k ) p 1- k = { K ( k ') p, k.5 1 + k ' ln( ) 1 - k ' (3) - 영역 의해석. 4. (4) (5) w-plane z-plane [8]. sn (the Jacoi elliptic function). K(1/ x ) 1 x = sn( w, ) w x K(1/ x ) w = K(1/ x ') h G ε ε r -w / H I J F s h O w/ A E B w-planed w/+g w / ε ε r z-plane -x c -x -1 -s'' -w'' w'' s'' 1 x x c F G H I J O A B D E 그림 4. Fig. 4. onformal mapping tranformation for Region. (1) () (4) (5) 73

THE JOURNAL OF KOREAN INSTITUTE OF ELETROMAGNETI ENGINEERING AND SIENE. vol. 7, no. 8, Aug. 16. w-plane z-plane. K(1/ x ) w 1 A: w'' = sn(, ) w x (6) K(1/ x ) w 1 B: s '' = sn( ( + g), ) w x K(1/ x ) 1 E: xc = sn( ( s / + jh), ) w x (7) (8) z-plane I, (9) (1). K( k1) = e e r K( k ') 1 (9) 그림 5. Fig. 5. onformal mapping tranformation for Region. w'' 1 - ( s ''/ x ) k k k c 1 =, 1 ' = 1-1 s '' 1 - ( w''/ xc ) -3 영역 의해석 (1) 5.., (11) 5 HA. [9]. s h w s h -, if > - w' p p = { w, elsewhere. (11) HA GB ( frineg1) GB PW ( frineg ). HA GB (1). w' fringe1= e h (1) GB ( frringe ) I, PW. 5, (13). fringe1 fringe 3= fringe1 + fringe (13) -4 전이구조특성임피던스및유효유전율 TEM,, (14). e eff ' ' K( k) / K( k ) + e rk( k1) / K( k1 ) + 3 / = ' ' K( k) / K( k ) + K( k1) / K( k1 ) + 3 / (14) 74

-FGPW Fig. 6. haracteristic impedance of the transition as a function of s/h(cal: calculated, sim: simulated). w=.889 mm, g=.54 mm and h=.54 mm. Fig. 6. (cal:, sim: ) w=.889 mm, g=.54 mm, h=.54 mm.,. Z = 1 6p [ ( ) / ( ) ( ) / ( ) / ] ' ' e K k K k eff + K k1 K k1 + 3 (15) PW., Microwave studio ST EM. 6. EM 8 GHz, 1 GHz.3 %. (s),. EM 3.3 %( 1.9 %),.,. RT/Duroid 588.54 mm(ε r =.) 5.76 mm,.38 mm,.76 mm PW 98. 5 98 PW. Klopfenstein, S 11 pole 9 GHz 7.6 mm [1]. Klopfenstein λ/, (Γ m ).. PW, Klopfenstein 5 98. 7 7.6 mm.13 mm 1.5 mm Klpofenstein.,.,. slot-line coupled. 초광대역전이구조설계및측정결과 PW -PW. PW 그림 7. Fig. 7. The ottom ground shape of designed transition: Top (red dots) and ottom plane(lack solid lines). 75

THE JOURNAL OF KOREAN INSTITUTE OF ELETROMAGNETI ENGINEERING AND SIENE. vol. 7, no. 8, Aug. 16. 할 수 있으며, 간단한 rectangular 패치의 경우, 공진 주파 수는 다음 식 (16)으로 표현된다. [11] m n = [( ) + ( ) ] lg e r wg g lt lcpw wm wt wcpw s 5.8 7.6 5.8.76.76.76.38 (16) 여기서, c는 빛 속도이며, w 는 선로 두께(w =.76 mm), l 는 비아 사이의 길이, m과 n은 모드의 index를 나타낸다. 전이구조가 방사체가 되는 것을 막기 위해, f 공진 주파 수가 고려되어져야 한다. 본 논문에서는 4 GHz까지의 광대역 성능을 나타내기 위해 전이구조에 4개의 비아 (1.85 mm 간격)를 이용하였다. 그림 8에 제작된 전이구조의 그림을 도시하였으며, 삽 입손실 및 반사손실의 측정을 위하여 ack-to-ack 구조로 제작하였다. 그림 9에는 측정된 전이구조 및 시뮬레이션 결과를 비교하였다. 제작된 전이구조는 9 4 GHz 이상 의 대역에서 전이구조 당 삽입손실 1 db 이하 및 반사손 실 1 db 이상을 만족하였다. 유전율이 낮은 기판을 이용 하여 높은 PW 임피던스(98옴)와 마이크로스트립 선로 (5옴)의 정합으로 인해 9 GHz 부근의 반사손실이 비교적 작으며, 이는 비매칭 정합의 전이구조 특성이라 할 수 있다. 5 GHz 부근의 측정상의 반사손실이 작은 부 g g 1 전이구조 크기 단위 lm 마이크로스트립 전이구조 성능 비교 표. -FGPW Tale. Performance comparison of microstrip-to-fgpw transitions. 최대 반사손실 설계 수식 참고문헌 동작 주파수 삽입손실 유무 [] D 4 GHz 1.5 db 1 db 무 [3] 85 11 GHz 1.5 db 17 db 무 [4] D 36 GHz 1.5 db 1 db 무 This 9 over 1 db 1 db 유 work 4 GHz S1 S-parameter [db] f mn c 마이크로스트립 표 1. -PW ( : mm) Tale 1. Summary of the transition dimenstions(unit: mm). -1 S11 - -3 Simulated Simulated Measured Measured -4 5 1 15 5 3 35 4 Frequency [GHz] 윗면 Top 아랫면 Bottom 제작된 전이구조의 모습 그림 8. Fig. 8. The faricated microstrip-to-pw transition. 76 제작된 전이구조 시뮬레이션 및 측정 결과 그림 9. Fig. 9. Insertion loss and return loss of the transition: measured(thick solid lines) versus simulated(dot lines) values. 분은 기판 가공상의 오차 및 측정 커넥터와 마이크로스 트립 선로의 부착 상에서 오는 비매칭 정도로 예상된다. 표 에 여러 참고 문헌과의 전이구조 성능을 비교하였 다. 낮은 유전율의 가판을 이용하였고, PW의 임피던스 를 높게하여 임피던스 변환기로써 전이구조를 설계한 점 을 고려했을 때, 본 논문에서 제시한 전이구조는 낮은 삽 입 손실 및 초광대역의 특성을 가지고 있음을 확인하였 다. 특히 전이구조의 설계 수식을 제시하여 설계의 명확

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