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1 韓國電磁波學會論文誌第 18 卷第 11 號 2007 年 11 月論文 이중기판결함접지구조를이용한비대칭윌킨슨전력분배기 An Unequal Wilkinson Power Divider Using Defected Ground Structure in Double Layered Substrate 임종식 구재진 오성민 정용채 * 안달 Jongsik Lim Jae-Jin Koo Seongmin Oh Yongchae Jeong* Dal Ahn 요약 종래의 DGS를이용한초고주파회로의메탈패키징 (metal packaging) 시존재했던 DGS의접지면접촉문제를해결하고자, 본논문에서는이중기판결함접지구조구조를제안하고, 이를 1:4 비대칭전력분배기에적용한응용예를제시한다. 이중기판에구현된사각형 DGS는종래와같이마이크로스트립선로의특성임피던스를표준형선로보다크게증가시킨다. 이중기판 DGS 구조를형성하기위하여제2유전체기판이 DGS가구현된기판면의바닥접지면에접합된다. 따라서제2유전체기판이메탈패키지바닥면에장착되므로, DGS가직접패키지접촉되는것을막을수있다. 초고주파회로응용예를보이기위해, 이중기판 DGS를이용하여패키지접지문제를해결한 1:4 비대칭전력분배기의설계및측정결과가제시되는데, 시뮬레이션과측정결과에있어서잘일치하는특성을보인다. Abstract A novel 1:4 unequal wilkinson power divider using rectangular-shaped defected ground structure(dgs) in double layered substrate is proposed for removing the ground problem of DGS in packaging. Rectangular-shaped DGS produces the transmission line having much higher characteristic impedance than standard microstrip line. The proposed unequal divider is composed of DGS and double layered substrate in order to be free from the ground problem of DGS patterns in packaging in metal housings. The second substrate is attached to the first substrate which contains DGS pattern on its ground plane at the bottom side to form the double layered substrate. In order to show the validity of the proposed DGS in the double layered substrate, a 1:4 unequal power divider is designed and measured. The predicted and measured performances are shown with an excellent agreement between them. Key words : Unequal Power Divider, DGS, Double Layered Substrate Ⅰ. 서론무선신호를두경로이상으로분배해주는윌킨슨전력분배기는 1960년에최초로그구조가소개된이래각종무선통신용회로및시스템을구성하는데있어서신호의분배와결합을위해가장널리 사용되는초고주파회로가운데하나이다 [1]. 전송선로소자로구성한윌킨슨전력분배기는기본적으로수동회로이므로가역성을가져서결합기로도사용가능한데, 기본형윌킨슨전력분배기에서는입력단자로입사된신호가두출력단자에같은크기의전력으로분배되어나타난다. 그런데만약 1:N의전 이논문은순천향대학교차세대 BIT 무선부품지역혁신센터에의하여지원된연구결과입니다. 순천향대학교전기통신공학과 (Department of Electrical and Communication Engineering, Soonchunhyang University) * 전북대학교전자정보공학부 (Department of Electronic and Information Engineering, Chonbuk National University) 논문번호 : 수정완료일자 : 2007 년 11 월 6 일 1291

2 韓國電磁波學會論文誌第 18 卷第 11 號 2007 年 11 月 력분배비에서 N>1인비대칭비율의경우에는, 어느한쪽경로전송선로의특성임피던스가 1:1 구조의표준값인 70.7 Ω보다높은값이요구된다 [2]. 예를들어간단한예인 N=2나 N=3인경우에는각각 103 Ω 과 132 Ω의높은특성임피던스를갖는전송선로가어느한경로에요구된다. 그러나표준형마이크로스트립선로의경우, 특별한문제없이구현이가능한임피던스의한계가 100~120 Ω 정도라는문제가심각하게제기될수있다 [3]. 더구나비대칭분배비율이 4 이상이라면 158 Ω 이상의임피던스가필요하므로더욱문제가심각해진다. 이러한문제를해결하기위한방편으로결함접지구조 (Defected Ground Structure: DGS) 를이용하여등가의인덕턴스를크게증가시켜서높은특성임피던스를갖는전송선로를구현하는방법이제시되었다 [4]~[6]. 결함접지구조는전송선로의접지면에특정한기하학적패턴으로구현되는데, 등가의인덕턴스와캐패시턴스가전송선로에부가되어전송선로의특성임피던스를크게높이는데유용한수단이다. DGS는또한표준형전송선로의전송특성에는보이지않는특정주파수차단특성이있어서저역통과여파기와유사한전송특성을얻고자할때에도많이사용된다. DGS는마이크로스트립전송선로에구현된종래의 PBG(Photonic Bandgap) 구조에비하여 DGS 선로단일소자 (unit element) 의정의와등가회로추출이매우용이하여무선회로설계시응용이매우용이한구조이다. 따라서 DGS는무선회로의소형화나성능개선에자주응용되는데, DGS 를활용하여새로운형태의무선회로를설계하거나더나아가서는종래에구현이불가능했던무선회로들을일부구현가능케하는등의장점이있다 [4]~[9]. 그러나 DGS가우수한회로응용능력이있음에도불구하고접지면을식각해내는구조로인하여금속하우징 (housing) 에장착할경우에바닥접지면이하우징면에접합되어 DGS의장점을살릴수없다는문제가있었다. 따라서패키징 (packaging) 문제, 즉 DGS의접지면문제를해결하는것이그간풀어야할과제로인식되고있었다. 본논문에서다루고있는주제인전력분배기에있어서도, 종래의 DGS 를이용한윌킨슨전력분배기의경우, 우수한비대칭분배특성에도불구하고금속하우징에패키징되었 을경우, 접지면에삽입된 DGS의구조가하우징과접합하게되는문제점이있었다. 따라서본논문에서는이문제를해결하기위해서, 바닥면에식각된 DGS 패턴이보이지않도록이중기판을이용하여전력분배기를설계한다. 이를통하여그간많이지적되어왔던패키징과정에서발생하는 DGS의접지면문제를해결하면서높은임피던스를갖는선로를구현하고, 이를활용하여 DGS 의접지면문제가해결된고비율의비대칭윌킨슨전력분배기를구현하는방법을제안하고자한다. Ⅱ. 이중기판 DGS 를지닌마이크로스트립선로 그림 1은종래의 DGS 선로및제안하는구조즉, 하우징에서 DGS의접지면문제를해결할수있는이중구조 DGS 마이크로스트립선로의옆단면도를보여주고있다. 먼저그림 1(a) 는종래의 DGS를지닌마이크로스트립선로의옆단면도이다. 이그림에서알수있듯이, 종래에는바닥접지면이노출되어있었으므로, 만약에금속하우징에삽입될때유전체면이바로하우징면에접합하게되므로 DGS의전기적특성이사라지는문제가있었다. 이런문제를해결하기위하여본논문에서는그림 1(b) 와같은이중기판 DGS 전송선로를제안한다. 제안하는구조를살펴보면제2유전체기판이 DGS 면에그대로접합된다. 이때제2유전체기판상면의금속면은그림 1(c) 와같이완전히제거되어도좋고, 그림 1(b) 와같이 DGS 면적보다더넓은면적 ("A" 로표시 ) 에대해서만선택적으로제거해도된다. 어떤경우든지제1기판의바닥접지금속면과제2기판의바닥접지금속면은서로동일한전위를갖는접지면을형성해야하므로다수의 via-hole을통하여연결시켜줘야한다. 이와같은구조를취하면제1유전체기판에식각된 DGS 패턴이전체적인 PCB 바닥면에서보이지않으므로금속하우징에장착할수있는장점이있다. 따라서그간많이지적되어왔던패키징문제가없으면서도 DGS의장점을이용하여높은임피던스를갖는선로를구현하고, 이를활용하여고비율의비대칭윌킨슨전력분배기를구현할수있다. 1292

3 이중기판결함접지구조를이용한비대칭윌킨슨전력분배기 DGS substrate Microstrip Line lower (ground) plane (a) DGS 1st substrate Microstrip Line 1st substrate lower (ground) plane A 2nd substrate upper plane 2nd substrate (b) Via hole 2nd substrate lower (ground) plane 그림 2. 일반적인 1:N 비대칭윌킨슨전력분배기회로구조 Fig. 2. Topology of 1:N unequal Wilkinson power dividers. (c) 그림 1. 마이크로스트립전송선로와결함접지구조의옆단면구조 (a) 종래의구조, (b) 제안하는이중기판결함접지구조, (c) 단순화한이중기판결함접지구조 Fig. 1. Side views of microstrip line and DGS (a) Conventional structure, (b) proposed structure using double-layered substrate, (c) simplified side view for (b). Ⅲ. 이중기판 DGS 를응용한비대칭전력분배기의설계 그림 2는기본적인윌킨슨전력분배기의기본적인회로를보여주고있다. 만약에전력분배비가 1:N (N>1) 의비대칭이라면특성임피던스 Z 3 는매우큰값이요구된다. 그러나가장널리사용되는초고주파용전송선로인마이크로스트립선로는구현가능한임피던스한계값에제한이있으므로, N이클수록구현가능성의문제가심각하게된다. 이것을표 1 에서확인할수있는데, 표 1은비대칭비율 (N) 을 1 에서 6까지바꾸었을때임피던스값의변화를보여주고있다. 가령 N=4의경우에 Z 3=158 Ω인데, 이값은일반적인마이크로스트립선로의구현한계보다훨씬높은값이다. 이렇게 150 Ω 이상의높은임피던스를갖는마이크로스트립선로를구현하기위하여다양한형태의 DGS를삽입할수있다. 본논문에서는이중기판결 표 1. 1:N 비대칭윌킨슨전력분배기의분배비에따른특성임피던스 Table 1. The characteristic impedance of 1:N unequal Wilkinson power divider. N Z 2[Ω] Z 3[Ω] R int[ω] R 2[Ω] R 3[Ω] 함접지구조를지닌전송선로를이용하여 1:4의비대칭윌킨슨전력분배기를구현하기위하여구조가간단하고등가의부가인덕턴스가큰사각형형태의 DGS를선택하였다. 사각형 DGS는등가의인덕턴스가큰반면상대적으로등가의캐패시턴스가작아종래의미앤더 DGS보다높은임피던스구현에더유리하다. 그림 3은이중기판구조에서의사각형 DGS와마이크로스트립선로를위에서내려다본그림으로보여주고있다. 비록그림 3에서는이중기판구조가보이지않으나, DGS는제1유전체기판의바닥접지면에구현된다. 본논문에서는유전율이 2.2이고두께가 31 mils인기판을사용하여이중기판 DGS 선로를설계하고, 이를이용하여 1:4 비대칭전력분배기를설계한다. 먼저 W 1 과 W 2 는제1유전체기판의접지면에있는사각형 DGS의크기이고, W M 은최상면마이크로스트립선로의폭이다. 이사각형 DGS 1293

4 韓國電磁波學會論文誌第 18 卷第 11 號 2007 年 11 月 그림 Ω 마이크로스트립선로를위한사각형형태의이중기판 DGS Fig. 3. Rectangular-shaped double layered DGS for 158 Ω microstrip line. 그림 5. 이중기판 DGS 선로의특성임피던스를계산하기위한전송선로모델 Fig. 5. Transmission line model to calculate the characteristic impedance of double layered DGS line. 도록조절되었다. 이제그림 5에서처럼 DGS 선로의특성임피던스를편의상 Z DGS 이라하자. 그러면중심주파수에서전기적길이 (θ) 는 π/2인데, 이때반사계수 (Γ) 의크기는최대이며 S 11 과 Γ는식 (1) 과같은관계가있다. 일단 Γ의크기가결정되면식 (2) 에의하여한쪽이단락된상태에서 DGS 선로의입력 그림 4. 그림 3 의 DGS 선로의 EM 시뮬레이션 S- parameter Fig. 4. EM Simulation S-parameter of the DGS line shown in Fig. 3. 가마이크로스트립선로의아래접지면에식각될때등가의인덕턴스가크게증가한다. 그러나등가의인덕턴스의증가에비하여추가되는캐패시턴스는극히작은값이된다. 따라서결과적으로특성임피던스가크게증가한것으로나타나게된다. 그림 4는 W 1 =30 mm, W 2 =5 mm, W M =0.26 mm로취했을때, 이중기판 DSG 선로에대한 EM 시뮬레이션특성을보여준다. 시뮬레이션특성에서나타난 S 11 값이 db인데, 이로부터그림 3의 DGS 마이크로스트립선로가 158 Ω의특성임피던스를갖는다는사실을알수있다. DGS 마이크로스트립선로의특성임피던스를구하는과정을그림 5를이용하여설명할수있다. 그림 5는 DGS 마이크로스트립선로의특성임피던스를계산하기위한단순화한전송선로모델을나타낸다. 먼저그림 3의전송특성에의하면 DGS 선로의입력측반사특성 (S 11 ) 은중심주파수에서 db이다. 선로의길이는중심주파수에서 λ/4가되 임피던스가계산된다. 따라서식 (3) 에의하여 Z DGS 가결정되는데, 만약에이 DGS 선로가비대칭전력분배기에사용되면 Z DGS 값이곧그림 2에서의 Z 3 가된다. 이와같이이중기판결함접지구조를지닌마이크로스트립전송선로의높은임피던스값을이용하여, DGS의접지문제가해결된다양한분배비율을갖는비대칭윌킨슨전력분배기를설계할수있다. 본논문에서는한예로 1:4 비대칭분배기를제작, 측정하였는데, 그결과를다음장에제시하고자한다. S 11 [db]=20 log Γ (1) Z in =Z 0 1+ Γ 1- Γ (2) Z 3 = Z in Z 0 =Z 0 1+ Γ 1- Γ (3) Ⅳ. 이중기판 DGS 를응용한비대칭분배기의제작및측정 위와같이제안된사각형구조의이중기판 DGS 를이용하여 1:4 비대칭전력분배기를설계및제작하고, 그성능을측정하였다. 그림 6은본논문에서설계, 제작한 1:4 비대칭전력분배기의레이아웃인 1294

5 이중기판결함접지구조를이용한비대칭윌킨슨전력분배기 그림 6. 이중기판 DGS 가삽입된 1:4 비대칭전력분배기레이아웃 Fig. 6. Layout of the proposed 1:4 unequal power divider with DGS and double layered substrate. 데, 사각형형태의 DGS가이중기판의사이즉, 제 1 유전체기판의바닥접지면에표시되어있다. 회로패턴주변의원들은다수의 via-hole을가리킨다. 한편, 이그림에는제2유전체기판의구조는별도로표시되어있지않으나, 실제회로구현시또하나의유전체기판을아래에중첩시켜이중기판구조를형성해야한다. 두출력측경로에있는전송선로의특성임피던스는앞에서보인그림 2의스케매틱회로의 R 2 와 R 3 를측정에용이하도록 λ/4 선로로변환한것이다. 1:4 분배비를위한이상적인격리저항 (R int ) 값은 125 Ω이다. 하지만실제로는임의의모든저항값에대하여칩저항이가용할수있는것이아니므로, 본논문의실험에서는상용으로쓰이는저항값중에서 125 Ω에가장가까운 130 Ω을사용하였다. 그림 7은제안하는이중기판 DGS를이용하여설계한 1:4 비대칭전력분배기의 3차원구조를나타내는그림이다. 두기판이서로맞닿아이중기판구조를형성하고있음을이그림을통하여알수있다. 그림 8(a) 와 (b) 는제안한전력분배기를구현하기위하여, 제1, 제2유전체기판을제작하여각면의사진을보인것이다. 제1유전체기판의바닥접지면에 DGS가구현되어있으며, 동시에제2유전체기판의상면에 DGS보다넓은면적의영역에유전체가 그림 7. 이중기판 DGS 를응용한 1:4 비대칭전력분배기의 3 차원구조 Fig. 7. Three-dimensional structure of the 1:4 divider using DGS and double layered substrate. 노출되어있다. 물론상기의그림 1(c) 를통하여이미설명하였듯이, 제2유전체기판의상면금속면은모두제거되어도된다. 이그림에서알수있듯이두유전체기판의바닥면은동일한접지면이되어야하므로회로패턴사이의빈공간에다수의 via-hole을연결하였다. Via-hole은또한회로를금속하우징에 (a) (c) 그림 8. 제안한 1:4 비대칭전력분배기의제작된사진 (a) 제 1 유전체기판, (b) 제 2 유전체기판, (c) 금속하우징에실장된전력분배기 Fig. 8. Photograph of the fabricated 1:4 unequal power divider (a) Substrate 1, (b) Substrate 2, (c) packaged divider in a metal housing. (b) 1295

6 韓國電磁波學會論文誌第 18 卷第 11 號 2007 年 11 月 실장할때나사의체결위치를지정하기도하므로현실적으로필요한부분이다. 그림 8(c) 는실제로제작하여금속하우징안에실장한 1:4 비대칭전력분배기의사진을보여주고있다. 이그림을통하여, 본논문에서제안한이중기판 DGS를이용한비대칭윌킨슨전력분배기가금속하우징에실장되어도접지문제가없음을알수있다. S-Parameter[dB] S 21 S 31 S 32 S 22 S 11 S 11 S 21 S 22 S 31 S S S freq, GHz (a) 그림 9는본논문에서제안하는 1:4 비대칭전력분배기의시뮬레이션된 S-parameter 특성을나타낸다. 먼저그림 9(a) 는회로설계도구인 Agilent 社의 advanced design system(ads) 를이용하여이상적인전송선로로구성된 1:4 전력분배기의이론적특성이고, 그림 9(b) 는 Ansoft 社의전자기적시뮬레이션도구인 high frequency structure simulator(hfss) 를사용하여수행한 EM 시뮬레이션결과이다. 그림 9(a) 의경우, S 21 과 S 31 은중심주파수에서각각 db, db로이상적인 1:4 분배비를보이고있으며, 그림 9(b) 의경우에도이와유사하게 S 21 과 S 31 이각각 db, db이다. 특히그림 9(b) 는그림 8에보인이중기판의 DGS와분배기회로구조를그대로시뮬레이션한결과인데, 이상적인특성인그림 9(a) 와매우유사하다. 이로써이중기판 DGS 및이를이용한비대칭전력분배기구조가논리적으로타당함을알수있다. 그림 10은그림 8의전력분배기의측정된성능을보여주고있는데, 중심주파수에서 S 21 과 S 31 이각각 db, db이다. 실제측정결과는예측결과와매우잘일치하고있는데, 시뮬레이션에이어측정결과로도본논문에서제안한구조의논리적타당성을확인할수있다. 측정결과를보면중심주파수 1.5 GHz를중심으로하여각단자에서의정합 (matching, S 11, S 22, S 33 ), 두출력단자간격리 (b) 그림 9. 이중기판 DGS 를이용하여설계한 1:4 비대칭전력분배기의시뮬레이션특성 (a) 이상적인회로소자로구성한경우의시뮬레이션결과 (Agilent ADS), (b) EM 시뮬레이션결과 (Ansoft HFSS) Fig. 9. Simulation data of the proposed 1:4 unequal power divider with double layered DGS(Agilent ADS) (a) Ideal performance, (b) EM simulation(ansoft HFSS). 그림 10. 제작된 1:4 비대칭전력분배기의측정된 S-parameter Fig. 10. Measurement S-parameters of the fabricated 1:4 unequal power divider. 1296

7 이중기판결함접지구조를이용한비대칭윌킨슨전력분배기 (isolation, S 32), 그리고정확한 1:4의두출력전력간의분배비 (S 21, S 31 ) 를확인할수있다. Ⅴ. 결론본논문에서는종래의 DGS가갖는금속하우징실장시 DGS의접지면접촉문제를해결하기위하여이중기판 DGS를제안하고, 이를응용하는한예로써 1:4 비대칭윌킨슨전력분배기를설계, 제작및측정하였다. 이중기판 DGS의구조를이용하여 158 Ω의특성임피던스를갖는이중기판 DGS 마이크로스트립선로를설계하여이를 1:4 비대칭전력분배기구조에삽입하였다. 이중기판구조를사용하였으므로식각된패턴이전체회로의바닥면에서보이지않으므로금속하우징에아무런문제없이장착할수있었다. 설계된회로의시뮬레이션결과는이상적인특성에매우근접하였으며, 실제로금속하우징에실장된상태에서측정한성능도시뮬레이션결과와잘일치하는우수한성능을보여주었다. 본연구팀은본논문에서제안한방법을향후에지속적으로응용하기위하여이중기판 DGS 구조를다른종류의초고주파회로에널리적용하는연구를지속적으로수행할예정이다. 참고문헌 [1] E. J. Wilkinson, "An N-way hybrid power divider", IRE Trans. Microwave Theory Tech., vol. 8, pp , Jan [2] D. M. Pozar, Microwave Engineering, Second Edition, John Wiely and Sons. Inc., New York, pp , [3] K. C. Gupta, et al., Microstrip Lines and Slotlines, Norwood, MA, Artech House, [4] J. S. Lim, S. -W. Lee, C. -S. Kim, J. -S. Park, D. Ahn, and S. Nam, "A 4:1 unequal Wilkinson power divider", IEEE Microwave and Wireless Components Letters, vol. 11, no. 3, pp , Mar [5] J. S. Lim, C. -S. Kim, J. -S. Park, D. Ahn, and S. Nam, "Design of 10 db 90 branch line coupler using microstrip line with defected ground structure", IEE Electronics Letters, vol. 36, no. 21, pp , Oct [6] J. S Lim, G. -Y. Lee, Y. -C. Jeong, D. Ahn, and K. -S. Choi, "A 1:6 unequal Wilkinson power divider", 36th European Microwave Conference Proceedings, Manchester, pp , Sep [7] D. Ahn, J. S. Park, C. S. Kim, J. Kim, Y. Qian, and T. Itoh, "A design of the low-pass filter using the novel microstrip defected ground structure", IEEE Trans. Microwave Theory Tech., vol. 49, no. 1, pp , Jan [8] J. S. Lim, J. S. Park, Y. T. Lee, D. Ahn, and S. Nam, "Application of defected ground structure in reducing the size of amplifiers", IEEE Microwave and Wireless Component Letters, vol. 12, no. 7, pp , Jul [9] J. S. Lim, Y. C. Jeong, D. Ahn, and S. Nam, "Improvement in performance of power amplifiers by defected ground structure", IEICE Trans. Electron., vol. E87-C, no. 1, pp , Jan

8 韓國電磁波學會論文誌第 18 卷第 11 號 2007 年 11 月 임종식 1991 년 2 월 : 서강대학교전자공학과 ( 공학사 ) 1993 년 2 월 : 서강대학교전자공학과 ( 공학석사 ) 2003 년 2 월 : 서울대학교전기컴퓨터공학부 ( 공학박사 ) 1993 년 2 월 ~1999 년 3 월 : 한국전자통신연구원위성통신기술연구단, 무선방송기술연구소선임연구원 2003 년 3 월 ~2003 년 7 월 : 서울대학교 BK21 정보기술사업단박사후연구원 2003 년 7 월 ~2004 년 9 월 : 특허청특허심사관 2004 년 9 월 ~2005 년 2 월 : 한국전자통신연구원디지털방송연구단전파기술연구그룹선임연구원 2005 년 3 월 ~ 현재 : 순천향대학교전기통신공학과교수 [ 주관심분야 ] 초고주파무선회로 / 부품설계, 능동 / 수동소자모델링및회로응용, 주기구조의모델링및회로응용등 정용채 1989년 2월 : 서강대학교전자공학과 ( 공학사 ) 1991년 2월 : 서강대학교전자공학과 ( 공학석사 ) 1996년 8월 : 서강대학교전자공학과 ( 공학박사 ) 1991년 2월~1998년 2월 : 삼성전자정보통신본부선임연구원 1998년 3월~현재 : 전북대학교전자정보공학부교수및전북대학교 IDEC WG 책임교수 [ 주관심분야 ] RF 및 Microwave 회로해석및설계, 전력증폭기및선형화기설계등 구재진 2006 년 2 월 : 순천향대학교정보기술공학부 ( 공학사 ) 2006 년 3 월 ~ 현재 : 순천향대학교전기통신시스템공학과석사과정 [ 주관심분야 ] 초고주파무선회로 / 부품설계, 능동 / 수동소자모델링및회로응용, 주기구조의모델링및회로응용등 안 달 1984 년 2 월 : 서강대학교전자공학과 ( 공학사 ) 1986 년 2 월 : 서강대학교전자공학과 ( 공학석사 ) 1990 년 8 월 : 서강대학교전자공학과 ( 공학박사 ) 1990 년 8 월 ~1992 년 2 월 : 한국전자통신연구원선임연구원 1992 년 3 월 ~ 현재 : 순천향대학교전기통신공학과교수 [ 주관심분야 ] RF, 마이크로파수동소자해석및설계등 오성민 2006년 2월 : 순천향대학교정보기술공학부 ( 공학사 ) 2006년 3월~현재 : 순천향대학교전기통신시스템공학과석사과정 [ 주관심분야 ] 초고주파무선회로 / 부품설계, 능동 / 수동소자모델링및회로응용, 주기구조의모델링및회로응용등 1298

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