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1 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE Oct.; 25(10), ISSN (Print)ISSN X (Online) Rotman Design of Rotman Lens for Curved Array Antenna with Minimal Phase Error 박주래 박동철 Joo-Rae ParkDong-Chul Park* 요약 Rotman. Rotman,,. Rotman 3,,, V,. Abstract We propose a design method of a Rotman lens for curved array antenna applicable to conformal array. In this paper, design equations are derived to obtain an array curve, transmission line lengths of a Rotman lens in conjunction with a curved array antenna, and the phase error of a Rotman lens based on these design equations is minimized through the beam curve optimization procedure and the refocusing procedure. Rotman lenses designed by the proposed design equations and design procedures still maintain 3 focal points, can feed a convex or concave array antenna with circular curve, parabolic curve, V-shaped curve, etc as well as a straight line array antenna, and have minimal phase error. Key words: Beam Curve Optimization, Curved Array Antenna, Phase Error, Refocusing, Rotman Lens. 서론,, [1],[2]. Rotman Rotman Turner [3],,,, (beam forming network) [4],[5]. Rotman. (Agency for Defense Development) * (Department of Radio Science & Engineering, Chungnam National University) Manuscript received July ; Revised September 30, 2014 ; Accepted October 6, (ID ) Corresponding Author: Dong-Chul Park ( c Copyright The Korean Institute of Electromagnetic Engineering and Science. All Rights Reserved. 1077

2 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct Rotman 3. (parallel plate region) (array curve)(beam curve), (array antenna) TEM (transmission line). 3. 0,. Rotman [6].,,,,.,, [6],[7]. Rotman,.. Rotman 3 [1],[4],, [8],[9], [6],[9],[10],[11], [12]. (Geometrical Optics) Rotman. Rotman,,.,., Rotman [12]. Rotman 3,,, V,., Rotman., Rotman.. 곡선배열안테나용 Rotman 렌즈의설계식 Rotman. 1 Rotman 그림 1. Rotman Fig. 1. Principle of Rotman lens. 1078

3 Rotman sin cos (2) (3) 그림 2. Rotman Fig. 2. Coordinates of Rotman lens.,. Rotman. 2 Rotman. 3, F 1 (Fcos, Fsin), F 2 (Fcos, Fsin), F 0 (G, 0). G (on-axis focal length), F (off-axis focal length), F 1 F 2 (focal angle).. O 1, O 2.,. 2-1 배열포트의위치와전송선의길이 sin cos (1) (1)(3) P (X a, Y a ). Q (U, V). W P Q, W 0 O 1 O 2. F 1. F, G, W-W 0, U, V, X a, Y a V m, f, g, w, u, v, x a, y a. (1)(3) (4)(6). a (4) a cos (5) (6) sin sin sin cos cos cos cos cos cos cos g, f,, (u, v) (x a, y a ) w. 1079

4 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct 빔포트의위치,. (7), (8). Uyguroglu [10] [11]. sin cos (7) sin cos (8) (7), (8) H 1 (X b, Y b ), O 1 H. P 1 Q 1, W 1. P 2 Q 2, W 2. H 1. Q 1 (U 1, V 1 ), Q 2 (U 2, V 2 ). ((U 1, V 1 ), (0, 0), (U 2, V 2 )). H, X b, Y b, X a1, Y a1, X a2, Y a2, U 1, V 1, U 2, V 2 V m, h, x b, y b, x a1, y a1, x a2, y a2, u 1, v 1, u 2, v 2. (7), (8) (9), (10). b cos (9) b sin (10) (9), (10). sin sin a a cos a a sin cos cos a a a a sin sin sin a a a a sin sin sin a a a a a a a a a a a a a a a a ((u 1, v 1 ), (0, 0), (u 2, v 2 )), (x b, y b ). 2-3 배열안테나의좌표 Rotman F [3].,,. V m (b) R,. 3 (c) F L. 3(d) V

5 Rotman (a) (a) Straight line (b) (b) Circular curve Q(U, V) H 1 P Q H 1 O 1 O 2 H 1. sin cos (15). 1,. 1, 빔곡선최적화절차 (c) (c) Parabolic curve 그림 3. Fig. 3. Coordinates of array antenna. (d) V (d) V-shaped curve (11) sin sin (12) ln (13) sin (14) (11)(14) S m.. 빔곡선최적화및재초점절차 Rotman. (15) (9), (10), Q 1 (u 1, v 1 ) Q 2 (u 2, v 2 ). Q 1 v 1 1 0, Q 2 v 2 1 0,. Q 1 u 1 Q 2 u 2. (Q 1, O 2, Q 2 ).., [3],[6],[9],[10]. 3-2 재초점절차 1081

6 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct [12]. Rotman. Rotman. 3-1, (off-axis focal points),,. F. g.. Rotman Rotman,., 직선배열안테나 Rotman g=1.6, f=1.44, =1.1, =40, =50. [6], F V m. Rotman, 0. f=1.4502, =1.0992, = Rotman,., (off-axis focal points). 5 Rotman,.. 시뮬레이션결과 Rotman,,, V 그림 4. Fig. 4. Shapes of lens-fed straight line array antenna. 1082

7 Rotman 그림 5. Fig. 5. Phase error of lens-fed straight line array antenna., 3,. 0 3 Rotman %. 그림 6. Fig. 6. Shapes of lens-fed convex circular curve array antenna. 4-2 원곡선배열안테나 Rotman, Rotman g=1.6, f=1.27, = 1.1, =40, =50, =30. f=1.3207, =1.0999, = Rotman,. 그림 7. Fig. 7. Phase error of lens-fed convex circular curve array antenna.. 7 Rotman, %. 1083

8 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct 포물선배열안테나 Rotman, Rotman g=1.6, f=1.66, =1.1, =40, =50, f L = f L F L V m. f=1.6472, =1.0973, = Rotman,.,... 9 Rotman,. 3 그림 8. Fig. 8. Shapes of lens-fed concave parabolic curve array antenna. 그림 9. Fig. 9. Phase error of lens-fed concave parabolic curve array antenna %. 4-4 V 자형곡선배열안테나 Rotman V, Rotman V g=1.6, f=1.66, =1.1, =40, =50, =75. f=1.6458, =1.0965, = Rotman V,.,. V.. 11 Rotman V, 1084

9 Rotman 그림 10. V Fig. 10. Shapes of lens-fed concave V-shaped curve array antenna Rotman,,, V 3.,., 3., Rotman,,,.. 결론 그림 11. V Fig. 11. Phase error of Rotman lens-fed concave V-shaped curve array antenna % Rotman. Rotman,,. Rotman,,, V 3,. 1085

10 THE JOURNAL OF KOREAN INSTITUTE OF ELECTROMAGNETIC ENGINEERING AND SCIENCE. vol. 25, no. 10, Oct Rotman. References [1] Lars Josefsson, Patrik Persson, Conformal Array Antenna Theory and Design, John Wiley & Sons, [2] R. C. Hansen, Phased Array Antennas, John Wiley & Sons, [3] W. Rotman, R. F. Turner, "Wide angle microwave lens for line source applications", IEEE Trans. Antennas Propagat., vol. AP-11, pp , Nov [4] D. H. Archer, "Lens-fed multiple beam arrays", Microwave J., vol. 27, pp , Sep [5] A. F. Peterson, E. O. Rausch, "Scattering matrix integral equation analysis for the design of a waveguide Rotman lens", IEEE Trans. Antennas Propagat., vol. 47, pp , May [6] R. C. Hansen, "Design trades for Rotman lenses", IEEE Trans. Antennas Propagat., vol. 39, pp , Apr [7] J. P. Shelton, "Focusing characteristics of symmetrically configured bootlace lenses", IEEE Trans. Antennas Propagat., vol. AP-26, pp , Jul [8] D. Archer, R. J. Prickett, and C. P. Hartwig, "Multi-beam array antenna", U. S. Patent 3,761,936, Sep [9] T. Katagi, S. Mano, and Shin-Ichi Sato, "An improved design method of Rotman lens antennas", IEEE Trans. Antennas Propagat., vol. AP-32, pp , May [10] R. Uyguroglu, A. Y. Oztoprak, and C. Ergun, "Improved phase performance for Rotman lens", International Journal of RF and Microwave Computer-Aided Engineering, vol. 23, pp , Nov [11],, "Rotman ",, 25(8), pp , [12] Joo-Rae Park, Dong-Chul Park, "Phase error minimization by refocusing Rotman lens", 2013 Asia-Pacific Microwave Conference Proceedings, pp , Nov : ( ) : ( ) : : [ 주관심분야 ] RF, : ( ) : () : University of California, Santa Barbara () : Ruhr University, Bochum, Germany : IEEE MTT Korea Chapter Chairman : IEEE EMC Korea Chapter Chairman : : Wireless 1976: [ 주관심분야 ] Microwave and Millimeterwave Passive Components, Antennas, EMI/EMC 1086

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