本論文目的為設計創新的多輸入多輸出天線陣列饋電電路，由4輸入4輸出巴特勒矩陣為基礎，設計3輸入4輸出饋電電路，其能夠使天線陣列輻射無偏移角度的主波束。由於高頻率的電磁波路徑損耗較為嚴重，因此採用基板合成波導設計，未來也更方便利用多層板疊構技術，將天線陣列與饋電電路整合，以縮小整體尺寸。
本研究設計三版3輸入4輸出饋電電路，其在近地軌道衛星通訊之地對空頻段12 GHz至14.5 GHz擁有良好的相位控制：第一版設計輸出相位差分別為–90度、0度、90度，可形成一個主波束無偏移角度以及兩個主波束分別偏移±31度；第二版設計較第一版不同在於，其由中間端埠饋入時可形成的主波束峰值在±38度，由兩側端埠饋入時僅由其中兩個端埠輸出，分別形成偏移±14度的主波束，形成的增益較低但波束寬較寬；第三版設計將第二版的輸出相位差做微調，可形成一個主波束無偏移角度以及兩個主波束分別偏移±48度，且三版的傳輸效率皆為70%左右。 

The purpose of this paper is to design an innovative multi-input multi-output (MIMO) antenna array feed circuit. Based on the 4-input and 4-output Butler matrix, 3-input and 4-output feed circuit is designed, which can make the antenna array radiation without offset angle of the main beam. Due to the serious path loss of high-frequency electromagnetic waves, the substrate-integrated waveguide (SIW) design is adopted. In the future, it will be more convenient to use the multi-layer board stacking technology to integrate the antenna array with the feed circuit to reduce the overall size.
In this study, three versions of 3-input and 4-output feed circuits are designed, which have good phase control in the ground-to-space frequency band of 12 GHz to 14.5 GHz for low-Earth orbit satellite communication: the output phase difference of the first version design is –90 degrees, 0 degrees, 90 degrees, which can form a main beam with no offset angle and two main beams offset by ±31 degrees respectively; the second version design is different from the first version, when it is fed from the middle port, the peak value of the main beam that can be formed is ±38 degrees. When it is fed from the two side ports, only two ports are output, forming a main beam with an offset of ±14 degrees, and the resulting gain lower but wider beam width; the third version design fine-tunes the output phase difference of the second version, which can form a main beam with no offset angle and two main beams offset by ± 48 degrees, and the transmission efficiency of the three versions are about 70%.

[1] M. M. Alam, "Microstrip antenna array with four port Butler matrix for switched beam base station application," 2009 12th International Conference on Computers and Information Technology, Dhaka, Bangladesh, Dec. 2009, pp. 531-536, doi: 10.1109/ICCIT.2009.5407295.
[2] O. U. Khan, "Design of X-band 4×4 Butler Matrix for Microstrip Patch Antenna Array," TENCON 2006 - 2006 IEEE Region 10 Conference, Hong Kong, China, Nov. 2006, doi: 10.1109/TENCON.2006.343831.
[3] Y. Liu, O. Bshara, I. Tekin and K. R. Dandekar, "A 4 by 10 series 60 GHz microstrip array antenna fed by butler matrix for 5G applications," 2018 IEEE 19th Wireless and Microwave Technology Conference (WAMICON), Sand Key, FL, USA, Apr. 2018, doi: 10.1109/WAMICON.2018.8363899.
[4] N. Chater, T. Mazri, M. Benbrahim, A. Charkaoui, "Optimized wideband steerable antenna array using an 8x8 Butler matrix," 2021 International Electronics Symposium (IES), Surabaya, Indonesia, Sep. 2021, doi: 10.1109/IES53407.2021.9594044.
[5] P. H. Re, C. Alistarh, S. Podilchak, G. Goussetis, J. Thompson and J. Lee, "Millimeter-Wave FMCW Radar Development using SIW Butler Matrix for Time Domain Beam Steering," 2019 16th European Radar Conference (EuRAD), Paris, France, 2019, pp. 141-144.
[6] N. Tiwari and T. R. Rao, "A switched beam antenna array with butler matrix network using substrate integrated waveguide technology for 60 GHz communications", in IEEE Advances in Computing Communications and Informatics, pp. 2152-2157, August 2015, doi: 10.1109/ICACCI.2015.7275935.
[7] T. Djerafi and K. Wu, "A Low-Cost Wideband 77-GHz Planar Butler Matrix in SIW Technology," in IEEE Transactions on Antennas and Propagation, vol. 60, no. 10, pp. 4949-4954, Oct. 2012, doi: 10.1109/TAP.2012.2207309.
[8] C. J. Chen and T.H. Chu, "Design of a 60-GHz substrate integrated waveguide Butler matrix-A systematic approach", in IEEE Transactions on Microwave Theory and Techniques, vol. 58, pp. 1724-1733, July 2010, doi: 10.1109/TMTT.2010.2050097.
[9] Z. Chen, X. Wu and F. Yang, "A compact SIW butler matrix with straight delay lines at 60 GHz," 2017 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, San Diego, CA, USA, 2017, pp. 2141-2142, doi: 10.1109/APUSNCURSINRSM.2017.8073113.
[10] Q. L. Yang, Y. L. Ban, K. Kang, C. Y. D. Sim and G. Wu, "SIW Multibeam Array for 5G Mobile Devices," in IEEE Access, vol. 4, pp. 2788-2796, June 2016, dol: 10.1109/ACCESS.2016.2578458.
[11] Q. L. Yang, Y. L. Ban, Q. Q. Zhou and M. Y. Li, "Butler matrix beamforming network based on substrate integrated technology for 5G mobile devices," 2016 IEEE 5th Asia-Pacific Conference on Antennas and Propagation (APCAP), Kaohsiung, Taiwan, 2016, pp. 413-414, doi: 10.1109/APCAP.2016.7843268.
[12] S. Dey, N. S. Kiran and S. Dey, "SIW Butler Matrix Driven Beam Scanning Array For Millimeter Wave 5G Communication," 2020 IEEE Asia-Pacific Microwave Conference (APMC), Hong Kong, Hong Kong, Dec. 2020, pp. 709-711, doi: 10.1109/APMC47863.2020.9331670.
[13] H. J. Riblet, "The Short-Slot Hybrid Junction," Proceedings of the IRE, vol. 40, no. 2 , pp. 180-184, Feb. 1952, doi: 10.1109/JRPROC.1952.274021.
[14] C. J. Chen and T. H. Chu, "Design of 60-GHz SIW short-slot couplers", Asia Pacific Microwave Conference, IEEE, pp. 2096-2099, Dec. 2009, doi: 10.1109/JRPROC.1952.274021.
[15] O. Konc, D. Maassen, F. Rautschke and G. Boeck, "Wideband substrate integrated waveguide Ku-band coupler," 2016 21st International Conference on Microwave, Radar and Wireless Communications (MIKON), Krakow, Poland, May 2016, doi: 10.1109/MIKON.2016.7491958.
[16] K. Wu, D. Deslandes and Y. Cassivi, "The Substrate Integrated Circuits - A New Concept for High-Frequency Electronics and Optoelectronics," TELSKIS 2003, Nis, Serbia and Montenegro, pp. Oct. 2003.
[17] J. E. Rayas-Sanchez and V. Gutierrez-Ayala, "A General EM-Based Design Procedure for Single-Layer Substrate Integrated Waveguide Interconnects with Microstrip Transitions", IEEE MTT-S Int. Microwave Symp. Dig., Atlanta, GA, Jun. 2008, pp. 983-986, doi: 10.1109/MWSYM.2008.4632999.
[18] David. M. Pozar, "Microwave.Engineering," Fourth Edition, John Wiley & Sone,Inc., 2012, pp. 324-328.
[19] David. M. Pozar, "Microwave.Engineering," Fourth Edition, John Wiley & Sone,Inc., 2012, pp. 343-346.
[20] A. Askarian, G. Moradi, "Modified Transition For Substrate Integrated Waveguide (SIW) Structures," Bulletin de la Société Royale des Sciences de Liège, Vol. 85, 2016, p. 203 – 214.
[21] B. Kunooru, S. V. Nandigama, D. R. Krishna, R. Gugulothu and S.Bhalke, "Studies on Microstrip to SIW transition at Ka-Band," 2019 TEQIP III Sponsored International Conference on Microwave Integrated Circuits, Photonics and Wireless Networks (IMICPW), Tiruchirappalli, India, May 2019, pp. 379-382,doi: 10.1109/IMICPW.2019.8933234.
[22] J. Lian, Y. Ban, C. Xiao and Z. Yu, "Compact Substrate-Integrated 4 × 8 Butler Matrix With Sidelobe Suppression for Millimeter-Wave Multibeam Application," in IEEE Antennas and Wireless Propagation Letters, vol. 17, no. 5, pp. 928-932, May 2018, doi: 10.1109/LAWP.2018.2825367.
[23] F. Ren, W. Hong and K. Wu, "W-band series-connected patches antenna for multibeam application based on SIW Butler matrix," 2017 11th European Conference on Antennas and Propagation (EUCAP), Paris, France, 2017, pp. 198- 201, doi: 10.23919/EuCAP.2017.7928649.
[24] C. H. Hsieh, Y. T. Lin, H. C. Jhan and Z. M. Tsai, "A Novel Concept for 2D Butler Matrix with Multi-Layers Technology," 2018 Asia-Pacific Microwave Conference (APMC), Kyoto, Japan, Nov. 2018, pp. 533-535, doi: 10.23919/APMC.2018.8617245.