由於環行器可運用於國防及商業電子元件之微波傳輸，故其研究及進展備受重視及關注。本學位論文中，作者以鋁表面鍍銀模式做為較佳之中心帶線，且成功設計出中心帶線之pattern在中心頻率0.9GHz時，頻寬比可達25.46%之環形器。利用頻率0.9GHz進行環行模擬分析，以尋找最佳中心帶線和鐵氧體半徑比值，除了一般比值0.985外，另外發現比值0.375也可達到良好的環行效果。此外，作者在模擬實驗中發現環行器尺寸中會有個極限值，並模擬使用極薄的鐵氧體材料鍍在中心帶線之表面兩側，結果還能達到我們所要的環行效果。另研究發現帶線表面維持潔度的確可提升環行效果，當金屬帶線經過抗氧化處理後，對於環行效果可達均一性。
作者相信本論文內容含許多可用資料，並在國防及商業科技上具有應用價值。

As the circulator can be used in defense and commercial electronic components of the microwave transmission, so the progress of this study earn much attention. In this dissertation, the authors use the silver plating on the two side of surface of aluminum as our stripline, and successfully design the center line pattern at the center frequency of 0.9GHz. The bandwidth ratio is up to 25.46% of the circulator. Using the frequency of 0.9GHz for circulator simulation analysis to find the best stripline and ferrite ratio, in addition to the general ratio of 0.985, this study also found that 0.375 can also achieve good circulatory effect.
Moreover, the author found that in the simulation experiment, the circulator size would have a limit, and simulate the use of very thin ferrite material plated on both sides of the surface of the stripline, the results can achieve our desired circulatory effect. Meanwhile, this study found that the stripline surface to maintain a cleanliness can enhance the circulatory effect, when the metal stripline after oxidation treatment, the circulatory effect can be uniform.
The author believes that the content of this paper is of valuable, and can be applied on the national defense and commercial technology.

第一章 緒論 8
第二章 電磁波在鐵氧體的行為 11
2.1 鐵氧體材料的基本特性 11
2.2 磁方程式 15
2.3 磁導係數張量 16
2.4 電子在鐵氧體中的傳播和行為 18
2.5 損耗的影響 20
第三章 環行器的原理與設計 24
3.1 環行器介紹 24
3.2 環行條件推導 26
3.3 圓盤結和雙Y圓盤結理論 27
3.4 磁場範圍的選擇 37
第四章 環行器模擬與設計 41
4.1 鐵氧體模擬参數 41
4.2 雙Y圓盤結環行器模擬與設計 41
第五章 結果與驗證 47
5.1 環行器尺寸極限探討 47
5.2 鐵氧體薄度極限探討 50
5.3 環行器中中心帶線和鐵氧體半徑比例之關係 57
5.4 表面清潔度對環行器微波傳輸之響應 69
5.5 中心帶線材料對環行器微波傳輸之響應 71
第六章 結論與未來展望 74
参考資料 76

[1] J. Helszajn, “The Stripline Circulator – Theory and Practice” Published by John Wiley & Sons, Inc. Published simultaneously in Canada, 2008.
[2] J. Baden Fuller, Ferrites at Microwave Frequencies, London: Peter Peregrinus, 1987
[3] C.P. Hartwig & D.W. Readey, “Ferrite Film Circulator”, vol.41, no.3, 1st , March, 1970
[4] D. M. Pozar, Microwave Engineering, 3rd ed. NJ: John Wiley & Sons, 2005.
[5] J. Helszajn, The Stripline Circulators: Theory and Practice, John Wiley & Sons, 2008.
[6] D. K. Linkhart, Microwave Circulator Design, 2nd Edition, Artech House Microwave Library, 2014.
[7] P. H. Martha, “Microwave applications of soft ferrites”, J. Magn. Magn. Mater., vol.215-216, pp. 171-183, Jun. 2000
[8] 陳振瑋, “4G 頻段夾心帶線型環行器研製”,碩士論文, 國立清華大學, 2013.
[9] 吳詩嶢, “4G 頻段低損耗及寬頻之環行器研發”,碩士論文, 國立清華大學, 2016.
[10] 傅國欽, “磁性材料之環行傳輸介質研究”,碩士論文, 國立清華大學, 2012.
[11] J. B. Davies and P. Cohen, “Theoretical design of symmetrical Junction stripline circulators”, IEEE Trans. Microwave Theory Techn., vol. MTT-11, no. 6, pp. 506– 512, Nov. 1963.
[12] Y. Konishi, “Lumped element Y circulator”, IEEE Trans. Microwave Theory Techn., vol. MTT- 13, no. 6, pp. 852–864, Nov. 1965.
[13] J. Helszajn, “Frequency response of quarter-wave coupled non-reciprocal stripline junctions”, IEEE Trans. Microwave Theory Techn., vol. 21, no. 8, pp. 533-537, Aug. 1973.
[14] W. Marynowski and J. Mazur, “Study of nonreciprocal devices using three-strip ferrite coupled line”, Prog. Electromagn. Res., vol. 118, pp. 487-504, 2011.
[15] Y. Naito and N. Tanaka, “Broad-Banding and changing operation frequency of circulator”, IEEE Trans. Microwave Theory Techn., vol. MTT-19, pp. 367–372, Apr. 1971.
[16] J. Helszajn and M. E. Powlesland, “Low-loss high-peak-power microstrip circulators”, IEEE Trans. Microwave Theory Techn., vol. MTT-29, no.6, pp. 572-578, Jun. 1981.
[17] J. Helszajn, “Circulators using planar WYE resonators”, IEEE Trans. Microwave
Theory Techn., vol. MTT-29, no. 7, Jul. 1981
[18] J. Helszajn, “Standing wave solutions of planar irregular hexagonal and WYE resonators”, IEEE Trans. Microwave Theory Techn., vol. MTT-29, NO. 6, Jun. 1981.
[19] J. Helszajn, and R. D. Baars, “Synthesis of wide-band planar circulators using narrow coupling angles and undersized disk resonators”, IEEE Trans. Microwave
Theory Techn., vol. MTT-39, no. 10, pp. 1681–1687, Oct. 1991.
[20] J. Helszajn, “Synthesis of octave-band quarter-wave coupled semi-tracking stripline junction circulators”, IEEE Trans. Microwave Theory Tech., vol. MTT-43, vol. 3, pp. 573–578, Mar. 1995.
[21] E. Schwartz, “Broadband matching of resonant circuits and circulators”, IEEE Trans.
Microwave Theory Techn., vol. MTT- 16, no. 3, pp.158-65, Mar. 1968.
[22]. Hogan, C. Lester (January 1952). "The Ferromagnetic Faraday Effect at
Microwave Frequencies and its Applications - The Microwave Gyrator". The
Bell System Technical Journal 31 (1): 1–31. in which the four-port Faraday
rotation circulator is proposed.
[23]. Jump up Hogan, C. Lester (1953), "The Ferromagnetic Faraday Effect at
Microwave Frequencies and its Applications", Reviews of Modern Physics 25
(1): 253–262, doi:10.1103/RevModPhys.25.253
[24] 蔡育超,“一對二高功率高速射頻切換裝置研製”,碩士論文, 國立清華大學, 2012.
[25] J. Helszain, “The synthesis of quarter-wave coupled circulators with Chebyshev characteristics”, IEEE Trans. Microwave Theory Techn, vol. MTT-20, no. 11, pp. 367-72, Nov. 1972.
[26] J. Helszajn, and D. J. Lynch, “Cut-off space of cloverleaf resonators with electric and magnetic walls”, IEEE Trans. Microwave Theory Techn,, vol. MTT-40, no. 8, pp. 1620–1629, Aug. 1992.
[27] J. Renpei, W. Chongyue, “Optimum design for WYE-junction circulator”, IEEE
Trans. Magn., vol.24, no. 6, pp. 2820-2822, Nov. 1988.
[28] J. Helszajn, “Fabrication of very weakly and weakly magnetized microstrip circulators”, IEEE Trans. Microwave Theory Techn., vol. MTT-46, no. 5, pp. 439– 449, May. 1998.
[29] J. L. Young and C. M. Johnson, “A compact recursive trans-impedance green’s function for the inhomogeneous ferrite microwave circulator”, IEEE Trans.
Microwave Theory Techn., vol. 52, no. 7, pp. 1751-1759, Jul. 2004.
[30] Y. Wang, B. Peng, W. L. Zhang, and K. Tan, “CPW circulators with barium ferrite thin film”, J. Electron. Sci. Tech., vol. 8, no. 4, pp. 351-355, Dec. 2010.

[31] 魏克珠, 李士根, 蔣仁培,“微波鐵氧體新器件”第一版 國防工業出版社, 1995.
[32] 金重勳, 主編“磁性技術手冊”初版 中華民國磁性技術協會,(2002) 164-165.
[33] T. H. Chang, “Gyromagnetically-induced transparency for ferrites,” Am. J. Phys. Vol. 84, no. 4, pp. 279-283, April 2016.
[34] M. Darques, J. D. L. T. Medina, L. Piraux, L. Cagnon and I. Huynen, “Microwave circulator based on ferromagnetic nanowires in an alumina template”,
Nanotechnology, vol. 21, no. 14, 145208, March 2010.
[35] T. Jensen, V. Krozer and C. Kjaergaard, “Realisation of microstrip junction circulator using LTCC technology”, Electronics Letters, vol. 47, no. 2, Jan. 2011.
[36] J. Wang, A. Yang, Y. Chen, Z. Chen, A. Geiler, S. M. Gillette, V. G. Harris and C. Vittoria, “Self biased Y-junction circulator at Ku band”, IEEE Microw. Wirel.
Compon. Lett., vol. 21, no. 6, pp. 292-294, Jun. 2011.
[37] B. Peng, H. Xu, H. Li, W. Zhang, Y. Wang and W. Zhang, “Self-Biased microstrip junction circulator based on barium ferrite thin films for monolithic microwave integrated circuits”, IEEE Trans. Magn., vol. 47, no. 6, pp. 1674-1677, Jun. 2011.
[38] L. Chao, H. Oukacha, E. Fu, V. J. Koomson and M. N. Afsar, “Millimeter wave complementary metal–oxide–semiconductor on-chip hexagonal nano-ferrite circulator”, J. Appl. Phys., Apr. 2015.
[39] K. M. Sliwa, M. Hatridge, A. Narla, S. Shankar, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, “Reconfigurable Josephson circulator/directional amplifier”, Phys. Rev. X 5, 041020, Nov. 2015.
[40] T. Miura, M. Kobayashi, H. Nagata, and Y. Konishi, “Optimization of lumped element circulator based on eigenvalue evaluation and structural improvement”,
IEEE Trans. Microwave Theory Techn., vo. 44, no. 12, pp. 2648–2654, Dec. 1996.
[41] P. H. Cheng and R. M. Narayanan, “Design of active circulators using high-speed operational amplifiers”, IEEE Microw. Wirel. Compon. Lett., vol. 20, no. 10, pp.
575-577, Oct. 2010.
[42] A. J. Baden Fuller, “Ferrites at Microwave Frequencies”, Peter Peregrinus, London, 1987.
[43] Martha Pardavi-Horvath,“Microwave Applications of Soft Ferrites ”, Journal of Magnetism and Magnetic Materials 215-216 (2000) 171-183.
[44] 北京大學物理系教授 虞福春 & 鄭春開, “電動力學” , 2006.
[45] J. D. Jackson, Classical Electrodynamics, 3rd ed. New York: Wiley, 1999.
[46] H. How, S. A. Oliver, S. W. McKnight, P. M. Zaveracky, N. E. McGruer, C. Vittoria, and R. Schmidt, “Influence of nonuniform magnetic field on a ferrite junction circulator”, IEEE Trans. Microwave Theory Techn., vol. 47, no. 10, pp. 1982–1989, Oct. 1999.
[47] C. P. Hartwig and D. W. Readey,”Ferrite Film Circulator”, J. Appl. Phys. Vol. 41, No.3, pp.1351, 1970.
[48] O. Zahwe, B. Sauviac, and J. J. Rousseau, “Fabrication and Measurement of a Coplanar Circulator with 65 mm YIG thin film”, Progress in Electromagnetics Research Letters, vol. 8, pp. 35 ~ 41, 2009.
[49] 宋文佳, “微帶結環行器設計與仿真研究” 電子科技大學碩士學位論文, 2009.
[50] Yu-Wei Su, “Fabrication and characterization of ferromagnetic film for RF/microwave crosstalk suppression”, Thesis for Master of Science in Chemical Engineering, September 2007.
[51] “微帶結環行器設計與仿真研究” 杭州電子科技大學碩士學位論文, 2015.