隨著近年來數位通訊工業的蓬勃發展，微波通訊電路的開發與設計進步的相當快速，高效能的無線通訊系統是相當重要的，而微波濾波器扮演了不可或缺並且相當重要的角色。本論文的主要目的為合成實現高選擇度之類橢圓濾波器，首先先探討此電路與傳統設計的巴特沃斯、柴比雪夫、和橢圓濾波器之架構與響應差異，然後針對文獻中缺乏完整合成理論之類橢圓濾波器，推導出其等效電路與特徵函數，再利用數學演算法，以此為原型進行最佳化的近似合成。
在本論文中，把先前學者所提出的架構原型，以三種不同的方式進行最佳化合成，以方便適用於不同需求之頻率響應。並對最佳化之結果、原始電路、以及傳統濾波器三者，進行頻率響應與電路實現難易程度的比較。最後，透過實際製作此類橢圓濾波器，並進行量測與模擬比較，證實了本研究方法的正確性。

Quasi-elliptic microwave filters with step stubs had been proposed recently. However, the synthesis procedures and design equations are not well developed yet. This thesis studies the optimization and realization of this type of quasi-elliptic filters. We adopt the prototype from the literature and use a modified algorithm to improve the optimization. Three optimization schemes are discussed to improve the response, and compare with the traditional function. Finally, the proposed method and design are verified by simulations and experiment.

[1.1] J. A. G. Malherbe, “Pseudo-elliptic bandstop filter with 1:2:3 harmonic ratio stubs,” Elec. Lett., vol. 49, No. 2, pp. 130~132, Jan. 2013.
[1-2] P. I. Richards, “Resistor-Transmission-Line Circuits,’’ Proc. IRE, vol. 36, No. 2, pp. 217-220, Feb. 1948.
[1-3] Y. Zhang, K. A. Zaki, J. A. Ruiz-Cruz, and A. E. Atia, “Analytical Synthesis of Generalized Multi-band Microwave Filters”, in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, 2007, pp. 1273-1276.
[2-1] H. J. Orchard and G. C. Temes, “Filter Design Using Transformed Variables”, IEEE Trans. On Circuit Theory, vol. 15, No. 4, pp. 385~408, Dec. 1968.
[2-2] Y. Zhang, K. A. Zaki, J. A. Ruiz-Cruz, and A. E. Atia, “Analytical Synthesis of Generalized Multi-band Microwave Filters”, in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, 2007, pp. 1273-1276
[3-1] P. I. Richards, “Resistor-Transmission-Line Circuits,’’ Proc. IRE, vol. 36, No. 2, pp. 217-220, Feb. 1948.
[3-2] J. A. G. Malherbe, “Pseudo-elliptic bandstop filter with 1:2:3 harmonic ratio stubs,” Elec. Lett., vol. 49, No. 2, pp. 130~132, Jan. 2013.
[3-3] R. Levy and I. Whiteley, “Synthesis of Distributed Elliptic-Function Filters from Lumped-Constant Prototypes,” IEEE Trans. On Microwave Theory and Techniques, vol. 14, No. 11, pp. 506-517, Nov. 1966.
[3-4] B. M. Schiffman and G. L. Matthaei, “Exact Design of Band-stop Microwave Filters,” IEEE Trans. On Microwave Theory and Techniques, vol. 12, No. 1 pp. 6-15, Jan. 1964.
[3-5] B. M. Schiffman, “A Multiharmonic Rejection Filter Designed by an Exact Method,” IEEE Trans. On Microwave Theory and Techniques, vol. 12, No.5, pp. 512-516, May 1964.
[3-6] B. M. Schiffman and L.Young, “Design Tables for an Elliptic-Function Band-Stop Filter (N=5),” IEEE Trans. On Microwave Theory and Techniques, vol. 14, No. 10, pp. 474-482, Oct. 1964.
[3-7] A. I. Zverev, Handbook of Filter Synthesis, John Wiley & Sons, Inc., New York, 1967, pp. 169-289.
[3-8] R. Levy, “A General Equivalent Circuit Transformation for Distributed Networks,” IEEE Trans. On Circuit Theory, vol. 12, No. 3, pp. 457-458, Sept. 1965.
[3-9] Y. Zhang, K. A. Zaki, J. A. Ruiz-Cruz, and A. E. Atia, “Analytical Synthesis of Generalized Multi-band Microwave Filters”, in IEEE MTT-S Int. Microw. Symp. Dig., Honolulu, HI, 2007, pp. 1273-1276.
[3-10] R. Levy, “Filters with Single Transmission Zeros at Real or Imaginary Frequencies,” IEEE Trans. On Microwave Theory and Techniques, vol. 24, No. 4, pp. 172~181, Apr. 1976.
[3-11] P. I. Richards, “A Special Class of Functions with Positive Real Part in a Half-Plane,’’ J. Duke Math., vol. 14, No. 3, pp.777-786, Sep. 1947.
[5.1] J. A. G. Malherbe, “Pseudo-elliptic bandstop filter with 1:2:3 harmonic ratio stubs,” Elec. Lett., vol. 49, No. 2, pp. 130~132, Jan. 2013.