微波濾波器合成理論可區分為兩種，第一種為以傳輸線在通帶中心頻率近似倒轉器及諧振器來設計濾波器，故此方式僅適用窄頻設計。第二種則根據傳輸線特性，在Richards’ domain上精確合成原型濾波器，再轉換成欲實現之濾波器架構，故此方法並無設計頻寬限制。本論文分別以上述兩種角度，探討近似及精確合成設計平行耦合線濾波器之差異，清楚指出近似設計方式產生誤差的具體原因，並據此提出改良的電路結構與設計方法。另外，在平行耦合線濾波器設計中有一常見問題，即設計頻寬越寬，輸入與輸出級耦合線間距越窄，因此曾有文獻以Tapped-Line結構取代輸入與輸出級耦合線，使得電路更容易製作，並提供通帶外傳輸零點，本論文提出了一個新的可自由控制傳輸零點之Tapped-Line結構。最後，本論文提出利用八分之一波長耦合線來設計濾波器的新方法，可以將傳統耦合線濾波器的整體長度縮小一半。本論文已經透過電磁模擬及電路實作的方式，驗證了所有上述新設計新方法的正確性。

Microwave filter synthesis can be categorized into two types. One uses transmission lines to approximate inverters and resonators at the center frequency of a passband, therefore, it is only suitable for narrowband applications. The other is by exact synthesis in Richards’ domain without bandwidth limitation. This study compares parallel coupled-line (PCL) filters designed by these two methods. The causes of the approximation errors of the first method are clearly identified and improved designs are proposed. In the design of parallel coupled-line filters, the gaps between the coupled lines of the input and output stages are often too narrow to be realizable when the required bandwidth is wide. To solve this problem, some studies had proposed to replace these coupled-line sections with tapped-line structures. This not only makes circuit implementation easier but introduces ultra transmission zeros near the passband. This study proposes a new tapped-line design to further control the frequencies of these transmission zeros. Finally, a compact filter is proposed by using one-eighth-wavelength coupled-line sections. This successfully reduces the size of traditional coupled-line filters by half. All the proposed designs in this study have been verified by electromagnetic simulations and measurements of fabricated circuits.

[1.1] S. B. Cohn, “Parallel-Coupled Transmission-Line-Resonator Filters,” IEEE Trans. Microwave Theory Tech., vol. 6, pp. 223-231, Apr. 1958.

[1.2] G. L. Matthaei, “Design of Parallel-Coupled Resonator Filters,” IEEE Microw. Mag., vol. 8, no 5, pp. 78-87, Oct. 2007.

[1.3] J. S. Wong, “Microstrip Tapped-Line Filter Design,” IEEE Trans. Microw. Theory Tech., vol. 27, no. 1, pp. 44–50, Jan. 1979.

[1.4] H. -M. Lee, Microwave Filter Deigns with Different Component Q, Different Mode Velocities, and Dual-Band Characteristics, National Cheng Kung University, Dissertation for Doctor of Philosophy, Jan. 2006, Chap. 3, pp.37-43.

[1.5] M. C. Horton and R. J. Wenzel, “General Theory and Design of Optimum Quarter-Wave TEM Filters,” IEEE Trans. Microwave Theory Tech., vol. 13, no. 3, pp. 316-327, May 1965.

[1.6] G. L. Matthaei, “Direct-Coupled Bandpass Filters with λ0/4 Resonator,” IRE Int. Conv. Record, vol. 6, pt. 1, pp. 98-111, 1958.

 
[1.7] S. Zhang and L. Zhu, “Synthesis Method for Even-Order Symmetrical Chebyshev Bandpass Filters with Alternative J/K Inverters and λ0/4 Resonators,” IEEE Trans. Microw. Theory Techn., vol. 61, no 2, pp. 808-816, Feb. 2013.

[1.8] C. -J. Chen, “Design of Parallel-Coupled Dual-Mode Resonator Bandpass Filters,” IEEE Trans. Compon., Packag., Manuf. Techn., vol. 6, no. 10, pp. 1542–1548, Oct. 2016.

[2.1] S. B. Cohn, “Parallel-Coupled Transmission-Line-Resonator Filters,” IEEE Trans. Microwave Theory Tech., vol. 6, pp. 223-231, Apr. 1958.

[2.2] G. L. Matthaei, “Design of Parallel-Coupled Resonator Filters,” IEEE Microw. Mag., vol. 8, no 5, pp. 78-87, Oct. 2007.

[2.3] H. -M. Lee, Microwave Filter Deigns with Different Component Q, Different Mode Velocities, and Dual-Band Characteristics, National Cheng Kung University, Dissertation for Doctor of Philosophy, Jan. 2006, Chap. 3, pp.37-43.

[2.4] G. L. Matthaei, “Direct-Coupled Bandpass Filters with λ0/4 Resonator,” IRE Int. Conv. Record, vol. 6, pt. 1, pp. 98-111, 1958.

[2.5] H. -M. Lee, Microwave Filter Deigns with Different Component Q, Different Mode Velocities, and Dual-Band Characteristics, National Cheng Kung University, Dissertation for Doctor of Philosophy, Jan. 2006, Chap. 3, pp.31.
 
[3.1] S. B. Cohn, “Parallel-Coupled Transmission-Line-Resonator Filters,” IEEE Trans. Microwave Theory Tech., vol. 6, pp. 223-231, Apr. 1958.

[3.2] G. L. Matthaei, “Design of Parallel-Coupled Resonator Filters,” IEEE Microw. Mag., vol. 8, no 5, pp. 78-87, Oct. 2007.

[3.3] H. -M. Lee, Microwave Filter Deigns with Different Component Q, Different Mode Velocities, and Dual-Band Characteristics, National Cheng Kung University, Dissertation for Doctor of Philosophy, Jan. 2006, Chap. 3, pp.37-43.

[3.4] M. C. Horton and R. J. Wenzel, “General Theory and Design of Optimum Quarter-Wave TEM Filters,” IEEE Trans. Microwave Theory Tech., vol. 13, no. 3, pp. 316-327, May 1965.

[3.5] Q. -X. Hong, Automated Implementation and Analysis of Interdigital Band-Pass Filters, Institute of Computer and Communication Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., Thesis for Master of Science, July 2017.

[4.1] G. L. Matthaei, “Direct-Coupled Bandpass Filters with λ0/4 Resonator,” IRE Int. Conv. Record, vol. 6, pt. 1, pp. 98-111, 1958.

[4.2] S. Zhang and L. Zhu, “Synthesis Method for Even-Order Symmetrical Chebyshev Bandpass Filters With Alternative J/K Inverters and λ0/4 Resonators,” IEEE Trans. Microw. Theory Techn., vol. 61, no 2, pp. 808-816, Feb. 2013.
 
[4.3] C. -J. Chen, “Design of Parallel-Coupled Dual-Mode Resonator Bandpass Filters,” IEEE Trans. Compon., Packag., Manuf. Techn., vol. 6, no. 10, pp. 1542–1548, Oct. 2016.

[4.4] R. J. Wenzel, “Synthesis of Combline and Capacitively Loaded Interdigital Bandpass Filters of Arbitrary Bandwidth,” IEEE Trans. Microw. Theory Techn., vol. 19, no 8, pp. 678-686, Aug. 1971.

[4.5] S. B. Cohn, “Parallel-Coupled Transmission-Line-Resonator Filters,” IEEE Trans. Microwave Theory Tech., vol. 6, pp. 223-231, Apr. 1958.

[5.1] G. L. Matthaei, “Design of Parallel-Coupled Resonator Filters,” IEEE Microw. Mag., vol. 8, no 5, pp. 78-87, Oct. 2007.

[5.2] S. B. Cohn, “Parallel-Coupled Transmission-Line-Resonator Filters,” IEEE Trans. Microwave Theory Tech., vol. 6, pp. 223-231, Apr. 1958.

[5.3] H. -M. Lee, Microwave Filter Deigns with Different Component Q, Different Mode Velocities, and Dual-Band Characteristics, National Cheng Kung University, Dissertation for Doctor of Philosophy, Jan. 2006, Chap. 3, pp.37-43.

[5.4] M. C. Horton and R. J. Wenzel, “General Theory and Design of Optimum Quarter-Wave TEM Filters,” IEEE Trans. Microwave Theory Tech., vol. 13, no. 3, pp. 316-327, May 1965.
 
[5.5] G. L. Matthaei, “Direct-Coupled Bandpass Filters with λ0/4 Resonator,” IRE Int. Conv. Record, vol. 6, pt. 1, pp. 98-111, 1958.

[5.6] S. Zhang and L. Zhu, “Synthesis Method for Even-Order Symmetrical Chebyshev Bandpass Filters with Alternative J/K Inverters and λ0/4 Resonators,” IEEE Trans. Microw. Theory Techn., vol. 61, no 2, pp. 808-816, Feb. 2013.

[5.7] C. -J. Chen, “Design of Parallel-Coupled Dual-Mode Resonator Bandpass Filters,” IEEE Trans. Compon., Packag., Manuf. Techn., vol. 6, no. 10, pp. 1542–1548, Oct. 2016.

[5.8] R. J. Wenzel, “Synthesis of Combline and Capacitively Loaded Interdigital Bandpass Filters of Arbitrary Bandwidth,” IEEE Trans. Microw. Theory Techn., vol. 19, no 8, pp. 678-686, Aug. 1971.