臺灣博碩士論文加值系統

本論文提出一種全對稱及半對稱的鼠競環混成器及耦合器，且此架構可以實現阻抗轉換及任意功率分配等特性。其中阻抗轉換特性是指輸入輸出埠的阻抗值可以不同，而任意功率分配特性則是指兩個輸出埠的功率比值可以為任意值。由於其半對稱的特性，傳統的奇偶模電路拆分法以及其相關的分析方法並不再適用。本論文提出兩種訊號激發的方法用來轉換原本的四埠混成器或耦合器變成為相關的兩埠網路。緊接著，本篇論文會詳細地演示S域濾波器合成方法，此方法可以用來合成這些兩埠網路。由於使用Ｓ域合成技術，所有關於濾波響應的規格皆為使用者可自定義，例如中心頻、頻寬、反射損耗的水平高度以及切比雪夫濾波響應的階數。此外，本論文也推導了一組簡單的設計方程式用來實現不等功率分配的特性。使用這些方程式，等功率分配的全對稱及半對稱鼠競環混成器可以被轉換成具有任意功率分配的鼠競環耦合器，其耦合器所有其它的規格皆跟原本的混成器相同。四個鼠競環電路被實作用來驗證本論文所提出的分析以及合成方法。其中兩個被製造的電路分別為六階全對稱鼠競環混成器以及五階半對稱鼠競環混成器。另外兩個則分別為二比一以及十比一功率分配五階半對稱鼠競環耦合器，且兩者同時具有輸入輸出埠分別為五十及七十歐姆的阻抗轉換特性。

This thesis proposes the full- and half-symmetric rat-race ring hybrids/couplers, in which the impedance transformation and arbitrary power division characteristics can be implemented. The impedance transformation property implies that the input and output port impedances can be different. The arbitrary power division property implies that the power ratio at two output ports can be arbitrary values. Because of the half-symmetry, the conventional even- and odd-mode partition and corresponding analysis method cannot be applied. Two signal-excitation methods are proposed to reduce the original four-port rat-race ring hybrids or couplers into corresponding two-port networks. Next, the S-domain filter synthesis method is demonstrated in this thesis in detail, and this method can be adopted to synthesize these two-port networks. Duo to the S-domain synthesis technique, all the specifications of filtering responses are user-defined such as a center frequency, a bandwidth, a return loss level, and an order of the Chebyshev response. In addition, the simplified design equations for realizing the unequal power division characteristics are derived in this thesis. By using these equations, the equal power division full- and half-symmetric rat-race ring hybrids can be transformed into the arbitrary power division rat-race ring couplers which other specifications are the same as original hybrids. Four rat-race ring circuits are implements to verify proposed analysis and synthesis methods. Two of these fabricated circuits are a sixth-order full-symmetric rat-race ring hybrid and a fifth-order half-symmetric rat-race ring hybrid, respectively. The other two circuits are the 3-dB and 10-dB power division fifth-order half-symmetric rat-race ring couplers with input/output impedance transformation of 50/70 ohm.

摘要 ...... i
Abstract ...... ii
誌謝 ...... iii
Table of Contents ...... v
List of Figures ...... vii
List o fTables ...... xi

1 Introduction ...... 1
1.1 LiteratureSurvey ...... 1
1.2 Motivation and Contribution ...... 5
1.3 Organization ...... 6

2 Fundamental Theory ...... 7
2.1 Conventional Rat-Race Ring Structure ...... 7
2.2 Filter Synthesis in S-domain ...... 10
2.2.1 Richards’ Transformation ...... 10
2.2.2 Synthesized Function of S-Domain Highpass Prototype ......13
2.2.3 Element Extraction ...... 14
2.2.4 Kuroda Identities ...... 17
2.3 Types of Microstrip Coupled Lines ...... 18
2.3.1 Lange coupler structure ...... 18
2.3.2 Enhanced Coupled Lines ...... 19
2.4 Configurations of Parallel Coupled Lines ...... 20
2.4.1 Open-Ended Parallel Coupled Lines ...... 20
2.4.2 Short-Ended Parallel Coupled Lines ...... 21
2.5 Phase Inverter ...... 21

3 Full- and Half-Symmetric Rat-Race Ring Hybrid With or Without Impedance Transformation ...... 23
3.1 Analysis of the proposed rat-race ring hybrid ...... 23
3.2 Synthesis and design flow of the proposed rat-race ring hybrid ...... 26
3.2.1 Sixth-Order Full-Symmetric Rat-Race Ring Hybrid ...... 27
3.2.2 Fifth-Order Half-Symmetric Rat-Race Ring Hybrid ...... 30
3.2.3 Fifth-Order Half-Symmetric Rat-Race Ring Hybrid With 70-ohm Output Impedance ...... 33
3.3 Fabrication and measurement of the proposed rat-race ring hybrid ...... 34
3.3.1 Sixth-Order Full-Symmetric Rat-Race Ring Hybrid ...... 35
3.3.2 Fifth-Order Half-Symmetric Rat-Race Ring Hybrid ...... 40
3.4 Summary ...... 46

4 Full- and Half-Symmetric Rat-Race Ring Coupler With Unequal Power Division ...... 49
4.1 Analysis of The Core Ring of Proposed Rat-Race Ring Coupler ...... 49
4.2 Synthesis and Simplified Design Equations of Proposed Rat-Race Ring Coupler ...... 54
4.2.1 Source Division Technique ...... 54
4.2.2 Half Circuits of Proposed Rat-Race Ring Coupler ...... 55
4.2.3 Simplified Design Equations ...... 59
4.3 Fabrication and Measurement of The Proposed Rat-Race Ring Coupler ...... 61
4.3.1 Circuit Layout and Implementation ...... 61
4.3.2 Simulation and Measurement ...... 66
4.4 Summary ...... 70

5 Conclusions ...... 71
Bibliography ...... 74
博士候

[1] R. Levy and S. B. Cohn, ”A history of microwave filter research, design, and develop- ment,” IEEE Trans. Microw. Theory Techn., vol.32, pp. 1055-1067, Sep. 1984.

[2] R. J. Wenzel, ”Exact design of TEM microwave networks using quarter-wave lines,” IEEE Trans. Microw. Theory Techn., vol. 12, pp. 94-111, Jan. 1964.

[3] S. Darlington, ”Synthesis of reactance-four-poles which produce prescribed insertion loss characteristics,” J. Math. Phys., vol. 18, pp. 257-353, Sep. 1939.

[4] P. I. Richards, ”General impedance-function theory,” Quart. Appl. Math, vol. 6, pp.21-29, 1948.

[5] P. I. Richards, ”Resistor-transmission-line circuits,” Proc. IRE, vol. 34, pp.217-220, Feb., 1948.

[6] B. A. Lippmann, ”Theory of directional couplers,” M.I.T. Rad. Lab. p., no. 860, Dec. 1945.

[7] M.I.T. Rad. Lab. Series. New York: McGraw-Hill, 1948, no. 8, pp.308-311.

[8] J. Reed and G. J. Wheeler, ”A method of analysis of symmetrical four-port networks,” IRE Trans. Microw. Theory Tech., vol. 4, pp. 246-252, Oct. 1956.

[9] S. March, ”A wideband stripline hybrid ring,” IEEE Trans. Microw. Theory Techn., vol. 16, no. 6, pp. 361, Jun. 1968.

[10] J. L. B. Walker, ”Improvements to the design of the 0-180 degree rat race coupler and its application to the design of balanced mixers with high LO to RF isolation,” in IEEE MTT-S Int. Microw. Symp. Dig., Denver, CO, USA, 1997, pp. 747-750 vol.2.

[11] M. -H. Murgulescu, E. Penard, and I. Zaquine, ”Design formulas for generalised 180° hy- brid ring couplers,” Electron. Lett., vol.30, no.7, pp.573-574, March 1994.

[12] T. Wang and K. Wu, ”Size-reduction and band-broadening design technique of uniplanar hybrid ring coupler using phase inverter for M(H)MIC’s,” IEEE Trans. Microw. Theory Techn., vol.47, no.2, pp.198-206, Feb. 1999.

[13] T.T.Mo, Q.Xue, and C.H.Chan, ”A broadband compact microstrip rat-race hybrid using a novel CPW inverter,” IEEE Trans. Microw. Theory Techn., vol.55, no.1, pp.161-167, Jan. 2007.

[14] S.Rehnmark,”Wide-band balanced line microwave hybrids,”IEEE Trans. Microw. Theory Techn., vol.25, no.10, pp.825-830, Oct. 1977.

[15] C. -Y. Chang, and C. -C. Yang, ”A novel broad-band Chebyshev-response rat-race ring coupler,” IEEE Trans. Microw. Theory Techn., vol.47, no.4, pp.455-462, Apr. 1999.

[16] W.S.Chang,C.H.Liang,andC.Y.Chang,”Wideband high-isolation and perfect-balance microstrip rat-race coupler,” Electron. Lett., vol.48, no.7, pp.382-384, March 2012.

[17] S. Gruszczynski, and K. Wincza, ”Broadband rat-race couplers with coupled-line section and impedance transformers,” IEEE Microw. Wireless Compon. Lett., vol.22, no.1, pp.22- 24, Jan. 2012.

[18] K. S. Ang, and Y. C. Leong, ”Converting baluns into broadband impedance-transforming 180° hybrids,” IEEE Trans. Microw. Theory Techn., vol.50, no.8, pp.1990-1995, Aug. 2002.

[19] C.H.Chi and C.Y.Chang, ”A new class of wideband multisection 180 degree hybrid rings using vertically installed planar couplers,” IEEE Trans. Microw. Theory Techn., vol. 54, no. 6, pp. 2478-2486, June 2006.

[20] L. Chiu and Q. Xue, ”A Parallel-Strip Ring Power Divider With High Isolation and Ar- bitrary Power-Dividing Ratio,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 11, pp. 2419-2426, Nov. 2007.

[21] B.Li, X.Wu and W.Wu, ”A 10:1 Unequal Wilkinson Power Divider Using Coupled Lines With Two Shorts,” IEEE Microw. Wireless. Compon. Lett., vol. 19, no. 12, pp. 789-791, Dec. 2009.

[22] K. K. M. Cheng and P. W. Li, ”A Novel Power-Divider Design With Unequal Power- Dividing Ratio and Simple Layout,” IEEE Trans. Microw. Theory Techn., vol. 57, no. 6, pp. 1589-1594, June 2009.

[23] F. Lin, Q. X. Chu, Z. Gong and Z. Lin, ”Compact Broadband Gysel Power Divider With Arbitrary Power-Dividing Ratio Using Microstrip/Slotline Phase Inverter,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 5, pp. 1226-1234, May 2012.

[24] D. . Pozar, Microwave Engineering 3rd ed. New York: Wiley, 2005.

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

[26] J. Helszajn, Microwave Planar Passive Circuits and Filters. New York: Wiley, 1994.

[27] L. Weinberg, Network Analysis and Synthesis. New York: McGraw-Hill, 1962.

[28] E. A. Guillemin, Synthesis of Passive Networks. New York: Wiley, 1957.

[29] J.Lange, ”Interdigitated stripline quadrature hybrid,”IEEETrans. Microw. Theory Techn., vol.17, no.12, pp.1150-1151, Dec 1969.

[30] R.Waugh, and D.Lacombe, ”Unfolding the Lange coupler, ”IEEE Trans. Microw. Theory Techn., vol.20, no.11, pp.777-779, Nov. 1972.

[31] L. Zhu, and K. Wu, ”Multilayered coupled-microstrip lines technique with aperture com- pensation for innovative planar filter design,” in Proc. Asia-Pacific Microw. Conf., vol.2, pp.303-306, Nov 1999.

[32] S.Im, C.Seo, J.Kim, Y.Kim, andN.Kim, ”Improvement of microstrip open loop resonator filter using aperture,” in IEEE MTT-S Int. Microw. Symp. Dig., vol.3, pp.1801-1804 vol.3, June 2002.

[33] M. C. Velazquez-Ahumada, J. Martel, and F. Medina, ”Parallel coupled microstrip filters with ground-plane aperture for spurious band suppression and enhanced coupling,” IEEE Trans. Microw. Theory Techn., vol.52, no.3, pp.1082-1086, March 2004.

[34] C. H. Liang, W. S. Chang and C. Y. Chang, ”Enhanced Coupling Structures for Tight Couplers and Wideband Filters,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 3, pp. 574-583, March 2011.

[35] Y. W. Lin, Y. C. Chou and C. Y. Chang, ”A Balanced Digital Phase Shifter by a Novel Switching-Mode Topology,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 6, pp. 2361- 2370, June 2013.

[36] S. -G. Kim, and K. Chang, ”Ultrawide-band transitions and new microwave components using double-sided parallel-strip lines,” IEEE Trans. Microw. Theory Techn., vol.52, no.9, pp.2148-2152, Sept. 2004.

[37] K. -W. Wong, L. Chiu, and Q. Xue, ”Wideband parallel-strip bandpass filter using phase inverter,” IEEE Microw. Wireless Compon. Lett., vol.18, no.8, pp.503-505, Aug. 2008.

[38] K. S. Ang and I. D. Robertson, ”Analysis and design of impedance transforming planar Marchand baluns,” IEEE Trans. Microw. Theory Techn., vol.49, pp.402-406, Feb. 2001.

[39] C. H. Chi, C. H. Wu, W. T. Wang, C. H. Lai, D. C. Niu, and C. Y. Chang, ”A 10-110GHz fundamental/harmonic rat-race mixer,” in Proc. European Microw. Conf., pp.652-655, Oct. 2007.