針對三線平衡不平衡轉換器的電路模型，本論文提出了一個略為不同的電路分析方法，藉由黑田轉換恆等式的使用，可以直接萃取出一個1:-1的變壓器。因此三線平衡不平衡轉換器可直接視為兩個完全相等的二階濾波器對稱相接，兩邊唯一差別只在一個1:-1的變壓器。

本論文主要探討了三線平衡不平衡轉換器在窄頻應用時所產生的問題，從公式推導中發現是因為等效模型中的部分元件導納值過高的原因。針對第一類平衡不平衡轉換器作討論後發現，這結構中之一部分耦合線結構在窄頻時會難以實現，因此本論文提出了兩個解決此問題的四線平衡不平衡轉換器結構。此外，利用冗餘性的設計也可以降低等效模型中的導納值，本論文針對了三種不同的冗餘性設計進行了研究，除了分別探討其優缺點之外，並以電磁模擬去驗證此冗餘性設計的可行性。

最後，針對所提出的四線平衡不平衡轉換器，本論文提出了電磁模擬與實作量測的結果，證實這是一種可行的方法。實驗過程中並發現，短路銅柱的寄生電感會破壞此轉換器的平衡，因此有必要利用其他方法補償這寄生電感所產生的效應。

關鍵字：濾波器、平衡不平衡轉換器

This thesis provides a slightly different derivation of the network model for three-line baluns. Kuroda’s identity is used for the extraction of a 1:-1 ideal transformer. Three-line baluns can then be identified directly as two identical second-order filters connected side by side, symmetrically. The only difference is a 1:-1 ideal transformer.

The main part of this thesis is on the design of narrowband three-line baluns. The admittances of some transmission-line sections in the network model are too high to be realizable. One of the two coupled-line sections of Type I balun is found to be particularly critical. In order to solve this problem, two modified structures, with four coupled lines, are proposed. Introducing redundant components to the filter design can also lower the admittances. Three types of redundant designs are discussed and verified by electromagnetic simulations.

One of the proposed four-line balun is designed, fabricated, and measured. The results agree with the theory. In this experiment, it is also found that the parasitic inductance of via holes can cause output unbalance and must be compensated for a better performance.

Index Terms: Filter, and Balun.

[1.1] N. Marchand “Transmission-line Conversion Transformers”, Electronics, vol. 17, no. 12, pp. 142-145, Dec. 1944 .

[1.2] J. H. Cloete “Exact Design of the Marchand Balun”, Microw. J., vol. 23, no. 5, pp. 99-102, May 1980.

[1.3] J. H. Cloete “Graphs of Circuit Elements for the Marchand Balun”, Microw. J., vol. 24, no. 5, pp. 125-128, May 1981.

[1.4] K. Nishikawa, I. Toyoda, and T. Tokumitsu, “Compact and Broad-Band Three-Dimensional MMIC Balun,” IEEE Trans. Microw. Theory Tech., vol.47, no.1, pp.96-98, Jan. 1999.

[1.5] Y. J. Yoon, Y. Lu, R. C. Frye, M. Y. Lau, P. R. Smith, L. Ahlquist, and D. P. Kossives, “Design and Characterization of Multilayer Spiral Transmission-line Baluns,” IEEE Trans. Microw. Theory Tech., vol.47, no.9, pp.1841-1847, Sept. 1999.

[1.6] O. A. Glubokov and B. N. Shelkovnikov, “Broadband Balun in LTCC Technology Using Vertical Solenoid Coupled Transmission Lines,” , in 7th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Services Dig. 2005, pp.452-455.

[1.7] H. -M. Lee and C. -M. Tsai, “Exact Synthesis of Broadband Three-Line Baluns,” IEEE Trans. Microw. Theory Tech., , vol.57, no.1, pp.140-148, Jan. 2009.

[2.1] H. -M. Lee and C. -M. Tsai, “Exact Synthesis of Broadband Three-Line Baluns,” IEEE Trans. Microw. Theory Tech., , vol.57, no.1, pp.140-148, Jan. 2009.

[2.2] C. -M. Tsai and K.C. Gupta, “CAD Procedures for Planar Re-entrant Type Couplers and Three-line Baluns,” in IEEE MTT-S Int. Microw. Symp. Dig., 1993, pp. 1013-1016 .

[2.3] C. Cho and K. C. Gupta, “A New Design Procedure for Single-Layer and Two-Layer Three-Line Baluns,” IEEE Trans. Microw. Theory Tech., vol.46, no. 12, pp. 2514-2519, Dec. 1998.

[2.4] R. C. Johnson and H. Jasik, Antenna Engineering Handbook, 2nd ed. McGraw-Hill, New York, pp. 43-24, 1984.

[2.5] R. E. Dabrecht, “Coplanar Balun Circuits for GaAs FET High-Power Push-Pull Amplifiers,” in IEEE MTT-S Int. Microw. Symp. Dig., 1973, pp.309-312.

[2.6] B. Lee, D. Park, S. Park, and M. Park, “Design of New Three-Line Balun and its Implementation Using Multilayer Configuration,” IEEE Trans. Microw. Theory Tech., vol. 54, no.4, pp. 1405-1414, April 2006.

[2.7] R. Sato and E. Cristal, “Simplified analysis of coupled transmission-line networks,” IEEE Trans. Microw. Theory Tech., vol. 18, No. 3, pp. 122-131, March 1970.

[2.8] R. Levy and J. Helszajn, “Specific Equations for One and Two Section Quarter-Wave Matching Networks for Stub-Resistor Loads, ” IEEE Trans. Microw. Theory Tech., vol. MTT-30, no. 1, pp. 55-63, Jan. 1982.

[3.1] C. -M. Tsai and K. C. Gupta, “CAD Procedures for Planar Re-entrant Type Couplers and Three-line Baluns,” in IEEE MTT-S Int. Microw. Symp. Dig., 1993, pp. 1013-1016.

[3.2] V. K. Tripathi, “Asymmetric Coupled Transmission Lines in an Inhomogeneous Medium,” IEEE Trans. Microw. Theory Tech., vol. 23, pp. 734-739, Sept. 1975.

[3.3] C. -M. Tsai and K. C. Gupta, “A Generalized Model for Coupled Lines and its Applications to Two-Layer Planar Circuits” IEEE Trans. Microw. Theory Tech., vol.40, no. 12, pp. 2190-2199, Dec. 1992.

[4.1] M. Goldfarb and R. Pucel, “Modeling via hole grounds in microstrip,” IEEE Microw. Guided Wave Lett., vol. I , no. 6, pp. 135-137, June 1991.

[4.2] D. Swanson “Grounding Microstrip Lines With Via Holes,” IEEE Trans. Microw. Theory Tech., vol. 40, no. 8, pp. 1719-1721, Aug. 1992.

[5.1] H. -M. Lee and C. -M. Tsai, “Exact Synthesis of Broadband Three-Line Baluns,” IEEE Trans. Microw. Theory Tech., vol.57, no.1, pp.140-148, Jan. 2009.

[5.2] C. -M. Tsai and K. C. Gupta, “CAD Procedures for Planar Re-entrant Type Couplers and Three-line Baluns,” in IEEE MTT-S Int. Microw. Symp. Dig., 1993, pp. 1013-1016.

[5.3] R. Levy and J. Helszajn, “Specific Equations for One and Two Section Quarter-Wave Matching Networks for Stub-Resistor Loads, ” IEEE Trans. Microw. Theory Tech., vol. MTT-30, no. 1, pp. 55-63, Jan. 1982.

[5.4] R. Sato and E. Cristal, “Simplified analysis of coupled transmission-line networks,” IEEE Trans. on Microw. Theory Tech., vol. 18, No. 3, pp. 122-131, March 1970.

[5.5] M. Goldfarb and R. Pucel, “Modeling via hole grounds in microstrip,” IEEE Microwave Guided Wave Lett., vol. 1 , no. 6, pp. 135-137, June 1991.

[5.6] D. Swanson, “Grounding Microstrip Lines With Via Holes,” IEEE Trans. Microw. Theory Tech, vol. 40, No. 8, pp. 1719-1721, Aug. 1992.