在本篇論文中，我們利用碎型理論來設計應用在802.11b/a的多層陶瓷balun元件並且利用低溫共燒陶瓷的製程將之實作出來。利用碎型曲線在我們的balun設計中，可以減少balun所占的面積同時只需要幾層的金屬層。在電氣特性上，我們能夠得到良好的輸出平衡及相角差，同時反射損耗的頻寬也有1.3 GHz並且有良好的匹配。利用多層結構的低溫共燒陶瓷製程所實作出來的碎型balun所量測到的結果和模擬的結果非常相近同時呈現出令人滿意的特性。我們將碎型的balun和原型的Marchand balun作比較，假設以802.11b的頻率來比較的話, Koch’s和Minkowski曲線分別可以減少46.4%和50%的面積。最後，我們利用完成的碎型balun和碎型的帶通濾波器、碎型天線作整合來構成一個簡單的被動模組，模擬的過程將在這篇論文中被討論同時從這個模組的模擬結果我們得到一個令人滿意的特性。

A new multilayer ceramic balun with fractal curve for 802.11b/a is presented in this thesis. The fractal curve is implemented in balun design. By using the fractal geometry, the reduction in size of the proposed balun is evident and only several metal layers are used. Excellent results of amplitude balance and phase difference are obtained. In the mean time, there is a 1.3-GHz bandwidth of return loss and the design results in a good matching. The measured results of the LTCC multilayer ceramic balun with fractal curve agree well with the simulation. Satisfactory performance is also obtained. The dimension of the proposed Koch’s and Minkowski_1st balun can be reduced by about 46.4% and 50%, respectively. Finally, the fractal balun is combined with fractal band pass filter and fractal antenna to become a passive module. Simulation of the module has been carried out and we find satisfactory results.

Acknowledgement.……………………………………………………………i
Abstract (Chinese)…………………………………………………………iii
Abstract (English)……………………………………………………………iv
Contents………………………………………………………………………v
List of Figures……………………………………………………………vii
List of Tables…………………………………………………………………xii

Chapter1 Introduction…………………………………………………………1
1.1 The background……………………………………………………………1
1.2 The purpose and approach for study………………………………………2
1.3 Outline of the thesis…………………………………………………………4

Chapter2 LTCC………………………………………………………………5
2.1 What is LTCC………………………………………………………………5
2.2 LTCC Material System and Process………………………………………7
2.2.1 LTCC Material System………………………………………………7
2.2.2 Process Flow………………………………………………………12
2.3 LTCC Design Flow………………………………………………………19

Chapter3 Fractal Theory……………………………………………………23
3.1 Introduction of Fractal Theory…………………………………………23
3.2 Dimension Definition of Fractal Curve…………………………………25
3.3 Fractal Application in Microwave………………………………………28

Chapter4 Design of Fractal Balun……………………………………………32
4.1 Introduction of Balun Theory……………………………………………32
4.2 Realize the design of Fractal Balun for LTCC……………………………35
4.2.1 The Prototype of Balun…………………………………………36
4.2.2 Balun with Von Koch Curve……………………………………44
4.2.3 Balun with Minkowski_1st Curve……………………………………48
4.3 Performance Comparison…………………………………………………52
4.4 Design of Fractal Balun for 802.11a Application…………………………55

Chapter5 Measurement Results……………………………………………64
5.1 TRL Calibration and Measurement Method………………………………64
5.1.1 TRL Calibration……………………………………………………64
5.1.2 Balun Measurement Method…………………………………………66
5.1.3 Test Board and TRL Calibration Board……………………………67
5.2 The Measured Results of 2.4 GHz Balun……………………………68
5.2.1 Measured Result of Prototype Balun for 2.4 GHz…………………68
5.2.2 Measured Result of Fractal Balun with Von Koch Curve
for 2.4 GHz…………………………………………………………71
5.2.3 Measured Result of Fractal Balun with Minkowski Curve
for 2.4 GHz…………………………………………………………73
5.2.4 Analysis of Defect Mode…………………………………………75
5.2.5 Performance Improvement and Comparison Table with Simulation77
5.3 The Measured Results of Fractal Balun for 802.11a………………………86

Chapter6 Design of Passive Module ………………………………………99
6.1 The
Simulated Result of Combing Fractal Balun and BPF………………99
6.2 The Antenna Design for Module…………………………………………105
6.3 The Simulation Result of Passive Module………………………………107

Chapter7 Conclusion………………………………………………………111

Reference……………………………………………………………………113

Reference

[1] Lap Kun Yeung, member, IEEE, and Ke-Li Wu, senior member, IEEE, “An LTCCBalanced-to-Unbalanced extracted-pole band pass filter with complex load,”IEEE Trans. on Microwave Theory and Tech., vol.54, no.4, pp.1512-1518, Apr.,2006.
[2] 經濟部技術處IT IS計畫 / 產業分析師 林正益, “ 藍芽射頻元件整合技術概況 “
[3] Y. X. Guo, Z. Y. Zhang, and L.C. Ong, “Design of Miniaturized LTCC Baluns,”IEEE, pp.1567~1570, 2006
[4] 台大電信 電波組, 楊錫明, 郭宗男, “ LTCC Introduction,”
[5] Heli Jantunen, “ A Novel Low Temperature Co-Firing Ceramic (LTCC) material for Telecommunication Devices,” Department of Electrical Engineering and Infotech Oulu, University of Oulu.
[6] Dr.S. Vasudevan, “ The Effect of Processing Parameters and Surface Roughness of Conductor Traces on the Microwave Properties of LTCC Structure,” Ferro Corporation Electronic Materials Divison
[7] 盧慶儒 “低溫共燒多層陶瓷技術特點與應用,” http://www.digitimes.com.tw
[8] Dr.S. Vasudevan, “ What is LTCC?- Introduction,” http://www.ltcc.de/en/print.php
[9] http://www.nchc.org.tw/ 國家高速電腦中心SONNET 2.5D 高頻電路模擬軟體介紹
[10] http://www.nchc.org.tw/ 國家高速電腦中心HFSS 3D 高頻電路模擬軟體介紹
[11] SONNET User’s Guide, Sonnet Software,Inc.
[12] Ansoft HFSS Engineering Note, Ansoft Corporation.
[13] B. B. Mandelbrot, The Fractal Geometry of Nature. New York: W. H. Freeman and company, 1977
[14] http://en.wikipedia.org/wiki/Fractal
[15] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, New York: John Wiley & Sons, 1990.
[16] H. Lauwerier, Fractals: Endlessly repeated Geometrical Figures, Princeton, New Jersey: Princeton University Press, 1991.
[17] J-F Gouyet, Physics and Fractal Structures, New York: Springer, 1996
[18] Yamaguti, Masaya, M. Hata, and J. Kigami, Translations of Mathematical Mono-graphs Volume 167 : Mathematics of Fractals, Providence, Rhode Island: American Mathematical Society, 1993.
[19] H.-O. Peitgen, J.M. Henriques, and L. F. Penedo, Eds., Fractals in the Fundamental and Applications Sciences. Amsrerdam: North Holland, 1991.
[20] G.. P. Cherepanov, A. S. Balankin, and V. S. Inanova, “Fractal fracture mechanics,” Eng. Fracture mechan., vol.51, pp.997-1033,1995
[21] “ Fractal Dimension,” http://math.bu.edu/DYSYS/Chaos-game/node6.html
[22] Hirad Samavati, Ali Hajimiri, Arvin R. Shahani, Gitty N. Nasserbakht, and Thomas H. Lee, “Fractal Capacitors,” IEEE Journal of Solid-State Circuits, vol.
33, no.12, pp.2035-2041, Dec. 1998.
[23] Hani Ghali , Member, IEEE, and Tarek A. Moselhy, “Miniaturized Fractal Rat-Race, Branch-Line, and Coupled-Line Hybrids,” IEEE Trans. on
Microwave Theory and Techniques, vol.41, no.11, pp.2513-2520, Nov. 2004
[24] K. J. Vinory, Jose K. Abraharm, Vijay K. Varadan, “ On the relationship Between
Fractal Dimension and the performance of Multi-Resonant Dipole Antennas Using Koch Curves,” IEEE Trans. on Antennas and Propagat., vol. 51, no.9,
pp.1405-1414, Sep. 2003.
[25] Byoung Hwa Lee, Dong Seok Park, Sang Soo Park, and Min Cheol Park, Design of New Three-Line Balun and Its Implementation Using Multilayer
Configuration,” IEEE Trans. of Microwave Theory and Tech., vol.54, no.4, Apr.2006.
[26] Yong-Xin Guo, Senior Member,IEEE, Z.Y. Zhang, L.C. Ong, Senior Member, IEEE, and M. Y. W. Chia, Member, IEEE, “ A Novel LTCC Miniaturized
Dualband Balun,” in IEEE Microwave And Wireless components lett., vol.16, no.3, Mar. 2006.
[27] Zhen-Yu Zhang, Yong-Xin Guo, L.C. Ong, and M.Y.W. Chia “ A New Planar Marchand Balun,” IEEE MTT-S Dig., pp1207-1210, Jun. 2005.
[28] M. C. Tsai, “A new compact wideband balun,” IEEE MTT-S Dig.,vol.1pp.141-143 , 1993
[29]徐建榆, “射頻積體電路之電感及相關被動元件之研製,” pp44~45, 國立成功 大學微電子工程研究所,碩士論文
[30]余思嫻, “ 低溫陶瓷共燒平衡式頻率雙工器模組, “ pp7~8, 國立交通大學
[31] D.W. Lew, J.S. Park, D.Ahn, N.K.Kang, W.Lim and C.S. Yoo, “ A design of the ceramic multilayer chip balun,” IEEE MTT-S Dig., pp.1893-1896, 1999.
[32] C.W. Tang and C.Y. Chang, “LTCC-MLC chip-type balun realized by LC resonance method” , IEEE Electrics Letters 23rd, vol.68, no.11, pp.519-520,
May 2002
[33] Ching-Wen Tang and Choi-Yang Chang, “ Using buried capacitor in LTCC-MLC balun,” IEEE Electrics Letters 18th, vol.38, no.15, pp.801-802, July 2002.
[34] Ching-Wen Tang and Chi-Yang Chang, “ A Semi-Lumped Balun Fabricated By Low Temperature Co-fired Ceramic,” in IEEE MTT-S Digest, pp.2201-2204,
2002.
[35] H. Tanaka, N. Banba, S. Ari and T.Nishikawa, “ 2GHz one octave-band 90 degree hybrid coupler using coupled meander line optimized by 3D FEM,” in IEEE MTT-S Int. Microwave Symp.Dig., pp.903-906, 1994.
[36] S.-M. Wang, C.-H. Chen, and C.-Y. Chang, “ A Study of meandered micro-strip coupler with high directivity,” in IEEE MTT-S Int. Microwave Symp., Dig., pp.63-66, 2003.
[37] 蔡第奇, “平衡市元件之向量網路分析儀量測技術,” pp.9-12, 國立中山大學 碩士論文
[38] Agilent, “ TRL/ LRM Calibration,”
[39] Agilent, “ Multi-port & Balanced Device Measurement Application Note Series,”
[40] http://pages.cs.wisc.edu/~ergreen/honors_thesis/
fractal.html
[41] 陳岳忠, “用碎形結構來設計符合無線網路規格的天線,” 國立中山大學電機工程學系 碩士論文, 2006.
[42] 郭騏民, “使用低溫共燒陶瓷碎形濾波器之設計與實作,” 國立中山大學電機工程學系 碩士論文, 2006.