臺灣博碩士論文加值系統

本篇論文以理論推導計算、數值模擬和實驗方法應用於開放式共振腔來量測材料之介電常數和介電損耗。主要是在Ka-band的35GHz附近去做量測。實驗上是利用HP8510網路分析儀去做量測，主要量測材料是Teflon為樣本。數值模擬軟體主要是利用HFSS9.2去做數值分析。實驗所量測到的值和已知論文量測值比較，介電常數誤差約1%以下， 誤差30%以下。本論文主要是利用高耦合系數的共振腔去做量測，結果與大部分已知論文極為相近。

第一章 簡介.............................1
1.1 概述 1
1.1.1 介電常數和介電損耗 1
1.1.2 品質因子 2
1.1.3 材料的介電性質 6
1.2 介電常數的量測 7
1.2.1 傳統低頻介電常數量測法 7
1.2.2 各種高頻的量測法簡介 8

第二章 開放式共振腔理論推導與量測理論..10
2.1 高斯光束理論 10
2.1.1 簡介 10
2.1.2 高斯光束傳播方程式 10
2.1.3 高斯光束的高次模態 13
2.1.4 Hermite-Gaussian 模的共振頻率 14
2.2 介電材料在開放式共振腔的理論推導 15
2.2.1 簡介 15
2.2.2 量測樣品介電常數的理論推導 16
2.2.3 量測樣品介電損耗的理論推導 18
2.2.4 總結 20

第三章 模擬結果和討論..................21
3.1 高斯理論、HFSS模擬和實驗的驗証 22
3.1.1 驗證電場和磁場分佈是否符合 22
3.1.2 驗證腔體大小和頻率是否符合 23
3.1.3 理論計算spot size的大小和q軸向模態的關係 24
3.1.3 利用真空樣品檢驗公式 25
3.2 利用HFSS模擬實驗 26

第四章 實驗結果和討論..................28
4.1 實驗儀器和操作 28
4.1.1實驗儀器簡介 28
4.1.2實驗過程概述 29
4.2實驗結果及誤差 31
4.2.1 實驗結果和討論 31
4.2.2 量測誤差討論 35

第五章 結論............................37

附錄...................................38
Appendix A 空腔和放入樣品的的腔壁損耗關係 38
Appendix B 初略找放入樣品後基模共振頻率 41

參考文獻...............................42

[1] John David Jackson, Classical Electrodynamics 3rd edition. New York: John Wiley & Sons.
[2] David M. Pozar, Microwave Engineering 2ed edition. New York: John Wiley & Sons.
[3] William D. Callister, Jr. Materials Science And Engineering An Introduction. New York：John Willey & Son.
[4] G.W. Chantry, “The Measurement of the Properties of Materials,” IEEE Proc., vol.74, NO.1, Jan 1986.
[5] Joseph T. Verdeyen, Laser Electronics 3rd edition. Pearson.
[6] P.K.Yu; A.L.Cullen, “Measurement of Permittivity by Jeans of an Open Resonator .I. Theoretical”Proc.Roy.Soci. London., Vol.380,No.1788,pp.49-71.
[7] R.J.Cook, R.G.Jones,C.B.Rosenberg, “Comparison of Cavity and Open-Resonator Measurements of Permittivity and Loss Angle at 35GHz.”, IEEE Trans.Ins.Measur.,Vol.IM-23,No.4,December 1974.
[8] A.L. Cullen; P.K. Yu “The Accurate Measurement of Permittivity by Means of an Open Resonator.”, Proc.Roy.Soci. London., Vol.325,No.1563,pp.493-509.
[9] Jyh Sheen, “Study of microwave dielectric properties measurements by various resonance techniques.”, Measurement,Vol.37,(2005),pp.123-130.
[10] F. I. Shimabukuro, and C.Yeh, “Attenuation Measurement of Very Low Loss Dielectric Waveguides by the Cavity Resonator Method Applicable in the Millimeter/Submillimeter Wavelength Range.”, IEEE Trans. Microwave Theory tech.,vol.36,No.7, pp.1160-1166, July 1988.
[11] J.E. Degenford, And P.D. Coleman, “ A Qusi-Optical Perturbation Technique for Measuring Dielectric Constants”, Proc. of the IEEE. , Vol.54 (April 1966), pp.520-522.
[12] B. Komiyama, M.Kiyokama, and T. Matsui, “Open Resonator for Precision Dielectric Measurements in the 100 GHz Band”, IEEE Trans. Microwave Theory tech., Vol.39, No.10(Oct.1991), pp.1792-1796.
[13] Y.N. Noskov , “Method for Measuring Properties of High Relative Dielectric Constant Materials in a Cutoff Waveguide Cavity.”, IEEE Trans. Microwave Theory tech.,Vol.48, No.3,March 2000,pp.329-333.
[14] J. Krupka , “Precise measurements of the complex permittivity of dielectric materials at microwave frequencies.”, Materials Chemistry and Physics ,Vol.79 (2003), pp.195-198.
[15] H. Kogelnik and T. Li, “Laser Beams and Resonators.”, Proc. of the IEEE., Vol.54, No.10,Oct. 1966,pp.1312-1329.
[16] R.O. Bell and G. Rupprecht, “Measurement of Small Dielectric Losses in Material with a Large Dielectric Constant at Microwave Frequencies.”, IRE Tran. Micro. Theory and Techniques, May 1961, pp.239-242.
[17] J.Sheen, “Study of microwave dielectric properties measurements by various resonance techniques.”, Measurement , Vol.37(2005), pp.123-130.
[18] R.G. Carter, “Accuracy of Microwave Cavity Perturbation Measurements.”, IEEE Trans. Microwave Theory tech.,Vol.49,No.5,May 2001, pp.918-923.
[19] Z. Abbas, R.D. Pollard, and R.W. Kelsall, “ Complex Permittivity Measurements at Ka-Band Using Rectangular Dielectric Waveguide.”, IEEE Trans.Ins.Measur., Vol.50, No.5, Oct.2001, pp.1334-1342.
[20] J.H. Liu, C.L. Chen, H.T. Lue, and J.T. Lue, “A new Method Developed in Measuring the Dielectric Constants of Metallic Nanoparticles by a Microwave Double-Cavity Dielectric Resonator.”, IEEE Microwave and Wireless Components Letter, Vol.13, No.5, May 2003,pp.181-183.
[21] P. Hillion, “Hertz-Debye potential and pulse propagation.”, J.Phys.A:Math.Gen.31(1998), pp.547777-5484.
[22] L. Chen, C.K. Ong, and B.T.G. Tan, “Amendment of Cavity Perturbation Method for Permittivity Measurement of Extremely Low-Loss Dielectrics.”, IEEE Trans.Ins.Measur., Vol.48, No.6,Dec.1999, pp.1031-1037.
[23] J. Obrzut and R. Nozaki,“ Permittivity Measurements of High Dielectric Constant Films at Microwave Frequencies.”, IPC EXPO Technical,April 2-7,2000, pp.61-66.
[24] R.N. Clark and C.B. Rosenberg, “Fabry-Perot and open resonators at microwave and millimeter wave frequencies,2-300 GHz”, J.Phy.E:Sci. Instrum., Vol. 15, 1982., pp.9-24.
[25] R.G. Jones, B.Sc.,M.Sc., “Precise dielectric measurements at 35 GHz using an open microwave resonator.”, Proc.IEE,Vol.123,No.4,April 1976.pp.285-290.
[26] S. Wang, D. Xu and L.Hu, “Open resonator Technique For Measuring Multi-Layer Dielectrics.”, Asia Pacific Microwave Conference, 1997,pp.885-888.
[27] A.N. Deleniv and S.Gevorgian, “ Open Resonator Technique for Measuring Multilayered Dielectric Plates.” IEEE Trans. Microwave Theory tech.,Vol.53,No.9, Sept. 2005, pp.2908-2916.
[28] F.I. Shimabukuro, S. Lazar, M.R. Chernick, and H.B. Dyson, “A Qusi-Optical Method for Measuring the Complex Permittivity of Materials.”, IEEE Trans. Microwave Theory tech., Vol.MTT-32, No.7, July 1984, pp.659-665.
[29] A.E. Siegman, Lasers ,University Science Books.
[30] K.R. Chu, “微波物理與應用”講義, 清大物理系.
[31] K.R. Chu, “Time Domain Analysis of Open Cavities,”講義, 清大物理系.