由於微波通訊系統的快速發展，小型化和高功能已經成為微波元件的兩大主要需求。而微波介電材料更將是符合這些要求的最佳選擇，因為其高介電常數可以降低元件的尺寸，而高品質因數則又可以改善元件的微波特性，並且低的共振頻率溫度漂移係數則又可以降低由於溫度變化所產生的元件共振頻率漂移。如以上所言，本論文將分成兩大主題來討論：微波介電材料和微波濾波器。

一、 微波介電材料
由於AB2O6 (A=Mg, Zn; B=Ta, Nb)微波介電材料所設計出之介電共振子在微波頻段呈現出極佳的微波介電特性。因此，在以往AB2O6微波介電材料已被廣泛應用於微波介電共振子(DRs)之中。但是對於純的MgTa2O6、MgNb2O6、ZnTa2O6和ZnNb2O6微波介電材料而言，要將其使用在微波頻段時，其共振頻率溫度漂移係數仍然不夠好。其中，MgTa2O6和ZnTa2O6呈現出共振頻率溫度漂移係數而MgNb2O6和ZnNb2O6卻呈現出負的共振頻率溫度漂移係數。因此，在本研究中，我們將組合正共振頻率溫度漂移係數的MgTa2O6陶瓷和負共振頻率溫度漂移係數的MgNb2O6陶瓷來形成共振頻率溫度漂移係數趨近於零的MgTa2-xNbxO6微波介電陶瓷；並且組合正的共振頻率溫度漂移係數的ZnTa2O6陶瓷和負的共振頻率溫度漂移係數的ZnNb2O6陶瓷來形成共振頻率溫度漂移係數趨近於零的ZnTa2-xNbxO6微波介電陶瓷，此二種微波介電陶瓷都非常適合應用於微波元件之中。此外，其燒結及微波介電特性亦將在此章中一併詳盡探討。

二、 微波濾波器
微波濾波器已被廣泛應用於通訊系統之中，本研究中所研發出的AB2O6最佳微波介電材料將於後續中用來當作微波濾波器之基板材料。由於基板材料的高介電常數和高品質因數，所設計出的濾波器之功能將可以明顯的提升。首先，我們將組合修正型端點耦合微帶線和半波長共振腔來研發出一個寬頻和雙頻(2.45/5.2 GHz)帶通濾波器，此技巧將很容易地在止帶中產生三個傳輸零點來改善濾波器特性。其次，本文將組合修正型端點耦合微帶線、外框結構和半波長U型髮夾共振腔來完成一個三頻陶瓷帶通濾波器(1.57/2.45/5.2 GHz)。並且，在元件背面採用缺陷接地面結構(DGS)來產生第四個頻帶(3.5 GHz)而完成四頻陶瓷帶通濾波器(1.57/2.45/3.5/5.2 GHz)。其中，由於使用了高介電常數陶瓷基板以及共振器組合的技巧，此四頻陶瓷帶通濾波器的實際尺寸只有26.3 mm*9.9 mm，而且在止帶中總共產生了六個極深的傳輸零點來改善濾波器特性(1~7 GHz)，其所有濾波器的實測特性(頻率、頻寬、插入損、止帶拒斥等等)皆符合目前微波通訊系統之應用。

With the rapidly progress in the microwave communication systems, miniaturization and performance enhancement have become two main requirements of the microwave devices. Microwave dielectric substrates would be the best choice for these requirements, because high dielectric constant of the substrates would reduce the size of the devices, high quality factor of the substrates would improve the microwave characteristics of the devices, and low temperature coefficient of resonant frequency would reduce the shift of the operating frequencies due to the variation of temperature. As mentioned above, the main research of this dissertation is divided into two parts: microwave dielectric materials and microwave filters.

1. Microwave dielectric materials
AB2O6 (A=Mg, Zn; B=Ta, Nb) microwave dielectric ceramics have been developed as the microwave dielectric resonators (DRs) in the past, because the dielectric resonators fabricated by AB2O6 ceramics reveal the good microwave dielectric characteristics. However, the temperature coefficients of resonant frequency of MgTa2O6, MgNb2O6, ZnTa2O6, and ZnNb2O6 ceramics are still not good enough for the applications at the microwave frequency. In addition, MgTa2O6 and ZnTa2O6 ceramics reveal positive temperature coefficients of resonant frequency but the MgNb2O6 and ZnNb2O6 ceramics reveal negative temperature coefficients of resonant frequency. In this study, combining of MgNb2O6 ceramics (with negative temperature coefficients of resonant frequency) and MgTa2O6 ceramics (with positive temperature coefficients of resonant frequency) to form Mg(Ta1-xNbx)2O6 ceramics and combining of ZnNb2O6 ceramics (with negative temperature coefficients of resonant frequency) and ZnTa2O6 ceramics (with positive temperature coefficients of resonant frequency) to form Zn(Ta1-xNbx)2O6 ceramics, which all reveal near-zero temperature coefficients of resonant frequencyand are suitable for the applications of microwave communication devices. The sintering and microwave dielectric characteristics of the Mg(Ta1-xNbx)2O6 and Zn(Ta1-xNbx)2O6 dielectric ceramics are also investigated.

2. Wide-band, dual-band, tri-band, and tetra-band bandpass filters
Microwave filters have been widely used in the communication systems. The optimal microwave dielectric characteristics of AB2O6 ceramics developed in this thesis were adopted as the substrates of the filters. The performance of the filters was improved obviously due to the high dielectric constant and high quality factor of the microwave dielectric ceramic substrates. At first, a wide-band and a dual-band (2.45/5.2 GHz) bandpass filters are developed by the combination technique of modified end-coupled microstrip lines and half-wavelength ombination technique will generate three transmission zeros easily in the stop-band to improve the characteristics of the filters. And the next, the tri-band (1.57/2.45/5.2 GHz) bandpass filters are developed by the combination of modified end-coupled microstrip lines, outer-frame structures and half-wavelength U-shaped hairpin resonators. The Defected Grounded Structures (DGS) are add into the ground planes of the tri-band bandpass filters to generate the fourth frequency (3.5 GHz), hence, the tetra-band (1.57/2.45/3.5/5.2 GHz) bandpass filters are accomplished. In addition, due to the uses of the high dielectric constant ceramic substrates and the combination techniques, the size of this tetra-band bandpass filter is only 26.3 mm*9.9 mm. Besides, six deeply transmission zeros are generated in the stop-band to improve the characteristics of the filters (1~7 GHz), all the characteristics of this tetra-band filters (frequency, bandwidth, insertion loss, and stop-band rejection) are suitable for the applications of modern communication systems.

Abstract Ⅰ
Acknowledgement Ⅴ
Contents Ⅵ
Table Captions Ⅹ
Figure Captions ⅩI
Chapter 1 General Introduction 1
1-1 Microwave Dielectric Materials and Dielectric Resonators 1
1-2 Microwave Planar Filter 3
1-3 Motivation of the Research 4
1-4 Outline of the Thesis 5
Chapter 2 Theory 6
2-1 Microwave Dielectric Properties 6
2-2 Dielectric Resonators 8
2-3 Basic Theory of Microwave Filters 10
Chapter 3 Microwave Dielectric Properties of AB2O6 Ceramics 13
3-1 Introduction 13
3-2 Experimental Procedures 13
3-3 Results and Discussion 14
3-3-1 ZnTa2-xNbxO6 Microwave Dielectric Ceramics 14
3-3-1-1 Density and XRD Analysis 15
3-3-1-2 SEM Analysis 16
3-3-1-3 Microwave Dielectric Characteristics Analysis 16
3-3-1-4 ZnTa1.7Nb0.3O6 Microwave Dielectric Ceramics 17
3-3-2 MgTa2-xNbxO6 Microwave Dielectric Ceramics 18
3-3-2-1 XRD Analysis 19
3-3-2-2 SEM Analysis 19
3-3-2-3 Density and Dielectric Constant Analysis 19
3-3-2-4 Microwave Dielectric Characteristics Analysis 20
3-3-2-5 Mg(Ta1-xNbx)2O6 Microwave Dielectric Ceramics
(x=0.25~0.35) 21
3-4 Conclusions of AB2O6 Ceramics 22
Chapter 4 Fabrication of Microstrip Line Planar Filters on the
Microwave Dielectric Ceramic Substrates 24
4-1 Introduction 24
4-2 Analysis of Filters 25
4-2-1 Immittance Inverters 25
4-2-2 Coupling Analysis 25
4-2-2-1 Electric Coupling 26
4-2-2-2 Magnetic Coupling 27
4-2-2-3 Mixed Coupling 28
4-2-3 Microstrip Lines 28
4-2-4 Coupling Lines 30
4-2-5 End-Coupled Half-Wavelength Resonators Banspass Filters 32
4-3 Design and Fabrication Procedures 33
4-3-1 Design Procedures 33
4-3-1-1 Wide-Band and Dual-Band Bandpass Filters 33
4-3-1-2 Tri-Band and Tetra-Band Bandpass Filters 35
4-3-2 Fabrication Procedures 38
4-4 Results and Discussion 38
4-4-1 Wide-Band and Dual-Band Bandpass Filters 38
4-4-2 Tri-Band and Tetra-Band Bandpass Filters 39
4-5 Conclusions of Ceramic Bandpass Filters 40
Chapter 5 Conclusions and Future Works 41
5-1 Conclusions 41
5-2 Future Works 43
References 45
Tables 50
Figures 56

[1] R. D. Richtmyer, “Dielectric Resonators,” J. Appl. Phys., 10 (1939) 391-398.
[2] S. Kucheiko, J. W. Choi, H. J. Kim and H. J. Jung: “Microwave dielectric properties of CaTiO3-Ca(Al1/2Ta1/2)O3 Ceramic,” J. Am. Ceram. Soc., 79 (1996) 2739~2743.
[3] Y. C. Chen, P. S. Cheng, C. F. Yang and W. C. Tzou: “The microwave properties of (Ba,Sr)Sm2Ti4O12 Ceramics (0≦x≦0.1),” J. Mater. Sci. Let., 20 (2001) 1169~1171.
[4] K. Ezaki, Y. Baba, H. Takhashi, K. Shibata and S. Nakano: “Microwave Dielectric-Properties of CaO-Li2O-LN2O3-TiO3 Ceramics,” Jpn. J. Appl. Phys., 32 (1993) 4319~4322.
[5] W. Choi and K.Y. Kim: “The Effects of Nd2O3 on the microwave dielectric properties of BiNbO4 ceramics,” J. Mater. Res., 13 (1998) 2945~2949.
[6] Y. C. Chen, W. C. Tzou, C. F. Yang and P. S. Cheng: “The effect of the crystalline phase on the sintering and microwave dielectric properties of CuO-doped (Bi0.95Sm0.05)NbO4 Ceramics,” Jpn. J. Appl. Phys., 40 (2001) 3252~3255.
[7] M. H. Weng and C. L. Huang: “The Microwave dielectric properties and microstructure of Bi(Nb,Ta)O4 Ceramics,” Jpn. J. Appl. Phys., 38 (1999) 5949~5952.
[8] P. Laffez, G. Desgardin and B. Raveau: “Microwave Dielectric Properties of Doped Ba6-x(Sm1-yNdy)8+2x/3Ti18O54 Oxides,”J. Mater. Sci., 30 (1995) 267~273.
[9] T. Konoike and H. Yamura, “Dielectric ceramic composition for microwave frequencies,” U. S. Patent No. 4,585,774, 1986.
[10] H. Tamura, T. Konoike, Y. Sakabe and K. Wakino, ”Impoved high-Q dielectric resonator with complex perovskite structure,” J. Am. Cerm. Soc., 67 (1984) C59-61.
[11] M. Onoda, K. Kuwata, K. Kaneta, K. Yoyama and S. Nomura, “Ba(Zn1/3Nb2/3)O3-Sr(Zn1/3Nb2/3)O3 solid solution ceramics with temperature stable high dielectric constant and low microwave loss,” Jpn. J. Appl. Phys., 21 (1982) 1707-1710.
[12] Y. C. Heiao, L. Wu and C. C. Wei, “Microwave dielectric properties of (Zr,Sn)TiO4 ceramics,” Mat. Res. Bull., 23 (1988) 1687-1692.
[13] J. M. Wu and M. C. Chang, “Reaction sequence and effects of calcinations and sintering on microwave properties of (Ba,Sr)O-Sm2O3-TiO2 ceramics,” J. Am. Ceram. Soc., 73 (1990) 1599-1605.
[14] K. Wakino, K. Minai and H. Tamura, “Microwave characteristics of (Zr,Sn)TiO4 and BaO-PbO-Nd2O3-TiO2 dielectric resonator,” J. Am. Ceram. Soc., 67 (1984)278-281.
[15] S. Nishigaki, H. Kato, S. Yano and R. Kamimura, “Microwave dielectric properties of (Ba,Sr)O-Sm2O3-TiO2 ceramics,” Am. Ceram. Soc. Bull., 66 (1987) 1405-1410.
[16] R. levy, “Filters with Single Transmission Zeros at Real or Imaginary Frequencies,” IEEE Trans. Microw. Theory Tech., MTT-24 (1976) 172-181.
[17] A. E. Williams, “A Four-Cavity Elliptic Waveguide Filter,” IEEE Trans. Microw. Theory Tech., MTT-18 (1970) 1109-1114.
[18] J. S. Hong and M. J. Lancaster, “Coupling of Microstrip Squire Open-Loop resonators for Cross-Coupled Planar Microwave Filters,” IEEE Trans. Microw. Theory Tech., MTT-44 (1996) 2099-2109.
[19] J. S. Hong and M. J. Lancaster, “Cross-Coupled Micristrip Hairpin-Resonator Filters,” IEEE Trans. Microw. Theory Tech., MTT-46 (1998) 118-122.
[20] M. Makimoto ans S. Yamashita, “Bandpass Filters using Parallel Coupled Stripline Stepped Impedance Resonators,” IEEE Trans. Microw. Theory Tech., MTT-28 (1980) 1413-1417.
[21] S. B. Cohn, “Parallel-Coupled Transmission-Line-Resonator Filters,” IRE Trans. Microw. Theory Tech., MTT-6 (1958) 223-231.
[22] E. G. Cristal and S. Frankel, “Hairpin-Line and Hybrid Hairpin-Line/Half-Wave Parallel-Coupled-Line Filters,” IEEE Trans. Microw. Theory Tech., MTT-20 (1972) 719-728.
[23] S. B. Cohn, “Direct-Coupled-Resonator Filters,” proceedings of the IRE, 45 (1957) 187-196.
[24] E. G. Cristal, “Tapped-Line Coupled Transmission Lines with Applications to Interdigital and Combline Filters,” IEEE Trans. Microw. Theory Tech., MTT-23 (1975) 1007-1012.
[25] J. S. Wang, “Microstrip Tapped-Line Filter Design,” IEEE Trans. Microw. Theory Tech., MTT-27 (1979) 44-50.
[26] T. Negas, G. Yeager, S. Bell and N. Coats, “BaTi4O9/BaTi9O20–Based Ceramics Resulted for Modern Microwave Applications,” Am. Ceram. Soc. Bull., 72 (1993) 80~89.
[27] S. B. Desu and H. M. O’Bryan, “Microwave Loss Quality of BaZn1/3Ta2/3O3 Ceramics,” J. Am. Ceram. Soc., 68 (1985) 546~551.
[28] S. Nishigaki, H. Kato, S. Yano and R. Kamimura, “Microwave Dielectric properties of (Ba,Sr)O-Sm2O3-TiO2 Ceramics,” Am. Ceram. Soc. Bull., 66 (1987) 1405~1410.
[29] A. Kan, H. Ogawa and H. Ohsato, “Influence of microstructure on microwave dielectric properties of ZnTa2O6 ceramics with low dielectric loss,” J. Alloys and Compounds, 337 (2002) 303~308.
[30] H. J. Lee, I. T. Kim and K. S. Hong, “Dielectric properties of AB2O6 compounds at microwave frequencies (A = Ca, Mg, Mn, CO, Ni, Zn, and B = Nb, Ta,),” Jpn. J. Appl. Phys., 36 (1997) L1318~L1320.
[31] C. F. Chen, T.Y. Huang, and R. B. Wu, “Design of Dual- and Triple-Passband Filters Using Alternately Cascaded Multiband Resonators,” IEEE Trans. Microw. Theory Tech., MTT-54 (2006) 3550.
[32] C. H. Lee, C. I. Hsu, and H. K. Jhuang, “Design of a New Tri-Band Microstrip BPF Using Combined Quarter-Wavelength SIRs,” IEEE Microw. Wireless Compon. Lett., 16 (2006) 594-596.
[33] Cheng-Fu Yang, Chao-Chin Chan, Chien-Min Cheng and Ying-Chung Chen, “The Sintering and Microwave Dielectric Characteristics of MgTa1.5Nb0.5O6 Ceramics,” Journal of the European Ceramic Society, 25(2005)2849-2852.
[34] Wen-Cheng Tzou, Ying-Chung Chen, Cheng-Fu Yang and Chien-Min Cheng, “The sintering and microwave dielectric characteristics of Mg(Ta2-xNbx)O6 ceramics,” Materials Research Bulletin, 41(2006)1357-1363.
[35] Chien-Min Cheng, Ying-Chung Chen, Cheng-Fu Yang, Chao-Chin Chan, “Sintering and Compositional Effects on the Microwave Dielectric Characteristics of Mg(Ta1-xNbx)2O6 Ceramics with 0.25≦x≦0.35,” Journal of Electroceramics, 18(2007)155-160.
[36] W. D. Kingery, H. K. Bowen and D. R. Uhlmann, “Introduction to Ceramics,” 2th edition, Wiley, New York, (1986).
[37] G. Burns, “Solid State Physics,” (1985) 461.
[38] B. D. Silvermann, “Microwave Absorption in cubic Strontium Titanate,” Phys. Rev., 125 (1962) 1921-1930.
[39] C. H. Perry, D. J. McCarthy and G. Rupprecht, “Dielectric Dispersion of Some Pervoskite Zirconate,” Phys. Rev., 126 (1962) 1710-1721.
[40] David K. Cheng, “Field and Wave Electromagnetics” 2th edition, Addison Wesley, New York (1989) 406-410.
[41] B. W. Hakki and P. D. Coleman, “A Dielectric Resonator Method of Measuring Inductive Capacities in the Millimeter Range,” IRE Trans. Microw. Theory Tech., MTT-8 (1960) 402-410.
[42] W. E. Courtney, “Analysis and Evaluation of a Method of Measuring the Complex Permittivity and Permeability of Microwave Insulators,” IEEE Trans. Microw. Theory Tech., MTT-18 (1970) 476-485.
[43] Y. Kobayshi and M. Katoh, “Microwave Measurement od Dielectric Properties of Low-Loss Materials by the Dielectric Rod Resonator Method,” IEEE Trans. Microw. Theory Tech., MTT-33 (1985) 586-592.
[44] G. Matthaei, L. Young and E. M. T Jones, “Microwave Filters, Impedance-Matching Networks and Coupling Structures,” McGraw-Hill, New York, (1964).
[45] J. G. Hong and M. J. Lancaster, “Microstrip Filters for RF/Microwave Applications,” John Wiley & Sons, (2001).
[46] R. D. Shannon: “Dielectric polarizabilities of ions in oxides and fluorides,” J. Appl. Phys., 73 (1993) 348~366.
[47] JCPDS card No. 76-1826, 1997 JCPDS International Center for Diffraction Data Formerly by the Joint Committee on Power Diffraction Standards.
[48] JCPDS card No. 76-1827, 1997 JCPDS International Center for Diffraction Data Formerly by the Joint Committee on Power Diffraction Standards.
[49] D.A. Robinson, “Calculation of the dielectric properties of temperate and tropical soil minerals from ion polarizabilities using the Clausius-Mosotti equation,” Solid Sci. Soc. Am. J., 68 (2004) 1780.
[50] D. Kajfez and P. Guillon, “Dielectric resonators,” Artech House, Masachusetts, (1986) 345-361.
[51] J. T. Kuo, C. L. Hsu, and E. Shih, “Compact planar quasi-elliptic function filter with inline stepped-impedance resonators,” IEEE Trans. Microw. Theory Tech., MTT-55 (2007) 1747-1755.
[52] C. M. Tsai and H. M. Lee, “Improved Design Equations of the Tapped-Line Structure for Coupled-Line Filters,” IEEE Microw. Wireless Compon. Lett., 17 (2007) 244-246.
[53] Sheng Sun and Lei Zhu, “Coupling dispersion of parallel-coupled microstrip lines for dual-band filters with controllable fractional pass bandwidths,” IEEE MTT-S Int. Microwave Sym. Dig., (2005) 2195-2198.
[54] C. K. Liao and C. Y. Chang, “Modified parallel-coupled filter with two independently controllable upper stopband transmission zeros,” IEEE Microw. Wireless Compon. Lett., 15 (2005) 841-843.
[55] C. M. Cheng, Y. C. Chen, C. F. Yang, and C. C. Chan, “Sintering and compositional effects on the microwave dielectric characteristics of Mg(Ta1-xNbx)2O6 ceramics with 0.25≦x≦0.35,” J. Electroceramics, 18 (2007) 155.
[56] W. C. Tzou, Y. C. Chen, C. F. Yang, and C. M. Cheng, “Microwave dielectric characteristics of Mg(Ta1-xNbx)2O6 ceramics,” Mater. Res. Bull., 41 (2006) 1357.
[57] B. I. Bleaney and B. Bleaney, “Electricity and Magnetism,” 3th edition, Oxford, (1976).
[58] K. C. Gupta, R. Garg, I. Bahl, and P. Bhartis, “Micristrip Lines and Slotlines,” 2th edition, Artech House, Boston, (1996).
[59] E. O. Hammerstard and O. Jensen, “Accurate models for microstrip computer-aided design,” IEEE MTT-S Int. Microwave Sym. Dig., (1980) 407-409.
[60] R. Garg and I. J. Bahl, “Characteristics of coupled microstriplines,” IEEE Trans. MTT-28 (1980) 272.
[61] G. Mattaei, L. Young and E. M. T. Jones, “Microwave Filters, Impedance-Matching Networks, and Coupling Structures,” Artech House, Norwood, MA, (1980).
[62] M. L. Chuang, “Cascaded dual band coupled-fed microstrip open-loop filter”, Microw. Opt. Tech. Lett., 45 (2005) 519-522.
[63] M. Mokhaari, J. Bornemann, and S. Amari, “Compact Planar Ultra-Wide-Pass-Band Filters with Source-Load Coupling and Impedance Stubs,” Proc. of APMC2006.
[64] S. W. Ting, K. W. Tam, R. P. Martins, "Miniaturized microstrip lowpass filter with wide stopband using double equilateral U-shaped defected ground structure", IEEE Microw. Wireless Compon. Lett., 16 (2006) 240-242.