本篇論文主要分別介紹兩大部分，第一部分將介紹新開發的低損耗微波介電材料BaMg2(VO4)2，並嘗試利用不同比例的元素取代來補償其共振頻率溫度飄移係數，並用於低溫共燒製程；第二部分將設計一操作在2.45GHz頻段的濾波器，實作於不同尺寸之基板上後探討其微波特性。
第一部分首先要介紹(Ba1-xSrx)Mg2(VO4)2 (x = 0–1)陶瓷系統之微波介電特性。由實驗得知，以Sr2+來取代Ba2+時，共振頻率溫度飄移係數會往正值補償。當取代比例為x = 0.15，且燒結溫度在960oC時有最佳的微波介電特性，ε r ~ 13.1，Q×f~ 71,000 GHz，τf ~ -4.5 ppm/oC。然而，為了應用在低溫共燒製程，本實驗也測試了Ba0.85Sr0.15Mg2(VO4)2和銀共燒的反應，燒結溫度為930oC並持溫4小時，通過SEM和Line Scan的分析，可得知在陶瓷體與銀的介面處並沒有擴散現象，因此，Ba0.85Sr0.15Mg2(VO4)2為一可應用在LTCC製程且τf ~0的微波介電材料。
第二部分將設計一操作在2.45GHz的帶通濾波器。主體架構為U型共振器，為了改善在通帶的頻率響應，採用Source-Load coupling的耦合方式，以及在U型共振器內部加入一T-stub，在通帶的兩側各產生一個傳輸零點。最後，我們將電路實作在FR4、Al2O3、Ba0.85Sr0.15Mg2(VO4)2基板上，並量測其頻率響應。由量測的結果可得知，利用高介電係數及低損耗的材料做為電路基板時，確實能達到提升效能和縮小面積的需求。

In order to obtain a novel low-temperature co-fired ceramics (LTCC), the microwave dielectric properties of (Ba1-xSrx)Mg2(VO4)2 (x = 0–1) ceramics had been investigated. The τf value of (Ba1-xSrx)Mg2(VO4)2 ( x = 0–1) ceramics varied from -40 to 170 ppm/oC as x increased, and a near zero value was obtained at x = 0.15, where the εr and the Q×f value were 13.1 and 71,000 GHz at the sintering temperature of 960 oC for 4 h. Then, we designed and fabricated a bandpass filter on FR4、Al2O3、Ba0.85Sr0.15Mg2(VO4)2 substrates. According to the results of measurements, the performance of the filter was improved by using low-loss dielectric ceramics as the substrate.

[1] H. M. O’bryan, J. Thomson, and J. K. Plourde, “A new BaO–TiO2 compound with temperature- stable high permittivity and low microwave loss,” J. Am. Ceram. Soc., 57 [10] 450–453 (1974).
[2] G. Wolfram and H. E. Göbel, “Existence range, structural and dielectric properties of ZrxTiySnzO4 ceramics (x+y+z = 2),” Mater. Res. Bull., 16 [11] 1455–1463 (1981).
[3] J. H. Sohn, Y. Inaguma, S. O. Yoon, M. Itoh, T. Nakamura, S. J. Yoon, and H. J. Kim, “Microwave dielectric characteristics of ilmenite-type titanates with high Q values,” Jpn. J. Appl. Phys., 33 [9B] 5466–5470 (1994).
[4] Y. Ohishi, Y. Miyauchi, H. Ohsato, and K. I. Kakimoto, “Controlled temperature coefficient of resonant frequency of Al2O3–TiO2 ceramics by annealing treatment,” Jpn. J. Appl. Phys., 43 [6A] L749–L751 (2004).
[5] C. L. Huang, T. J. Yang, and C. C. Huang, “Low dielectric loss ceramics in the ZnAl2O4–TiO2 system as a τf compensator,” J. Am. Ceram. Soc., 92 [1] 119–124 (2009).
[6] W. F. Smith, 劉品均(譯), 施佑蓉(譯), 材料科學與工程, 第三版, 高立圖書, (2005).
[7] D. M. Pozar, Microwave engineering, Addison-Wesley (1998).
[8] D. Kajfez, “Basic principle give understanding of dielectric waveguides and resonators,” Microwave SysTFm News., 13, 152–161 (1983).
[9] D. Kajfez, A. W. Glisson, and J. James, “Computed model field distributions for isolated dielectric resonators,” IEEE Trans. Microwave Theory Tech., 32 [12] 1609–1616 (1984).
[10] 張盛富, 戴明鳳, 無線通信之射頻被動電路設計, 全華出版社, (1998).
[11] 鄭景太, 淺談高頻低損失介電材料, 工業材料, 176期, (2001).
[12] W. D. Kingery, H. K. Bowen, D. R. Uhlmann, 陳皇鈞(譯), “陶瓷材料概論,” 曉園出版社, (1988).
[13] 余樹楨, “晶體之結構與性質,” 渤海堂文化公司, (2007)
[14] M. R. Joung, J. S. Kim, M. E. Song, S. Nahm, J. H. Paik, and B. H. Choi , “Formation and microwave dielectric properties of the Mg2V2O7 ceramics,” J. Am. Soc., 92 [7] 1621–1624 (2009).
[15] R. Umemura, H. Ogawa, H. Ohsato, A. Kan, and A. Yokoi, “Microwave dielectric properties of low-temperature sintered Mg3(VO4)2 ceramic,” J. Eur. Ceram. Soc., 25 2865–2870 (2005).
[16] R. Umemura, H. Ogawa, and A. Kan “Low temperature sintering and microwave dielectric properties of (Mg3-xZnx)(VO4)2 ceramics,” J. Eur. Ceram. Soc., 26 2063–2068 (2006).
[17] E. K. Suresh, A. N. Unnimaya, A. Surjith, and R. Ratheesh, “New vanadium based Ba3MV4O15 (M = Ti and Zr) high Q ceramics for LTCC applications,” Ceram. Int., 39 3635–3639 (2013).
[18] G. G. Yao , and H. W. Zhang , “Novel series of Low-Firing Microwave Dielectrics Ceramics: Ca5A4(VO4)6 (A2+ = Mg, Zn),” J. Am. Ceram. Soc., 96[6] 1691–1693 (2013).
[19] R. L. Geiger, P. E. Allen, and N. R. Strader, VLSI Design Techniques for Analog and Digital Circuits, McGraw-Hill, (1990).
[20] R.A. Pucel, D. J. Masse, C.P. Hartwig, “Losses in microstrip”, 16 [6] 342–350 (1968)
[21] J. S. Hong and M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, John Wiley & Sons, (2001).
[22] G. Kompa, Practical Microstrip Design and Applications, Artech House, (2005).
[23] K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, “Microstrip Lines and Slotlines,” Second Edition, Artech House, (1996).
[24] G. L. Matthaei, L. Young, E. M. T. Jones, “Microwave filters, impedence matching networks and coupling structures,” Artech House, (1980).
[25] E. J. Denlinger, “Losses of microstrip lines,” IEEE Trans. Microwave Theory Tech. 28 [6] 513–522 (1980).
[26] X.C. Zhang, Z.Y. Yu, and J. Xu , “Design of Microstrip Dual-Mode Filters Based on Source-Load Coupling,” IEEE Microw. Wireless Compon. Lett., 18 [10] 677–679 (2008).
[27] M. Zhou, X. Tang, and F. Xiao, “Miniature Microstrip Bandpass Filter Using Resonator-Embedded Dual-Mode Resonator Based on Source-Load Coupling,” IEEE Microw. Wireless Compon. Lett., 20 [3] 139–141 (2010).
[28] H. A. Wheeler, “Transmission line properties of parallel strips separated by a dielectric sheet,” IEEE Trans. Microwave Theory Tech., 13 172–185 (1965).
[29] H. A. Wheeler, “Tramsmission line properties of a strip on a dielectric sheet on a plane,” IEEE Trans., MTT-25 631–647 (1977).
[30] I. Wolff, “Microstrip bandpass filters using degenerate modes of microstrip ring resonator,” Electron. Lett., 8 [12] 163–164 (1972).
[31] H. Liu, Y. Zhao, L. Shi, and H. Luo, “Dual-Mode Dual-Band Bandpass Filter Design Using Open-Loop Resonators,” Microw. Opt. Techn. Let. 54 [10] 2370–2372 (2012)
[32] J.S. Hong, H. Shaman, and Y.H. Chun, “Dual-Mode Microstrip Open-Loop Resonators and Filters,” IEEE Trans. Microw. Theory Tech., 55 [8] 1760–1770 (2007)
[33] B. W. Hakki and P. D. Coleman, “A dielectric resonator method of measuring inductive capacities in the millimeter range,” IEEE Trans. Microwave Theory Tech., 8 [4] 402–410 (1960).
[34] W. E. Courtney, “Analysis and evaluation of a method of measuring the complex permittivity and permeability of microwave insulators,” IEEE Trans. Microwave Theory Tech., 18 [8] 476–485 (1970).
[35] P. Wheless and D. Kajfez, “The use of higher resonant modes in measuring the dielectric constant of dielectric resonators,” IEEE Trans. Microwave Theory Tech., 85 [1] 473–476 (1985).
[36] Y. Kobayashi and M. Katoh, “Microwave measurement of dielectric properties of low-loss materials by the dielectric rod resonator method,” IEEE Trans. Microwave Theory Tech., 33 [7] 586–592 (1985).
[37]A. Grzechnik, P. F. McMillan, “High pressure behavior of Sr3(VO4)2 and Ba3(VO4)2,”Journal of Solid State Chemistry, 132, 156–162(1997)
[38] M. Azdouz, B. Manoun, M. Essehli, M. Azrour, L. Bih, S. Benmokhtar, A. Ait Hou, and P. Lazor, “Crystal chemistry, Rietveld refinements and Raman spectroscopy studies of the new solid solution series: Ba3-xSrx(VO4)2 (0≦x≦3),” J. Alloys Compd. 498 (2010) 42–51.