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研究生： 陳士軒
Chen, Shih-Hsuan
論文名稱： 介電陶瓷材料 (Mg0.95Zn0.05)2TiO4 與Ba(Ti1-xMx)4O9 (M = Zr、Sn)之微波特性探討及應用
Microwave Dielectric Properties and Applications of (Mg0.95Zn0.05)2TiO4 and Ba(Ti1-xMx)4O9 (M = Zr, Sn)
指導教授： 黃正亮
Huang, Cheng-Liang
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2010
畢業學年度： 98
語文別： 中文
論文頁數： 122
中文關鍵詞： 微波介電材料 、低損耗
外文關鍵詞： (Mg0.9Zn0.05)2TiO4, Dielectric properties, Low-loss
相關次數： 點閱：70  下載：1 
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    • 摘要
    此篇論文主要分為兩大部分來探討及研究，第一部份將介紹低損耗的介電材料，在(Mg0.95Zn0.05)2TiO4系統中試圖以具正值共振頻率溫度飄移係數的鈣鈦礦材料，CaTiO3 (+800 ppm/°C)、SrTiO3 (+1600 ppm/°C) 及Ca0.8Sr0.2TiO3 (+991 ppm/°C)調整溫度飄移係數使其為零。經由實驗的結果，得知0.93(Mg0.95Zn0.05)2TiO4–0.07Ca0.8Sr0.2TiO3有最佳的微波介電特性，其εr~17.86、Q×f ~ 133,600 GHz (at 10 GHz)及τf ~ –5 ppm/°C；而在Ba(Ti1-xMx)4O9系統中(M = Sn、Zr) 則是探討材料的微結構及微波介電特性。在M = Zr且x = 0.0125時在燒結溫度1300℃持溫4小時之下，可得到Ba(Ti0.9875Zr0.0125)4O9之最佳介電特性εr = 34.80，Q׃ ~ 63,700 GHz (at 8 GHz)，τf ~ 13 ppm/℃。而當M = Sn且x = 0.0125時在燒結溫度1270℃持溫4小時之下，可得到Ba(Ti0.9875Sn0.0125)4O9之最佳介電特性εr = 36.46，Q׃ ~ 50,600 GHz (at 7.2 GHz)，τf ~ 16.87 ppm/℃
    第二部份將介紹其在被動電路之應用,且實做於不同基板上探討元件尺寸的改善。將分別以 FR4、Al2O3及0.93(Mg0.95Zn0.05)2TiO4－0.07(Ca0.8Sr0.2)TiO3作為基板來設計一微帶線帶通濾波器，且藉由加入開路殘段而達到倍頻抑制的效果。濾波器的規格為：中心頻率 2.4 GHz、頻寬為 7 %，並使用電磁模擬軟體 IE3D來進行電腦模擬。

    Abstract
    There are two main subjects in this paper. First we will disduss two kinds of low loss dielectric materials, then try to make temperature coefficient of resonant freguency near zero and find out the best microwave dielectric properties. Second, there will be a discussion of passive component and improvement in different substrates.
    First, the improvement of τf of (Mg0.95Zn0.05)2TiO4 base on Mg2TiO4 structure followed up the introduced of (Mg0.95Zn0.05)2TiO4 have been investigated in this paper. In order to adjust the negative τf, CaTiO3, SrTiO3 and Ca0.8Sr0.2TiO3 peroveskite which have been add. The experiment result show that 0.93(Mg0.95Zn0.05)2TiO4－0.07(Ca0.8Sr0.2)TiO3 have the best microwave dielectric properties: εr ~17.86, Q×f ~133,600 GHz (at 10 GHz) and τf ~ –5 ppm/°C.
    Then, BaTi4O9-base microwave dielectric ceramics substute Ti4+ by Zr4+ and Sn4+ were synthesized using the solid-state reaction reaction froming Ba(Ti1-xMx)4O9 (M = Sn, Zr). When M = Zr and x=0.0125, we can obtain the best dielectric properties of Ba(Ti0.9875Zr0.0125)4O9 : εr = 34.80, Q׃ ~ 63,700 GHz (at 8 GHz), τf ~ 13 ppm/°C. With M = Sn and x=0.0125, the best dielectric properties, εr = 36.46, Q׃~50,600 GHz (at 7.2 GHz), τf ~ 16.87 ppm/°C were obtained for Ba(Ti0.9875Sn0.0125)4O9.
    Besides, with open-stub ring bandpass filter were studied in second section which achieved spurious responses suppression by open-stub and properly feed-in structure. We simulated it by electromagnetic simulation software (IE3D) at setting of center frequency 2.4 GHz and bandwidth 7 %. Also, we try to realized that the improvement of Insertion-Loss and circuit size at the substitution of substrates FR4, Al2O3 and 0.93(Mg0.95Zn0.05)2TiO4－0.07(Ca0.8Sr0.2)TiO3 for the microstrip bandpass filter.

    目 錄 摘要.................................................................................................................................III Abstract...........................................................................................................................V 誌謝................................................................................................................................VII 目錄...............................................................................................................................VIII 表目錄...........................................................................................................................XII 圖目錄..........................................................................................................................XIII 第一章 緒論.................................................................................................................1 1-1 前言......................................................................................................................1 1-2 研究目的..............................................................................................................1 第二章 介電材料原理...............................................................................................3 2-1微波陶瓷材料之介電特性分析...........................................................................3 2-1-1 介電常數（Dielectric constant：K）....................................................3 2-1-2 介電品質因數（Quality factor：Q）.........................................................6 2-1-3 共振頻率之溫度係數（ ）.....................................................................8 2-2 介電共振器(Dielectric Resonator, DR)原理.....................................................9 2-3 燒結原理............................................................................................................12 2-3-1 燒結的種類.............................................................................................12 2-3-2 液相燒結理論.........................................................................................14 2-3-3 陶瓷體燒結的三過程.............................................................................15 2-4 尖晶石結構.......................................................................................................16 2-5 鈦鐵礦結構.......................................................................................................18 2-6 鈣鈦礦結構.......................................................................................................20 2-7 BaTi4O9結構.....................................................................................................20 第三章 微帶線及濾波器之原理..........................................................................23 3-1 濾波器簡介........................................................................................................23 3-2 微帶線原理........................................................................................................26 3-2-1 微帶傳輸線及其傳輸組態....................................................................26 3-2-2 微帶線各項參數公式計算及考量........................................................27 3-3 微帶線諧振器種類...........................................................................................34 3-4 諧振器間的耦合形式.......................................................................................37 3-4-1 電場耦合................................................................................................38 3-4-2 磁場耦合................................................................................................41 3-4-3 混和耦合................................................................................................44 3-5 諧振器間耦合量................................................................................................46 3-6 環形諧振器(Ring Resonator)[36]....................................................................47 3-6-1 簡介........................................................................................................47 3-6-2 環狀諧振器的頻率模態........................................................................47 3-6-3 輸入阻抗的計算[37]..............................................................................49 3-6-4 方形環狀諧振器(square ring)帶通濾波器[39]...................................50 3-6-5 反對稱(skew-symmetric)饋入結構......................................................56 3-6-6 方形環狀諧振器阻抗的選定................................................................58 第四章 實驗程序與量測方法..............................................................................60 4-1 微波介電材料的製備.......................................................................................60 4-1-1 原始粉末之配置與球磨........................................................................60 4-1-2 煆燒成相.................................................................................................60 4-1-3 壓模.........................................................................................................61 4-1-4 燒結.........................................................................................................61 4-2 微波介電材料的特性分析與量測....................................................................63 4-2-1 XRD分析.................................................................................................63 4-2-2 環境式電子顯微鏡（ESEM）分析........................................................63 4-2-3 密度之量測.............................................................................................63 4-2-4 微波介電特性之量測.............................................................................64 4-3 濾波器之製作與量測........................................................................................71 4-3-1 濾波器設計規格.....................................................................................71 4-3-2 濾波器製作.............................................................................................72 4-3-3 濾波器量測.............................................................................................72 第五章 實驗結果與討論........................................................................................74 5-1 (1-x)(Mg0.95Zn0.05)2TiO4－xSrTiO3微波特性之探討.......................................75 5-1-1 (1-x)(Mg0.95Zn0.05)2TiO4－xSrTiO3系統之XRD相組成分析.............75 5-1-2 (1-x)(Mg0.95Zn0.05)2TiO4－xSrTiO3系統之SEM微結構分析.............75 5-1-3 (1-x)(Mg0.95Zn0.05)2TiO4－xSrTiO3系統之密度分析...........................76 5-1-4 (1-x)(Mg0.95Zn0.05)2TiO4－xSrTiO3系統之介電特性分析...................76 5-2 (1-x)(Mg0.95Zn0.05)2TiO4－xCaTiO3微波特性之探討......................................80 5-2-1 (1-x)(Mg0.95Zn0.05)2TiO4－xCaTiO3系統之XRD相組成分析............80 5-2-2 (1-x)(Mg0.95Zn0.05)2TiO4－xCaTiO3系統之SEM微結構分析............81 5-2-3 (1-x)(Mg0.95Zn0.05)2TiO4－xCaTiO3系統之密度分析..........................81 5-2-4 (1-x)(Mg0.95Zn0.05)2TiO4－xCaTiO3系統之介電特性分......................82 5-3 (1-x)(Mg0.95Zn0.05)2TiO4－x(Ca0.8Sr0.2)TiO3微波特性之探............................86 5-3-1 (1-x)(Mg0.95Zn0.05)2TiO4－x(Ca0.8Sr0.2)TiO3系統之XRD相組成分析 ............................................................................................................................86 5-3-2 (1-x)(Mg0.95Zn0.05)2TiO4－x(Ca0.8Sr0.2)TiO3系統之SEM微結構分析 ............................................................................................................................87 5-3-3 (1-x)(Mg0.95Zn0.05)2TiO4－x(Ca0.8Sr0.2)TiO3系統之密度分析.............87 5-3-4 (1-x)(Mg0.95Zn0.05)2TiO4－x(Ca0.8Sr0.2)TiO3系統之介電特性分析.....88 5-4 Ba(Ti1-xZrx)4O9微波特性之探討......................................................................93 5-5 Ba(Ti1-xSnx)4O9微波特性之探討....................................................................101 5-6 濾波器的響應..................................................................................................107 5-6-1 FR4基板...............................................................................................107 5-6-2 Al2O3基板.............................................................................................109 5-6-3 0.93(Mg0.95Zn0.05)2TiO4－0.07(Ca0.8Sr0.2)TiO3基板..........................111 第六章 結論與未來展望.....................................................................................115 參考文獻......................................................................................................................117 表 目 錄 表4-1 三種不同基板之參數..................................................................................71 表5-1 相關材料之微波介電特性..........................................................................74 表5-2 相關材料的晶體結構與系統......................................................................74 表5-3 相關材料之微波介電特性..........................................................................93 表5-4 Ba(Ti1-xZrx)4O9在不同比例下的晶格常數及分子體積............................95 表5-5 Ba(Ti1-xZrx)4O9在不同比例下的計算所得的離子極化率變化................95 表5-6 Ba(Ti1-xSnx)4O9在不同比例下的晶格常數及分子體積..........................102 表5-7 FR4基板之電路佈局尺寸........................................................................107 表5-8 以FR4為基板之濾波器特性表................................................................108 表5-9 Al2O3基板之電路佈局尺寸......................................................................109 表5-10 以Al2O3為基板之濾波器特性表.............................................................111 表5-11 0.93(Mg0.95Zn0.05)2TiO4－0.07(Ca0.8Sr0.2)TiO3基板之電路佈局尺寸...111 表5-12 0.93(Mg0.95Zn0.05)2TiO4－0.07(Ca0.8Sr0.2)TiO3基板之濾波器特性.......113 表5-13 三種不同基板之濾波器特性比較............................................................114 表6-1 Ba(Ti1-xMx)4O9 (M = Zr, Sn)系統之最佳微波介電特性.........................115 圖目錄 圖2-1 極化頻率分佈圖............................................................................................4 圖2-2 空間電荷極化................................................................................................4 圖2-3 方向極化........................................................................................................4 圖2-4 離子極化........................................................................................................5 圖2-5 電子極化........................................................................................................5 圖2-6 電磁波由介質1( )入射到介質2( )..................................................9 圖2-7 電磁波發生全反射之情形............................................................................9 圖2-8 圓柱形DR電場分布圖................................................................................11 圖2-9 圓柱型DR中各種mode之外部與內部功率傳輸比.................................12 圖2-10 燒結時孔隙形狀變化之示意圖..................................................................13 圖2-11 燒結時孔隙在晶界移動示意圖..................................................................16 圖2-12 尖晶石單位晶胞內各原子之排列..............................................................17 圖2-13 尖晶石的空隙種類......................................................................................18 圖2-14 鈦鐵礦結構..................................................................................................19 圖2-15 鈣鈦礦結構..................................................................................................20 圖2-16 TiO6結構圖..................................................................................................21 圖2-17 BaTi4O9 unit-cell structure.........................................................................21 圖2-18 pentagonal prism tunnel structure............................................................22 圖2-19 TiO6長鏈結構..............................................................................................22 圖2-20 pentagonal prism tunnel structure............................................................22 圖2-21 application of BaTi4O9................................................................................22 圖3-1 .四種主要濾波器形式的傳輸特性圖............................................................24 圖3-2 .三種濾波器的低通原型圖............................................................................25 圖3-3 .微帶線之外觀圖............................................................................................27 圖3-4 .微帶線之電場與磁場分佈圖........................................................................27 圖3-5 .步階阻抗不連續處之示意圖 (a)實際結構 (b)等效電路..........................32 圖3-6 .微帶線開路端效應........................................................................................33 圖3-7 .直角彎折效應之結構圖與等效電路圖.......................................................34 圖3-8. 四分之一波長微帶線短路傳輸線................................................................35 圖3-9. 指叉型(interdigital)濾波器..........................................................................36 圖3-10 二分之一波長微帶線諧振器的傳輸線示意圖...........................................36 圖3-11 平行耦合線濾波器.......................................................................................37 圖3-12 U型諧振器與U型濾波器...........................................................................37 圖3-13 正方形開迴路諧振器與開迴路諧振器濾波器...........................................37 圖3-14 微帶線共振器之電場強度分佈圖(a) 短路(b) 開路......................38 圖3-15 幾種電場耦合的共振器佈局.......................................................................38 圖3-16 兩電場耦合的共振器之等效電路圖...........................................................39 圖3-17 當 以及 的等效π型網路...................................................40 圖3-18 表示電場耦合使用導納反轉子的另一種等效電路圖...............................40 圖3-19 微帶線共振器之磁場強度分佈圖(a) 短路 (b) 開路....................41 圖3-20 幾種磁場耦合的共振器佈局.......................................................................42 圖3-21 兩磁場耦合的共振器之等效電路圖...........................................................42 圖3-22 當 以及 的等效T型網路................................................43 圖3-23 表示磁場耦合使用阻抗反轉子的另一種等效電路圖..............................43 圖3-24 幾種混和耦合的共振器佈局.......................................................................44 圖3-25 兩混和耦合的共振器之等效電路圖..........................................................45 圖3-26 使用J-inverter & K-inverter分別代表電場、磁場耦合的等效電路圖 ......................................................................................................................45 圖3-27 (a)單一諧振器之諧振頻率量測 (b)單一諧振器之諧振頻率響應..........46 圖3-28 (a)耦合結構之頻率響應量測 (b)耦合結構之頻率響應量測示意圖......47 圖3-29 方形環狀諧振器..........................................................................................51 圖3-30 環狀諧振器駐波情形..................................................................................52 圖3-31 封閉迴路環狀微帶線..................................................................................52 圖3-32 方形環狀諧振器濾波器..............................................................................53 圖3-33 方形環狀諧振器電路上視圖......................................................................53 圖3-34 方形環狀諧振器側視圖..............................................................................54 圖3-35 方形環狀諧振器等效電路圖......................................................................54 圖3-36 濾波器等效電路..........................................................................................55 圖3-37 不同饋入結構示意圖..................................................................................56 圖3-38 不同饋入結構之S21參數頻率響應圖......................................................57 圖3-39 不同饋入結構之S11參數頻率響應圖......................................................57 圖3-40 不同的阻抗值Z之S21參數頻率響應圖...................................................58 圖3-41 不同的阻抗值Z之S11參數頻率響應圖..................................................59 圖4-1 實驗流程圖..................................................................................................62 圖4-2 Courtney hold基本架構.............................................................................64 圖4-3 量測用模具組..............................................................................................65 圖4-4 辨別TE mode 和TM mode之方法..........................................................65 (a)TE mode耦合量小(耦合線圈垂直).......................................................65 (b)TM mode耦合量大(耦合線圈水平)......................................................65 圖4-5 (a)TE011 mode (b)TE012 mode..................................................................67 圖4-6 單顆DR放入測量系統內測量介電常數...................................................69 圖4-7 兩顆DR放入測量系統內測量品質因數...................................................70 圖4-8 開路殘段環型濾波器...................................................................................71 圖4-9 濾波器量測架構...........................................................................................73 圖5-1 (1-x) M2ZT－xST 在1270℃不同比例下之X-ray繞射圖.....................77 圖5-2 0.94 M2ZT－0.06ST 在不同燒結溫度下之X-ray繞射圖......................77 圖5-3 0.94 M2ZT－0.06ST之SEM圖..................................................................78 圖5-4 0.94 M2ZT－0.06ST之EDS圖..................................................................79 圖5-5 0.94 M2ZT－0.06ST系統之介電常數及密度與燒結溫度關係圖...........79 圖5-6 0.94 M2ZT－0.06ST系統之Q×f值及溫度飄移係數與燒結溫度關係圖 .......................................................................................................................80 圖5-7 (1-x) M2ZT－xCT 在1270℃不同比例下之X-ray繞射圖......................83 圖5-8 0.92 M2ZT－0.08CT 在不同燒結溫度下之X-ray繞射圖.....................83 圖5-9 0.92 M2ZT－0.08CT之SEM圖.................................................................84 圖5-10 0.92 M2ZT－0.08CT之EDS圖.................................................................85 圖5-11 0.92 M2ZT－0.08CT系統之介電常數及密度與燒結溫度關係圖...........85 圖5-12 0.92 M2ZT－0.08CT系統之Q×f值及溫度飄移係數與燒結溫度關係 .......................................................................................................................86 圖5-13 (1-x) M2ZT－xCST 在1240℃不同比例下之X-ray繞射圖..................89 圖5-14 0.93 M2ZT－0.07CST 在不同燒結溫度下之X-ray繞射圖...................89 圖5-15 0.93 M2ZT－0.07CST之SEM圖..............................................................90 圖5-16 0.93 M2ZT－0.07CST之EDS圖...............................................................91 圖5-17 0.93 M2ZT－0.07CST系統之介電常數及密度與燒結溫度關係圖........91 圖5-18 0.93 M2ZT－0.07CST系統Q×f值及溫度飄移係數與燒結溫度關係 ......................................................................................................................92 圖5-19 Ba(Ti1-xZrx)4O9微波介電材料在1300℃的XRD......................................94 圖5-20 Ba(Ti0.9875Zr0.0125)4O9微波介電材料在不同燒結溫度之XRD.................94 圖5-21 Ba(Ti1-xZrx)4O9在不同比例下之溫度飄移係數與分子體積關係圖........97 圖5-22 Ba(Ti0.9875Zr0.0125)4O9之SEM圖................................................................98 圖5-23 Ba(Ti0.9875Zr0.0125)4O9之密度及介電常數與燒結溫度關係圖..................99 圖5-24 Ba(Ti0.9875Zr0.0125)4O9之Q×f值及溫度漂移係數與燒結溫度關係圖....100 圖5-25 Ba(Ti1-xSnx)4O9微波介電材料在1300℃的XRD....................................101 圖5-26 Ba(Ti0.9875Sn0.0125)4O9微波介電材料在不同燒結溫度之XRD...............102 圖5-27 Ba(Ti1-xSnx)4O9在不同比例下之溫度飄移係數與分子體積關係圖......103 圖5-28 Ba(Ti0.9875Zr0.0125)4O9之SEM圖..............................................................104 圖5-29 Ba(Ti0.9875Sn0.0125)4O9之密度及介電常數與燒結溫度關係圖................105 圖5-30 Ba(Ti0.9875Sn0.0125)4O9之Q×f值及溫度漂移係數與燒結溫度關係圖....106 圖5-31 具開路殘段環形帶通濾波器....................................................................107 圖5-32 FR4基板之濾波器實作照片....................................................................108 圖5-33 FR4基板之電腦模擬圖............................................................................108 圖5-34 FR4基板之實作量測圖............................................................................108 圖5-35 Al2O3基板之濾波器實作照片..................................................................110 圖5-36 Al2O3基板之電腦模擬圖..........................................................................110 圖5-37 Al2O3基板之實作量測圖..........................................................................110 圖5-38 0.93(Mg0.95Zn0.05)2TiO4-0.07(Ca0.8Sr0.2)TiO3基板之濾波器實作照片..112 圖5-39 0.93(Mg0.95Zn0.05)2TiO4-0.07(Ca0.8Sr0.2)TiO3基板之電腦模擬圖..........113 圖5-40 0.93(Mg0.95Zn0.05)2TiO4-0.07(Ca0.8Sr0.2)TiO3基板之實作量測圖..........113

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