近幾年，個人通訊蓬勃發展且訴求輕、薄、短小，所以在天線的體積設計上要求小型化，本論文對一些縮小化的天線做分析與模擬，首先是較早期縮小化PIFA天線的分析，之後利用短路的特性設計出具有縮小且可調的雙頻特性，而因為短路所造成的頻寬問題，把短路置換成晶片電阻來改善，這些縮小化的過程中天線增益都會下降，利用於天線上加一覆蓋層以改善。
另外對於現在較熱門的藍芽系統天線，本論文中使用了ACPS（Asymmetrical Coplanar Striplines）結構來設計，並對其參數影響作一完整探討，而用此結構設計可以得到比傳統矩形微帶天線還寬的頻寬。
論文最後，因為天線結構小，應用FDTD（Finite Difference Time Domain）所需的模擬時間需要很長，於是在論文中學習一新的演算法ADI（Alternating-Direction Implicit）-FDTD，且利用此演算法來模擬幾個簡單結構。

In recent years, the demand for portable radio communication has been increasing which requires low profile, light weight and small size antennas. Therefore, the size of the antenna is required to be as small as possible. In this thesis, some of the compact antennas will be analyzed and simulated. The early-stage PIFA antenna will be investigated first, and then the shorting pin characteristics to design compact and dual band antenna was utilized. Because the shorting pin will lead to the decrease of bandwidth, replacement of the shorting pin by using chip-resistor could improve this characteristic. The compactness of antennas will lead to the decrease of the gain. In order to improve the gain of antennas, the combination of substrate and superstrate configuration with very high permittivity material is used.
For the consideration of Bluetooth system, we use the ACPS (Asymmetrical Co-planar Striplines) structure to design the antenna. Using this structure in the design will obtain a promotion in bandwidth compared with the conventional rectangular microstrip antenna.
Because the size of the antenna is small, the time to simulate this structure by the FDTD (Finite Difference Time Domain) method is too long. In order to solve this problem, this thesis mainly study a new FDTD algorithm based on the Alternating-Direction Implicit method, and use this algorithm to simulate some simple structures.

目錄

目錄 Ⅰ
圖表目錄 Ⅲ
第一章 序論 1
1.1 概述 1
1.2 FDTD（Finite Difference Time Domain）介紹 1
1.3 論文大綱 2
第二章 FDTD 基本理論 4
2.1 FDTD的演算法 4
2.1.1 Yee的FDTD演算法 4
2.1.2 穩定準則的處理 7
2.2 激發源的處理 8
2.2.1 邊緣電壓激發方式 8
2.2.2 同軸式饋入線電壓源 9
2.2.3 阻抗性電壓源激發 11
2.3 非均勻網格之有限差分時域法 12
2.3.1 理論 13
第三章 傳統與縮小化的矩形微帶天線分析與模擬 16
3.1 傳統矩形微帶天線（rectangular microstrip antenna） 16
3.1.1 一般特性 16
3.1.2 基本理論分析 18
3.1.3 模擬結果討論 19
3.2 平面倒F型天線的分析與模擬 23
3.2.1 平面倒F型天線（PIFA：Planar Inverted-F Antennas）介紹 23
3.2.2 PIFA天線的特性分析 24
3.2.3 共振頻率與頻寬探討 25
3.2.4 模擬結果 26
3.3 小型化天線的分析與模擬 28
3.3.1 開槽微帶天線特性分析 28
3.3.2 短路柱對微帶天線的特性分析 29
3.3.3 加上短路柱天線的模擬結果分析 29
3.3.4 具有晶片電阻負載對微帶天線的特性分析 32
3.3.5 微帶天線加入晶片電阻的模擬結果與分析 33
3.4 具有增強增益的微帶天線 33
3.4.1 介紹 33
3.4.2 模擬結果 34
第四章 分析積體化倒F型天線在藍芽系統的應用 37
4.1 積體化平面型倒F天線（PIFA）分析 37
4.2 使用不對稱的共面帶線設計一個積體化倒F型天線 41
4.2.1 不對稱共面帶線（Asymmetric coplanar striplines） 42
4.2.2 開路端的校正 43
4.2.3 短路端的校正 45
4.2.4 天線的設計 47
4.2.5 模擬結果與討論 48
第五章 ADI（Alternating-Direction Implicit）演算法的分析與模擬 57
5.1 介紹 57
5.2 2D ADI-FDTD數值公式 57
5.3 討論ADI-FDTD數值的穩定度 59
5.4 2D TE wave ADI-FDTD模擬結果 62
5.5 使用3D ADI-FDTD演算法模擬一個矩形微帶天線 64
第六章 結論 66
參考文獻 67
附錄 A . ADI-FDTD 3D公式 71

圖表目錄

圖2-1 FDTD電場及磁場的空間網格配置圖 4
圖2-2 FDTD交替計算時間步階圖 7
圖2-3 一個微帶線激發實例圖 8
圖2-4 連接平板天線與同軸線的結構 10
表2-1 同軸線區域與天線區域的交界面plane2處理 11
圖2-5 包圍電磁場的表面積分路徑封閉曲線的邊緣長度定義 14
圖3-1 微帶天線(microstrip antenna)的基本結構圖 16
圖3-2 阻抗性電壓源饋入的矩形微帶天線 17
圖3-3 典型交叉極化比值與矩形微帶天線長寬比之對應關係 17
表3-1 均勻與非均勻切割的比較 19
圖3-4 使用FDTD方法比較均勻與非均勻切割方法 20
圖3-5 在resonant frequency觀看相位的變化 20
圖3-6 當饋入點在y=b/2，x=0∼a移動時S11的變化情形 21
圖3-7 當饋入點在x=a/2，y=0∼b移動時S11的變化情形 21
圖3-8 非均勻切割方法中鄰近網格的尺寸變化倍率 22
圖3-9 使用阻抗性電壓源饋入與同軸線饋入 22
圖3-10 平面倒F型天線結構 23
圖3-11 共振頻率與短路金屬板的關係 24
圖3-12 輻射金屬片的尺寸與短路金屬板的寬度變化在輻射金屬板的表面電流變化情形 25
圖3-13 當短路金屬板寬度小於L1時與PIFA的頻寬關係 26
圖3-14 PIFA結構 26
表3-2 PIFA的模擬參數 27
圖3-15 PIFA天線高度變化跟共振頻率的關係 27
圖3-16 短路金屬板的寬度短路金屬板的寬度對天線共振頻率的影響 27
圖3-17 加上短路柱天線的模擬結構 29
表3-3 加上短路柱天線的模擬參數 29
圖3-18 加上了短路柱後矩形微帶天線的折返損耗 30
圖3-19 加入金屬短路柱天線在 模態電場示意圖 30
圖3-20 天線共振頻率與金屬短路柱的位置變化關係 31
圖3-21 加入不同的晶片電阻阻值對天線頻率、頻寬的變化 33
圖3-22 PIFA天線加上一具有高介電常數的負載 34
表3-4 PIFA加上高介電常數負載的模擬參數 34
圖3-23 天線的折返損耗與頻率 34
圖3-24 天線的增益 35
圖3-25 增加高介電常數負載的厚度對天線增益變化 36
圖4-1 PIFA應用於藍芽的天線結構 37
表4-1 PIFA結構於藍芽天線的相關參數 37
圖4-2 天線的折返損耗與頻率 38
圖4-3 天線的輸入阻抗 38
圖4-4 天線遠場輻射場型 39
圖4-5 不同的S變化對天線頻率的影響 39
表4-2 S的距離變化對天線的頻率與阻抗關係 39
表4-3 改變天線其他參數對頻寬的影響 39
圖4-6 d2對天線頻率的影響 39
圖4-7 三種倒F型天線（IFAs）：（a）傳統線型IFA；（b）平面倒F型天線PIFA；（c）積體化的IFA 41
圖4-8 積體化倒F型天線IIFA使用ACPS線製造 42
圖4-9 ACPS lines 結構 42
圖4-10 （a）特徵阻抗（b）有效介電常數在厚度為1.57mm的FR4基板金屬線寬的關係 43
圖4-11 等效的有效開路端長度概念 44
圖4-12 等效的有效開路端長度 44
圖4-13 等效的有效短路端長度概念 45
圖4-14 等效的有效短路端長度 45
圖4-15 （a）特徵阻抗（b）有效介電常數在厚度為0.76mm的FR4基板金屬線寬的關係 46
圖4-16 在厚度為0.76mm的FR4基板上，端點的校正 46
圖4-17 IIFA的等效網路 47
圖4-18 用ACPS lines設計的天線結構 48
表4-4 IIFAs參數 48
圖4-19 使用網路分析儀所量到的折返損耗 49
圖4-20 模擬的折返損耗與阻抗圖 49
圖4-21 h的改變與S11及頻率關係 50
表4-5 h的改變對天線特性的影響 50
圖4-22 S的改變與S11及頻率關係 51
表4-6 S的改變對天線特性的影響 51
圖4-23 W的改變與S11及頻率關係 52
表4-7 W的改變對天線特性的影響 52
圖4-24 P的改變與S11及頻率關係 53
表4-8 P的改變對天線特性的影響 53
圖4-25 GL的改變與S11及頻率關係 53
表4-9 GL的改變對天線特性的影響 54
表4-10 接地面的面積大小對天線特性的影響 54
圖4-26 基板厚度對天線的影響 54
圖4-27 ACPS lines所製作的天線，其輻射場型（a）在遠場的E-plane（b）在遠場的H-plane 55
圖4-28 阻抗性電壓源不同方向饋入觀看其折返損耗結果（a）FDTD模擬結果（b）實際量測結果 56
圖5-1 ADI-FDTD在2D TE Wave的流程圖 59
圖5-2 ADI-FDTD程式處理上的概念 61
圖5-3 激發源處理的程序（a）傳統的FDTD（b）ADI-FDTD 61
圖5-4 2D ADI-FDTD TE wave自由空間模型 62
圖5-5 在觀察點正規化 場量隨時間變化關係 63
表5-1 ADI-FDTD與傳統FDTD時間上的比較 63
圖5-6 3D ADI-FDTD 處理流程圖 64
圖5-7 矩形微帶天線的結構 64
表5-2 模擬參數 65
圖5-8 使用ADI-FDTD所模擬的天線結果 65

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