論文摘要 : 
     介質EBG有非常多的好處，它可以配置成反射面，也可以配置為覆蓋層，這兩種配置皆可以提升天線的輻射特性，並且和金屬的EBG相比，可以有更低的歐姆損耗。根據EBG的結構配置可以分為三大類，即一維的柱狀排列，二維的平面式排列，及三維的立體狀結構。三維的立體狀結構有更多的好處以及更多的設計自由度，然而因為實作上的困難，使得其在微波上的研究及應用受到侷限。受惠於積層製造技術以及奈米科技的進步，複雜的3D陶瓷或介質結構已能被製作出來。考量EBG整體結構的整體尺寸以及對製程精度的要求，我們認為28GHz的毫米波頻段是個適合嘗試採用積層製造技術來製備天線元件的候選頻段。 
     在此論文中，我們將先設計一個工作在28GHz的典型平面式woodpile EBG。EBG的各項設計參數將被仔細分析並且探討它們對天線性能上的影響。之後，此論文提出一個弧形的EBG設計。我們發現弧形的EBG可以改善天線的輻射場型，提供更好的指向性。散射參數及輻射場型等天線參數皆有提供以證明在偶極天線上，弧形狀的設計可以比平面式的設計提供更佳的性能。

Abstract :
Dielectric electromagnetic band-gap (EBG) has many advantages. It can be configured as a reflector, or be configured as a superstrate. Both of this two configurations can improve antenna radiation preference with lower conduction loss as compared to metallic EBG. In general, EBG can be categorized into three groups according to their geometric configuration, which are one-dimensional rods, two-dimensional planar surfaces, and three-dimensional volumetric structures. The 3D structure has more advantages and design flexibility, however, due to the difficulties in prototyping, studies and applications in microwave field is limited. Thanks to the progress in additive manufacturing and nano-technology, dielectric or ceramic complex 3D structure is able to be fabricated. Considered the overall size of an EBG structure and the accuracy required of the fabrication process, 28GHz mmWave band is a good candidate, which has the feasibility of applying additive manufacturing in the production of antenna parts.
In this thesis, a classic planar woodpile EBG working at 28GHz will be designed. Design parameters will be carefully analyzed and studied their effects on antenna performances. After that, a curved dielectric EBG with be proposed. It was found that a curved EBG can improve radiation pattern, providing higher directivity of the antenna. Antenna parameters such as scattering parameters and radiation patterns are provided to validate that the curved design provides better performance with a dipole antenna than the planar one.

目錄
 
中文摘要	I
英文摘要	III
目錄	V
圖目錄	VII 
表目錄	XII
第一章、緒論	1
1.1 研究背景	1
1.2 研究目的與文獻探討	2
1.3 論文架構	12
第二章、毫米波天線及電磁帶隙結構	13
2.1 毫米波天線應用與設計	13
2.2 電磁帶隙結構特性	17
第三章、平面電磁帶隙設計	27
3.1 EBG單元設計	27
3.2 偶極天線與EBG結構平面大小	34
3.3 EBG結構參數分析	43
第四章、弧形電磁帶隙設計	53
4.1. 弧形電磁帶隙結構	53
4.2. 弧形EBG弧度與層數分析	61
4.2.1 弧度分析	61
4.2.2 焦點分析	66
4.2.3 厚度分析	73
4.3弧形結構與平面結構相比在特性上的優缺點	78
第五章、結論	81
參考文獻	83
 
圖目錄
圖 1.1. (a) 平面結構的Woodpile EBG  (b) 圓柱形結構的Woodpile EBG俯視圖  (c) 圓柱形結構的Woodpile EBG側視圖 [1]	4
圖 1.2. (a) 只有天線做輻射的輻射場型圖 (b) 平面Woodpile EBG結構天線的輻射場型圖 (c) 平面Woodpile EBG結構擺放置天線上方產生輻射 [1]	5
圖 1.3. 圓柱形Woodpile EBG結構天線的輻射場型圖 [1]	5
圖 1.4. (a) Mushroom-like EBG  (b) Hairpin resonator EBG  [2]	6
圖 1.5. Uniplanar compact  EBG結構 [3]	7
圖 1.6. UC-EBG結構和Cross Slot的貼片天線陣列結構 [3]	8
圖 1.7. UC-EBG結構和Cross Slot的貼片天線陣列側視結構 [3]	8
圖 1.8. (a) 常規的2*2微帶陣列天線項視圖 (b) 用於2*2微帶陣列的交叉堆疊EBG覆板天線 (c) 圓柱棒EBG可覆蓋2*2微帶陣列天線 [4]	9
圖 1.9. (a) 每一層交叉疊放的方向示意圖 (b) 每一層做交叉疊放後的EBG結構俯視圖 [5]	10
圖 1.10. (a) 每一層做交叉疊放後的EBG結構側視圖 (b) 每一層做交叉疊放後的EBG結構透視圖 [5]	11
圖 2.1. 布拉格散射原理說明 [24]	17
圖 2.2. (a) 1-D ; (b) 2-D ; (c) 3-D光子晶體的簡示圖 [28]	22
圖 2.3. (a) 1-D ; (b) 2-D ; (c) 3-D光子晶體在空間中的呈現 [29]	22
圖 2.4. 3-D的光子晶體 [30]	24
圖 2.5. 能隙 (band gap) 呈現 [31]	25
圖 3.1. unit cell 單位晶元模擬圖	27
圖 3.2. unit cell 單位晶元邊界條件之反射係數圖	28
圖 3.3. unit cell 模擬俯視圖(間距為參數c)	29
圖 3.4. unit cell 單位晶元之模擬圖(柱寬參數a、柱長參數b)	29
圖 3.5. 柱寬參數a變化之反射係數圖	30
圖 3.6. 柱長參數b變化之反射係數圖	31
圖 3.7. 高介電常數 ε_r 參數變化之反射係數圖	32
圖 3.8. 低介電常數 ε_r 參數變化之反射係數圖	33
圖 3.9. dipole天線之模擬圖	35
圖 3.10. dipole天線之反射係數圖	36
圖 3.11. dipole天線之輻射場型圖	36
圖 3.12. dipole天線放置woodpile EBG中心之模擬俯視圖	37
圖 3.13. 平面woodpile EBG模擬之輻射場型圖	38
圖 3.14. 平面woodpile EBG模擬之反射係數圖	38
圖 3.15. 參數mdx變化之結構側視圖	39
圖 3.16. 參數mdx變化之輻射場型圖	40
圖 3.17. 參數mdx變化之反射係數圖	40
圖 3.18. (a) dipole水平擺放至EBG結構中心之模擬圖 (b) dipole垂直擺放至EBG結構中心之模擬圖	41
圖 3.19. dipole天線水平擺放與垂直擺放至EBG結構中心之輻射場型圖	42
圖 3.20. (a) X軸方向結構面積變大之模擬圖 (b) Y軸方向結構面積變大之模擬圖	44
圖 3.21.結構面積X軸方向變大與面積不變化之輻射場型圖	45
圖 3.22. 結構面積Y軸方向變大與面積不變化之輻射場型圖	46
圖 3.23. 結構面積軸向變化之輻射場型圖	47
圖 3.24. (a) EBG結構層數四層之模擬圖 (b) EBG結構層數六層之模擬圖 (c) EBG結構層數八層之模擬圖	48
圖 3.25. EBG結構層數四層與六層之輻射場型圖	49
圖 3.26. EBG結構層數四層與八層之輻射場型圖	50
圖 3.27. EBG結構層數變化之輻射場型圖	51
圖 4.1. (a) dipole天線放置弧形woodpile EBG中心之模擬圖 (b) dipole天線放置弧形woodpile EBG中心之模擬側視圖	55
圖 4.2. 弧形woodpile EBG模擬之輻射場型圖	56
圖 4.3. 弧形woodpile EBG模擬之反射係數圖	56
圖 4.4. 參數pdy變化之結構側視圖	57
圖 4.5. 參數pdy變化之輻射場型圖	58
圖 4.6. 參數pdy變化之反射係數圖	58
圖 4.7. 弧形EBG結構與平面EBG結構圖	59
圖 4.8. 弧形EBG結構與平面EBG結構之輻射場型圖	60
圖 4.9. (a) 弧形woodpile EBG彎曲45度之模擬圖 (b) 弧形woodpile EBG彎曲45度之模擬側視圖	62
圖 4.10. (a) 弧形woodpile EBG彎曲90度之模擬圖 (b) 弧形woodpile EBG彎曲90度之模擬側視圖	62
圖 4.11. (a) 弧形woodpile EBG彎曲180度之模擬圖 (b) 弧形woodpile EBG彎曲180度之模擬側視圖	63
圖 4.12. 弧形woodpile EBG彎曲45度與90度之輻射場型圖	64
圖 4.13. 弧形woodpile EBG彎曲90度與180度之輻射場型圖	65
圖 4.14. 弧形woodpile EBG彎曲變化之輻射場型圖	66
圖 4.15. 彎曲45度焦點間距變化之結構側視圖	67
圖 4.16. 彎曲45度焦點間距變化之輻射場型圖	67
圖 4.17. 彎曲45度焦點間距變化之反射係數圖	68
圖 4.18. 彎曲90度焦點間距變化之結構側視圖	68
圖 4.19. 彎曲90度焦點間距變化之輻射場型圖	69
圖 4.20. 彎曲90度焦點間距變化之反射係數圖	69
圖 4.21. 彎曲180度焦點間距變化之結構側視圖	70
圖 4.22. 彎曲180度焦點間距變化之輻射場型圖	71
圖 4.23. 彎曲180度焦點間距變化之反射係數圖	71
圖 4.24. 三種最佳彎曲焦點間距之輻射場型圖	72
圖 4.25. 三種最佳彎曲焦點間距之反射係數圖	73
圖 4.26. (a) 弧形EBG結構層數四層之模擬圖 (b) 弧形EBG結構層數六層之模擬圖 (c) 弧形EBG結構層數八層之模擬圖	74
圖 4.27. 弧形EBG結構層數四層與六層之輻射場型圖	75
圖 4.28. 弧形EBG結構層數四層與八層之輻射場型圖	76
圖 4.29. 弧形EBG結構層數變化之輻射場型圖	77
圖 4.30. 八層弧形EBG結構與八層平面EBG結構之輻射場型圖	79




















表目錄
表 3.1. Unit cell介電常數與長柱參數分析表	52
表 3.2. 平面woodpile EBG結構增益值之參數分析表	52
表 4.1. 弧形EBG結構其對應比較參數之增益值分析表	80

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