一直以來，粉末的介電特性量測需要考慮諸多變因，例如: 孔隙率、密度、濕度、雜質等因素[1]-[3]，導致目前無法直接量測粉末的介電特性。常見的介電測量方法中，例如: 傳輸線法 (Transmission Line)與共振腔法 (Resonant Cavity)等，需要對於材料進行加工[4]-[6]，而這將花費時間和金錢來達成量測需求，在製備樣品的過程中也可能會出現缺陷。因此，本研究在探討一種無需混合高分子聚合物的情況下，可直接測量粉末材料複介電係數的方法。
這項研究為粉狀材料的介電特性量測，使用的共振腔頻率為2.45 GHz，以複合模型(Hybrid Model)進行模擬。使用不同大小的氧化鋁粉末作為樣品，裝在鐵氟龍容器中，並放置共振腔內金屬柱的上方，通過強化電場法（Field - Enhanced Method, FEM）強化頻率響應，向量網路分析儀(Vector Network Analyzer, VNA)會接收材料的訊號，然後使用高頻結構模擬器 (High Frequency Structure Simulator, HFSS)針對複合模型的模擬結果進行比較，透過分析得到材料的共振頻率和品質因子得到複介電係數。為了與理論值作比較，使用四個經典的有效介質理論模型(Maxwell-Garnett (MG), symmetrical Bruggeman (sBM), Landau-Lifshitz-Looyenga (LLL), Lichtenecker’s logarithmic (LOG))來取得粉末的複介電特性理論值，檢驗本研究探討的複介電係數量測方法準確性，其中，LLL模型的數據誤差最小。另外，本研究發現在奈米尺度下，隨著氧化鋁粉末尺寸的減小，會因為表面積效應(surface effect)，導致複介電係數增加的現象。本研究成果—複合模型量測方式能夠直接而準確量測分析粉狀材料的複介電係數。

The dielectric measurement of the powdery material has always required considering many variables, e.g. porosity, density, humidity, impurity, etc.[1]-[3], which makes it difficult to directly measure the dielectric properties of the powder. The common dielectric measurement methods, such as Transmission Line, Resonant Cavity, etc. require material processing[4]-[6], which will spend time and money to match the demands, and manufacturing defects might occur. Therefore, we proposed a method that can measure the dielectric constant of materials in powder, without mixing the polymer and that is more convenient than other existing methods.

This work used a simulation-based Hybrid Model to do the dielectric measurement of powdery materials at a frequency of 2.45 GHz. Alumina powders of various sizes were used as samples, packed in a Teflon container, and then placed on the top of the central rod within a resonant cavity to obtain the frequency responses by the enhanced-field method (EFM). A vector network analyzer (VNA) received the experimental frequency response, which was then compared with the simulated results of the Hybrid Model by a full-wave simulator (high-frequency structure simulator, HFSS). Contour maps were established to map the samples' resonant frequencies and quality factors to their complex permittivities. Four classical effective medium theory models (Maxwell-Garnett (MG), symmetrical Bruggeman (sBM), Landau-Lifshitz-Looyenga (LLL), Lichtenecker’s logarithmic (LOG)) were considered to examine the proposed method with the LLL model best fitting the data. The results obtained by our method agreed well with that suggested by Looyenga’s formula for the powdery alumina. Also, as the size of the alumina powder decreases, its complex permittivity tends to increase due to the surface effect. This method serves as a fast and accurate way to directly characterize the dielectric properties of the powdery material.

第一章 緒論··············································3
1.1 前言··············································3
1.2 微波··············································5
1.3 複介電係數········································6
1.4 極化機制··········································8
1.5 散射參數··········································12
第二章 微波共振腔的設計與介紹····························15
2.1 共振腔體結構······································15
2.2品質因子··········································19
2.3 共振腔電磁場結構與公式推導························22
2.4 參數映射圖········································25
第三章 實驗方式與材料選擇································27
3.1 實驗架設··········································27
3.2 材料的選擇—氧化鋁································28
3.3 氧化鋁在不同粒徑下的SEM分析圖···················30
3.4 複合材料epoxy/ alumina的製備方式···················34
第四章 實驗量測分析與修正································36
4.1 複合材料epoxy/ alumina的介電特性量測···············36
4.2 純氧化鋁粉末量測··································39
4.3 液滴模型··········································43
4.4 複合模型的修正—壓縮複合模型······················49
第五章 有效介質理論······································55
5.1 有效介質理論模型··································55
5.2 實驗與模擬········································57
5.3 不同粒徑下的氧化鋁粉末之介電係數的實驗與理論比較··60
5.4 氧化鋁粉末在不同粒徑下的複介電係數趨勢分析·····68
5.5 Hybrid Model與LLL Model討論·····················73
第六章 結論··············································75
附錄 參考文獻············································77

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