The Study of Measurement and Analysis in Dielectric Materials of Microwave and The Application to Antenna Design
李政達、林明星，許崇宜
E-mail: 9510785@mail.dyu.edu.tw
ABSTRACT
Since microwave dielectric materials may greatly influence the performance of high-frequency devices, accurate characterization of microwave dielectric materials becomes very important in high-frequency circuit design. Although many methods have been proposed for measuring the constitutive parameters of a dielectric in the literature, they usually have some limitations. Among those methods, the procedure that employs an open-ended coaxial probe (referred to as the OECP method) is usually favorable, for it is relatively easy to use, simple, nondestructive, and of broad band in nature. In this study, the author will use an HP coaxial probe to measure the reflection coefficients of a material under test (MUT). From these coefficients, the frequency-dependent dielectric constants of a MUT can be computed using the formulas derived in this thesis. The computed dielectric constants are compared with those using the HP 85070D dielectric measurement system to validate the derived formulas. Moreover, with the help of these formulas, measured dielectric constants using a standard HP coaxial probe and those using a simplified laboratory-made open-ended coaxial probe are compared and studied. It is found that the low-cost dielectric measurement system established here can replace the expensive HP 85050D system. Finally, a microwave substrate with its high dielectric constant measured using this low-cost system is applied to design a chip antenna.
Keywords : microwave base plate, dielectric parameters measurement, open-ended coaxial probe, chip antenna Table of Contents
封面內頁 簽名頁 授權書．．．．．．．．．．．．．．．．．．．．．．．．．iii 中文摘要．．．．．．．．．．．．
．．．．．．．．．．．．iv 英文摘要．．．．．．．．．．．．．．．．．．．．．．．．v 誌謝．．．．．．．．．
．．．．．．．．．．．．．．．．．vi 目錄．．．．．．．．．．．．．．．．．．．．．．．．．．vii 圖目錄．．．
．．．．．．．．．．．．．．．．．．．．．．x 表目錄．．．．．．．．．．．．．．．．．．．．．．．．．xiv 第 一章 緒論 1-1 研究之背景與目的．．．．．．．．．．．．．．．．．．1 1-2 文獻回顧．．．．．．．．．．．．．．
．．．．．．．．．2 1-3 論文輪廓．．．．．．．．．．．．．．．．．．．．．．．5 第二章 介電係數與量測法 2-1 微 波介電材料．．．．．．．．．．．．．．．．．．．．6 2-1.1 介電質．．．．．．．．．．．．．．．．．．．．．
．6 2-1.2 介電係數．．．．．．．．．．．．．．．．．．．．9 2-1.3 集總電路模式．．．．．．．．．．．．．．．．
．．11 2-1.4 電磁場模式．．．．．．．．．．．．．．．．．．．12 2-1.5 頻率變化之影響．．．．．．．．．．．．．
．．．13 2-1.6 Cole-Cole方程式．．．．．．．．．．．．．．．．13 2-2 介電係數量測法．．．．．．．．．．．．．
．．．．．15 2-2.1 微帶天線法．．．．．．．．．．．．．．．．．．．16 2-2.2 微帶線共振法．．．．．．．．．．．
．．．．．．．18 2-2.3 同軸探針法．．．．．．．．．．．．．．．．．．．22 2-3 量測法之適用性評估．．．．．．
．．．．．．．．．．23 第三章 終端開路同軸探棒量測法 3-1 終端開路同軸探棒．．．．．．．．．．．．．．．．
．25 3-2 等效模型及算式．．．．．．．．．．．．．．．．．．26 3-3 進階等效模型及算式．．．．．．．．．．．．
．．．．29 3-4 全波模擬法驗證．．．．．．．．．．．．．．．．．．31 3-5 校正．．．．．．．．．．．．．．．．
．．．．．．．．34 3-6 實驗設備及方法．．．．．．．．．．．．．．．．．．37 3-7 HP 85070D介電係數量測系統．
．．．．．．．．．．40 第四章 量測結果與討論 4-1 等效模型與HP 85070D之量測準確度分析．．．．．43 4-2 自製簡易 型同軸探棒之準確度．．．．．．．．．．．50 第五章 微波介電材料於天線上之應用 5-1 天線於高介電微波陶瓷材料上 之設計．．．．．．．．55 5-2 以天線驗證準確之介電常數值．．．．．．．．．．．58 5-3 雙頻晶片天線之實作與量測
．．．．．．．．．．．．．59 第六章 結論．．．．．．．．．．．．．．．．．．．．．．．．．．．72 參考文獻 ．
．．．．．．．．．．．．．．．．．．．．．．．．．．．73 附錄 附錄A 電磁模擬軟體簡介．．．．．．．．．．．
．．．．77 附錄B 天線原理簡介．．．．．．．．．．．．．．．．．．81 附錄C 無線區域網路技術簡介．．．．．．
．．．．．．．． 85 圖目錄 圖2.1 材料之四種極化機構示意圖．．．．．．．．．．．．．8 圖2.2 極化對頻率之響應圖
．．．．．．．．．．．．．．．．8 圖2.3 平行板電容與介電質．．．．．．．．．．．．．．．．9 圖2.4 介電常數與 介電損失之複數平面．．．．．．．．．．．10 圖2.5 交流電源下平行板電容等效電路．．．．．．．．．．．11 圖2.6 微帶天線之共振頻率與介電常數關係圖(使用IE3D模擬) 16 圖2.7 微帶天線與T型微帶天線之介電常數量測範圍．．．．
．17 圖2.8 T-型微帶線共振器 (a)模擬架構；(b)實體圖．．．．．．19 圖2.9 FR4板模擬與量測之S12比較(模擬使用IE3D) ．
．．．19 圖2.10 微帶線耦和共振器 (a)半波長微帶線耦和共振器； (b)半波長環型微帶線耦和共振器．．．．．．．．．
．20 圖2.11 差動微帶線共振器．．．．．．．．．．．．．．．．21 圖2.12 量測示意及等效電路模型圖．．．．．．．
．．．．．23 圖3.1 HP coaxial probe．．．．．．．．．．．．．．．．．．26 圖3.2 同軸探棒量測系統 (a)量測示意圖
；(b)量測實體圖．．． 26 圖3.3 同軸探棒量測示意圖．．．．．．．．．．．．．．．．27 圖3.4 等效電路模型．．．．
．．．．．．．．．．．．．．．27 圖3.5等效電容模型．．．．．．．．．．．．．．．．．．．29 圖3.6天線輻射模式 之等效電路模型．．．．．．．．．．．．30 圖3.7 模擬與量測值的差距 (a)Δρ;(b) Δψ．．．．．．．．．33 圖3.8 校正 用之同軸探棒模擬結構．．．．．．．．．．．．．35 圖3.9 同軸探棒校正後之Smith Chart (a)探棒開路(air)； (b)接觸待測 介質(water) ．．．．．．．．．．．．．36 圖3.10 同軸探棒之等效電路示意圖．．．．．．．．．．．．36 圖3.11 網路 分析儀及校正套件-1 (a)HP安捷倫E5071A 網路分析儀；(b) 85033E 3.5mm校正套件．．．．．．37 圖3.12 網路分析儀及校 正套件-2 (a)安立知MS4624B 網路分析儀；(b) 3.5mm校正套件．．．．．．．．．．38 圖3.13 自製簡易型同軸探棒 (a)N-Type Probe；(b)SMA Probe．38 圖3-14 HP Coaxial Probe與自製簡易型同軸探棒．．．．．．．39 圖3-15 HP 85070D 介電量測系統 (a)HP Coaxial Probe & 短路校正器；(b)HP 85070D軟體界面．．．．．．．．41 圖4.1 量測法之 準確度比較- 液態介質 (a)蒸餾水；(b)甲醇； (c)酒精．．．．．．．．．．．．．．．．．．．．．．45 圖4.2 量測法之 準確度比較-固 體介質 (a)微波陶瓷；(b)FR4．46 圖4.3 量測法之 準確度比較-液態介質 (a)蒸餾水；(b)甲醇； (c)酒精．．．．．．．．．．
．．．．．．．．．．．．48 圖4.4 量測法之 準確度比較-固體介質 (a)微波陶瓷；(b)FR4．49 圖4.5 模擬與量測值之相位差
．．．．．．．．．．．．．．．50 圖4.6 三種不同型式探棒之 準確度比較-液態介質 (a)蒸餾水； (b)甲醇；(c)酒精．．．
．．．．．．．．．．．．．．52 圖4.7 三種不同型式探棒之 準確度比較-固體介質 (a)微波陶瓷；(b)FR4．．．．．．．
．．．．．．．．．53 圖5.1 基本曲折型晶片天線之S11(HFSS模擬) ．．．．．．．56 圖5.2 改良為雙頻段曲折型晶片天 線A. (a)設計概念； (b)改善成果．．．．．．．．．．．．．．．．．．．．57 圖5.3 晶片天線A.及測試基板 (a)HFSS模擬 架構圖；(b)實體圖57 圖5.4 改變介電常數對晶片天線頻率點之影響(HFSS模擬值) ．58 圖5.5 晶片天線A.之S11模擬與量測 值( =31) ．．．．．．．59 圖5.6 改良為雙頻段之曲折型晶片天線(晶片天線B.)．．．．．60 圖5.7 晶片天線B.及測試基板 實體圖 (a)MSL feed； (b)CPW feed．．．．．．．．．．．．．．．．．．． 61 圖5.8 晶片天線B.之S11模擬與量測值 (a)MSL；(b)CPW feed．62 圖5.9 天線場型實測圖．．．．．．．．．．．．．．．．．．63 圖5.10 晶片天線B.於2.45 GHz 模擬與實測之輻射場形(MSL feed) (a)E-plane(max = 4.34 dB); (b)H-plane(max = 3.75 dB) ．63 圖5.11 晶片天線B.於5.25 GHz模 擬與實測之輻射場形(MSL feed) (a)E-plane(max = 3.83 dB); (b)H-plane(max = 0.73 dB) ．64 圖5.12 晶片天線B.於2.45 GHz模擬 與實測之輻射場形(CPW feed) (a)E-plane(max = 5.1 dB); (b)H-plane(max = 4.65 dB) ．64 圖5.13 晶片天線B.於5.25GHz模擬與 實測之輻射場形(MSL feed) (a)E-plane(max = 4.22 dB); (b)H-plane(max = 0.82 dB) ．65 圖5.14 晶片天線B.及測試基板實體圖(
測試基板接地面縮短3 mm) (a)MSL feed；(b)CPW feed．．．．．．．．．．．．．67 圖5.15 縮短測試基板接地面對頻率點 的影響(實測值) (a)MSL feed； (b)CPW feed．．．．．．．．．．．．．68 圖5.16 修正載板後晶片天線A.於2.45 GHz之輻射 場形(MSL feed) (a)E-plane(max = 3.43 dB); (b)H-plane(max = 3.58 dB) ． 69 圖5.17修正載板後晶片天線A.於5.25 GHz之輻射場 形(MSL feed) (a)E-plane(max = 4.06 dB); (b)H-plane(max = 2.27 dB) ．69 圖5.18 修正載板後晶片天線A.於2.45 GHz之輻射場 形(CPW feed) (a)E-plane(max = 4.2 dB); (b)H-plane(max = 3.12 dB) ．70 圖5.19修正載板後晶片天線A.於5.25 GHz之輻射場 形(CPW feed) (a)E-plane(max = 3.06 dB); (b)H-plane(max = 1.29 dB) ．70 表目錄 表2.1 25℃參考液(蒸餾水與甲醇)之Cole-Cole 參數．．．．．．14 表2.2 Rectangular Patch Antenna之靈敏度．．．．．．．．．．17 表2.3 T-Pattern Antenna之靈敏度
．．．．．．．．．．．．．17 表2.4 T-resonator對FR4的量測結果．．．．．．．．．．．．19 表2.5 各種量測法之適用 性比較．．．．．．．．．．．．．．24 表5.1晶片天線B.之增益實測值．．．．．．．．．．．．．．65 表5.2修正載板 後之晶片天線A. 之增益實測值．．．．．．．71
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