近年來，由於無線通訊的發展，射頻積體電路(RFIC)已經越來越複雜，而且隨著我們對商品的要求—執行速度越來越快，體積越來越小，功能越來越多，射頻積體電路的設計則更為重要。然而，設計射頻積體電路是更後端的工作，在設計電路之前，還有許多努力要做，舉個例子說:研究積體電路製作材料的人住在地下室，利用模擬軟體研究電路元件特性參數的住人在一樓，設計電路的人住在二樓，由這個例子可以看出，在設計電路的人真正開始設計之前，還有許多的人做了很多的努力。

而本篇論文，正是住在一樓的我們利用電磁模擬軟體Fasthenry來模擬並分析螺旋型電感，並且透過我們的實驗方法協助欲了解螺旋型線圈電感特性的人，可以更節省時間與金錢成本，快速的對利用Fasthenry這套電磁模擬軟體模擬各式螺旋型電感的流程以及方法有深入的了解。並且利用這樣的研究方法找出特性最佳，電感品質最好的螺旋型線圈結構以提供給電路設計者使用。

本論文將會從最開始如何設計一個正確的Fasthenry螺旋型電感結構開始，再詳細敘述如何針對Fasthenry設計出一個完整或不完整的基底，並且加以驗證，而且利用導入自動化模擬流程，不但可以大幅的縮短使用者編寫輸入檔所花的時間，也可以避免因人為輸入所產生的結構錯誤，再利用本論文所使用的自動化程式對不同結構的螺旋型線圈與基底進行模擬實驗。還有就螺旋型線圈的形狀產生不同的結構輸入檔，並且針對各種螺旋型電感的結構差異，設計出具有代表性的測試結構並且將它們所模擬出的測值交叉比對，將它們依照操作變因找出相對得測試結構，觀察並驗證趨勢是否正確，並藉此研究如何利用不同的設計結構來達到最好的螺旋型線圈電感效能。

In recent years, due to the development of wireless communications, RF integrated circuits (RFIC) has become increasingly complex and as our demand of products- implementation of the speed faster and faster, smaller and smaller, faster ,and more efficient, radio frequency integrated circuit design seems to be much more important and difficult. However, the design of RF integrated circuits is a back-end work. Namely, the people who study the integrated circuit production materials live in the basement, the people who use simulation software to simulate circuit elements’ parameters live on the first floor, and the integrate circuit designers live on the second floor. We could know that before a designer start to design a circuit, there are many people who have done a lot of effort.

We live on the first floor! We use an electromagnetic simulation software – Fasthenry to simulate and analysis spiral inductors, and help others to learn more about spiral inductor characteristics through our experiments, and it would certainly save a lot of time, money and effort for them. This thesis can also let people get familiar with how to simulate spiral inductor by Fasthenry, and find the best quality inductor for designer.

This paper will identify how to design a proper Fasthenry spiral inductor structure input file, and then described the details about how to design a Fasthenry complete or incomplete substrate structure. Furthermore, we use an automated simulation program, it would not only shorten the time that user have to spent, but also avoided input errors. We also developed some different versions of automated simulation program, we offered three different shapes of spiral inductor structures automated program, ex: rectangular, hexagonal, and octagonal spiral inductors. We designed some test structures to observe whether the trend of inductance and resistance of spiral inductor is right, and find out how to design a better spiral inductor.

中文摘要……………………………………………………………………………1
英文摘要……………………………………………………………………………2
目錄…………………………………………………………………………………3圖目錄………………………………………………………………………………6
表目錄………………………………………………………………………………10

第一章 緒論 12
1.1 電感，自感，互感，感應係數k………………………………………14
1.1.1 電感 …………………………………………………………14
1.1.2 自感，互感，感應係數k…………………………………….15
1.2 螺旋型電感(Spiral inductor) ……………………………………17
1.3 射頻積體電路(RFIC) ………………………………………………18
1.4 電磁模擬軟體Fasthenry …………………………………………19
1.5 基板(substrate)電性，電阻率(rho) ……………………………20
1.6螺旋型電感等效模型圖(equivalent model) ……………………21
1.7品質因子(Quality factor)…………………………………………23


第二章 使用電磁模擬軟體Fasthenry來建構模擬螺旋型電感 27
2.1 建構一個正確的Fasthenry螺旋型線圈模型……………………27
2.2建構一個正確的螺旋型線圈基底 …………………………………32
2.3 進階的基底結構設計格式…………………………………………35
2.3.1 平行十等分分割法基底結構模型…………………………37
2.3.2 九宮格法基底結構模型……………………………………43


第三章 電感準確性驗證 — Fasthenry模擬出來的電感與科學園區晶圓製
造公司的經驗公式的比較 49
3.1 分別利用Fasthenry與園區經驗公式模擬抽取及計算螺旋型線圈 電感…………………………………………………………………49
3.2 計算園區經驗公式與Fasthenry模擬的電感之間的誤差………51
3.3 製程變異對螺旋型電感造成的影響………………………………54
3.3.1製程變異……………………………………………………54
3.3.2製程變異造成螺旋型電感金屬線線粗的改變……………56
3.3.3 操作頻率不同造成螺旋型電感的電感電阻值改變 ……61
3.3.4製程變異造成螺旋型電感金屬線線厚的改變……………64
3.3.5製程變異造成螺旋型電感與基底垂直距離的改變………….71


第四章 雙繞式，重疊式，平行式螺旋型線圈的模擬 74
4.1 雙繞式螺旋型線圈(Coupled Spiral) ………………………………74
4.2 重疊式螺旋型線圈(Stacked Spiral) ……………………………76
4.3 水平平行式螺旋型線圈(Parallel Spiral) ………………………78


第五章 基底結構材質測試以及自動化Fasthenry模擬流程 81
5.1 改變基底(substrate)的材質來觀察對電感及感應係數的影響…81
5.2 自動化Fasthenry螺旋型線圈結構模擬 …………………………86
5.3重疊式螺旋型線圈基底材質自動化程式模擬 ……………………88
5.3.1 重疊式螺旋型線圈 -十等分法基底切割結構自動化模擬實
驗 ……………………………………………………………88
5.3.2 重疊式螺旋型線圈 –十等分法基底切割結構自動化模擬實
驗 ……………………………………………………………92
5.4 雙繞式螺旋型線圈基底材質自動化程式模擬 ……………………97
5.4.1 雙繞式螺旋型線圈—十等分法基底切割結構自動化模擬實
驗 ……………………………………………………………98
5.4.2 雙繞式螺旋型線圈--九宮格法基底切割結構自動化模擬實
驗 ……………………………………………………………99
5.5 討論相同百分比，但分布不同造成的影響 ………………………102
5.6 基底紋路屏障(PGS，pattern ground shield)的螺旋型電感結構模
擬……………………………………………………………………107


第六章 各種螺旋型線圈結構以及基底設計結構的分析比較 116
6.1 虛擬金屬……………………………………………………………116
6.2 八角形螺旋型線圈…………………………………………………116
6.3 六邊形螺旋型線圈的模擬實驗與分析比較………………………121
6.4 代表結構比較………………………………………………………124
6.4.1 訂定操作變因並產生相對設計結構………………………124
6.4.2 操作變因電感比較關係圖…………………………………128
6.4.3 操作變因電阻比較關係圖…………………………………129
6.5電感形狀與基底結構Q值比較關係圖……………………………131


第七章 結論 134

第八章 未來展望 139

參考文獻 141

附錄 142
附錄A 142
製程變動造成垂直距離對電感電阻與理想Q值的影響表

附錄B 144
new_PGS_gen_spiral.pl節錄

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