臺灣博碩士論文加值系統

摘 要
本論文將設計一個優於先前學者所提出的電路，以線性組合的觀念設計出高階萬用濾波電路，其優點在於電路設計使用較少的主、被動元件，用單端輸入的主動元件及接地電容，大幅降低寄生電容的效應。
本論文以Mansour Moniri 和 Bashir Al-Hashimi兩位學者所提出的建構方塊為開端[1]，以線性組合的觀念設計出高階萬用濾波電路，其電路架構為單電壓輸入以及單電壓輸出，經由適當轉導的選擇，在輸出端可實現高通、低通、帶通、帶拒、全通等五種濾波器功能。本論文所使用的主動元件為：運算轉導放大器(Operational Transconductance Amplifier ; OTA) 及第二代電流控制傳輸器(Second generation Current Controlled Conveyor ; CCCII)。由於主動元件OTA及CCCII，其轉導值及內部Ｘ端本質電阻值，均可以偏壓電流予以調整，在電路設計時可以免除電阻的使用，電路結構簡單化。另外，元件輸入端為高阻抗，具有可直接串接前級電路的優點，一個n階通用濾濾波器僅需使用2n+4個主動元件及n個接地電容。
本論文所提出的電路均以HSPICE做為實際驗證的模擬工具，以聯華電子公司UMC05 LEVEL49 的製程參數做為在晶片化前的考量參數，因此本論文的濾波電路只要經過佈局（Layout）與Post Simulation就可以下線(Type out)作實際的驗證。本論文以Matlab作理論值的驗證，HSPICE所模擬數據與理論值均相當吻合，因此本論文所設計的電路，未來在實際的運用上均有很大的發展及參考之處。

Abstract
The voltage-mode high-order universal filter structure using linear combination approach has been studied ing this thesis [7-20]. A fundamental high-order multi-function ( lowpass , bandpass, and highpass ) filter structure is realized first. Different order output signals can be obtained from different nodes in the fundarnental filter structure. Therefore, the linear combination of the output signals of the fundamental filter structure maker any kinds of filtering functions. The synthesize voltage-mode high-order universal filter structure employs 2n+4 single-input active elements and n grounded capacitors.
The second-generation current controlled conveyors (CCCII) with electronically tunable inner resistance and used in the <a href="http://www.ntsearch.com/search.php?q=design&v=56">design</a>. Using nullator-and norator equivalent transformationk, the CCCII-based filter structure can be transformed into the operational Transconductance Amplifier based filter structure. Note that the transconductance of an OTA is also adjustable by the bias current.
H-Spice simulations are used for carrying out the comparison between CCCII-absed and OTA-based filter structures in terms of filtering performance, noise, and sensitivity analysis. Simulation results validate the theory predictons

目錄

第一章 緒論 1
第二章 電流式主動元件之介紹 2
2-1 等效Nullor Model模型 2
2-1.1　Nullor model： 3
2-1.2 Nullator model： 4
2-1.3 Norator model： 4
2-2 電流傳輸器(CC)的特性 6
2-2.1 第一代電流傳輸器(CCI) 7
2-2.2 第二代電流傳輸器﹙CCII﹚ 8
2-2.3第三代電流傳輸器(CCIII) 13
2-3 第二代電流控制傳輸器﹙CCCII﹚ 17
2-4 運算轉導放大器(OTA) 21
2-5 多輸出端電流式主動元件架構 25
第三章 以線性組合觀念設計電壓式OTA-C N階濾波電路 30
3-1 CCCII與OTA的轉換 31
3-2 建構式方塊及電壓傳輸矩陣電路合成法 37
3-3 一階電壓式OTA-C萬用濾波器電路 42
3-4 二階電壓式OTA-C萬用濾波器電路 45
3-5 三階電壓式OTA-C萬用濾波器電路 49
3-6 N階電壓式OTA-C萬用濾波器電路 53
3-7雜訊理論特性 60
3-7.1射雜訊（Shot Noise） 60
3-7.2熱雜訊（Thermal Noise） 61
3-7.3閃爍雜訊（Flicker Noise） 61
3-7.4爆裂雜訊（Burst Noise） 62
3-7.5累增雜訊（Avalanche Noise） 62
3-7.6積體電路元件之雜訊模型（Noise Models） 63
3-8靈敏度分析理論特性（Sensitivity Analysis） 65
3-8.1 電壓式OTA-C二階萬用濾波電路靈敏度分析 65
3-8.2 電壓式CCCⅡ-C二階萬用濾波電路靈敏度分析 67
第四章 以線性組合觀念設計電壓式OTA-C與CCCⅡ-C濾波電路特性功能上的比較 69
4-1 三階CCCⅡ-C萬用濾波電路轉移函式細部推導 70
4-2 三階OTA-C萬用濾波電路轉移函式細部推導 76
4-3 CCCⅡ與 OTA 濾波電路非理想分析 82
4-3.1 OTA 非理想電路 82
4-3.2 CCCⅡ 非理想電路 83
4-4 三階OTA-C與CCCⅡ-C萬用濾波電路模擬與特性功能上的比較 85
4-5 雜訊(Noise)比較 93
4-6 靈敏度（Sensitivity）比較 96
4-6.1二階電壓式OTA-C與CCCⅡ-C高通濾波電路靈敏度比較 97
4-6.2二階電壓式OTA-C與CCCⅡ-C低通濾波電路靈敏度比較 100
第五章 結論及未來研究方向 104
結論 104
未來發展及研究方向 110
參考文獻 111
附錄 115
作者簡歷 121

圖目錄

圖2-1 NULLATOR 與 NORATOR 模型 3
圖2-2 NULLATOR MODEL模型 4
圖2-3(A) 正型之NORATOR 5
圖2-3(B) 負型之NORATOR 5
圖2-4 CCI之元件符號 7
圖2-5 CCI之NULLOR等效模型 7
圖2-6 CCII之元件符號 8
圖2-7(A) CCII之NULLOR模型 9
圖2-7(B) CCII之簡化NULLOR模型 9
圖2-8(A) CCII+之內部電路結構 11
圖2-8(B) CCII-之內部電路結構 11
圖2-9 CCII之簡單應用 12
圖2-10 CCIII之元件符號 14
圖2-11 以雙輸出之CCII實現CCIII 14
圖2-12(A)電流加法器 14
圖2-12(B)加權電流加法器 15
圖2-13(A)電流放大器 15
圖2-13(B)電壓放大器 15
圖2-13(C) 傳輸阻抗放大器 15
圖2-13(D) 傳輸導納放大器 16
圖2-14 CCIII之CMOS內部電路 16
圖2-15 CCCII之元件符號及NULLOR模型 17
圖2-16(B) CCCII-之內部電路 19
圖2-17﹙A﹚CCCII模擬負電阻 19
圖2-17﹙B﹚可由偏壓電流控制之電壓放大器 19
圖2-17﹙C﹚可由偏壓電流控制之電流放大器 20
圖2-17 CCCII之基本應用電路 20
圖2-18 OTA之元件符號 21
圖2-19 OTA之NULLOR等效模型 21
圖2-20 OTA元件符號及NULLATOR-NORATOR等效模型 22
圖2-21 OTA之內部電路 23
圖2-22 OTA的應用電路 24
圖2-23複製正向電流源及反向電流源 26
圖2-24疊接電路複製正向電流源及反向電流源 26
圖2-25 CCCII(-/-)之電路符號及端點特性 27
圖2-26 CCCII(-/-)之內部電路圖 27
圖2-27 CFCCC IIP之電路符號及端點特性 28
圖2-28 CCCII(+/-)之內部電路圖 28
圖2-29 DO-CCCII之NULLOR模型 29
圖3-1 CCCII＋之元件符號 31
圖3-2 OTA＋之元件符號 31
圖3-3 正型OTA等效電路 33
圖3-4 正型OTA負輸入端接地等效電路 33
圖3-5 正型OTA負輸入端接地等效電路 33
圖3-6 CCCII之元件符號及NULLOR模型 33
圖3-7 CCCII + X端接地之NULLOR模型 33
圖3-8 負型OTA等效電路 34
圖3-9 負型OTA正輸入端接地等效電路 34
圖3-10 負型OTA正輸入端接地等效電路 34
圖3-11 CCCII - X端接地之NULLOR模型 35
圖3-12﹙A﹚CCCII與OTA模擬負電阻 35
圖3-12﹙B﹚可由偏壓電流控制之電壓放大器 35
圖3-12﹙C﹚可由偏壓電流控制之電流放大器 36
圖3-12 CCCII與OTA應用電路間轉換 36
圖3-13 一階CCCII-C濾波電路之建構方塊與其轉移函數 37
圖3-14 一階OTA濾波電路之建構方塊與其轉移函數 38
圖3-15 一階電壓式OTA濾波電路之建構方塊 38
圖3-16結構Ⅰ：一階電壓式OTA-C建構方塊 39
圖3-17結構Ⅱ：一階電壓式OTA-C萬用濾波器 44
圖3-18結構Ⅱ：二階OTA-C萬用濾波器 48
圖3-19結構Ⅱ：三階OTA-C萬用濾波器 52
圖3-20 N階OTA-C萬用濾波器 57
圖3-21 N階CCCⅡ-C 萬用濾波器 57
圖3-22 包含雜訊源之完整二極體小信號等效電路 63
圖3-23 包含雜訊源之完整電晶體小信號等效電路 63
圖3-24 包含雜訊源之完整場效電晶體小信號等效電路 63
圖3-25 電壓式OTA-C二階萬用濾波電路 65
圖3-26 電壓式CCCⅡ-C二階萬用濾波電路 67
圖4-1 三階CCCⅡ-C萬用濾波電路圖 70
圖4-2 三階OTA-C萬用濾波器 76
圖4-3 OTA非理想模型 82
圖4-4 CCⅡ非理想模型 83
圖4-5 (A)三階高通OTA-C與CCCⅡ-C濾波器大小響應圖 87
圖4-5 (B) 三階高通OTA-C與CCCⅡ-C濾波器相角響應圖 87
圖4-6 (A) 三階低通OTA-C與CCCⅡ-C濾波器大小響應圖 88
圖4-6 (B) 三階低通OTA-C與CCCⅡ-C濾波器相角響應圖 88
圖4-7 (A) 三階帶通OTA-C與CCCⅡ-C濾波器大小響應圖(分子為S2項) 89
圖4-7 (B) 三階帶通OTA-C與CCCⅡ-C濾波器相角響應圖(分子為S2項) 89
圖4-8 (A) 三階帶通OTA-C與CCCⅡ-C濾波器大小響應圖(分子為S項) 90
圖4-8 (B) 三階帶通OTA-C與CCCⅡ-C濾波器相角響應圖(分子為S項) 90
圖4-9二階高通CCCⅡ-C與OTA-C濾波電路雜訊分析圖 93
圖4-10二階低通CCCⅡ-C與OTA-C濾波電路雜訊分析圖 94
圖4-11 二階帶通CCCⅡ-C與OTA-C濾波電路雜訊分析圖 95
圖4-12 (A) 二階高通OTA-C濾波器NOMINAL、C1+5%、C1-5%靈敏度響應圖 98
圖4-12 (B) 二階高通OTA-C濾波器NOMINAL、C2+5%、C2-5%靈敏度響應圖 98
圖4-12 (C) 二階高通OTA-C濾波器NOMINAL及C1±5%;C2±5%靈敏度響應圖 98
圖4-12 (D) 二階高通CCCⅡ-C濾波器NOMINAL、C1+5%、C1-5%靈敏度響應圖 99
圖4-12 (E) 二階高通CCCⅡ-C濾波器NOMINAL、C2+5%、C2-5%靈敏度響應圖 99
圖4-12 (F) 二階高通CCCⅡ-C濾波器NOMINAL及C1±5%;C2±5%靈敏度響應圖 99
圖4-13 (A) 二階低通OTA-C濾波器NOMINAL、C1+5%、C1-5%靈敏度響應圖 101
圖4-13 (B) 二階低通OTA-C濾波器NOMINAL、C2+5%、C2-5%靈敏度響應圖 101
圖4-13 (C) 二階低通OTA-C濾波器NOMINAL及C1±5%;C2±5%靈敏度響應圖 101
圖4-13 (D) 二階低通CCCⅡ-C濾波器NOMINAL、C1+5%、C1-5%靈敏度響應圖 102
圖4-13 (E) 二階低通CCCⅡ-C濾波器NOMINAL、C2+5%、C2-5%靈敏度響應圖 102
圖4-13 (F)二階低通CCCⅡ-C濾波器NOMINAL及C1±5%;C2±5%靈敏度響應圖 102

表目錄

表2-1 CCII之工作電壓及電流的範圍 …………………………………13
表2-2 CCII其MOS電晶體之長寬比值 ………………………………13
表3-1 近年來發表的高階OTA-C濾波器之比較 ……………………………61
表4-1 Butterworth 多項式 次方之係數； ……………………76
表4-2 三階CCCII-C與 OTA-C濾波器之參數設定 …………………………89
表4-3 三階OTA-C與CCCⅡ-C轉移函數濾波電路模擬與理論差異表………94
表4-4 二階電壓式OTA-C與CCCⅡ-C高通濾波電路靈敏度比較………100
表4-5 二階電壓式OTA-C與CCCⅡ-C低通濾波電路靈敏度比較………...103
表5-1 本論文所提出濾波電路之優點與特色………………………………111

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