臺灣博碩士論文加值系統

高階濾波電路的合成方法，在主動濾波器設計的領域裡，一直是相當重要的主題。 在過去所發表的文獻中，對於電路的性能與結構上的簡化，仍然有諸多的限制。本論文提出一種新的電路合成法，利用信號加權的觀念，使用最少的主動、被動元件，可實現高階萬用濾波電路的電壓轉移函數。
信號加權合成法的電路架構是以輸入電壓信號加權轉為電流信號，注入一個基礎多功濾波電路而成。此基礎多功濾波電路可在不同的主動元件的輸出節點，產生高通、帶通、與低通等不同的濾波信號。這個以信號加權合成的濾波電路，經由主動元件內阻或轉導的調整，於同一個輸出端，實現高通、低通、帶通、帶拒及全通等五種濾波功能。 n 階電壓式萬用濾波電路僅需使用2n+2個單端輸入的主動元件(註：第二代電流控制傳輸器(Second generation Current Controlled Conveyor ， CCCⅡ) 或 運算轉導放大器(Operational Transconductance Amplifier ， OTA))，及 n 個接地電容器所組成。由於 OTA 的轉導及 CCCⅡ 之 X 端內阻均可由偏壓電流調整，電路設計時毋需再使用電阻器，大大簡化了電路結構。
利用Nullator-and-Norator的等效轉換，以 CCCⅡ設計的濾波電路可轉換為以 OTA 設計的濾波電路。因此本論文亦針對兩種主動元件所建構的萬用濾波電路分別在頻率響應、電路靈敏度及輸出雜訊的特性方面，進行理論值與 H-Spice 模擬值之分析比較。結果驗證了以 OTA 為主動元件的濾波電路具有較佳的特性，其模擬結果與理論推導結果吻合。

The voltage-mode high-order universal filter structure using weighting signal approach has been studied in this thesis. A fundamental high-order multi-function (low-pass, band-pass, and high-pass) filter structure is realized first. Different order output signals can be obtained from different nodes in the fundamental filter structure. Add the weighting of the voltage input signal (i.e., a transformed current signal) to each node in the fundamental structure and then the proposed voltage-mode high-order universal filter structure is obtained, which employs 2n+2 single-input active element and n grounded capacitors.
The second-generation current controlled conveyors (CCCIIs) with electronically adjustable inner resistance are used in the design. Using Nullator-and-Norator equivalent transformation, the CCCII-based filter structure can be transformed into the Operational Transconductance Amplifiers-based filter structure. Note that the transconductance g of an OTA is also tunable by the bias current.
H-Spice simulations are used for carrying out the comparison between CCCII-based and OTA-based filter structures in terms of filtering performance, noise, and sensitivity analysis. Simulation results validate the theory predictions.

目 錄

第一章 緒 論 9
第二章 電流式主動元件簡介 13
2-1 Nullor Model等效模型 13
2-2 電流傳輸器(Current Conveyer )的特性 16
2-2.1 第一代電流傳輸器(CCⅠ) 16
2-2.2 第二代電流傳輸器(CCⅡ) 17
2-2.3 第三代電流傳輸器(CCⅢ) 22
2-3 第二代電流控制電流傳輸器(CCCⅡ) 27
2-4 運算轉導放大器(OTA) 30
第三章 信號加權觀念設計電壓式CCCⅡ-C與OTA-C高階萬用濾波電路 35
3-1 理想CCCⅡ與OTA元件的等效轉換 35
3-2 多功能濾波電路之合成 40
3-2.1 二階電壓式CCCⅡ-C/OTA-C多功能濾波電路 43
3-2.2 三階電壓式CCCⅡ-C/OTA-C多功能濾波電路 45
3-2.3 N階電壓式CCCⅡ-C/OTA-C多功能濾波電路 47
3-3 以信號加權觀念設計萬用濾波電路 50
3-3.1 二階電壓式CCCⅡ-C/OTA-C萬用濾波器電路 51
3-3.2 三階電壓式CCCⅡ-C/OTA-C萬用濾波器電路 53
3-3.3 N階電壓式CCCⅡ-C/OTA-C萬用濾波電路 58
3-4靈敏度（Sensitivity）特性 62
3-4.1 二階電壓式CCCⅡ-C萬用濾波電路靈敏度分析 63
3-4.2 二階電壓式OTA-C萬用濾波電路靈敏度分析 64
3-5 雜訊(Noise)特性 66
3-5.1 射雜訊（Shot Noise） 66
3-5.2 熱雜訊（Thermal Noise） 67
3-5.3 閃爍雜訊（Flicker Noise） 68
3-5.4 爆裂雜訊（Burst Noise） 68
3-5.5 累增雜訊（Avalanche Noise） 69
3-5.6 積體電路元件之雜訊模型（Noise Models） 69
第四章 電壓式CCCⅡ-C與OTA-C高階萬用濾波電路之比較 71
4-1 CCCⅡ 與 OTA 非理想特性之比較 72
4-2 濾波特性(Filtering Performance)之比較 77
4-3 雜訊特性(Noise Performance)之比較 92
4-4 靈敏度特性(Sensitivity Performance)之比較 97
4-4.1 固定C2值，C1增加5% 97
4-4.2 固定C1值，C2增加5% 100
4-4.3 C1、C2同時增加5% 103
第五章 結論及未來研究方向 106
參 考 文 獻 109
附錄 113
作 者 簡 歷 116

圖 目 錄
圖2-1.1 Nullator模型 13
圖2-1.2 正型之Norator 圖2-1.3 負型之Norator 14
圖2-1.4 Nullator 與 Norator 模型 15
圖2-4 CCI之元件符號 17
圖2-5 CCI之Nullor等效模型 17
圖2-6 CCII之元件符號 18
圖2-7(a) CCII之Nullor模型 18
圖2-7(b) CCII之簡化Nullor模型 18
圖2-8(a) CCII+之內部電路結構 20
圖2-8(b) CCII-之內部電路結構 20
圖2-9 CCII之簡單應用 22
圖2-10 CCIII之元件符號 23
圖2-11 以雙輸出之CCII實現CCIII 23
圖2-12(a)電流加法器 23
圖2-12(b)加權電流加法器 24
圖2-13(a)電流放大器 24
圖2-13(b)電壓放大器 24
圖2-13(c) 傳輸阻抗放大器 25
圖2-13(d) 傳輸導納放大器 25
.圖2-14 CCIII之CMOS內部電路 26
圖2-15 CCCII之元件符號及Nullor模型 27
圖2-16(a) CCCII+之內部電路 28
圖2-16(b) CCCII-之內部電路 28
圖2-17 CCCII之基本應用電路 29
圖2-17 OTA元件符號及Nullator-Norator等效模型 30
圖2-18 OTA之內部電路 31
圖2-18複製正向電流源及反向電流源 33
圖2-19疊接電路複製正向電流源及反向電流源 33
圖2-20 CCCII(+/-)之內部電路圖 34
圖2-21 DO-CCCII之Nullor模型 34
圖 3-1.1 CCCⅡ 接腳圖 圖 3-1.2 OTA 接腳圖 36
圖3-1.3 正型OTA之Nullor等效電路 37
圖3-1.4 正型OTA負輸入端接地Nullor等效電路 37
圖3-1.5 正型OTA負輸入端接地Nullor等效電路 37
圖3-1.6 CCCII之元件符號及Nullor模型 37
圖3-1.7 CCCII + X端接地之Nullor模型 37
圖3-1.8 負型OTA之Nullor等效電路 38
圖3-1.9 負型OTA正輸入端接地Nullor等效電路 38
圖3-1.10 負型OTA正輸入端接地Nullor等效電路 38
圖3-1.11 CCCII X端接地之Nullor等效模型 38
圖3-1.12 CCCII與OTA應用電路間轉換 39
圖3-2.1 學者提出之電流式一階濾波電路之建構方塊與其轉移函數 41
圖3-2.2 差動輸入電壓式一階濾波電路之建構方塊 41
圖3-2.3 單端輸入一階電壓式多功能濾波電路之建構方塊 43
圖3-2.4單端輸入二階電壓式多功能濾波電路之建構方塊 44
圖3-2.5單端輸入三階電壓式多功能濾波電路 45
圖3-2.6 RC正規化網路 圖3-2.7 正規化之增益響應(f) 47
圖 3-2.8 單端輸入N階電壓式多功能濾波電路 49
圖3-3.1 單端輸入輸出一階電壓式OTA-C萬用濾波電路之建構方塊 50
圖3-3.2 單端輸入輸出二階電壓式OTA-C萬用濾波電路之建構方塊 51
圖3-3.3 單端輸入三階電壓式OTA-C萬用濾波電路 53
圖3-3.4 單端輸入輸出N階電壓式OTA-C萬用濾波電路 58
圖3-3.5 單端輸入輸出N階電壓式CCCⅡ-C萬用濾波電路 61
圖3-4.2 電壓式CCCⅡ-C二階萬用濾波電路 63
圖3-4.1 電壓式OTA-C二階萬用濾波電路 64
圖3-5.1 包含雜訊源之完整二極體小信號等效電路 69
圖3-5.2 包含雜訊源之完整電晶體小信號等效電路 69
圖3-5.3 包含雜訊源之完整場效電晶體小信號等效電路 70
圖4-1.1 OTA的非理想等效模型 72
圖4-1.2 CCCⅡ的非理想等效模型 73
圖4-1.3 OTA在+/-2.5伏特偏壓的轉導值工作範圍 75
圖4-1.4 CCCⅡ在+/-2.5伏特偏壓的轉導值工作範圍 75
圖4-1.5 OTA在+/-2.5伏特偏壓的轉導值頻率響應曲線 76
圖4-1.6 CCCⅡ在+/-2.5伏特偏壓的轉導值頻率響應曲線 76
圖4-2.1 三階CCCⅡ-C萬用濾波電路 77
圖4-2.2 (a)三階高通OTA-C與CCCⅡ-C濾波器大小響應圖 87
圖4-2.2 (b) 三階高通OTA-C與CCCⅡ-C濾波器相角響應圖 87
圖4-2.3 (a) 三階低通OTA-C與CCCⅡ-C濾波器大小響應圖 88
圖4-2.3 (b) 三階低通OTA-C與CCCⅡ-C濾波器相角響應圖 88
圖4-2.4 (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4-2.4 (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4-2.5 (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4-2.5 (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4-8 (a) 三階高通OTA-C濾波電路雜訊分析圖 93
圖4-8 (b) 三階高通CCCⅡ-C濾波電路雜訊分析圖 93
圖4-9 (a) 三階低通OTA-C濾波電路雜訊分析圖 94
圖4-9 (b) 三階低通CCCⅡ-C濾波電路雜訊分析圖 94
圖4-9 (a) 三階帶通OTA-C濾波電路雜訊分析圖 95
圖4-9 (b) 三階帶通CCCⅡ-C濾波電路雜訊分析圖 95
圖4-9 (a) 三階帶通OTA-C濾波電路雜訊分析圖 96
圖4-9 (b) 三階帶通CCCⅡ-C濾波電路雜訊分析圖 96
圖4-8 (a) 二階高通OTA-C濾波器靈敏度響應圖 98
圖4-8 (b) 二階高通CCCⅡ-C濾波器靈敏度響應圖 98
圖4-8 (a) 二階低通OTA-C濾波器靈敏度響應圖 99
圖4-8 (b) 二階低通CCCⅡ-C濾波器靈敏度響應圖 99
圖4-8 (a) 二階高通OTA-C濾波器靈敏度響應圖 100
圖4-8 (b) 二階高通CCCⅡ-C濾波器靈敏度響應圖 101
圖4-8 (a) 二階低通OTA-C濾波器靈敏度響應圖 101
圖4-8 (b) 二階低通CCCⅡ-C濾波器靈敏度響應圖 102
圖4-8 (a) 二階高通OTA-C濾波器靈敏度響應圖 104
圖4-8 (b) 二階高通CCCⅡ-C濾波器靈敏度響應圖 104
圖4-8 (a) 二階低通OTA-C濾波器靈敏度響應圖 105
圖4-8 (b) 二階低通CCCⅡ-C濾波器靈敏度響應圖 105

表 目 錄
表 1-1 近年來發表的高階OTA-C濾波電路之特性比較 10
表2-1 CCII之工作電壓及電流的範圍 19
表2-2 CCII其MOS電晶體之長寬比值 19
表 3-3.1 單端輸入電壓式OTA-C二階萬用濾波電路之元件延展性 52
表 3-3.2(a) 單端輸入電壓式OTA-C三階萬用濾波電路之元件延展性 56
表 3-3.2(b) 單端輸入電壓式OTA-C三階萬用濾波電路之元件延展性 57
表 4-2.1(a) 單端輸入電壓式CCCⅡ-C三階萬用濾波電路之元件延展性 79
表 4-2.1(b) 單端輸入電壓式CCCⅡ-C三階萬用濾波電路之元件延展性 80
表4-2.2 三階CCCII-C濾波器之參數設定 85
表4-2.3 三階OTA-C濾波器之參數設定 86
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 91
表4-4.1 OTA-C及CCCⅡ-C C1+5%之靈敏度 97
表4-4.2 OTA-C及CCCⅡ-C C2+5% 之靈敏度 100
表4-4.3 OTA-C及CCCⅡ-C C1, C2 +5% 之靈敏度 103

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