臺灣博碩士論文加值系統

以運算轉導放大器(OTA)及電容器有系統的實現N階萬用濾波電路，一直是眾多學者研究的課題之一。線性組合法與信號加權法為實現N階萬用濾波電路提供了兩個有系統且規律的方法。以線性組合觀念設計OTA-C電壓式N階萬用濾波電路之架構需要2n+4個單端輸入OTA及n個接地電容器；以信號加權觀念設計OTA-C電壓式N階萬用濾波電路需要2n+2個單端輸入OTA及n個接地電容器。本論文的研究主要是比較線性組合法與信號加權法設計之OTA-C電壓式N階萬用濾波電路在濾波性能（Filtering performance）、雜訊（Noise）、靈敏度（Sensitivity）、元件分佈（Component spread）及串接能力（cascadability）之差異。
本論文的第二章分別介紹Nullor模型(Nullor model)、電流式主動元件、運算轉導放大器（OTA）及其內部電路實現之方法。第三章利用建構方塊法說明線性組合法與信號加權法實現N階萬用濾波電路之觀念。第四章為針對線性組合法與信號加權法所設計OTA-C電壓式高階萬用濾波電路進行特性之比較。分別實現三階之高通、低通及帶通濾波器以驗證線性組合法與信號加權法之可行性，再比較兩種設計法實現之二階全通濾波器在濾波性能、雜訊、靈敏度、元件分佈及串接能力分析比較。
由於線性組合法實現電壓式N階萬用濾波電路之架構較以信號加權法設計多了兩個主動元件，雜訊源較多，所以理論上信號加權法的特性會較佳，經過模擬驗證與理論分析比較之後，信號加權法在濾波性能、雜訊及靈敏度方面，表現確實較線性組合法佳。信號加權法因其輸入端路徑較線性組合法多，造成其輸入阻抗降低，使得其串接能力表現較線性組合法差。線性組合法在其電壓轉移函數之分子部分較信號加權法簡潔，因此線性組合法元件分佈較小。
論文中的電路均以HSPICE做為驗證的模擬工具，使用UMC05 LEVEL49 的製程參數，經過HSPICE與MATLAB的驗證後，兩種設計方法所實現之高通、低通及帶通濾波部分，其實驗值與理論值十分吻合；另外比較兩種設計法在濾波性能、雜訊、靈敏度、元件分佈及串接能力方面，可以提供設計濾波電路者進一步之參考，期能在未來設計出高濾波性能、低雜訊、低靈敏度、較小的元件分佈及高串接能力之濾波電路。

Many Operational Transconductance Amplifier (OTA)-based nth-order voltage-mode universal filter structures were proposed. Very recently, both linear combination and singnal weighting approaches archieve two new nth-order voltage-mode universal filter structures. The former employs 2n+4 single-input OTAs and n grounded capacitors. The latter employs 2n+2 single-input OTAs and n grounded capacitors. In this study, we have done the comparison between linear combination and weighting signal approaches in terms of filtering performance, noise, sensitivity, component spread and cascadability.

H-spice simulations with UMC05 Level 49 parameters are used to do the comparison. When non-ideal active devices are considered, differences in frequency responses of the linear combination and weighting signal approaches will be observed. Clearly these differences can be attributed to non-ideal active devices. In the research of OTA-C filters, weighting signal approach is better than linear combination method in terms of filtering performance, noise and sensitivity because the signal weighting method uses two fewer single-ended-input OTAs than the linear combination approach. As we know, for the universal nth-order, the number of capacitors needed should be at least n and to achieve the independent tunability of each coefficient at least 2n+2 OTAs are required. In this sense our technique needs the fewest element, which should be very important for integration. In terms of component spread and cascadability, linear combination method is better than weighting signal approach. This is because the signal weighting method have more input path than linear combination approach.
This paper offers the signal weighting and linear combination approaches differences in terms of filtering performance, noise, sensitivity, component spread and cascadability. We have to make the most of this comparsion’s conclusions, which should be very useful for filters implemented using linear combination and singnal weighting approaches archieve nth-order voltage-mode universal filter structures.

第一章 緒論……………………………………………………………1
第二章 電流式主動元件介紹…………………………………………6
2-1 Nullor模型 …………………………………………………6
2-2 電流傳輸器(CC)的特性 ……………………………………8
2-2.1 第一代電流傳輸器(CCI) ……………………………9
2-2.2 第二代電流傳輸器(CCII)……………………………10
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)……………………………16
2-4 運算轉導放大器(OTA) ……………………………………20
2-5 多輸出端電流式主動元件架構 ……………………………24
第三章 線性組合法與信號加權法設計通用N階濾波器 ……………27
3-1 CCCⅡ-C與OTA-C轉換規則 …………………………………27
3-2 建構方塊 ……………………………………………………33
3-3 線性組合法N階通用濾波器(OTA-C)電路架構 ……………39
3-4 信號加權法N階通用濾波器(OTA-C)電路架構 ……………41
3-5 靈敏度分析 …………………………………………………43
3-6 雜訊分析 ……………………………………………………44
3-6.1 射雜訊（Shot Noise）………………………………44
3-6.2 熱雜訊（Thermal Noise） …………………………45
3-6.3 閃爍雜訊（Flicker Noise） ………………………45
3-6.4 爆裂雜訊（Burst Noise） …………………………46
3-6.5 累增雜訊（Avalanche Noise） ……………………46
3-6.6 積體電路元件之雜訊模型（Noise Models）………46
第四章 線性組合法與信號加權法設計N階通用濾波器(OTA-C)
的比較…………………………………………………………48
4-1 線性組合法設計三階通用濾波器(OTA-C)電路之驗證……48
4-2 信號加權法設計三階通用濾波器(OTA-C)電路之驗證……54
4-3 線性組合法與信號加權法設計二階通用濾波器(OTA-C)
電路之比較 …………………………………………………60
4-3.1 Filtering performance …………………………59
4-3.2 Noise ………………………………………………67
4-3.3 Sensitivity ………………………………………69
4-3.4 Component spread …………………………………75
4-3.5 Cascadability ……………………………………78
4-4 比較結果與電路的優點 ……………………………………83
第五章 結論及未來研究方向…………………………………………85
參考文獻 …………………………………………………………………87
附錄 ………………………………………………………………………91
作者簡歷 …………………………………………………………………103

圖2-1 Nullor模型 6
圖2-2 Nullator與Norator模型 7
圖2-3(a) 正型Norator模型 8
圖2-3(b) 負型Norator模型 8
圖2-4 CCI之元件符號 9
圖2-5 CCI之Nullor等效模型 9
圖2-6 CCII之元件符號 10
圖2-7(a) CCII之Nullor模型 10
圖2-7(b) CCII之簡化Nullor模型 11
圖2-8(a) CCII+內部電路結構 11
圖2-8(b) CCII-內部電路結構 12
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 電流加法器 14
圖2-13 加權電流加法器 15
圖2-14 CCIII應用於放大器之設計 15
圖2-15 CCIII之CMOS內部電路 16
圖2-16 CCCII之元件符號及Nullor模型 17
圖2-17(a) CCCII+之內部電路結構 18
圖2-17(b) CCCII-之內部電路結構 18
圖2-18 CCCII之基本應用電路 19
圖2-19 新的CCCII內部電路 20
圖2-20 OTA之元件符號 21
圖2-21 OTA之Nullor等效模型 21
圖2-22 OTA元件符號及Nullator-Norator等效模型 22
圖2-23 OTA之內部電路 23
圖2-24 OTA的應用電路 24
圖2-25 複製正向電流源及反向電流源 25
圖2-26 疊接電路複製正向電流源及反向電流源 26
圖3-1 CCCII+之元件符號 27
圖3-2 OTA+之元件符號 27
圖3-3 正型OTA之Nullor等效電路圖 29
圖3-4 正型OTA負輸入端接地Nullor等效電路 29
圖3-5 正型OTA負輸入端接地Nullor等效電路 30
圖3-6 CCCII之元件符號及Nullor模型 30
圖3-7 CCCII + X端接地之Nullor模型 30
圖3-8 負型OTA之Nullor等效電路 31
圖3-9 負型OTA正輸入端接地Nullor等效電路 31
圖3-10 負型OTA正輸入端接地Nullor等效電路 31
圖3-11 CCCII - X端接地之Nullor模型 31
圖3-12 CCCII與OTA應用電路間轉換 32
圖3-13 線性組合法一階建構方塊的型式 34
圖3-14 線性組合法二階濾波電路方塊的型式 36
圖3-15 信號加權法一階建構方塊的型式 37
圖3-16 信號加權法二階濾波電路方塊的型式 38
圖3-17 線性組合觀念設計OTA-C電壓式N階萬用濾波電路 39
圖3-18 信號加權觀念設計OTA-C電壓式N階萬用濾波電路 42
圖3-19 包含雜訊源之完整二極體小信號等效電路 46
圖3-20 包含雜訊源之完整電晶體小信號等效電路 47
圖3-21 包含雜訊源之完整場效電晶體小訊號等效電路 47
圖4-1 線性組合法設計三階通用濾波器(OTA-C)電路結構 49
圖4-2(a) 高通濾波器之頻率響應 53
圖4-2(b) 低通濾波電路之頻率響應 53
圖4-2(c) 帶通濾波電路之頻率響應 53
圖4-3 信號加權法設計三階通用濾波器(OTA-C)電路結構 54
圖4-4(a) 高通濾波之頻率響應 58
圖4-4(b) 低通濾波之頻率響應 58
圖4-4(c) 帶通濾波之頻率響應 58
圖4-5 運算轉導放大器（OTA）轉導值與偏壓電流值 59
圖4-6 運算轉導放大器（OTA）非理想模型 61
圖4-7 線性組合觀念設計OTA-C電壓式二階萬用濾波電路 62
圖4-8 信號加權觀念設計OTA-C電壓式二階萬用濾波電路 63
圖4-9 二階線性組合法與信號加權法全通濾波之頻率響應（增益） 65
圖4-10 二階線性組合法與信號加權法全通濾波之頻率響應（相位） 66
圖4-11 線性組合法全通雜訊分析 68
圖4-12 信號加權法全通雜訊分析 68
圖4-13 線性組合法全通濾波頻率漂移 72
圖4-14 線性組合法全通濾波頻率漂移 72
圖4-15 信號加權法全通濾波頻率漂移 73
圖4-16 信號加權法全通濾波頻率漂移 73
圖4-17（a）信號加權法低通濾波器C=5pf 77
圖4-17（b）信號加權法低通濾波器C=20pf 77
圖4-18 電壓放大器等效電路 78
圖4-19 單一顆OTA輸出、入阻抗 79
圖4-20 單一顆OTA輸入導納圖 79
圖4-21單一顆OTA輸出導納圖 80
圖4-22 線性組合法輸入導納圖 80
圖4-23 信號加權法輸入導納圖 81
圖4-24 線性組合法輸出導納圖 81
圖4-25 信號加權法輸出導納圖 82

表4-1 Butterworth 多項式n=1~7次方之係數 52
表4-2 信號加權法之濾波信號實現方法 55
表4-3 信號加權法之轉導值與偏壓電流值 57
表4-4 信號加權法之轉導值與偏壓電流值 65
表4-5 線性組合與信號加權法之元件個數 67
表4-6 線性組合法與信號加權法頻率漂移 74
表4-7 線性組合法與信號加權法實現二階全通參數值 75
表4-8 線性組合法與信號加權法特性比較表 83
表4-9 近年來發表的OTA-C 電壓式N階濾波電路之比較 84

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