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研究生： 林永福
Lin, Yung-Fu
論文名稱： 多階雜訊塑形之三角積分調變器之設計
Design of Multi-Stage Noise Shaping Sigma-Delta Modulator
指導教授： 劉濱達
Liu, Bin-Da
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年： 2005
畢業學年度： 93
語文別： 英文
論文頁數： 76
中文關鍵詞： 雜訊塑形 、三角積分調變器
外文關鍵詞： noise shaping, sigma-delta modulator
相關次數： 點閱：113  下載：7 
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    • 　　在本論文中，我們提出一個以新型雜訊塑形函數為基礎的三角積分調變器。此函數最大的特點在於以一非整數階的雜訊塑型函數來取代一般常用的整數階函數。由數學分析以及模擬結果可以證明，在取樣比率適中的情況下，此非整數階雜訊塑形函數相對於一般的多階雜訊塑形函數，具有更高的雜訊抑制能力。考量實際應用所需，我們亦提出兩種整數型近似方法來逼近所提出的非整數型雜訊塑形函數︰Padé近似法以及三角近似法。其中三角近似法的逼近率可以達到近乎百分之百。
    　　為了驗證提出的新型雜訊塑形函數，我們設計一個二階對二階的多級雜訊塑形三角積分調變器。根據MATLAB軟體的模擬結果顯示，在超取樣比率為40的情況下，採用9.6 MHz的取樣頻率及120 KHz的輸入頻寬，此三角積分調變器的訊號對雜訊及諧波失真比可達到95dB。

    　In this thesis, the design methodology of sigma-delta modulator with a novel noise shaping technique is proposed. A fractional-order noise shaping function instead of the commonly used integer-order noise shaping is presented and analyzed. The proposed fractional function is proven to acquire a more efficient noise shaping ability than its integer counterpart. For practical implementation consideration, the order of the noise-shaping function still has to be converted from fractional number to integer. Therefore two numerical approximation functions, Padé approximation and trigonometric approximation, are adopted and proposed respectively.
    　In order to verify the proposed noise-shaping algorithm, a sigma-delta modulator with 2-to-2 MASH architecture is constructed and verified with MATLAB simulation tool. At an oversampling ratio of 40, simulation results reveal that a peak SNDR of 95 dB can be achieved with a signal bandwidth of 120 kHz for the sampling frequency of 9.6 MHz.

    Table of Contents i Acknowledgement iii Abstract iv List of Figures vi List of Tables ix Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Thesis Organization 3 Chapter 2 Fundamentals of Sigma-Delta Converter 4 2.1 Introduction 4 2.1.1 Nyquist-Rate Converters 5 2.1.2 Oversampling Converters 6 2.2 Sigma-Delta Modulator 10 2.2.1 Noise-Shaping 12 2.3 Sigma-Delta Modulator Structures 17 2.3.1 Single-Stage Structure 17 2.3.2 Multi-Stage Structure 18 2.3.3 Multi-Bit Quantization Structure 21 2.4 Summary 22 Chapter 3 Analysis of the Proposed Noise Shaping Algorithm 23 3.1 Effective Noise Shaping 24 3.1.1 Numerical Analysis of Proposed Noise Shaping 26 3.2 Rational Function Approximation 29 3.2.1 Proposed Trigonometric Approximation Function 33 3.3 Summary 36 Chapter 4 Realization of the 2-to-2 MASH Sigma-Delta Modulator 37 4.1 Proposed First-Qrder Modulator 37 4.1.1 Multi-Stage Noise Shaping (MASH) Architecture 39 4.1.2 Stability 45 4.2 Behavior of the Proposed SDM 47 4.3 Circuit of the Proposed SDM 54 4.3.1 Model of Integrator 54 4.3.2 Non-Ideal Issues 56 4.3.3 Parasitic Capacitors 57 4.3.4 Settling Time 57 4.3.5 Finite Opamp Gain 58 4.4 Circuit Simulation 60 4.4.1 Design of Opamp 61 4.4.2 Design of Quantizer 64 4.4.3 Design of Sigma-Delta Modulator 66 4.5 Summary 69 Chapter 5 Conclusions and Future Works 71 5.1 Conclusions 71 5.2 Future Works 72 References 73

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