Σ-Δ調變器技術具有雜訊塑型之特性，可將量化過程中產生的雜訊及諧波推往高頻帶，進而達到高解析度的類比數位轉換，因為如此，Σ-Δ調變器技術被廣泛的應用於許多領域。隨著Σ-Δ調變器的階數增加，雜訊塑型效果將越為顯著，其整體性能越佳，但遺憾的是，當Σ-Δ調變器的階數大於二階時，會引發穩定性的問題，導致穩定輸入範圍受到很大的限制；本論文針對此問題，提出一個新型適應性Σ-Δ調變器，透過適應性法則調整雜訊轉移函數的極點位置，使得雜訊轉移函數之頻帶外增益下降，達到增加穩定輸入範圍的目的，經由模擬及實作驗證，可以有效地大幅提升穩定輸入範圍。

Noise shaping is one of the distinguishing characteristics of the sigma-delta modulation technique that separates it from other types of pulse-width modulation schemes. In sigma-delta modulation, unwanted noise and harmonics caused by quantization are intentionally pushed toward the high-frequency band in order to achieve high resolution data conversion within the signal bandwidth. Due to its robust, high in-band linearity, the sigma-delta modulation technique finds numerous applications in industry. Generally speaking, as the order of a sigma-delta modulator increases, the modulator performance becomes better, which unfortunately comes along with a decrease in the modulator’s stable input range. This thesis presents a novel adaptive law which is capable of on-line tuning the loop filter of a sigma-delta modulator and reducing the out of band gain of the resulting noise transfer function when the modulator input is large, thereby widening the stable input range of the modulator without significant sacrifice of the performance. The simulation and experimental results prove the effectiveness of the proposed adaptive sigma-delta modulator.

第一章 序論 1
1-1 研究動機及目的 1
1-2 文獻回顧 2
1-3 論文組織 5
第二章 Σ-Δ調變器調變技術及原理簡介 7
2-1 Σ-Δ調變器之發展沿革 7
2-2 低階Σ-Δ調變器 9
2-2.1 一階Σ-Δ調變器 10
2-2.2 二階Σ-Δ調變器 17
2-3 高階Σ-Δ調變器 19
2-4 Σ-Δ調變器的穩定性分析 21
2-4.1 雜訊轉移函數之頻帶外增益 22
2-4.2 線性化根軌跡法 24
第三章 新型適應性Σ-Δ調變器 28
3-1 新型適應性Σ-Δ調變器架構介紹與分析 28
3-1.1 架構推導 28
3-1.2 調整係數選取 30
3-2 適應性法則 33
3-2.1 最陡下降法 34
3-2.2 評價函數(cost function)選取 37
第四章 模擬與電路實現驗證 44
4-1 新型適應性Σ-Δ調變器架構模擬 44
4-1.1 性能指標 44
4-1.2 新型適應性Σ-Δ調變器架構模擬結果 45
4-1.3 各種適應性Σ-Δ調變器性能比較 54
4-2 新型適應性Σ-Δ調變器架構電路實現 55
4-2.1 硬體電路簡介 55
4-2.2 實測結果 61
第五章 結論 68
參考文獻 70

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