對於積分三角類比數位轉換器的穩定性研究

Abstract

由於更好的雜訊平移效果,使用高階積分三角轉換器能達到更好的信號解析度。但是對於純微分器形式雜訊轉移函數的高階積分三角轉換器而言,假如我們不使用多位元的量化器，則此積分三角轉換器容易傾向不穩定。因此,為何高階的積分三角轉換器容易導致系統的不穩定變成了一個值得有趣且值得探討的問題。在這篇論文中,我們推導出一個量化器輸入的雜訊能量模型去解釋高階積分三角轉換器的不穩定性,然後利用MATLAB/SIMULINK的模擬環境,我們也探討了一些二階到四階積分三角轉換器的穩定性結果。最後我們介紹了一些已發表研究有關於分析穩定度的方法以及單位元或多位元積分三角轉換器的穩定準則。

Higher-order sigma-delta modulators can achieve higher resolution by pushing more quantization noise outside the band of interest (better noise shaping effect). But higher-order modulators with pure differentiation noise transfer function are prone to be unstable unless we utilize the multi-bit quantizer. Therefore, one of an interesting problem is that why the higher-order modulator’s order drive the system to be unstable. In this thesis, we derivate a noise power of the quantizer input to illustrate the instability proneness for higher-order modulators, and the stability results for second to fourth-order modulators with single and multi-bit quantizer are investigated by MATLAB/SIMULINK simulations. Finally, we introduce the stability analytic way and several stability criteria of the single-bit and multi-bit sigma-delta modulators, which have been proposed from published researches.