曹恆偉臺灣大學：電信工程學研究所王勝賢Wang, Sheng-XianSheng-XianWang2007-11-272018-07-052007-11-272018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/58630CD 音樂為高音質音樂的標準之一，其取樣頻率為44.1 kHz且解析度有16位元。由於近年來對高音質音樂需求增加，所以應用於音頻之數位/類比轉換器所扮演的角色也就越來越重要。如何同時達到消費性電子產品的低成本需求、專業錄音用途所引頸期盼的廣域動態範圍和高線性度、以及可攜式產品要求的低功率消耗，這將是極富挑戰的研究課題。 傳統應用於音頻之數位/類比轉換器是採用多位元的R-2R 梯形電阻架構。其操作原理是利用賦有加權二進位電流源來達成訊號格式轉換的目的。然而，梯形電阻架構容易受到製成變異而導致電阻值（或者是電流源）不匹配；此外，切換器轉換過程所產生的短時脈衝波也會對音樂訊號造成干擾，上述之變異及干擾都會造成聽覺上的不適。雖然該架構經過適當地校正之後，效能上會有所提昇，但校正時所耗費的成本卻是相當昂貴。 1位元超取樣三角積分數位/類比轉換器的問世，克服R-2R 電阻架構數位/類比轉換器的問題。由於數位電路對製成變異的容忍度較類比電路佳，以及近年來CMOS製成進步，晶片密度變大且成本降低，因此1位元超取樣三角積分數位/類比轉換器利用複雜的數位電路取代原本較敏感的類比電路。然而，為了達到CD 音樂的高音質要求，1位元三角積分調變器若非使用高階調變器即是增加超取樣頻率。1位元高階三角積分調變器會遭遇穩定度的問題；太大的超取樣頻率則會增加類比重建濾波器的設計困難度。為了克服應用於CD音頻之1位元超取樣三角積分數位/類比轉換器所面臨的困難，採用多位元的三角積分調變器是必然的趨勢。 本篇論文設計與實現應用於CD音樂之數位/類比轉換器之多位元超取樣三角積分調變系統，並且呈現出最佳化數位三角積分調變系統的演算法，最後使用FPGA驗證此演算法所設計之硬體。此調變系統由三個主要電路組成。首先是負責升頻的數位內插式濾波器；再者為使用多位元三階架構的數位三角積分調變器；最後則是Data-Weighted Averaging的電路，其目的是為了減緩類比元件不匹配所產生的干擾效應。CD-AUDIO is a high-quality audio standard that supports 16-bit linear pulse-code modulation (PCM) with sampling rate 44.1 kHz. The growth of CD-AUDIO has increased the demands of audio digital-to-analog converters (DAC) that meet the low-cost needs of consumer applications, achieves the wide dynamic range and high linearity required for the professional studio and also low power demand for portable products. Conventional multi-bit audio DAC’s use an R-2R resistor ladder to obtain a binary weighted range of current source equal to the number of bits to be converted. While properly adjusted, the DAC’s using the R-2R resistor ladder can function well but are extremely dependent on the tolerances of resistor networks and on matched and glitch-free electronic switches. Hence, the conventional DAC’s are typically rather expensive products. The use of 1-bit Delta-Sigma (∆-Σ) modulator with the oversampling technique eliminates the resistor matching problem by trading digital complexity for desired insensitivity to analog non-idealities. However, in order to achieve the requirement of high resolution, the high order or high oversampling ratio 1-bit modulator will be needed. Although the achievable resolution does improve in ∆-Σ modulators employing a 1- bit quantizer, these improvements diminish rapidly due to the in-stability of high order modulator. In addition, because of the substantial out-of-band quantization noise power in delta-sigma modulators, the design of analog output filters for oversampled DACs can be quite difficult. One solution to the above problems is to use a multi-bit quantizer in the ∆-Σ modulators. In this thesis, we have simulated and implemented a complete third-order multibit ∆-Σ modulation system for CD-AUDIO digital-to-analog converter. It consists of a 64X digital interpolation filter to bring the input sample rate up to the modulator rate, a multibit ∆-Σ modulator to reduce the word length by trading off the out-of-band noise, and dynamic element matching to dynamically swap the unit-element with mismatch problem caused by process variance.Acknowledgements……………………………………………………I Abstracts……………………………………………………………III Table of Contents...………………………………………………V List of Figures……………………………………………………IX List of Tables……………………………………………………XIII CHAPTER 1 Introduction………………………………………P1 1.1 Motivation………………………………………………………1 1.2 Organization in the thesis…………………………………2 CHAPTER 2 Fundamentals of Δ-Σ Modulators………………P3 2.1 Introduction……………………………………………………3 2.2 Quantization and Quantization Error…………………….4 2.2.1 Performance Metrics……………………………………….7 2.2.1.1 Signal-to-Noise ratio (SNR)………………………….7 2.2.1.2 Signal-to-noise plus Distortion Ratio (SNDR)…..8 2.2.1.3 Dynamic range (DR)…………………………….….…..9 2.2.1.4 Effective Number of Bit’s (ENOB’s)..….….….10 2.2.2 Single-bit Quantization………………………………..10 2.2.3 Multi-bit Quantization………………………………….11 2.3 Oversampling Technique…………………………………….12 2.4 Sigma-Delta (Δ-Σ) Modulators…………………………….16 2.4.1 First-Order Noise-Shaping……………………………..18 2.4.2 Second-Order Noise-Shaping…………………………...21 2.4.3 High-Order Noise-Shaping…………………….….…...23 2.4.3.1 Single-loop topology………………………….….….24 2.4.3.2 Cascaded topology………………………...….….….30 CHAPTER 3 The Mismatch and Stability of Multibit Δ-ΣModulators…………………………........................P33 3.1 Introduction………………………………………………...33 3.2 The Mismatch of Multibit Δ-Σ Modulators …………...34 3.3 The Approaches for improved Linearity……………....36 3.3.1 Dynamic Element matching………………………….……36 3.3.1.1 Dynamic Element Randomization………………………38 3.3.1.2 Dynamic Element Rotation…………………………….40 3.3.1.3 Individual Level Averaging………………………….41 3.3.1.4 Data-Weighted Averaging…………………………....42 3.3.1.5 Vector-Based Mismatch shaping……………………..44 3.3.1.6 Element selection using tree structure………….44 3.4 The Stability of Delta-Sigma modulator……………….45 CHAPTER 4 The Design Strategy of Multibit Δ-ΣModulation System…………………….….............................P49 4.1 Introduction………………………………………………….50 4.2 The Synthesis of NTF……………………………………...50 4.2.1 NTF Zero Optimization…………………………………..51 4.2.2 NTF Pole Optimization…………………………………..52 4.3 The Architecture of the Δ - Σ Modulator…………….54 4.4 Design of Digital Interpolation Filter……………….57 4.4.1 Interpolation by L……………………………………...57 4.4.2 Filter Specification…………………………………...59 4.4.3 Multistage Filter Topology…………………………….60 4.4.4 Filter Design Considerations………………………….64 4.4.4.1 Half-band Filter……………………………………...65 4.4.4.2 Cascade Integrator Comb (CIC) Filters……………67 4.4.4.3 Poly-phase Filter……………………………………..69 4.5 Hardware Design Technique………………………………..71 CHAPTER 5 The Simulation and Implementation of Multibit Δ-Σ Modulation System………………………………………….P75 5.1 Introduction………………………………………………….75 5.2 The Realization of Δ - Σ Modulator…………………...75 5.3 The Implementation of Data Weighted Averaging……..83 5.4 The Realization of Interpolation Filters…………….92 CHAPTER 6 Conclusions……………………………………..P97 APPENDIX ……………………………………………………….P99 Bibliography…………………………………………………..P1034144274 bytesapplication/pdfen-US數位內插式濾波器三角積分調變器數位/類比轉換器超取樣線性度動態範圍製成變異Audio DACDelta-Sigma ModulatorOversampling Technique1-bit QuantizerMulti-bit quantizerdigital interpolation filterdata-weighted averaging(DWA)Noise-ShapingHalf-band filterCIC filterthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/58630/1/ntu-95-R92942111-1.pdf