Principles of Sigma Delta Conversion for Analog to Digital Converters.pdf

Motorola

Digital Signal

Processors

Principles of Sigma-Delta

Modulation for Analog-to-

Digital Converters

Sangil Park, Ph. D.

Strategic Applications

Digital Signal Processor Operation

MOTOROLA

APR8

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Table

of Contents

SECTION 1

ntroduction

1-1

SECTION 2

Conventional Analog-to-Digital Converters

2-1

SECTION 3

Quantization Error in A/D Conversion

3-1

SECTION 4

Oversampling and Decimation Basics

4-1

SECTION 5

Delta Modulation

5-1

SECTION 6

Sigma-Delta modulation for A/D Converters

(Noise Shaping)

6-1

6.1 Analysis of Sigma-Delta Modulation in

Z-Transform Domain

6-6

SECTION 7

Digital Decimation Filtering

7-1

7.1 Comb-Filter Design as a Decimator

7-5

7.2 Second Section Decimation FIR Filter

7-10

SECTION 8

Mode Resolution by Filtering the Comb-Filter

Out put with Half-Band Filters

8-1

SECTION 9

Summary

9-1

REFERENCES

References-1

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iii

Illustrations

Figure 2-1

Figure 2-2

Figure 2-3

Generalized Analog-to-Digital Conversion Process

Conventional Analog-to-Digital Conversion Process

Spectra of Analog and Sampled Signals

2-2

2-3

2-5

Figure 3-1

Figure 3-2

Quantization Error

Noise Spectrum of Nyquist Samplers

3-3

Figure 4-1

Comparison Between Nyquist Samplers and 2X

Oversamplers

Anti-Aliasing Filter Response and Noise Spectrum of

Oversampling A/D Converters

Frequency Response of Analog Anti-Aliasing Filters

Simple Example of Decimation Process

4-3

Figure 4-2

Figure 4-3

Figure 4-4

4-5

4-6

4-7

Figure 5-1

Delta Modulation and Demodulation

5-2

Figure 6-1

Derivation of Sigma-Delta Modulation from

Delta Modulation

Block Diagram of Sigma-Delta Modulation

S-Domain Analysis of Sigma-Delta Modulator

Block Diagram of First-Order Sigma-Delta A/D

Converter

Input and Output of a First-Order Sigma-Delta

Modulator

Z-Domain Analysis of First-Order Noise Shaper

Spectrum of a First-Order Sigma-Delta

Noise Shaper

Figure 6-2

Figure 6-3

Figure 6-4

6-1

6-2

6-3

6-5

Figure 6-5

Figure 6-6

Figure 6-7

6-6

6-7

6-9

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