Principles of Sigma Delta Conversion for Analog to Digital Converters.pdf
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Motorola
Digital Signal
Processors
Principles of Sigma-Delta
Modulation for Analog-to-
Digital Converters
by
Sangil Park, Ph. D.
Strategic Applications
Digital Signal Processor Operation
MOTOROLA
APR8
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ty/Affirmative Action Employer.
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
MOTOROLA
iii
I
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
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
MOTOROLA
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