Sigma-Delta Modulators for IC Analog-to-Digital Converters

angelweishan

Sigma-Delta Modulators for Integrated Circuit Analog-to-Digital Converters

HARVARD UNIVERSITY
The Graduate School OF Arts and Sciences

Philip David Steiner


CONTENTS
1 Introduction
   1.1 Modeling of Sigma-Deita Modulaturs .
   1.2 Overview ..
   1.3 Contributions

2 Nyquist, Oversampled, and Noise Shaping A/D Converters
   2.1 Sampling and Quantization
      2.1.1 Sampling ..
      2.1.2 Quantization
      2.1.3 Modeling the Quantizer
   2.2 Performance Specification of A/D Converters
      2.2.l Specifications for Ideal Converters
      2.2.2 Errors in Non Ideal Converters
      2.2.3 Physical Sources of Noise
   2.3 Nyquist Rate :ADC Architectures
      2.3.l The Flash ADC
      2.3.2 The Successive Approximation .ADC
    2.-4 Oversampled and Noise Shaping A/D Converters
       2.-4.1 Oversampling ......... .
       2.-4.2 Noise Shaping A/D Converters


3 Sigma-Delta Analog-to-Digital Converters
   3.1 Ideal Sigma-Delta Modulation ...
      3.1.1 The First Order Modulator
      3.1.2 Higher Order ~Iodulation . . .
      3.1.3 Stability of Higher Order Modulators
      3.1.-1 Sampled Data and Continuous-Time Modulators
      3.1.5 Pattern Noise and Idle Tones
      3.1.6 Higher Order NTF-s
   3.2 Circuits Issues ....
      3.2.1 The Integrator
      3.2.2 Integrator Non-Idealities .
      3.2.3 Physical Noise in the Integrator.
      3.2.-1: The Quantizer/.illC and DAC
   3.3 Sigma-Delta ~Iodulator Architectures
      :3.3.1 Interpolative Sigma-Delta Architectures
      3.3.2 Stabilization Techniques for Interpolative Architectures
      3.3.3 Architectural Techniques for Eliminating Idle Tones
      3.3.4: MESH Modulators . . . . . .
   3.4: Analysis of Sigma-Delta Modulators
      3.4.1 Linear Analysis Method . . .
      3.4.2 nonlinear Analysis Approaches

4 State Space Description of Sigma-Delta J.\tIoduIators
4-1:.1 Linear Systems ............ .
.. L2 Interpolative Sigma-Delta Modulators
4-1:.2.1 General Form of Interpolative Sigma-Delta ~Iodulation
4-1:.2.2 Pseud~Linear Systems Analysis .. . .
4-1:.3 Diagonal Form of the Interpolative Modulators
4-1:.3.1 Classes of Diagonal Modulators . . . . . .
4-1:.3.2 Diagonal Modulation and Transfer Functions
4-1:.3.3 Diagonal Modulation and Complex Numbers
4-1:.3.-1: Diagonal Systems and Modulator Order
4-I:A Non-Diagonal Forms and Implemented Systems .
5 Stability of Interpolative l.\tlodulators
5.1 Stability Measures for E-~ Modulators.

5 .. 1.1 Practical Considerations .
5.1.2 A Definition of Stability.
The First Order Modulator ..

5.2.1 Dynamics of the First Order Modulator
5.2.2 Stability of the First Order Modulator
5.3 Second Order Sigma-Delta Modulators . . . .


5.3.1 The General Second Order Modulator 145
5.3.2 The Two Parameter Modulator . . . . 148
5.3.3 Dynamics of The Two Parameter System with Constant Input 151
5.3.4 Stability for Constant Inputs 155
5.3.5 A Design E.."{ample . . 164
5.3.6 Time Varying Inputs . 167
5.4 Higher Order Modulators . . .
5.4.1 Generalized First Order Systems
5.4.2 Shifted First Order Systems . . .
5.4.3 Stability of Higher Order Parallel ~Iodulators
6 Multi-Bit Modulators
6.1 Multi-bit Modulators and Linearity .
6.2 Improving Linearity in Multi-Bit Modulators
6.2.1 Element Trimming ..... .
6.2.2 Dynamic Element :\[atching .
6.2.3 Digital Error Correction
6.2.4 Dual Quantizer Systems
6.3 A Summary of Multi-Bit Methods
7 The l\'IDQ l\'Iodulator
7.1 Modified Dual-Quantizer Approach ..
7.1.1 The Modified Design . . . . .
7.1.2 Extensions to Higher Order Modulators
7.2 Simulation Results . . . . . . . . . . . . .
7.2.1 Specifications for the Simulations .
7.J_?.- Simulation Results for the Second Order MDQ Modulator .
7.2.3 Non Ideal Components ........ .
7.2.4 Non Linearity in the State Quantizer .
Higher Order Simulation Results . . .

7.3 Discussion of Results . . . . . 230
8 Conclusions and Future Work 234
8.1 Future \Vork ... _ . 238
A Proofs For Chapter 4 241
A.1 Proof of Theorem ·U . . 241
A.2 Proof of Theorem -L2 . 242
B Measures of Stability in L-~ Modulators 245
C Proofs For Chapter 5 247
C.l Proof of Theorem 5.3 . 247
C.2 Proof of Theorem 5A . 261
C.3 Proof of Theorem 5.5 . 263
C.4 Proof of Theorem 5.6 . 264
C.5 Proof of Theorem 5.7 . 266
C.6 Proof of Theorem 5.8 . 267
D Program Listings 268
Bibliography 274

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