Bandpass Sigma Delta Modulators

by Van Engelen, Jurgen; Van De Plassche, Rudy

• ISBN13: 9780792386988
• ISBN10: 0792386981
• Format: Hardcover
• Copyright: 1999-05-01
• Publisher: Kluwer Academic Pub

Summary

Sigma delta modulation has become a very useful and widely applied technique for high performance Analog-to-Digital (A/D) conversion of narrow band signals. Through the use of oversampling and negative feedback, the quantization errors of a coarse quantizer are suppressed in a narrow signal band in the output of the modulator. Bandpass sigma delta modulation is well suited for A/D conversion of narrow band signals modulated on a carrier, as occurs in communication systems such as AM/FM receivers and mobile phones. Due to the nonlinearity of the quantizer in the feedback loop, a sigma delta modulator may exhibit input signal dependent stability properties. The same combination of the nonlinearity and the feedback loop complicates the stability analysis. In Bandpass Sigma Delta Modulators, the describing function method is used to analyze the stability of the sigma delta modulator. The linear gain model commonly used for the quantizer fails to predict small signal stability properties and idle patterns accurately. In Bandpass Sigma Delta Modulators an improved model for the quantizer is introduced, extending the linear gain model with a phase shift. Analysis shows that the phase shift of a sampled quantizer is in fact a phase uncertainty. Stability analysis of sigma delta modulators using the extended model allows accurate prediction of idle patterns and calculation of small-signal stability boundaries for loop filter parameters. A simplified rule of thumb is derived and applied to bandpass sigma delta modulators. The stability properties have a considerable impact on the design of single-loop, one-bit, high-order continuous-time bandpass sigma delta modulators. The continuous-time bandpass loop filter structure should have sufficient degrees of freedom to implement the desired (small-signal stable) sigma delta modulator behavior. Bandpass Sigma Delta Modulators will be of interest to practicing engineers and researchers in the areas of mixed-signal and analog integrated circuit design.

Table of Contents

Preface	xv
Introduction	1	(4)
Quantization and Sampling	5	(14)
Signals	5	(1)
Quantization	6	(1)
Quantization Error Analysis	6	(6)
White Noise Approximation	7	(2)
Harmonic Distortion and Intermodulation	9	(2)
Non-Ideal Quantization	11	(1)
Sampling	12	(2)
Non-Ideal Sampling	13	(1)
Performance Definitions	14	(3)
Conclusions	17	(2)
Noise Shaping Concepts	19	(18)
Oversampling	19	(1)
Error Feedback	20	(2)
Architectures	22	(6)
Sigma Delta Modulator	22	(2)
Multi Stage Noise Shaping (MASH)	24	(1)
Other Architectures	25	(3)
Decimation and Filtering	28	(1)
System Overview	29	(1)
Design Considerations	30	(5)
Stability	30	(1)
Loop Filter Topologies	30	(2)
Implicit Input Filtering	32	(1)
Continuous-time vs. Discrete-time Loop Filters	33	(1)
One-bit vs. Multi-bit Quantizers	34	(1)
Conclusions	35	(2)
Performance	37	(22)
Linear Prediction	37	(5)
Lowpass Modulator Example	39	(1)
Optimal NTF zero placement	40	(2)
Idle Patterns, Dead Zones and Tones	42	(9)
Idle Patterns and Dead Zones	42	(1)
Tones	43	(8)
Dither and Chaotic Modulators	51	(2)
Dither	51	(2)
Chaotic Modulators	53	(1)
Non-Ideal Implementation	53	(5)
Limited gain	53	(3)
Noise	56	(1)
Crosstalk and Distortion	57	(1)
Conclusions	58	(1)
Stability	59	(48)
Definitions	59	(4)
Stability Analysis Methods and Criteria	63	(3)
Describing Function Method	66	(4)
Second Order Lowpass SDM	67	(1)
Third Order Lowpass SDM	68	(2)
Quantizer Modeling	70	(1)
Phase Uncertainty of a Sampled Quantizer	70	(10)
Analysis	71	(3)
Closed Form Expressions	74	(3)
Approximation	77	(1)
Extended Describing Function Quantizer Model	78	(2)
Prediction of Limit Cycles	80	(4)
Phase Criterion	80	(3)
Amplitude and Phase of Limit Cycles	83	(1)
Small Signal Stability	84	(15)
Second Order Lowpass Example	85	(2)
Third Order Lowpass Modulator Example	87	(1)
Low-and Highpass Modulators	88	(4)
Rule of Thumb	92	(2)
Bandpass Modulators	94	(3)
Discussion	97	(2)
Large Signal Stability	99	(3)
Analysis	99	(2)
Stabilization Techniques	101	(1)
Relationship to the Noise Model	102	(2)
Conclusions	104	(3)
Design of Continuous time Bandpass SDMs	107	(14)
Design Goals	107	(1)
Design Considerations Overview	107	(2)
Design Methodology	109	(2)
Continuous time to Discrete time Transformation	111	(3)
Subsampling in Continuous time SDMs	114	(3)
Bandpass Loop Filter Structures	117	(2)
Conclusions	119	(2)
SDM Implementations	121	(34)
Digital Test Set-Up	121	(2)
Discrete Fourth Order bandpass SDM	123	(9)
Application	123	(1)
Discrete Time Filter Design	124	(1)
Continuous Time Filter Design	125	(3)
Implementation	128	(1)
Measurements	129	(3)
Fully Integrated Sixth Order bandpass SDM	132	(20)
Discrete Time Filter Design	132	(2)
Continuous Time Filter Design	134	(3)
Implementation	137	(4)
Measurements	141	(9)
Further Remarks	150	(2)
Comparison	152	(2)
Conclusions	154	(1)
Conclusion and Discussion	155	(8)
References	163	(2)
List of Acronyms	165	(2)
List of Symbols	167	(2)
Modulator Response to Input Signals	169	(4)
Root Locus Search Method	173	(4)
Algorithm for Finding a Stability Boundary	177	(2)
Example VHDL description of a digital SDM	179	(4)
About the Authors	183	(2)
Index	185