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CMOS SigmaCMOS Sigma--Delta Converters Delta Converters ––From Basics to StateFrom Basics to State--ofof--thethe--ArtArt
RocRocííoo del Rdel Ríío, o, BelBeléénn PPéérezrez--VerdVerdúú and Josand Joséé M. de la RosaM. de la Rosa
{rocio,belen,jrosa}@imse.cnm.es
KTH, Stockholm, April 23-27
Basic Concepts and ArchitecturesBasic Concepts and Architectures
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2. Fundamentals of 2. Fundamentals of ΣΔΣΔ ADCsADCs
3. Discrete3. Discrete--Time Time ΣΔΣΔ ModulatorsModulators
OversamplingOversampling
Quantization noise shapingQuantization noise shaping
Basic architectureBasic architecture
Classification of Classification of ΣΔΣΔ ADCsADCs
OUTLINEOUTLINE
SingleSingle--bit singlebit single--quantizer architecturesquantizer architectures
Dual quantizationDual quantization
MultiMulti--bit quantizationbit quantization
Bandpass Bandpass ΣΔΣΔ modulatorsmodulators
1. Introduction1. Introduction
4. Continuous4. Continuous--Time Time ΣΔΣΔ ModulatorsModulatorsBasic concepts and topologiesBasic concepts and topologies
Synthesis methodsSynthesis methods
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Introduction: Introduction: Basic ADC processBasic ADC processBasic ADC process
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Introduction: Introduction: Basic ADC processBasic ADC processBasic ADC process
Sampling process
Limits the input signalfrequency
Speed of the ADC
Quantization process
Limits the input signalaccuracy
Resolution of the ADC
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Introduction: Introduction: Resolution vs. conversion rateResolution vs. conversion rateResolution vs. conversion rate
CMOS ADCsCMOS ADCs
ΣΔΣΔ ADCsADCs
Nyquist ADCsNyquist ADCs
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Introduction: Introduction: QuantizationQuantizationQuantization
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Introduction: Introduction: QuantizationQuantizationQuantization
[Enge99]
Quantization input-output characteristic
Quantization error White noise model
- If x varies randomly from sample to sample
- If the # of quantizer levels is high
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Introduction: Introduction: Quantization Quantization Quantization --- white noise modelwhite noise modelwhite noise model
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Oversampling
Classification of ADCs
Nyquist-rate ADCs (M~1)
Oversampling ADCs (M>>1)
Introduction: Introduction: SamplingSamplingSampling
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PSD of oversampled quantization noise
Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: OversamplingOversamplingOversampling
In-Band Noise power (IBN or PQ)
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Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: Performance MetricsPerformance MetricsPerformance Metrics
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Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: Performance MetricsPerformance MetricsPerformance Metrics
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Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: Quantization Noise ShapingQuantization Noise ShapingQuantization Noise ShapingProcessing of the quantization error
In-band noise power and effective resolution
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Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: Basic Basic Basic ΣΔΣΔΣΔ ADC architectureADC architectureADC architecture
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SigmaSigma--DeltaDeltaADCADC
NyquistNyquistADCADC
HIGHHIGH--SELECTIVITY ANALOG FILTER SELECTIVITY ANALOG FILTER for antifor anti--aliasingaliasing
Overall resolution obtained using Overall resolution obtained using HIGHHIGH--ACCURACY ANALOG BLOCKSACCURACY ANALOG BLOCKS
LOWLOW--SELECTIVITY ANALOG FILTER SELECTIVITY ANALOG FILTER for antifor anti--aliasing (1st/2nd order)aliasing (1st/2nd order)
High overall resolution obtained using High overall resolution obtained using LOW/MODERATELOW/MODERATE--ACCURACY ANALOG BLOCKSACCURACY ANALOG BLOCKS
HIGHHIGH--SELECTIVITY DIGITAL FILTERSELECTIVITY DIGITAL FILTER
EASIER AND MORE ROBUST IN MODERN CMOSEASIER AND MORE ROBUST IN MODERN CMOS
Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: NyquistNyquistNyquist---rate vs. rate vs. rate vs. ΣΔΣΔΣΔ ADCsADCsADCs
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H(z) with large gainwithin the signal band
1st1st--order order ΣΔΣΔMML L thth--order order ΣΔΣΔMM
Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: BasicBasic ΣΔΣΔΣΔM architectureM architectureM architecture
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DT ΣΔM CT ΣΔM
Low-Pass ΣΔM Band-Pass ΣΔM
Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: Classification of Classification of ΣΔΣΔΣΔMsMsMsNature of the signals being handled: Low-pass vs. Band-pass
Dynamics of the loop filter: Discrete-Time vs. Continuous-Time
Number of bits of the embedded quantizer: single-bit vs. multi-bit
Number of quantizers employed: single-loop, cascade, etc..
Type of primitives available in the fabrication technology…
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H(z) with large gainwithin the signal band
L L thth--order order ΣΔΣΔMM
Oversampling, Oversampling, OSROSR
Order of the shaping, Order of the shaping, LL
Resolution of the Resolution of the internal quantizer, internal quantizer, BB
Speed of analog circuitry Speed of analog circuitry
Stability of the Stability of the ΣΔΣΔM M
Linearity of the DAC Linearity of the DAC
L B
Fundamentals of Fundamentals of ΣΔΣΔ ADCs: ADCs: Basic control parametersBasic control parameters
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DTDT--ΣΔΣΔMs: Ms: 1st1st--order LPorder LP ΣΔΣΔΣΔ ModulatorModulatorModulator
Using a linear model for the quantizer
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DTDT--ΣΔΣΔMs: Ms: 1st1st--order LPorder LP ΣΔΣΔΣΔ ModulatorModulatorModulator
Ramp input & 1-bit quantizer
Sinewave input & 3-bit quantizer
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Noise pattern
DTDT--ΣΔΣΔMs: Ms: 1st1st--order LPorder LP ΣΔΣΔΣΔ ModulatorModulatorModulator
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DTDT--ΣΔΣΔMs: Ms: 2nd2nd--order LPorder LP ΣΔΣΔΣΔ ModulatorModulatorModulator
1st-order ΣΔ Modulator
2nd-order ΣΔ Modulator
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DTDT--ΣΔΣΔMs: Ms: 2nd2nd--order LPorder LP ΣΔΣΔΣΔ ModulatorModulatorModulator
Linear analysis
Output spectrum and noise pattern
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purepure--differentiator FIRdifferentiator FIR NTFNTFProne to instabilityProne to instability
2nd2nd--order order ΣΔΣΔMM
L L thth--order order ΣΔΣΔMM
Stable for inputs inif
[Candy85]
High-order ΣΔ loops areonly conditionally stable [OptE90]
IIRIIR NTFNTFss
Zeros at Zeros at zz = 1= 1
Gain adjusted to satisfy
[Lee87]
Butterworth/Chebyshev polesButterworth/Chebyshev poles
(1)(1)(1)(1)
DTDT--ΣΔΣΔMs: Ms: HighHigh--order Singleorder Single--loop loop ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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OPTIMIZED IIROPTIMIZED IIR NTFNTFss
Complex zeros at |Complex zeros at |z z | = 1 with optimal | = 1 with optimal positions within the signal bandpositions within the signal band
[Schr93]
Butterworth/Chebyshev polesButterworth/Chebyshev poles
(2)(2)
(2)(2)(1)(1)
5th5th--order NTForder NTF((OSR OSR = 64)= 64)
IIRIIR NTFNTFss
Zeros at Zeros at zz = 1= 1
Gain adjusted to satisfy
[Lee87]
Butterworth/Chebyshev polesButterworth/Chebyshev poles
(1)(1)
DTDT--ΣΔΣΔMs: Ms: HighHigh--order Singleorder Single--loop loop ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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(2)(2)
Distributed feedback andDistributed feedback anddistributed feedforward inputdistributed feedforward input
(1)(1)
(2)(2) Feedforward summationFeedforward summation+ local resonators+ local resonatorsComplexity (many feedback/feedforward coeffs)Complexity (many feedback/feedforward coeffs)
Large spread of coeffs (area, power)Large spread of coeffs (area, power)
DTDT--ΣΔΣΔMs: Ms: HighHigh--order Singleorder Single--loop loop ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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Systematic loss of resolution, but:
MASH MASH ΣΔΣΔMsMs
Each stage re-modulates a signal containing the quantization error in the previous one.
Digital processing is used to cancel out all quantization errors, but that in the last stage.
Error Cancellation Logic (ECL)Error Cancellation Logic (ECL)
d > 1, interstagecoupling
Smaller than for single loopsIndependent of OSR
HIGHHIGH--ORDER STABLE OPERATIONORDER STABLE OPERATION is ensured by cascading low-order stages (Li = 1, 2).
Relationships among ECL and ΣΔM to be fulfilled for perfect cancellation (NOISE LEAKAGENOISE LEAKAGE).
Performance close to idealPerformance close to ideal
Small spread of analog coeffsSmall spread of analog coeffsECL can be easily implementedECL can be easily implemented
Suited at low oversamplingSuited at low oversampling
DTDT--ΣΔΣΔMs: Ms: HighHigh--order Cascade order Cascade ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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11--11--1 1 ΣΔΣΔMM [Mats87]
4th4th--order 2order 2--stage cascadestage cascade22--2 2 ΣΔΣΔMM
4th4th--order 3order 3--stage cascadestage cascade22--11--1 1 ΣΔΣΔMM
[Kare90]
[Yin94]
22--1 1 ΣΔΣΔMM [Longo88]22--22--1 1 ΣΔΣΔMM [Vleu01]22--11--11--1 1 ΣΔΣΔMM [Rio00]22--22--2 2 ΣΔΣΔMM [Dedic94]
Noise leakage precludes the cascading ofa large number of stages to be practical
DTDT--ΣΔΣΔMs: Ms: HighHigh--order Cascade order Cascade ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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Element TrimmingElement TrimmingAnalog CalibrationAnalog CalibrationDigital CorrectionDigital Correction
Increased dynamic rangeIncreased dynamic range
Better stability propertiesBetter stability properties
DAC nonDAC non--linearities are directly linearities are directly added to the inputadded to the input
B can trade for OSR (wideband)
More aggressive high-order NTFs
The linearity of the ΣΔM will beno better than that
Correcting DAC errorsCorrecting DAC errors
DEM techniquesDEM techniques
Decorrelating DAC errorsDecorrelating DAC errorsfrom the inputfrom the input
FULLFULL--PARALLEL ADC/DACPARALLEL ADC/DAC(Typically B < 6)
DAC linearity limited byDAC linearity limited bycomponent mismatchcomponent mismatch
Dual quantizationDual quantization
Introducing DAC errorsIntroducing DAC errorsat a nonat a non--critical positioncritical position
POSSIBLE APPROACHESPOSSIBLE APPROACHES
DTDT--ΣΔΣΔMs: Ms: MultiMulti--bitbit ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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Increased dynamic rangeIncreased dynamic range
Better stability propertiesBetter stability properties
DAC nonDAC non--linearities are directly linearities are directly added to the inputadded to the input
B can trade for OSR (wideband)
More aggressive high-order NTFs
The linearity of the ΣΔM will beno better than that
ELEMENT SELECTIONELEMENT SELECTIONLOGICLOGIC
FULLFULL--PARALLEL ADC/DACPARALLEL ADC/DAC(Typically B < 6)
DAC linearity limited byDAC linearity limited bycomponent mismatchcomponent mismatch
Elements selected to make DAC errors independent of the input signal
Dynamic Element Matching (DEM)Dynamic Element Matching (DEM)
Algorithms that try to average the error in each DAC level to zero (to push DAC errors to high freq.)
Randomization: Distortion transforms into white noiseRotation: Distortion moves out of band (CLA)Mismatch-shaping: 1st/2nd order (ILA, DWA, DDS)
DTDT--ΣΔΣΔMs: Ms: MultiMulti--bitbit ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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Combines 1-bit and multi-bit quantizers (linearity/reduced error)
Dual QuantizationDual Quantization
LeslieLeslie--SinghSingharchitecturearchitecture
[Lesl90]Concept applied to singleConcept applied to single--loop loop ΣΔΣΔMsMs [Hair91]
Concept applied to cascade Concept applied to cascade ΣΔΣΔMsMs [Bran91]
L-0 cascade ΣΔMSuffers from noise leakageMulti-bit quantization does not improve stability
Improved stabilityNoise leakage
Multi-bit quantization usually applied only in the last stage
DAC errors shaped by L-LNRelaxes DAC requirements
Noise leakage (inherent to cascades)
DTDT--ΣΔΣΔMs: Ms: DualDual--quantizationquantization ΣΔΣΔΣΔ ModulatorsModulatorsModulators
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DTDT--ΣΔΣΔMs: Ms: Bandpass Bandpass ΣΔΣΔΣΔ Modulators Modulators Modulators ––– IF DigitizationIF DigitizationIF Digitization
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DTDT--ΣΔΣΔMs: Ms: Bandpass Bandpass ΣΔΣΔΣΔ Modulators Modulators Modulators
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DTDT--ΣΔΣΔMs: Ms: Bandpass Bandpass ΣΔΣΔΣΔ Modulators Modulators Modulators
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DTDT--ΣΔΣΔMs: Ms: Bandpass Bandpass ΣΔΣΔΣΔMs Ms Ms ––– Signal band location Signal band location Signal band location
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DTDT--ΣΔΣΔMs: Ms: LPLPLP---tototo---BP Transformation Method BP Transformation Method BP Transformation Method
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DTDT--ΣΔΣΔMs: Ms: LPLPLP---tototo---BP Transformation Method BP Transformation Method BP Transformation Method
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DTDT--ΣΔΣΔMs: Ms: LPLPLP---tototo---BP Transformation Method BP Transformation Method BP Transformation Method
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DTDT--ΣΔΣΔMs: Ms: Bandpass Bandpass ΣΔΣΔΣΔ Modulators Modulators Modulators Other BP-ΣΔM architectures
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DTDT--ΣΔΣΔMs: Ms: Bandpass Bandpass ΣΔΣΔΣΔ ADCs ADCs ADCs --- DecimationDecimationDecimation
Bandpass decimation
Efficient decimation
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Continuous-Time ΣΔMs
CT front (loop filter) partDT back (quantizer) partSampling inside the loop
CTCT--ΣΔΣΔMs: Ms: Basic ConceptsBasic ConceptsBasic Concepts
Discrete-Time ΣΔMs
DT loop filterAll internal signals are DTSampling at the input
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AA Filter
Pros of CT-ΣΔMs
Implicit anti-aliasing filterLess impact of sampling errorsNo input switches – potentially better for low-voltage supplyNo “settling” error at the loop filter circuitryPotentially larger operation speed with less power consumptionNo sampling of the noise at the input capacitorsReduced digital noise coupling
Counters of CT-ΣΔMs
Very involved dynamic due to the combination of non-linearity, CT and DTlarger impact of circuit non-linearitiesTime constant tuning is needed for correct loop filteringLarge sensitive to time uncertainty (“jitter”)
CTCT--ΣΔΣΔMs: Ms: Basic ConceptsBasic ConceptsBasic Concepts
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Linear analysis of CT-ΣΔMs, assuming [Bree01]:
Linear model for the quantizerDAC gain is unity in the signal bandwidth
Example: Lth-order, B-bit single-loop architecture
CTCT--ΣΔΣΔMs: Ms: Basic ConceptsBasic ConceptsBasic Concepts
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DT-to-CT synthesis method: pulse invariant transformation (freq. domain)
Find an equivalent DT ΣΔM that fulfils the required specificationsBased on a DT-to-CT equivalence [Cher00]
Open-loop configuration
CTCT--ΣΔΣΔMs: Ms: Synthesis MethodsSynthesis MethodsSynthesis Methods
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Application of DT-to-CT method to cascade CT ΣΔMs
Every state variable and DAC output must be connected to the integrator input of theulterior stages in the cascade [Ortm01]Increases the number of analog components (transconductors and amplifiers)
DT-to-CT
CTCT--ΣΔΣΔMs: Ms: Synthesis MethodsSynthesis MethodsSynthesis Methods
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Direct synthesis method [Bree01]Uses the desired NTF as a starting point, (as for the DT case)An Inverse Chevychev distribution of the NTF zeros has advantages in terms of SNR and stability
Application to cascade architectures [Tort06]Optimum placement of poles/zeroes of the NTFSynthesis of both analog and digital part of the cascade CT ΣΔ ModulatorReduced number number of analog components
DT-to-CT
MethodDirect
Method
CTCT--ΣΔΣΔMs: Ms: Synthesis MethodsSynthesis MethodsSynthesis Methods
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1 1.5
2 2.5
0 0.20.40.60.81
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σc(%)σgm(%)
SN
R L
oss
(dB
)
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1.5
2
2.5
0 0.20.40.60.81
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σc(%)σgm(%)
Direct synthesis of cascade architectures (I) [Tort06]
Sensitivity to mismatch (gm,C)A 2-1-1 example
DT-to-CT synthesis method Direct synthesis method
CTCT--ΣΔΣΔMs: Ms: Synthesis MethodsSynthesis MethodsSynthesis Methods
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Direct synthesis of cascade architectures (II) [Tort06]
CTCT--ΣΔΣΔMs: Ms: Synthesis MethodsSynthesis MethodsSynthesis Methods
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A case study: A 12-bit@20MHz, 4-b, 2-1-1 CT ΣΔM for VDSL [Tort06]D
irect
synt
hesi
sm
etho
d
CTCT--ΣΔΣΔMs: Ms: Synthesis MethodsSynthesis MethodsSynthesis Methods
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[Bree01] L. Breems and J.H. Huijsing, Continuous-Time Sigma-Delta Modulation for A/D Conversion in Radio Receivers. Kluwer Academic Publishers, 2001.
[Cherr00] J.A. Cherry and W.M. Snelgrove, Continuous-Time Delta-Sigma Modulators for High-Speed A/D Conversion. Kluwer Academic Publishers, 2000.
[Enge99] J.V. Engelen and R. van de Plassche, BandPass Sigma-Delta Modulators: Stability Analysis, Performance and Design Aspects. Kluwer Academic Publishers, 1999.
[Geer02] Y. Geerts, M. Steyaert and W. Sansen: “Design of Multi-bit Delta-Sigma A/D Converters”. Kluwer, 2002.
[Mede99] F. Medeiro, B. Pérez-Verdú, and A. Rodríguez-Vázquez, Top-Down Design of High-Performance Sigma-Delta Modulators. Kluwer Academic Publishers, 1999.
[Nors97] S.R. Norsworthy, R. Schreier, and G.C. Temes (Editors), Delta-Sigma Data Converters: Theory, Design and Simulation. IEEE Press, New York 1997.
[Pelu99] V. Peluso, M. Steyaert, and W. Sansen, Design of Low-Voltage Low-Power CMOS Delta-Sigma A/D Converters. Kluwer Academic Publishers, 1999.
[Rabi99] S. Rabii and B.A. Wooley, The Design of Low-Voltage, Low-Power Sigma-Delta Modulators. KluwerAcademic Publishers, 1999.
[Rio06] R. del Río, F. Medeiro, B. Pérez-Verdú, J.M. de la Rosa and A. Rodríguez-Vázquez, CMOS Cascade Sigma-Delta Modulators for Sensors and Telecom: Error Analysis and Practical Design. Springer, 2006.
[Rodr03] A. Rodríguez-Vázquez, F. Medeiro and E. Janssens, CMOS Telecom Data Converters. KluwerAcademic Publishers, 2003.
[Rosa02] J.M. de la Rosa, B. Pérez-Verdú, and A. Rodríguez-Vázquez, Systematic Design of CMOS Switched-Current Bandpass Sigma-Delta Modulators for Digital Communication Chips. Kluwer Academic Publishers, 2002.
[Shoa95] O. Shoaei, Continuous-Time Delta-Sigma A/D Converters for High Speed Applications. Ph.D. Dissertation, Carleton University, 1995.
General ReferencesGeneral References