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CMOS SigmaCMOS Sigma--Delta Converters Delta Converters ––From Basics to StateFrom Basics to State--ofof--thethe--ArtArt
Basic Concepts and ArchitecturesBasic Concepts and ArchitecturesAngelAngel RodríguezRodríguez--VázquezVázquez
Basic Concepts and ArchitecturesBasic Concepts and ArchitecturesAngel Angel RodríguezRodríguez--VázquezVázquez
Materials in this course have been contributed by Fernando Medeiro, José M. de la Rosa, Rocío del Río, Belén Pérez-Verdú and Angel Rodríguez-Vázquez
Barcelona, 29-30 / Septiembre / 2010
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OUTLINEOUTLINE1. Introduction1. Introduction
2. Fundamentals of 2. Fundamentals of ADCsADCs OversamplingOversampling
Quantization noise shapingQuantization noise shaping
Basic architectureBasic architecture
Cl ifi ti fCl ifi ti f ADCADC
3. Discrete3. Discrete--Time Time ModulatorsModulators Classification of Classification of ADCsADCs
Si lSi l bit i lbit i l titi hit thit t SingleSingle--bit singlebit single--quantizerquantizer architecturesarchitectures
Dual quantizationDual quantization
MultiMulti--bit quantizationbit quantization MultiMulti bit quantizationbit quantization
BandpassBandpass modulatorsmodulators
4. Continuous4. Continuous--Time Time ModulatorsModulators
Basic concepts and topologiesBasic concepts and topologies
Synthesis methodsSynthesis methods
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Introduction: Introduction: Basic ADC ProcessBasic ADC Process
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Introduction: Introduction: QuantizationQuantization
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OversamplingIntroduction: Introduction: SamplingSampling
p g
Classification of ADCs
Nyquist-rate ADCs (M~1)
Oversampling ADCs (M>>1)
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Introduction: Introduction: Taxonomy of ADCsTaxonomy of ADCs
Sampling process
Limits the input signalLimits the input signal frequency
Speed of the ADC Speed of the ADC
Quantization process
Limits the input signal accuracy
Resolution of the ADC
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Introduction: Introduction: Taxonomy of ADCsTaxonomy of ADCs
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Introduction: Introduction: About ADC taxonomyAbout ADC taxonomy
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Introduction: Introduction: Resolution vs. conversion rateResolution vs. conversion rateCMOS ADCsCMOS ADCs
ADCsADCs
NyquistNyquist ADCsADCs
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Introduction: Introduction: Quantization errorQuantization error Quantization output-input characteristicQ p p
Quantization error White noise model
- If x varies randomly from sample to sampley p p
- If the # of quantizer levels is high
[Enge99]
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Introduction: Introduction: Quantization error noise modelQuantization error noise model
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PSD of oversampled quantization noise
Fundamentals of Fundamentals of ADCs: ADCs: OversamplingOversampling
PSD of oversampled quantization noise
In-Band Noise power (IBN or PQ)
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Fundamentals of Fundamentals of ADCs: ADCs: OversamplingOversampling
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Fundamentals of Fundamentals of ADCs: ADCs: Performance metricsPerformance metrics
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Fundamentals of SD ADCs: Fundamentals of SD ADCs: Quantization noise shapingQuantization noise shaping Processing of the quantization error
I b d i d ff ti l ti In-band noise power and effective resolution
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Fundamentals of Fundamentals of ADCs: ADCs: Basic Basic ADC architectureADC architecture
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Fundamentals of Fundamentals of ADCs: ADCs: NyquistNyquist--rate vs. rate vs. ADCsADCs
NyquistNyquistADCADC
SiSi D ltD ltSigmaSigma--DeltaDeltaADCADC
HIGHHIGH--SELECTIVITY ANALOG FILTER SELECTIVITY ANALOG FILTER for antifor anti--aliasingaliasing
LOWLOW--SELECTIVITY ANALOG FILTER SELECTIVITY ANALOG FILTER for antifor anti--aliasing (1st/2nd order)aliasing (1st/2nd order)for antifor anti--aliasingaliasing
Overall resolution obtained using Overall resolution obtained using HIGHHIGH--ACCURACY ANALOG BLOCKSACCURACY ANALOG BLOCKS
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
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H(z) with large gain
Fundamentals of Fundamentals of ADCs: ADCs: Basic Basic M architectureM architecture
within the signal band
1st1st--order order MML L thth--order order MM
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H(z) with large gain
Fundamentals of Fundamentals of ADCs: ADCs: Basic Basic M architectureM architecture
within the signal band
1st1st--order order MML L thth--order order MM
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Fundamentals of Fundamentals of ADCs: ADCs: Classification of Classification of MsMs Nature of the signals being handled: Low-pass vs. Band-pass
Low-Pass M Band-Pass M
Dynamics of the loop filter: Discrete-Time vs. Continuous-Time
DT M CT M
Number of bits of the embedded quantizer: single bit vs multi bit 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 gainL BFundamentals of Fundamentals of ADCs: ADCs: Basic control parametersBasic control parameters
within the signal bandL
L L thth--order order MM
Oversampling, Oversampling, OSROSR
Order of the shaping, Order of the shaping, LL
Speed of analog circuitry Speed of analog circuitry
Resolution of the Resolution of the internal quantizer, internal quantizer, BB
Stability of the Stability of the M M
Linearity of the DACLinearity of the DACLinearity of the DAC Linearity of the DAC
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H(z) with large gainL BFundamentals of Fundamentals of ADCs: ADCs: Basic control parametersBasic control parameters
within the signal bandL
L L thth--order order MM
Oversampling, Oversampling, OSROSR
Order of the shaping, Order of the shaping, LL
Speed of analog circuitry Speed of analog circuitry
Resolution of the Resolution of the internal quantizer, internal quantizer, BB
Stability of the Stability of the M M
Linearity of the DACLinearity of the DACLinearity of the DAC Linearity of the DAC
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DTDT-- Ms: Ms: 1st1st--order LP order LP modulatormodulator
Using a linear model for the quantizer
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DTDT-- Ms: Ms: 1st1st--order LP order LP ModulatorModulator
Ramp input & 1-bit quantizer
Sinewave input & 3 bit quantizerSinewave input & 3-bit quantizer
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Noise pattern
DTDT-- Ms: Ms: 1st1st--order LP order LP modulatormodulator
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DTDT-- Ms: Ms: 2nd2nd--order LP order LP modulatormodulator
1st-order Modulator
2nd-order Modulator
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DTDT-- Ms: Ms: 2nd2nd--order LP order LP modulatormodulator
Linear analysis
Output spectrum and noise pattern
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2nd2nd--order order MM
DTDT-- Ms: Ms: HighHigh--order singleorder single--loop loop modulatorsmodulators
Stable for inputs inif
[Candy85]
L L thth--order order MM
purepure--differentiator FIRdifferentiator FIR NTFNTFProne to instabilityProne to instability
High-order loops areonly conditionally stable [OptE90]only conditionally stable [ p ]
IIRIIR NTFNTFss [Lee87]
Zeros at Zeros at zz = 1= 1 Butterworth/Chebyshev polesButterworth/Chebyshev poles
(1)(1)(1)(1)
Gain adjusted to satisfy
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DTDT-- Ms: Ms: HighHigh--order singleorder single--loop loop modulatorsmodulators
OPTIMIZED IIROPTIMIZED IIR NTFNTFss [Schr93]
(2)(2)
5th5th--order NTForder NTF((OSR OSR = 64)= 64)
Complex zeros at |Complex zeros at |z z | = 1 with optimal | = 1 with optimal positions within the signal bandpositions within the signal band
Butterworth/Chebyshev polesButterworth/Chebyshev poles
IIRIIR NTFNTFss [Lee87]
(2)(2)(1)(1)
Zeros at Zeros at zz = 1= 1 Butterworth/Chebyshev polesButterworth/Chebyshev poles
(1)(1)
Gain adjusted to satisfy
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Di t ib t d f db k dDi t ib t d f db k d
DTDT-- Ms: Ms: HighHigh--order singleorder single--loop loop modulatorsmodulators
Distributed feedback andDistributed feedback anddistributed feedforward inputdistributed feedforward input
(1)(1)
(2)(2) Feedforward summationFeedforward summation+ local resonators+ local resonators Complexity (many feedback/feedforward coeffs)Complexity (many feedback/feedforward coeffs)
Large spread of coeffs (area power)Large spread of coeffs (area power) Large spread of coeffs (area, power)Large spread of coeffs (area, power) Not suited at low oversampling (standNot suited at low oversampling (stand--alone)alone)
(2)(2)
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Error Cancellation Logic (ECL)Error Cancellation Logic (ECL)
DTDT-- Ms: Ms: HighHigh--order cascade order cascade modulatorsmodulators
HIGHHIGH--ORDER STABLE OPERATIONORDER STABLE OPERATION is ensured by cascading low-order stages (Li = 1, 2).
d > 1, interstagecoupling
by cascading low order stages (Li 1, 2).
Relationships among ECL and M to be fulfilled for perfect cancellation (NOISE LEAKAGENOISE LEAKAGE).
coupling
Systematic loss of resolution, but:
MASH MASH MsMs
Smaller than for single loops Independent of OSR
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
Performance close to idealPerformance close to ideal
Small spread of analog coeffsSmall spread of analog coeffs ECL can be easily implementedECL can be easily implemented
quantization errors, but that in the last stage. Suited at low oversamplingSuited at low oversampling
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DTDT-- Ms: Ms: HighHigh--order cascade order cascade modulatorsmodulators
11--11--1 1 MM [Mats87]
22--2 2 MM [Kare90]
22--1 1 MM [Longo88] 22--22--1 1 MM [Vleu01]
Noise leakage precludes the cascading of4th4th--order 2order 2--stage cascadestage cascade 22--11--11--1 1 MM [Rio00]
22--22--2 2 MM [Dedic94]
Noise leakage precludes the cascading ofa large number of stages to be practical
4th4th--order 3order 3--stage cascadestage cascade22--11--1 1 MM [Yin94]
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DTDT-- Ms: Ms: MultiMulti--bit bit modulatorsmodulators
Increased dynamic rangeIncreased dynamic rangeB can trade for OSR (wideband)
Better stability propertiesBetter stability properties
DAC nonDAC non--linearities are directly linearities are directly added to the inputadded to the input
More aggressive high-order NTFs
FULLFULL--PARALLEL ADC/DACPARALLEL ADC/DAC(Typically B < 6)
DAC linearity limited byDAC linearity limited bycomponent mismatchcomponent mismatchadded to the inputadded to the input
The linearity of the M will beno better than that
( yp y ) pp
POSSIBLE APPROACHESPOSSIBLE APPROACHES
Element TrimmingElement Trimming Analog CalibrationAnalog Calibration
Correcting DAC errorsCorrecting DAC errors
DEM techniquesDEM techniques
Decorrelating DAC errorsDecorrelating DAC errorsfrom the inputfrom the input
Dual quantizationDual quantization
Introducing DAC errorsIntroducing DAC errorsat a nonat a non--critical positioncritical position
Digital CorrectionDigital Correction
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ELEMENT SELECTIONELEMENT SELECTION
DTDT-- Ms: Ms: MultiMulti--bit bit modulatorsmodulators
ELEMENT SELECTIONELEMENT SELECTIONLOGICLOGIC
Increased dynamic rangeIncreased dynamic rangeB can trade for OSR (wideband)
Better stability propertiesBetter stability properties
DAC nonDAC non--linearities are directly linearities are directly
( )
More aggressive high-order NTFs
FULLFULL--PARALLEL ADC/DACPARALLEL ADC/DAC(T pi ll B < 6)
DAC linearity limited byDAC linearity limited byomponent mi m t homponent mi m t hadded to the inputadded to the input
The linearity of the M will beno better than that
(Typically B < 6) component mismatchcomponent mismatch
Elements selected to make DAC errors independent of the input signal
Dynamic Element Matching (DEM)Dynamic Element Matching (DEM)
Elements selected to make DAC errors independent of the input signal
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 noise Rotation: Distortion moves out of band (CLA) Mismatch-shaping: 1st/2nd order (ILA, DWA, DDS)
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DTDT-- Ms: Ms: DualDual--quantization quantization modulatorsmodulators
Combines 1-bit and multi-bit quantizers (linearity/reduced error)
Dual QuantizationDual Quantization
LeslieLeslie--SinghSinghLeslieLeslie SinghSingharchitecturearchitecture
[Lesl90]Concept applied to singleConcept applied to single--loop loop MsMs [Hair91]
L-0 cascade M
Improved stability Noise leakage L 0 cascade M
Suffers from noise leakage Multi-bit quantization does
not improve stability
Concept applied to cascadeConcept applied to cascade MsMs [Bran91]Concept applied to cascade Concept applied to cascade MsMs [Bran91]
Multi-bit quantization usually applied only in the last stage
DAC errors shaped by L-LNRelaxes DAC requirements
Noise leakage (inherent to cascades)
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DTDT-- Ms: Ms: BandpassBandpass modulators modulators –– IF digitizationIF digitization
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DTDT-- Ms: Ms: BandpassBandpass modulators modulators
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DTDT-- Ms: Ms: BandpassBandpass modulators modulators
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DTDT-- Ms: Ms: BandpassBandpass Ms Ms –– Signal band location Signal band location
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DTDT-- Ms: Ms: LPLP--toto--BP transformation method BP transformation method
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DTDT-- Ms: Ms: LPLP--toto--BP transformation method BP transformation method
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DTDT-- Ms: Ms: LPLP--toto--BP transformation method BP transformation method
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DTDT-- Ms: Ms: BandpassBandpass SD Modulators SD Modulators
Other BP M architectures Other BP-M architectures
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DTDT-- Ms: Ms: ADCs ADCs -- DecimationDecimation
Bandpass decimation Bandpass decimation
Effi i t d i ti Efficient decimation
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CTCT-- Ms: Ms: Basic conceptsBasic concepts
Discrete-Time Ms
DT loop filter All internal signals are DT Sampling at the input
Continuous-Time Ms
CT f t (l filt ) t CT front (loop filter) part DT back (quantizer) part Sampling inside the loop
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CTCT-- Ms: Ms: Basic conceptsBasic concepts
AA Filter
Pros of CT-Ms
Implicit anti-aliasing filterImplicit anti aliasing filter Less impact of sampling errors No input switches – potentially better for low-voltage supply No “settling” error at the loop filter circuitry P t ti ll l ti d ith l ti Potentially larger operation speed with less power consumption No sampling of the noise at the input capacitors Reduced digital noise coupling
Counters of CT-Ms Counters of CT Ms
Very involved dynamic due to the combination of non-linearity, CT and DT
larger impact of circuit non linearities larger impact of circuit non-linearities Time constant tuning is needed for correct loop filtering Large sensitive to time uncertainty (“jitter”)
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Linear analysis of CT-Ms assuming [Bree01]:
CTCT-- Ms: Ms: Basic conceptsBasic concepts
Linear analysis of CT Ms, assuming [Bree01]:
Linear model for the quantizer DAC gain is unity in the signal bandwidth
Example: Lth-order, B-bit single-loop architecture
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C h i h d l i i f i (f d i )
CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
DT-to-CT synthesis method: pulse invariant transformation (freq. domain)
Find an equivalent DT M that fulfils the required specifications Based on a DT-to-CT equivalence [Cher00]
Open-loop configuration
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DT-to-CT synthesis method: State-Space Representation (time domain)
CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
DT-to-CT synthesis method: State-Space Representation (time domain) Operation of the loop filter is described by state-space equations Can be applied to an arbitrary feedback DAC waveform [Olia03b]
Equivalent DT system
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CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
Application of DT-to-CT method to cascade CT Ms
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) Increases the number of analog components (transconductors and amplifiers)
DT-to-CT
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Direct synthesis method [Bree01]
CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
ec sy es s e od [ ee0 ] 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 A li ti t d hit t [T t06] Application to cascade architectures [Tort06]
Optimum placement of poles/zeroes of the NTF Synthesis of both analog and digital part of the cascade CT Modulator Reduced number number of analog components Reduced number number of analog components
DT-to-CT
MethodDirect
Method
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Direct synthesis of cascade architectures (I) [Tort06]
CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
Direct synthesis of cascade architectures (I) [Tort06]
Sensitivity to mismatch (gm,C) A 2-1-1 example
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A 2-1-1 example
14
16
18
oss
(dB
)
10
12
14
10
12
SN
R L
o
6
8
1 1.5
2 2.5
0 0.20.40.60.81
8
c(%)gm(%)1
1.5
2
2.5
0 0.20.40.60.81
4
c(%)gm(%)
c
DT-to-CT synthesis method Direct synthesis method
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Direct synthesis of cascade architectures (II) [Tort06]
CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
Direct synthesis of cascade architectures (II) [Tort06]
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A case study: A 12 bit@20MHz 4 b 2 1 1 CT M for VDSL [Tort06]
CTCT-- Ms: Ms: Synthesis methodsSynthesis methods
A case study: A 12-bit@20MHz, 4-b, 2-1-1 CT M for VDSL [Tort06]ho
dth
esis
met
Dire
ct s
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General ReferencesGeneral References
[Bree01] L. Breems and J.H. Huijsing, Continuous-Time Sigma-Delta Modulation for A/D Conversion in RadioReceivers. Kluwer Academic Publishers, 2001.
[Cherr00] J.A. Cherry and W.M. Snelgrove, Continuous-Time Delta-Sigma Modulators for High-Speed A/DConversion. Kluwer Academic Publishers, 2000.
[Enge99] J V Engelen and R van de Plassche BandPass Sigma-Delta Modulators: Stability Analysis[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 andSimulation. IEEE Press, New York 1997.
[Pelu99] V. Peluso, M. Steyaert, and W. Sansen, Design of Low-Voltage Low-Power CMOS Delta-Sigma A/DConverters. 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 CascadeSigma- Delta Modulators for Sensors and Telecom: Error Analysis and Practical Design. Springer,20062006.
[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 AcademicPublishers, 2002.
[Shoa95] O. Shoaei, Continuous-Time Delta-Sigma A/D Converters for High Speed Applications. Ph.D.Dissertation, Carleton University, 1995.