EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 1EE247Lecture 24Oversampled ADCs– Why oversampling?– Pulse-count modulation– Sigma-delta modulation• 1-Bit quantization• Quantization error (noise) spectrum• SQNR analysis• Limit cycle oscillations–2ndorder ΣΔ modulator• Dynamic range • Practical implementation– Effect of various nonidealities on the ΣΔ performanceEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 2The Case for OversamplingNyquist sampling:Oversampling:• Nyquist rate fN= 2B• Oversampling rate M = fs/fN>> 1fs>2B +δFreqBSignal“narrow”transitionSamplerAA-Filter“Nyquist”ADCDSP=MFreqBSignal“wide”transitionSamplerAA-FilterOversampledADCDSPfsfsfNfs >> fN??EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 3Nyquist v.s. Oversampled ConvertersAntialiasing|X(f)|frequencyfrequencyfrequencyfBfB2fsfBfsInput SignalNyquist SamplingOversamplingfS~2fBfS>> 2fBfsAnti-aliasing FilterEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 4Oversampling Benefits• No stringent requirements imposed on analog building blocks • Takes advantage of the availability of low cost, low power digital filtering• Relaxed transition band requirements for analog anti-aliasing filters• Reduced baseband quantization noise power• Allows trading speed for resolutionEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 5ADC ConvertersBaseband Noise• For a quantizer with step size Δ and sampling rate fs:– Quantization noise power distributed uniformly across Nyquist bandwidth ( fs/2)– Power spectral density:– Noise is aliased into the Nyquist band –fs/2 to fs/222esse1N(f)f12 f⎛⎞Δ==⎜⎟⎝⎠-fBf s /2-fs/2fBNe(f)NBEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 6Oversampled ConvertersBaseband NoiseBBBBff2Beffs2BsBs2B0BB0BB0ssB1SN(f)df df12 f2f12 fwhere for f f /2S122f SSSfMfwhere M oversampling ratio2f−−⎛⎞Δ==⎜⎟⎝⎠⎛⎞Δ=⎜⎟⎜⎟⎝⎠=Δ=⎛⎞==⎜⎟⎜⎟⎝⎠==∫∫-fBf s /2-fs/2fBNe(f)NBEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 7Oversampled ConvertersBaseband Noise2X increase in MÆ 3dB reduction in SBÆ ½ bit increase in resolution/octave oversamplingBB0BB0ssB2f SSSfMfwhere M oversampling ratio2f⎛⎞==⎜⎟⎜⎟⎝⎠==To increase the improvement in resolution: Embed quantizer in a feedback loopÆPredictive (delta modulation)ÆNoise shaping (sigma delta modulation)EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 8Pulse-Count ModulationVin(kT)Nyquist ADCt/T012OversampledADC, M = 8t/T012Vin(kT)Mean of pulse-count signal approximates analog input!EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 9Pulse-Count Spectrumf Magnitude• Signal: low frequencies, f < B << fs• Quantization error: high frequency, B … fs/ 2• Separate with low-pass filter!EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 10Oversampled ADCPredictive Coding• Quantize the difference signal rather than the signal itself• Smaller input to ADC Æ Buy dynamic range• Only works if combined with oversampling• 1-Bit digital output• Digital filter computes “average” ÆN-Bit output +_vINDOUTPredictorADCEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 11Oversampled ADCDecimator:• Digital (low-pass) filter• Removes quantization error for f > B• Provides most anti-alias filtering• Narrow transition band, high-order• 1-Bit input, N-Bit output (essentially computes “average”)fs= MfNFreqBSignal“wide”transitionSamplerAnalogAA-FilterE.g.Pulse-CountModulatorDecimator“narrow”transitionfs1= M fNDSPModulatorDigitalAA-Filterfs2= fN+ δ1-Bit Digital N-BitDigitalEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 12Modulator• Objectives:– Convert analog input to 1-Bit pulse density stream– Move quantization error to high frequencies f >>B– Operates at high frequency fs>> fN• M = 8 … 256 (typical)….1024• Since modulator operated at high frequencies Æ need to keep circuitry “simple”Æ ΣΔ = ΔΣ ModulatorEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 13Sigma- Delta ModulatorsAnalog 1-Bit ΣΔ modulators convert a continuous time analog input vINinto a 1-Bit sequence dOUTH(z)+_vINdOUTLoop filter1b Quantizer (comparator)fsDACEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 14Sigma-Delta Modulators• The loop filter H can be either switched-capacitor or continuous time• Switched-capacitor filters are “easier” to implement + frequency characteristics scale with clock rate• Continuous time filters provide anti-aliasing protection• Loop filter can also be realized with passive LC’s at very high frequenciesH(z)+_vINdOUTfsDACEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 15Oversampling A/D Conversion• Analog front-end Æ oversampled noise-shaping modulator• Converts original signal to a 1-bit digital output at the high rate of (2MXB)• Digital back-end Æ digital filter• Removes out-of-band quantization noise• Provides anti-aliasing to allow re-sampling @ lower sampling rate1-bit@ fsn-bit@ fs/MInput Signal Bandwidth B=fs/2MDecimation FilterOversamplingModulatorfsfs= sampling rateM= oversampling ratiofs/MEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 161stOrder ΣΔ ModulatorIn a 1storder modulator, simplest loop filter Æ an integrator+_vINdOUT∫H(z) =z-11 – z-1DACEECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 171stOrder ΣΔ ModulatorSwitched-capacitor implementationVi-+φ1φ2φ21,0dOUT+Δ/2-Δ/2EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 181stOrder ΔΣ Modulator• Properties of the first-order modulator:– Analog input range is equal to the DAC reference– The average value of dOUTmust equal the average value of vIN– +1’s (or –1’s) density in dOUTis an inherently monotonic function of vINÆ linearity is not dependent on component matching– Alternative multi-bit DAC (and ADCs) solutions reduce the quantization error but loose this inherent monotonicity & relaxed matching requirements+_vINdOUT∫-Δ/2≤vIN≤+Δ/2DAC-Δ/2 or +Δ/2EECS 247 Lecture 24: Oversampling Data Converters © 2005 H. K. Page 191stOrder ΣΔ ModulatorInstantaneous quantization errorTally of quantization error1-Bitquantizer1-Bit digital
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