EECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 1EE247Lecture 24• Interleaved ADCs• Oversampled ADCs– Why oversampling?– Pulse-count modulation– Sigma-delta modulation• 1-Bit quantization• Quantization error (noise) spectrum• SQNR analysis• Limit cycle oscillationsEECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 2Summary Last LecturePipelined ADCs (continued)– Effect gain stage, sub-DAC non-idealities on overall ADC performance• Digital calibration (continued)• Correction for inter-stage gain nonlinearity– Implementation • Practical circuits• Combining the digital bits• Stage implementation–Circuits–Noise budgetingEECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 3Time Interleaved Converters•Example: – 4 ADCs operating in parallel at sampling frequency fs– Each ADC converts on one of the 4 possible clock phases– Overall sampling frequency= 4fs– Note T/H has to operate at 4fs!• Extremely fast:Typically, limited by speed of T/H• Accuracy limited by mismatch among individual ADCs (timing, offset, gain, …)T/H4fsADCfsADCADCADCOutput Combiner VINDigital Outputfs+Ts/4fs+2Ts/4fs+3Ts/4EECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 4Oversampled ADCsEECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 5Analog-to-Digital Converters• Two categories:– Nyquist rate ADCs Æ fsigmax~ 0.5xfsampling• Maximum achievable signal bandwidth higher compared to oversampled type• Resolution limited to max. 12-14bits– Oversampled ADCs Æ fsigmax<< 0.5xfsampling• Maximum possible signal bandwidth lower compared to nyquist• Maximum achievable resolution high (18 to 20bits!)EECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 6The 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 Oversampled ADCs © 2008 H.K. Page 7Nyquist v.s. Oversampled ConvertersAntialiasing|X(f)|frequencyfrequencyfrequencyfBfB2fsfBfsInput SignalNyquist SamplingOversamplingfS ~2fBfS >> 2fBfsAnti-aliasing FilterEECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 8Oversampling 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 Oversampled ADCs © 2008 H.K. Page 9ADC 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 distributed over the Nyquist band –fs /2 to fs /222esse1N(f)f12 f⎛⎞Δ==⎜⎟⎝⎠-fBf s /2-fs /2fBNe(f)NBEECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 10Oversampled 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 Oversampled ADCs © 2008 H.K. Page 11Oversampled 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 loopÆNoise shaping (sigma delta modulation)EECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 12Pulse-Count ModulationVin(kT)Nyquist ADCt/T012OversampledADC, M = 8t/T012Vin(kT)Mean of pulse-count signal approximates analog input!EECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 13Pulse-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 Oversampled ADCs © 2008 H.K. Page 14Oversampled 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 +_vINDOUTPredictorADCDigitalFilterN-bit1-bitEECS 247 Lecture 24 Oversampled ADCs © 2008 H.K. Page 15Oversampled ADCDecimator:• Digital (low-pass) filter• Removes quantization error for f > B• Provides anti-alias filtering for DSP• 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 Oversampled ADCs © 2008 H.K. Page 16Modulator (AFE)• 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 Oversampled ADCs © 2008 H.K. Page 17Sigma- 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 Oversampled ADCs © 2008 H.K. Page 18Sigma-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
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