EE247 Lecture 24 Oversampled ADCs Why oversampling Pulse count modulation Sigma delta modulation 1 Bit quantization Quantization error noise spectrum SQNR analysis Limit cycle oscillations 2nd order modulator Dynamic range Practical implementation Effect of various nonidealities on the performance EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 1 The Case for Oversampling Nyquist sampling fs Signal narrow transition B Freq AA Filter fs 2B Sampler Nyquist ADC Oversampling fs fN Signal B Freq DSP wide transition fs M fN AA Filter Sampler Oversampled ADC DSP Nyquist rate fN 2B Oversampling rate M fs fN 1 EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 2 Nyquist v s Oversampled Converters Antialiasing X f Input Signal frequency fB Nyquist Sampling fB fs fS 2fB Anti aliasing Filter 2fs frequency Oversampling fB fS 2fB EECS 247 Lecture 24 Oversampling Data Converters fs frequency 2005 H K Page 3 Oversampling 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 resolution EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 4 ADC Converters Baseband Noise For a quantizer with step size and sampling rate fs Quantization noise power distributed uniformly across Nyquist bandwidth fs 2 Ne f NB fB fs 2 f s 2 fB Power spectral density N e f 2 1 fs 1 2 fs e2 Noise is aliased into the Nyquist band fs 2 to fs 2 EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 5 Oversampled Converters Baseband Noise fB SB f fB N e f d f B f B 2 1 df 1 2 fs Ne f 2 fB 12 f s 2 wh e re for f B f s 2 2 fs 2 SB0 12 2f S SB SB0 B B0 f M s f whe re M s ov e rsampling ratio 2 fB NB fB EECS 247 Lecture 24 Oversampling Data Converters fB f s 2 2005 H K Page 6 Oversampled Converters Baseband Noise 2f S SB SB0 B B0 f M s f whe re M s ov e rsampling ratio 2 fB 2X increase in M 3dB reduction in SB bit increase in resolution octave oversampling To increase the improvement in resolution Embed quantizer in a feedback loop Predictive delta modulation Noise shaping sigma delta modulation EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 7 Pulse Count Modulation Vin kT Vin kT Nyquist ADC 0 1 2 0 1 2 t T Oversampled ADC M 8 t T Mean of pulse count signal approximates analog input EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 8 Pulse Count Spectrum Magnitude f 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 9 Oversampled ADC Predictive Coding vIN ADC DOUT Predictor Quantize the difference signal rather than the signal itself Smaller input to ADC Buy dynamic range Only works if combined with oversampling 1 Bit digital output Digital filter computes average N Bit output EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 10 Oversampled ADC f Mf s1 N Signal wide transition B Freq Analog AA Filter f Mf s N E g Pulse Count Modulator Sampler Modulator Decimator narrow transition Digital AA Filter 1 Bit Digital f f s2 N DSP N Bit Digital Decimator 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 EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 11 Modulator 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 need to keep circuitry simple Modulator EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 12 Sigma Delta Modulators Analog 1 Bit modulators convert a continuous time analog input vIN into a 1 Bit sequence dOUT fs vIN H z dOUT DAC 1b Quantizer comparator Loop filter EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 13 Sigma 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 frequencies fs vIN H z dOUT DAC EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 14 Oversampling A D Conversion fs Input Signal Bandwidth B fs 2M Oversampling 1 bit Modulator fs fs M Decimation n bit Filter fs M fs sampling rate M oversampling ratio Analog front end oversampled noise shaping modulator Converts original signal to a 1 bit digital output at the high rate of 2MXB Digital back end digital filter Removes out of band quantization noise Provides anti aliasing to allow re sampling lower sampling rate EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 15 1st Order Modulator In a 1st order modulator simplest loop filter an integrator H z vIN z 1 1 z 1 dOUT DAC EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 16 1st Order Modulator Switched capacitor implementation 1 2 2 dOUT 1 0 Vi 2 2 EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 17 1st Order Modulator vIN 2 vIN 2 2 or 2 dOUT DAC Properties of the first order modulator Analog input range is equal to the DAC reference The average value of dOUT must equal the average value of vIN 1 s or 1 s density in dOUT is an inherently monotonic function of vIN 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 EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 18 1st Order Modulator Tally of quantization error Analog input 2 Vin 2 1 X 1 Bit quantizer 2 Q 3 Y z 1 1 1 z Sine Wave Integrator Comparator Instantaneous quantization error 1 Bit digital output stream 1 1 Implicit 1 Bit DAC 2 2 2 M chosen to be 8 low to ease observability EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 19 1st Order Modulator Signals 1st Order Sigma Delta X Q Y 1 5 Amplitude 1 0 5 X analog input Q tally of q error Y digital DAC output Mean of Y approximates X 0 0 5 T 1 fs 1 M fN 1 1 5 0 10 20 30 40 50 60 Time t T EECS 247 Lecture 24 Oversampling Data Converters 2005 H K Page 20 Modulator Characteristics Quantization noise and
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