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Berkeley ELENG 247A - Lecture Notes

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EE247 Lecture 23 Oversampled ADCs 1 Bit quantization Quantization error spectrum SQNR analysis Limit cycle oscillations 2nd order modulator Dynamic range Practical implementation Effect of various nonidealities on the performance EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 1 Oversampled ADCs Last Lecture Why Oversampling Allows trading speed for resolution Relaxed transition band requirements for analog antialiasing filters Reduced baseband quantization noise power Utilizes low cost low power digital filtering Issue of limit cycle oscillation spurious inband tones By simply increasing oversampling ratio 2X increase in sampling ratio 0 5 bit increase in resolution To achieve greater improvement in resolution Embed quantizer in a feedback loop Predictive delta modulation Noise shaping sigma delta modulation EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 2 Oversampling A D Conversion Signal BW fs 2M 1 bit fs n bit fs M Analog front end oversampled noise shaping modulator Converts original signal to a 1 bit digital output at the high rate of 2MX fsignal Digital back end digital filter Removes out of band quantization noise Provides anti aliasing to allow re sampling lower sampling rate EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 3 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 23 Oversampling Data Converters 2004 H K Page 4 Oversampled ADC f Mf s1 N Signal wide transition Freq B 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 23 Oversampling Data Converters 2004 H K Page 5 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 Better be simple Modulator EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 6 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 a comparator Loop filter EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 7 Sigma Delta Modulators The loop filter H can be either a switched capacitor or continuous time Switched capacitor filters are easier to implement and scale with the clock rate Continuous time filters provide anti aliasing protection Can be realized with passive LC s at very high frequencies fs vIN H z dOUT DAC EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 8 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 23 Oversampling Data Converters 2004 H K Page 9 1st Order Modulator Switched capacitor implementation 1 2 2 Vi dOUT 1 0 2 2 EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 10 1st Order Modulator vIN 2 vIN 2 dOUT 2 or 2 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 EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 11 1st Order Modulator Tally of quantization error Analog input 2 Vin 2 1 Bit quantizer 1 2 3 X Q Y z 1 1 z 1 Sine Wave Integrator Comparator Instantaneous quantization error EECS 247 Lecture 23 Oversampling Data Converters 1 Bit digital output stream 1 1 Implicit 1 Bit DAC 2 2 2 2004 H K Page 12 1st Order Modulator Signals 1st Order Sigma Delta X Q Y 1 5 X analog input Q tally of q error Y digital DAC output Amplitude 1 0 5 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 23 Oversampling Data Converters 2004 H K Page 13 Modulator Characteristics Quantization noise and thermal noise KT C distributed over fs 2 to fs 2 Total noise reduced by 1 M Very high SQNR achievable 20 Bits Inherently linear for 1 Bit DAC Quantization error independent of component matching Limited to moderate to low speed EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 14 Output Spectrum First order sigma delta A 0 79 fx 0 0628319 offset 0 020944 N 1024 K 30 30 Definitely not white Input 20 Skewed towards higher frequencies Amplitude dBWN 10 Tones 0 10 20 dBWN dB White Noise scale sets the 0dB line at the noise per bin of a random 1 1 sequence 30 40 50 0 0 1 0 2 0 3 Frequency f f s 0 4 0 5 sigma delta L1 sin m EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 15 Quantization Noise Analysis Integrator x kT H z z 1 1 z 1 Quantization Error e kT y kT Quantizer Model Sigma Delta modulators are nonlinear systems with memory very difficult to analyze directly Representing the quantizer as an additive noise source linearizes the system EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 16 Signal Transfer Function z 1 H z x kT 1 1 z H j 0 j H Sig j 1 1 s Integrator H z y kT Magnitude Signal transfer function low pass function 0 Y z H z H Sig z z 1 X z 1 H z f0 Delay EECS 247 Lecture 23 Oversampling Data Converters Frequency 2004 H K Page 17 Noise Transfer Function Qualitative Analysis vn2 vi vi 0 j vn2 f f0 2 veq vn2 f f0 vi vo 2 veq 2 veq vn2 f f0 2 0 j vo f0 2 0 j Frequency vo EECS 247 Lecture 23 Oversampling Data Converters 2004 H K Page 18 STF and NTF Quantization Error e kT Integrator x kT H z z 1 1 z 1 y kT Quantizer Model Signal transfer function Y z H z STF z 1 X z 1 H z Delay Noise transfer function NTF Y z 1 1 z 1 E z 1 H z EECS 247 Lecture 23 Oversampling Data Converters Differentiator 2004 H K Page 19 Noise Transfer Function NTF 1 Y z 1 z 1 E z 1 H z e j T 2 e j T 2 NTF j 1 e j T 2e j T 2 2 2e j T 2 j sin T 2 2e j T 2 …


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Berkeley ELENG 247A - Lecture Notes

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