EE247 Lecture 23 ADC figures of merit Oversampled ADCs Why oversampling Pulse count modulation Sigma delta modulation 1 Bit quantization Quantization error noise spectrum SQNR analysis Limit cycle oscillations 2nd order SD modulator Practical implementation Effect of various building block nonidealities on the SD performance EECS 247 Lecture 23 Oversampled ADCs 2010 Page 1 ADC Figures of Merit Objective Establish measure s to compare performance of various ADCs Can use FOM to combine several performance metrics to get one single number What are reasonable FOM for ADCs EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 2 ADC Figures of Merit FOM1 f s 2 ENOB This FOM suggests that adding an extra bit to an ADC is just as hard as doubling its bandwidth Is this a good assumption Ref R H Walden Analog to digital converter survey and analysis IEEE Journal on Selected Areas in Communications April 1999 EECS 247 Lecture 23 Data Converters Nyquist Rate ADC 2010 Page 3 Survey Data 1bit Octave Ref R H Walden Analog to digital converter survey and analysis IEEE Journal on Selected Areas in Communications April 1999 EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 4 ADC Figures of Merit FOM 2 Power f s 2 ENOB J conv Sometimes inverse of this metric is used In typical circuits power speed FOM2 captures this tradeoff correctly How about power vs ENOB One more bit 2x in power Ref R H Walden Analog to digital converter survey and analysis IEEE Journal on Selected Areas in Communications April 1999 EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 5 ADC Figures of Merit One more bit means 6dB SNR 4x less noise power 4x larger C Power Gm C increases 4x Even worse Flash ADC Extra bit means 2x number of comparators Each of them needs double precision Transistor area 4x Current 4x to keep same current density Net result Power increases 8x EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 6 ADC Figures of Merit FOM2 seems not entirely appropriate but somehow still standard in literature papers Tends to work because Not all power in an ADC is noise limited E g Digital power biasing circuits etc Better use FOM2 to compare ADCs with same resolution EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 7 ADC Figures of Merit FOM 3 Power Speed Compare only power of ADCs with approximately same ENOB Useful numbers 10b 9 ENOB ADCs 1 mW MSample sec Note the ISSCC 05 example 0 33mW MS sec 12b 11 ENOB ADCs 4 mW MSample sec EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 8 10 Bit ADC Power Speed Yoshioko ISSCC 05 EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 9 12 Bit ADC Power Speed Loloee ESSIRC 2002 EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 10 Performance Trend Bandwidth x Resolution Hz LSB 1 0E 12 1 0E 11 1 0E 10 2x 5 years 1 0E 09 1985 1990 EECS 247 Lecture 23 1995 2000 Pipelined ADCs and More 2005 2010 Page 11 ADC Architectures Slope type converters Successive approximation Flash Interpolating Folding Residue type ADCs Two step Flash Pipelined ADCs Time interleaved parallel converter Oversampled ADCs EECS 247 Lecture 23 Data Converters Nyquist Rate ADCs 2010 Page 12 Analog to Digital Converters Two categories Nyquist rate ADCs fsigmax 0 5xfsampling Maximum achievable signal bandwidth higher compared to oversampled type Resolution limited to max 14bits Oversampled ADCs fsigmax 0 5xfsampling Maximum possible signal bandwidth significantly lower compared to nyquist Maximum achievable resolution high 18 to 20bits EECS 247 Lecture 23 Oversampled ADCs 2010 Page 13 The Case for Oversampling Nyquist sampling fs Signal narrow transition B Freq AA Filter fs 2B d Sampler Nyquist ADC Oversampling DSP fs fN Signal B Freq wide transition fs M fN AA Filter Sampler Oversampled ADC DSP Nyquist rate fN 2B Oversampling rate M fs fN 1 EECS 247 Lecture 23 Oversampled ADCs 2010 Page 14 Nyquist v s Oversampled Converters Antialiasing Requirements X f Input Signal frequency fB Nyquist Sampling fB fs 2fs fS 2fB Anti aliasing Filter frequency Oversampling fB fs frequency fS 2fB EECS 247 Lecture 23 Oversampled ADCs 2010 Page 15 ADC Converters Baseband Noise For a quantizer with quantization step size D and sampling rate fs Quantization noise power distributed uniformly across Nyquist bandwidth fs 2 Ne f NB fs 2 fB fB f s 2 Power spectral density N e f D2 1 f s 12 f s e2 Noise is distributed over the Nyquist band fs 2 to fs 2 EECS 247 Lecture 23 Oversampled ADCs 2010 Page 16 Oversampled Converters Baseband Noise SB fB N e f df fB fB fB D2 1 df 12 f s Ne f 2 fB 12 f s D 2 NB whe re for f B f s 2 D2 fs 2 SB0 12 2f S SB SB0 B B0 f M s f whe re M s ov e rsam pling ratio 2 fB EECS 247 Lecture 23 fB fB Oversampled ADCs f s 2 2010 Page 17 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 further increase the improvement in resolution Embed quantizer in a feedback loop patented by Cutler in 1960s Noise shaping sigma delta modulation EECS 247 Lecture 23 Oversampled ADCs 2010 Page 18 Pulse Count Modulation 010 Nyquist ADC Vin 2 8FS 0 010 t Ts 1 2 1 2 t Ts 2 8 Vin 2 8FS Oversampled ADC M 8 0 Mean of pulse count signal approximates analog input EECS 247 Lecture 23 Oversampled ADCs 2010 Page 19 Pulse Count Output Spectrum Magnitude Digital filter 2 8 B fs 4 fs 2 f Signal band of interest low frequencies f B f s Quantization error high frequency B fs 2 Separate signal from Q error with digital low pass filter EECS 247 Lecture 23 Oversampled ADCs 2010 Page 20 Oversampled ADC Predictive Coding vIN Digital Filter 1 bit ADC DOUT N bit 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 Oversampled ADCs 2010 Page 21 Oversampled ADC wide transition B f f d s2 N f Mf s1 N Signal Freq Analog AA Filter f Mf s N E g Pulse Count Modulator Sampler Modulator Decimator narrow transition Digital AA Filter 1 Bit Digital DSP N Bit Digital Decimator Digital low pass filter Removes quantization noise for f B 1 Bit input fs1 MfN N Bit output fs2 fN d computes average Provides anti alias filtering for DSP Narrow transition band high order digital filters with high order consume significantly smaller power area compared to analog
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