Tones 5th order modulator A D DSP DC inputs Tones Dither kT C noise EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 1 5th Order Modulator 1 512 1 16 1 64 b1 b2 b1 1 X b2 1 10 1 k1z 1 k2z 1 k3z 1 k4z 1 1 z 1 1 z 1 1 z 1 1 z 1 I1 1 4 I2 a1 a1 1 4 I3 1 8 k5z 1 1 z 1 I4 I5 2 3 4 5 6 I 1 I 2 I 3 I 4 I 5 1 a2 a2 1 2 a3 a3 1 2 a4 a4 1 4 a5 a5 1 4 7 Q Comparator 1 1 Stable input range 0 3 0 3 1 Y see L20 L5 sim mdl and L20 L5 m A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 2 Output Spectrum dBWN Int Noise dBV 5th Order Noise Shaping 50 Tones at fs 2 Nfin exceed input Input 0 1V sinusoid 215 point DFT 30 averages 0 50 100 Output Spectrum Integrated Noise 30 averages 150 0 A D DSP 5 10 Frequency Hz 15 5 x 10 EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 3 Output Spectrum dBWN Int Noise dBV In Band Noise A D DSP 50 Output Spectrum Integrated Noise 30 averages 0 50 100 In Band quantization noise 120dB 150 0 1 2 3 Frequency Hz EECS 247 Lecture 21 Oversampled ADC Implementation 4 5 4 x 10 2002 B Boser 4 Output Spectrum dBWN Int Noise dBV 5th Order Noise Shaping 50 Input 0 1V sinusoid 215 point DFT 30 averages 0 50 150dB stopband attenuation needed to attenuate unwanted fs 2 Nfin components down to the in band quantization noise level 100 Output Spectrum Integrated Noise 30 averages 150 A D DSP 0 5 10 Frequency Hz EECS 247 Lecture 21 Oversampled ADC Implementation 15 5 x 10 2002 B Boser 5 Out of Band vs In Band Signals A digital low pass filter with suitable coefficient precision can eliminate out of band quantization noise No filter can attenuate unwanted in band components without attenuating the signal We ll spend some time making sure the components at fs 2 Nfin will not mix down to the signal band But first let s look at the modulator response to small DC inputs or offset A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 6 Output Spectrum dBWN Int Noise dBV Tones 50 Output Spectrum Integrated Noise 30 averages 2mV DC input 1V full scale 0 Simulation technique A random 1st input randomizes the noise and enables averaging Without the small tones are not visible 50 6kHz 12kHz 100 150 A D DSP 0 1 2 3 Frequency Hz 4 5 4 x 10 EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 7 Limit Cycles Representing a DC term with a 1 1 pattern e g 1 1 1 1 1 1 1 1 1 1 1 1 123 123 123 123 123 11 1 2 3 4 5 14 4444 4442 4444 4444 3 0 1444444444 24444444443 1 11 Spectrum fs f f 2 s 3 s K 11 11 11 A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 8 Limit Cycles Fundamental f f s VDC VDAC 3MHz 2mV 1V 6kHz Tone velocity df f s dVDC VDAC 3kHz V A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 9 Output Spectrum dBWN Int Noise dBV Tones A D DSP 6kHz 50 0 50 100 Output Spectrum Integrated Noise 30 averages 150 1 47 1 475 1 48 1 485 1 49 Frequency Hz EECS 247 Lecture 21 Oversampled ADC Implementation 1 495 1 5 6 x 10 2002 B Boser 10 Tones Tones follow the noise shape The fundamental of a tone that falls into a quantization noise null disappears VDC VFB f fs 10 5kHz 3MHz 3 5mV 1V A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 11 Output Spectrum dBWN Int Noise dBV Tones A D DSP 50 Output Spectrum Integrated Noise 30 averages 3 5mV DC input 0 50 100 150 0 1 2 3 Frequency Hz 4 5 4 x 10 EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 12 Tones In band tones look like signals Can be a big problems in some applications E g audio even tones with power below the quantization noise floor can be audible Tones near fs 2 can be aliased down into the signal band Since they are often strong even a small alias can be a big problem We will look at mechanisms that alias tones in the next lecture First let s look at dither as a means to reduce or eliminate inband tones A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 13 Dither DC inputs can of course be represented by many possible bit patterns Including some that are random but still average to the DC input The spectrum of such a sequence has no tones How can we get a SD modulator to produce such randomized sequences A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 14 Dither The target DR for our audio SD is 16 Bits or 98dB Let s choose the sampling capacitor such that it limits the dynamic range DR 1 2 VFS 2 k BT C k T C DR 1 B 2 2 VFS 109 8 A D DSP 1 2 k BT 50 5pF 1V 2 vn2 EECS 247 Lecture 21 Oversampled ADC Implementation k BT 9 V C 2002 B Boser 15 Dither 50 2mV DC input Output Spectrum dBWN No dither With dither 0 50 100 150 A D DSP 0 1 2 3 Frequency Hz 4 5 4 x 10 EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 16 Dither Output Spectrum dBWN 50 Dither at an amplitude which buries the inband tones has virtually no effect on tones near fs 2 0 50 100 No dither With dither 150 1 47 A D DSP 1 475 1 48 1 485 1 49 Frequency Hz 1 495 1 5 6 x 10 EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 17 kT C Noise So far we ve looked at noise added to the input of the SD modulator which is also the input of the first integrator Now let s add noise also to the input of the second integrator Let s assume a 4pF sampling capacitor This gives 1 4 x 32 V rms noise two uncorrelated 32 V samples per clock A D DSP EECS 247 Lecture 21 Oversampled ADC Implementation 2002 B Boser 18 Output Spectrum dBWN Int Noise dBV kT C Noise 50 2mV DC input No noise 1st Integrator 2nd Integrator 0 Noise from 2nd integrator smaller than 1st integrator noise shaped 50 Why 100 150 A D DSP 0 1 2 3 Frequency Hz 4 5 4 x 10 EECS 247 Lecture …
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