EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 1A/DDSPTones• 5thorder Σ∆ modulator– DC inputs– Tones– Dither– kT/C noiseEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 2A/DDSP5thOrder Modulator7Q6I_55I_44I_33I_22I_11Yb2b2b1b1a5a5a4a4a3a3a2a2a1a1k5z -11-z -1I5k4z -11-z -1I4k3z -11-z -1I3k2z -11-z -1I2k1z -11-z -1I1Comparator1Xsee L20_L5_sim.mdl and L20_L5.m+1 / -1Stable input range ~ -0.3 … +0.31/10 1 1/4 1/4 1/81/512 1/16-1/641 1/2 1/2 1/4 1/4EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 3A/DDSP5thOrder Noise ShapingInput: 0.1V, sinusoid215point DFT30 averages0 5 10 15x 105-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]Output SpectrumIntegrated Noise (30 averages)Tones at fs/2-Nfinexceed inputEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 4A/DDSPIn-Band Noise0 1 2 3 4 5x 104-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]Output SpectrumIntegrated Noise (30 averages)In-Band quantization noise:–120dB !EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 5A/DDSP5thOrder Noise ShapingInput: 0.1V, sinusoid215point DFT30 averages0 5 10 15x 105-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]Output SpectrumIntegrated Noise (30 averages)150dB stopband attenuation neededto attenuate unwanted fs/2-Nfincomponentsdown to the in-band quantization noise levelEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 6A/DDSPOut-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-Nfinwill not “mix” down to the signal band• But first, let’s look at the modulator response to small DC inputs (or offset) …EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 7A/DDSPΣ∆ Tones2mV DC input(1V full-scale)Simulation technique:A random 1stinput randomizes the noise and enables averaging. Without the small tones are not visible.0 1 2 3 4 5x 104-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]Output SpectrumIntegrated Noise (30 averages)6kHz12kHzEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 8A/DDSPLimit Cycles• Representing a DC term with a –1/+1 pattern … e.g.• Spectrum++−+−+−+−+−→444444444 3444444444 2144444444 344444444 213213213213213211110543211 1 1 1 1 1 1 1 1 1 1111K11311211sssfffEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 9A/DDSPLimit Cycles• Fundamental• Tone velocitykHz61V2mVMHz3===DACDCsVVffδkHz/V3==DACsDCVfdVdfδEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 10A/DDSPΣ∆ Tones1.47 1.475 1.48 1.485 1.49 1.495 1.5x 106-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]Output SpectrumIntegrated Noise (30 averages)6kHzEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 11A/DDSPΣ∆ Tones• Tones follow the noise shape• The fundamental of a tone that falls into a “quantization noise null” disappears …mV5.3MHz3kHz5.10V1===sFBDCffVVδEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 12A/DDSPΣ∆ Tones0 1 2 3 4 5x 104-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]Output SpectrumIntegrated Noise (30 averages)3.5mV DC inputEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 13A/DDSPΣ∆ Tones• In-band tones look like signals• Can be a big problems in some applications– E.g. audio à 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 in-band tonesEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 14A/DDSPDither• 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?EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 15A/DDSPDither• 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:()( )( )µV9 pF5.50V11022218.9221221==→====CTkvTkVTkDRCCTkVDRBnBFSBBFSEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 16A/DDSPDither0 1 2 3 4 5x 104-150-100-50050Frequency [Hz]Output Spectrum [dBWN]No ditherWith dither2mV DC inputEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 17A/DDSPDither1.47 1.475 1.48 1.485 1.49 1.495 1.5x 106-150-100-50050Frequency [Hz]Output Spectrum [dBWN]No ditherWith ditherDither at an amplitude which buries the in-band tones has virtually no effect on tones near fs/2EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 18A/DDSPkT/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 32µV rms noise(two uncorrelated 32µV samples per clock)EECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 19A/DDSPkT/C Noise• 2mV DC input • Noise from 2ndintegrator • smaller than 1stintegrator noise• shaped• Why?0 1 2 3 4 5x 104-150-100-50050Frequency [Hz]Output Spectrum [dBWN] / Int. Noise [dBV]No noise1st Integrator2nd IntegratorEECS 247 Lecture 21: Oversampled ADC Implementation © 2002 B. Boser 20A/DDSPkT/C Noise• Noise from 1stintegrator is added directly to the input• Noise from 2ndintegrator is first-order noise shaped• Noise from subsequent integrators is attenuated even furtherà Especially for high oversampling ratios, only the first 1 or 2 integrators add significant thermal noise. This is true also for other imperfections.7Q6I_55I_44I_33I_22I_11Yb2b2b1b1a5a5a4a4a3a3a2a2a1a1k5z -11-z -1I5k4z -11-z -1I4k3z -11-z -1I3k2z -11-z
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