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Berkeley ELENG 247A - Lecture Notes

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EECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 1EE247Lecture 26• Administrative–EE247 Final exam: – Date: Mon. Dec. 18th– Time: 12:30pm-3:30pm– Location: 241 Cory Hall– Extra office hours: Thurs. Dec. 14th,10:30am-12pm• Closed book/course notes• No calculators/cell phones/PDAs/computers• Bring two 8x11 paper with your own notes• Final exam covers the entire course material unless specified otherwiseEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 2EE247Lecture 26• Oversampled ADCs (continued)–2ndorder ΣΔ modulator• Dynamic range• Practical implementation– Effect of various building block nonidealities on the ΣΔperformance– Higher order ΣΔ modulators• Cascaded modulators (multi-stage)• Single-loop single-quantizer modulators with multi-order filtering in the forward pathEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 3Summary of Last LectureOversampled ADCs:– Allows trading speed for resolution – No stringent requirements imposed on analog building blocks – Takes advantage of low cost, low power digital filtering– Relaxed transition band requirements for analog anti-aliasing filters– Further reduction of baseband quantization noise power by combining oversampling with clever use of feedback• By simply increasing oversampling ratio: 2X increase in sampling ratio Æ 0.5-bit increase in resolution• Embedding the quantizer in a 1storder feedback loop Æ 1.5-bit increase is resolution per 2x increase in sampling rate• Problem: Limit cycle oscillations at levels exceeding quantization noise!EECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 41stOrder ΣΔLimit Cycle OscillationIn-band spurious tone with f ~ DC input level• Problem: quantization noise becomes periodic in response to low level DC inputs & could fall within passband of interest!• Solution:¾ Use dithering (inject noise-like signal at the input ): randomizes quantization noise- Circuit thermal noise if large enoughÆ acts as dither¾ Second order loopNoise Shaping FunctionFrequencyfBfNfs /2First-Order Noise ShapingIdeal Low-passDigital FilterEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 51stOrder ΣΔ ModulatorLinearized Model Analysis()11() () 1 () Yz z Xz z Ez−−=+−LPFHPFEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 62ndOrder ΣΔ Modulator• Two integrators in series• Single quantizer (typically 1-bit)• Feedback from output to both integrators• Tones less prominent compared to 1st orderEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 72ndOrder ΣΔ ModulatorLinearized Model Analysis()()112211 1Recursive drivation: 2Using the delay operator : ( ) ( ) 1 ( ) nn n n nYX E E EzYzzXz zEz−−−−− −=+− +=+−LPFHPFEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 82ndOrder ΣΔ ModulatorIn-Band Quantization Noise() ()()22222442512sin121512jfTfsMfsMBYQzeBsSSfNTFz dffTdffMπππ−=−=Δ≅Δ≈∫∫()()()()2124412 sin / for 1sNTF z zNTF fff Mπ−=−==>>EECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 9Quantization Noise2ndOrder ΣΔ Modulator vs 1stOrder Modulator4251512YSMπΔ≈2231312YSMπΔ≈Noise Shaping FunctionFrequencyfBfs /21stOrder Noise ShapingIdeal Low-passDigital Filter2nd-Order Noise ShapingEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 102ndOrder ΣΔ Modulator Dynamic RangeM DR (2nd) DR (1st)16 49 dB 33dB32 64 dB 42dB1024 139 dB 87dB242554544peak signal power10log 10logpeak noise power1 sinusoidal input, 122151215215 1510log 10log 50log2211.1XYXYXYSDRSSSTFSMSMSDRM MDR dBππππ⎡⎤⎡⎤==⎢⎥⎢⎥⎣⎦⎣⎦Δ⎛⎞==⎜⎟⎝⎠Δ==⎡⎤⎡⎤==+⎢⎥⎢⎥⎣⎦⎣⎦=− +50logM2X increase in MÎ15dB (2.5-bit) increase in DREECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 112ndOrder ΣΔ Modulator ExampleM Æ 256=28to allow some margin so that thermal noise dominants & provides dithering & also for ease of digital filter implementation Æ Sampling rate (2x20kHz + 5kHz)M = 12MHz (quite reasonable!)•Digital audio application•Signal bandwidth 20kHz•Resolution 16-bitmin16 98 Dynamic Range11.1 50log153bit dBDR dB MM−→=− +=EECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 12Limit Cycle Tones in 1stOrder & 2ndOrder ΣΔ Modulator• Higher oversampling ratio Æ lower tones•2ndorder much lower tones compared to 1st•2Xincrease in M decreases the tones by 6dB for 1storder loop and 12dB for 2ndorder loopRef: B. P. Brandt, et al., "Second-order sigma-delta modulation for digital-audio signal acquisition," IEEE Journal of Solid-State Circuits, vol. 26, pp. 618 - 627, April 1991.R. Gray, “Spectral analysis of quantization noise in a single-loop sigma–delta modulator with dc input,” IEEE Trans. Commun., vol. 37, pp. 588–599, June 1989.6dB12dB2ndOrder ΣΔ Modulator1stOrder ΣΔ ModulatorQuantization noiseEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 13ΣΔ ImplementationPractical Design Considerations• Internal node scaling & clipping• Effect of finite opamp gain & linearity• KT/C noise• Opamp noise• Effect of comparator nonidealities• Power dissipation considerationsEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 14Switched-Capacitor Implementation 2ndOrder ΣΔNodes Scaled for Maximum Dynamic Range• Modification (gain of ½ in front of integrators) reduce & optimize required signal range at the integrator outputs ~ 1.7x input full-scale (Δ)• Note: Non-idealities associated with 2ndintegrator and quantizer when referred to the ΣΔ input is attenuated by 1stintegrator high gainÆ The only building block requiring low-noise and accuracy is the 1stintegratorRef: B.E. Boser and B.A. Wooley, “The Design of Sigma-Delta Modulation A/D Converters,”IEEE J. Solid-State Circuits, vol. 23, no. 6, pp. 1298-1308, Dec. 1988.EECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 152ndOrder ΣΔ ModulatorExample: Switched-Capacitor ImplementationINDout• Fully differential front-end• Two bottom-plate integrators• 1-bit DAC is made of switches and VrefsEECS 247 Lecture 26: Oversampling Data Converters© 2006 H. K. Page 16Switched-Capacitor Implementation 2ndOrder ΣΔPhase 1• Sample inputs on 1ststage C1, sample output of


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Berkeley ELENG 247A - Lecture Notes

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