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Berkeley ELENG 247A - Lecture 28

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EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 1EE247Lecture 28• Administrative– Extra office hours next week @ 563 Cory:Wed. Dec. 12th,2pm-4pmThurs. Dec. 13th,10am-12pm– Project submission: • Deadline extended: Thurs. Dec. 13th or Frid. Dec. 14th• If you have chosen to do the project, please make an appointment with the instructor for 15mins per each project report to present the results:Thurs. Dec. 13th,after 1pm or Frid. Dec.14thafter 10amEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 2EE247Lecture 28• Higher order ΣΔ modulators– Cascaded ΣΔ modulators (MASH) (last lecture)– Forward path multi-order filter (continued)• Bandpass ΣΔ modulators • Testing of ΣΔ modulator front-end• Acknowledgements• Examples of systems utilizing analog-digital interface circuitry (not part of final exam)EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 3Higher Order ΣΔ Modulators(2) Multi-Order Filter• Zeros of NTF (poles of H(z)) can be strategically positioned to suppress in-band noise spectrum• Approach:Design NTF first and solve for H(z)() 1() () ()1() 1()HzYz Xz EzHz Hz=+++ΣE(z)X(z)Y(z)()HzΣY( z) 1NTF E(z) 1 H(z)==+EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 4Example: Modulator Specification• Example: Audio ADC– Dynamic range DR 18 Bits– Signal bandwidth B 20 kHz– Nyquist frequency fN44.1 kHz– Modulator order L 5– Oversampling ratio M = fs/fN64– Sampling frequency fs2.822 MHz• The order L and oversampling ratio M are chosen based on– SQNR > 120dBEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 5Noise Transfer Function, NTF(z)% stop-band attenuation Rstop=80dB, L=5 ... L=5; Rstop = 80;B=20000; [b,a] = cheby2(L, Rstop, B, 'high');% normalize b = b/b(1); NTF = filt(b, a, ...);104106-100-80-60-40-20020Frequency [Hz]NTF [dB]Chebychev 2 filter chosenÆ zeros in stop-bandEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 6Loop-Filter CharacteristicsH(z)() 1NTF() 1 ()1() 1YzEz HzHzNFT==+→=−104106-20020406080100Frequency [Hz]Loopfilter H [dB]EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 7Modulator TopologySimulation ModelQI_5I_4I_3I_2I_1Yb2b1a5a4a3a2a1K1 z -11 - z -1I1gDAC GainComparatorX-11 - z -1I2K2 z -11 - z -1I3K3 z -11 - z -1I4K4 z -11 - z -1I5K5 z +1-1FilterEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 8-40 -35 -30 -25 -20 -15 -10 -5 0-20-15-10-50510i1i2i3i4i5q Input [dBV]Loop filter peak voltages [V]Internal Node Voltages• Internal signal peak amplitudes are weak function of input level (except near overload)• Maximum peak-to-peak voltage swing approach +-10V! Exceed supply voltage!• Solutions:• Reduce Vref??• Node scalingIntegrator outputsQuantizer inputEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 9Node Scaling Example:3rdIntegrator Output Voltage Scaled by αK3 * α, b1 /α, a3 / α, K4 / α, b2 * αVnew=Vold* αQI_5I_4I_3I_2I_1Yb2b1a5a4a3a2a1K1 z -11 - z -1I1gDAC GainComparatorX-11 - z -1I2K2 z -11 - z -1I3K3 z -11 - z -1I4K4 z-11 - z -1I5K5 z EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 10Node Voltage Scaling-40 -35 -30 -25 -20 -15 -10 -5 0-1.5-1-0.500.511.5In put [dBV]Loop fi lter peak voltages [V]α=1/10Æk1=1/10;k2=1;k3=1/4;k4=1/4;k5=1/8;a1= 1; a2=1/2;a3=1/2; a4=1/4;a5=1/4;b1=1/512;b2=1/16-1/64;g =1;• Integrator output range reasonable for new parameters• But: maximum input signal limited to -5dB (-7dB with safety) – fix?EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 11Input Range ScalingIncreasing the DAC levels by using higher value for g reduces the analog to digital conversion gain:Increasing VIN& g by the same factor leaves 1-Bit data unchangedgzgHzHzVzDINOUT1)(1)()()(≅+=Loop FilterH(z)ΣVINDOUT+1 or -1ComparatorgEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 12Scaled Stage 1 Modelg modified:From 1 to 2.5;ÆOverload input level shifted up by 8dB-40 -35 -30 -25 -20 -15 -10 -5 0-1.5-1-0.500.511.5Input [dBV]Loop filter peak voltages [V]+2dBEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 13Stability Analysis(not included in final exam)• Approach: linearize quantizer and use linear system theory!• One way of performing stability analysisÆ use RLocus in Matlab with H(z) as argument and Geff as variable• Effective quantizer gain• Can obtain Gefffrom simulation222yGeffq=H(z)ΣΣQuantizer Modele(kT)x(kT)y(kT)Geffq(kT)Ref: R. W. Adams and R. Schreier, “Stability Theory for ΔΣ Modulators,” in Delta-Sigma Data Converters- S. Norsworthy et al. (eds), IEEE Press, 1997EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 14Stability Analysis• Zeros of STF same as zeros of H(z)• Poles of STF vary with G• For G=0 (no feedback) poles of the STF same as poles of H(z)• For G=large, poles of STF move towards zeros of H(z)• Draw root-locus: for G values for which poles move to LHP (s-plane) or inside unit circle (z-plane) Æ system is stable()()()()()()() ()1GHzSTFGHzNzHzDzGNzSTFDz GNz⋅=+⋅=⋅→=+⋅EECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 15Modulator z-Plane Root-Locus•As Geffincreases, poles of STF move from • poles of H(z) (Geff= 0) to • zeros of H(z) (Geff= ∞)• Pole-locations inside unit-circle correspond to stable STF and NTF• Need Geff> 0.45 for stabilityGeff = 0.45z-Plane Root Locus0.6 0.7 0.8 0.9 1 1.1-0.4-0.3-0.2-0.100.10.20.30.4Increasing GeffUnit CircleEECS 247 Lecture 28: Oversampled ADCs Cont'd & Final Remarks © 2007 H. K. Page 16-40 -35 -30 -25 -20 -15 -10 -5 0 500.20.40.60.8Input [dBV]Effective Quantizer GainGeff=0.45stable unstable• Large inputs Æ comparator input grows• Output is fixed (±1)Æ GeffdropsÆ modulator unstable for large inputs• Solution:• Limit input amplitude• Detect instability


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Berkeley ELENG 247A - Lecture 28

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