EECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 1EE247Lecture 26• This lecture is taped on Wed. Nov. 28thdue to conflict of regular class hours with a meeting• Any questions regarding this lecture could be discussed during regular office hours or in class at the next lecture• Please hand in your homework #8 solution to Yida Duan, otherwise bring it to H.K.’s office hour • Regular office hours held today, Nov. 29th., 2:30 to 3:30pm, @ 563 Cory HallEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 2EE247Lecture 26• Oversampled ADCs 1storder ΣΔ modulator (continued)• In-band quantization noise analysis & dynamic range• Issue: DC input results in periodic tones Æ limit cycle oscillations–2ndorder ΣΔ modulator• Dynamic range• Practical implementation– Effect of various building block nonidealities on the ΣΔperformance–ExampleEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 3Summary of Last LectureOversampled ADCs:–Reduction of baseband quantization noise power by combining oversampling with clever use of feedback around the quantizer–Allows trading speed for resolution –No stringent requirements imposed on analog building blocks (more today) –Takes advantage of low cost, low power digital filtering available in fine-line CMOS technologyEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 41stOrderSigma- Delta ModulatorsAnalog 1-Bit ΣΔ modulators convert a continuous time analog input vINinto a 1-Bit digital sequence DOUTH(z)+_VINDOUTLoop filter1b Quantizer (comparator)fsDACEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 51stOrder ΣΔ Modulator1storder modulator, simplest loop filter Æ an integrator+_VINDOUT∫H(z) =z-11 – z-1DACNote: Non-linear system with memory Æ difficult toanalyzeEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 61stOrder ΣΔ ModulatorSTF and NTFSignal transfer function:1() ()STF Delay() 1 ()Yz HzzXz Hz−== = ⇒+Noise transfer function:erentiator Diff 1)(11)()(NTF1⇒−=+==−zzHzEzYIntegratorΣQuantizerModelQuantizationError e(kT)x(kT)y(kT)11H( )1zzz−−=−ΣEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 7Noise Transfer Function()()()()()1/2 /2/2/2/2 /2/2()11 set() 1 ()()(1 )=222sin/22sin/22sin /2where 1/Thus: ()=2sin /2=2sin /jTjT jTjT jTjTjT jjTsYzNTF z z eEz HzeeNTF j e eejTee TTeTfNTF f T fωωωωωωωπωπωωωωωπ−−−−−−−−−⎛⎞⎜⎟⎜⎟⎝⎠⎡⎤⎣⎦⎡⎤⎣⎦== =− =+−=−==×==()2 () () ()syefNf NTFf Nf=EECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 8First Order ΣΔ ModulatorNoise Transfer CharacteristicsNoise Shaping FunctionfrequencyfBfNfs /2First-Order Noise ShapingLow-passDigital FilterKey Point:Most of quantization noise pushed out of frequency band of interest()22() () ()4sin / ( )yeseNf NTFf NfffNfπ=⋅=⋅EECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 9Quantizer Error• For quantizers with many bits• Let’s use the same expression for the 1-Bit case• Use simulation to verify validity • Experience: Often sufficiently accurate to be useful, with enough exceptions to be careful()1222Δ=kTeEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 10First Order ΣΔ ModulatorSimulated Noise Transfer Characteristic0 0.1 0.2 0.3 0.4 0.5-40-30-20-1001020Frequency [f /fs] Amplitude [ dBWN ]Simulated output spectrumComputed NTFSignal()2() 4sin /ysNf ffπ=• Confirms assumption of quantization noise being white at insertion point• Linearized model seems to be accurateEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 11First Order ΣΔ ModulatorIn-Band Quantization Noise()() ()()()()2221222222231sin / 112sin121312jfTfsMfsMsBYQzeBsQNTF z zNTF f 4 f f for MSSfNTFz dffTdffSMππππ−−=−=−=>>=Δ≅Δ→≈∫∫Total in-band quantization noiseEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 121stOrder ΣΔDynamic RangeM DR16 33 dB32 42 dB1024 87 dB2X increase in MÎ9dB (1.5-Bit) increase in dynamic range222332322full-scale signal power10log 10loginband noise power1 sinusoidal input, 1221312929910log 10log 30log22XQXQXQSDRSSSTFSMSMSDR M MDRππππ⎡⎤⎡⎤==⎢⎥⎢⎥⎣⎦⎢⎥⎣⎦Δ⎛⎞==⎜⎟⎝⎠Δ==⎡⎤⎡⎤==+⎢⎥⎢⎥⎣⎦⎣⎦=−3.4 30logdB M+EECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 13Oversampling and Noise Shaping• ΣΔ modulators have interesting characteristics– Unity gain for input signal VIN– Significant attenuation of in-band quantization noise injected at quantizer input– Performance significantly better than 1-Bit noise performance possible for frequencies << fs• Increase in oversampling (M = fs/fN>> 1) improves SQNR considerably–1storder ΣΔ: DR increases 9dB for each doubling of M– To first order, SQNR independent of circuit complexity and accuracy• Analysis assumes that the quantizer noise is “white”– Not entirely true in practice, especially for low-order modulators– Practical modulators suffer from other noise sources also (e.g. thermal noise)EECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 141stOrder ΣΔ ModulatorResponse to DC Input3Y2Q1XDC Input=1/11 FSz -11-z -1IntegratorComparator• Matlab & Simulink model from Lecture 25 used• Input Æ DC at 1/11 full-scale levelEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 151stOrder ΣΔResponse to DC Input• DC input A = 1/11• Output spectrum shows DC component plus distinct tones!!• Tones frequency shaped the same as quantization noiseÆ More prominent at higher frequenciesÆ Seems like periodic quantization “noise”0 0.1 0.2 0.3 0.4 0.5-40-20020Frequency [ f /fs ]Amplitude [ dBWN ]DC ComponentEECS 247 Lecture 26: Oversampling Data Converters© 2007 H. K. Page 16Limit Cycle Oscillation-111+110-19+18-17+16-15+14-13+12+11DC input 1/11 ÆPeriodic sequence:0 10 20 30 40 50-0.4-0.200.20.4Time [t/T]OutputFirst order
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