EE247 Lecture 26 This lecture is taped on Wed Nov 28th due 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 Hall EECS 247 Lecture 26 Oversampling Data Converters 2007 H K Page 1 EE247 Lecture 26 Oversampled ADCs 1st order modulator continued In band quantization noise analysis dynamic range Issue DC input results in periodic tones limit cycle oscillations 2nd order modulator Dynamic range Practical implementation Effect of various building block nonidealities on the performance Example EECS 247 Lecture 26 Oversampling Data Converters 2007 H K Page 2 Summary of Last Lecture Oversampled 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 technology EECS 247 Lecture 26 2007 H K Page 3 Oversampling Data Converters 1st Order Sigma Delta Modulators Analog 1 Bit modulators convert a continuous time analog input vIN into a 1 Bit digital sequence DOUT fs VIN H z DOUT DAC Loop filter EECS 247 Lecture 26 1b Quantizer comparator Oversampling Data Converters 2007 H K Page 4 1st Order Modulator 1st order modulator simplest loop filter an integrator z 1 H z 1 z 1 VIN DOUT DAC Note Non linear system with memory difficult to analyze EECS 247 Lecture 26 2007 H K Page 5 Oversampling Data Converters 1st Order Modulator STF and NTF Integrator H z x kT Quantization Error e kT z 1 1 z 1 Signal transfer function Y z H z STF z 1 X z 1 H z y kT Quantizer Model Delay Noise transfer function NTF EECS 247 Lecture 26 Y z 1 1 z 1 E z 1 H z Oversampling Data Converters Differentiator 2007 H K Page 6 Noise Transfer Function NTF Y z 1 1 z 1 E z 1 H z set z e j T e j T 2 e j T 2 2 NTF j 1 e j T 2e j T 2 2e j T 2 j sin T 2 2e j T 2 e j 2 sin T 2 2sin T 2 e j T 2 where T 1 f s Thus NTF f 2 sin T 2 2 sin f f s 2 N y f NTF f Ne f EECS 247 Lecture 26 2007 H K Page 7 Oversampling Data Converters First Order Modulator Noise Transfer Characteristics Noise Shaping Function 2 N y f NTF f N e f Low pass Digital Filter 2 4 sin f f s N e f First Order Noise Shaping frequency fB fN fs 2 Key Point Most of quantization noise pushed out of frequency band of interest EECS 247 Lecture 26 Oversampling Data Converters 2007 H K Page 8 Quantizer Error For quantizers with many bits e2 kT 2 12 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 EECS 247 Lecture 26 2007 H K Page 9 Oversampling Data Converters First Order Modulator Simulated Noise Transfer Characteristic Amplitude dBWN 20 Signal Simulated output spectrum Computed NTF Confirms assumption of quantization noise being white at insertion point Linearized model seems to be accurate 10 0 10 20 N y f 4 sin f f s 30 2 40 0 0 1 EECS 247 Lecture 26 0 2 0 3 Frequency f fs 0 4 Oversampling Data Converters 0 5 2007 H K Page 10 First Order Modulator In Band Quantization Noise NTF z 1 z 1 2 NTF f 4 sin f f s 2 B SY for M 1 2 SQ f NTF z z e 2 jfT df B fs 2M fs 2M SQ 2 1 2 2sin fT df f s 12 2 1 2 3 M 3 12 EECS 247 Lecture 26 Total in band quantization noise 2007 H K Page 11 Oversampling Data Converters 1st Order Dynamic Range S full scale signal power DR 10log 10log X inband noise power SQ 1 SX 2 2 SQ 2 sinusoidal input STF 1 2 1 2 3 M 3 12 9 SX M3 SQ 2 2 M DR 16 32 1024 33 dB 42 dB 87 dB 9 9 DR 10log 2 M 3 10log 2 30log M 2 2 DR 3 4dB 30log M 2X increase in M 9dB 1 5 Bit increase in dynamic range EECS 247 Lecture 26 Oversampling Data Converters 2007 H K Page 12 Oversampling and Noise Shaping 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 1st order 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 13 1st Order Modulator Response to DC Input Matlab Simulink model from Lecture 25 used Input DC at 1 11 full scale level 1 X DC Input 1 11 FS EECS 247 Lecture 26 2 Q z 1 1 1 z Integrator 3 Y Comparator Oversampling Data Converters 2007 H K Page 14 1st Order Response to DC Input DC input A 1 11 Amplitude dBWN DC 20 Component Output spectrum shows DC component plus distinct tones 0 Tones frequency shaped the same as quantization noise More prominent at higher frequencies 20 40 0 0 1 0 2 0 3 0 4 0 5 Frequency f fs EECS 247 Lecture 26 Seems like periodic quantization noise 2007 H K Page 15 Oversampling Data Converters Limit Cycle Oscillation DC input 1 11 Periodic sequence First order sigma delta DC input 1 2 1 0 4 3 1 0 2 4 1 Output 1 0 0 2 0 4 0 10 20 30 40 50 Time t T 5 1 6 1 7 1 8 1 9 1 10 1 11 1 Average 1 11 EECS 247 Lecture 26 Oversampling Data Converters 2007 H K Page 16 1st Order Limit Cycle Oscillation Amplitude In band spurious tone with f DC input level First Order Noise Shaping fB fN Frequency fs 2 Problem quantization noise becomes periodic in response to low level DC inputs could fall within passband of interest Solution Use dithering inject noise like signal at the input randomizes quantization noise If circuit thermal noise is large enough acts as dither Second order loop EECS 247 Lecture 26 2007 H K Page …
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