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Upsampling II Zero padding results in higher sampling rate However, this does not mean that mirror spectra occur only at multiples of the sampling frequency Imaging, i.e. replica in between 0..2 Low pass filter removes images – Result in frequency domain: Replica only at k x f s – Result in time domain: Zeros move on real signal curve Stephan Henzler Mixed-Signal-Electronics 2012/13 38
Fractional Sample Rate Conversion Purpose: Change sample rate by a non-integer factor L/M Two possibilities: – Up-sampling by L, down-sampling by M – Down-sampling by M, than up-sampling by L The order of up- and down-sampling may be exchanged without any change in the input/output behavior if the decimation factor M and the interpolation factor L are relatively prime. Stephan Henzler Mixed-Signal-Electronics 2012/13 39
Page 1 and 2: Mixed-Signal-Electronics PD Dr.-Ing
Page 3 and 4: Stephan’s ambition for this cours
Page 5 and 6: Administratives Lecture: Stephan He
Page 7 and 8: The Macroscopic World is Purely Ana
Page 9 and 10: Topics of MSE Course Structure of
Page 11 and 12: Recommended Literature Analog Integ
Page 13 and 14: Constraints of Mixed Signal Circuit
Page 15 and 16: Generic Structure of Mixed-Signal S
Page 17 and 18: Representation of Discrete Time Sig
Page 19 and 20: Inverse Z-Transformation Methods f
Page 21 and 22: Representation of Discrete Time Sig
Page 23 and 24: low-pass low-pass low-pass Aliasing
Page 25 and 26: amplitude fsampling = 1 f signal,2
Page 27 and 28: Anti Aliasing Filter No brick wall
Page 29 and 30: Practical Sampling: Sample & Hold
Page 31 and 32: Xsh(!) = ¡ 1 j!¿ Sampling with Fi
Page 33 and 34: generalization X(s) = Relation Betw
Page 35 and 36: Downsampling II Mathematically dow
Page 37: Upsampling Stephan Henzler Mixed-Si
Page 41 and 42: Example for Simple Anti Aliasing Fi
Page 43 and 44: Transistor Description (for hand ca
Page 45 and 46: Chapter 2 Sample and Hold Circuits
Page 47 and 48: Sample & Hold Circuit Stephan Henzl
Page 49 and 50: Sample & Hold: Clock Feed-Through 3
Page 51 and 52: 5. 6. Clock jitter Sample & Hold Ci
Page 53 and 54: Impact of Jitter on S&H Performance
Page 55 and 56: Noise due to jitter: Jitter Effect
Page 57 and 58: S&H with Correlated Double Sampling
Page 59 and 60: Noise of Sampled Signals: kT/C-Nois
Page 61 and 62: Closed Loop Track & Hold Circuit 1
Page 63 and 64: Closed Loop Track & Hold Circuit 3
Page 65 and 66: Summary Sample & Hold Circuits Step
Page 67 and 68: Resistor Realizations in MOS Techno
Page 69 and 70: Resistor Realizations in MOS Techno
Page 71 and 72: Switched Capacitor Resistor Emulati
Page 73 and 74: Resistor Equivalents Stephan Henzle
Page 75 and 76: Parameter Variations in SC Circuits
Page 77 and 78: Implementation of Integrated Capaci
Page 79 and 80: Vertical Parallel Plate Capacitor S
Page 81 and 82: Limitations of SC-Equivalence Steph
Page 83 and 84: Limitations of SC-Equivalence Switc
Page 85 and 86: Switched Capacitor Integrators Step
Page 87 and 88: z-Transformation Approximation on
Page 89 and 90:
Analysis of Switched-Capacitor Circ
Page 91 and 92:
Impact of Parasitic Capacitances C
Page 93 and 94:
Switched Capacitor Amplifier Stepha
Page 95 and 96:
SC Amplifier: Output Signal Stephan
Page 97 and 98:
Superposition Theorem in SC Circuit
Page 99 and 100:
Ideal Digital-to-Analog Conversion
Page 101 and 102:
DAC Gain Error Stephan Henzler Mixe
Page 103 and 104:
Ideal Analog-to-Digital Conversion
Page 105 and 106:
Quantization in A/D-Converters Step
Page 107 and 108:
Quantization in A/D-Converters Sig
Page 109 and 110:
ADC Gain Error Stephan Henzler Mixe
Page 111 and 112:
Non-Linearity in Data Converters St
Page 113 and 114:
Nonlinearity in Data-Converters Ste
Page 115 and 116:
DAC Nonlinearity: Differential Nonl
Page 117 and 118:
ADC Nonlinearity: Integral Nonlinea
Page 119 and 120:
Dynamic ADC Measurement ADC conver
Page 121 and 122:
Harmonic Distortion Caused by Nonli
Page 123 and 124:
Effective Number of Bits An ideal
Page 125 and 126:
Other Useful Figures in Mixed-Signa
Page 127 and 128:
Non-Linearity Gain Compression Co
Page 129 and 130:
Superposition of Two Frequencies St
Page 131 and 132:
Non-Linearity Cross Modulation Co
Page 133 and 134:
Non-Linearity Intermodulation Two
Page 135 and 136:
Non-Linearity: Further Reading Rec
Page 137 and 138:
Chapter 5 Nyquist Rate Digital-to-A
Page 139 and 140:
max value bus voltage follower stri
Page 141 and 142:
Elmore Delay (cont.): Path Resistan
Page 143 and 144:
Elmore Delay (cont): Delay Approxim
Page 145 and 146:
Stephan Henzler Mixed-Signal-Electr
Page 147 and 148:
Normalized Delay 300 250 200 150 10
Page 149 and 150:
Stephan Henzler Mixed-Signal-Electr
Page 151 and 152:
Monotonicity in Binary Weighted DAC
Page 153 and 154:
Implementation of Binary Weighted D
Page 155 and 156:
High number of bits - large area Hi
Page 157 and 158:
Page 159 and 160:
R-2R-Ladder Network Stephan Henzler
Page 161 and 162:
Page 163 and 164:
SC-Amplifier with Controllable Capa
Page 165 and 166:
Thermometer Code Converters (method
Page 167 and 168:
Hybrid Converter Architectures Step
Page 169 and 170:
Charge Scaling DAC Compatibel with
Page 171 and 172:
Analog-to-Digital Converter Familie
Page 173 and 174:
Dual-Slope Analog-to-Digital Conver
Page 175 and 176:
Iterative Analog-to-Digital Convert
Page 177 and 178:
Converter with Successive Approxima
Page 179 and 180:
Converter with Successive Approxima
Page 181 and 182:
Modified SAR Algorithm Stephan Henz
Page 183 and 184:
Charge Redistribution SAR Converter
Page 185 and 186:
Charge Redistribution SAR Converter
Page 187 and 188:
Hybrid SAR Converters Search can b
Page 189 and 190:
Detailed SAR Architecture Let’s
Page 191 and 192:
Binary Weighted SAR Stephan Henzler
Page 193 and 194:
Algorithmic Analog-to-Digital Conve
Page 195 and 196:
Page 197 and 198:
Illustration in Robertson Diagram 2
Page 199 and 200:
Page 201 and 202:
Voltage Doubling in Algorithmic Con
Page 203 and 204:
Voltage Doubling in Algorithmic Con
Page 205 and 206:
Pipelined ADC 1 Going for pipeline
Page 207 and 208:
High-Speed ADC: Pipeline Processing
Page 209 and 210:
Impact of Comparator Offset on ADC
Page 211 and 212:
Impairments in SAR Algorithms Find
Page 213 and 214:
Redundant SAR Algorithms Stage qua
Page 215 and 216:
Subranging Principle quantization e
Page 217 and 218:
Linear Model of Subranging ADC Step
Page 219 and 220:
Linear Model of Subranging ADC Eff
Page 221 and 222:
General Pipeline SAR ADC Stephan He
Page 223 and 224:
Background Calibration for Stage Ga
Page 225 and 226:
Summary Pipeline ADC Stage errors
Page 227 and 228:
implemented as parallel connection
Page 229 and 230:
thermometer code one-hot code trans
Page 231 and 232:
Bubble Correction in Flash Converte
Page 233 and 234:
Interpolating Flash Converter Steph
Page 235 and 236:
Kickback Effect Especially in flas
Page 237 and 238:
Folding ADC: Operation Principle St
Page 239 and 240:
High-Speed ADC: Parallel Processing
Page 241 and 242:
Chapter 7 Comparators Stephan Henzl
Page 243 and 244:
Static Characteristics of Comparato
Page 245 and 246:
Operational Amplifier as Comparator
Page 247 and 248:
Comparator Propagation Delay Linea
Page 249 and 250:
Track & Latch Circuit I Stephan Hen
Page 251 and 252:
Principle of Track-and-Latch Stage
Page 253 and 254:
Latched Comparators I Standard arc
Page 255 and 256:
Track & latch circuit: Latched Comp
Page 257 and 258:
Current Mode (CML) Latch Combines
Page 259 and 260:
Elimination of Memory Effect Prech
Page 261 and 262:
Chapter 8 Oversampled Converters Si
Page 263 and 264:
Linear Model of Quantization Noise
Page 265 and 266:
Quantization Noise and Oversampling
Page 267 and 268:
Feasibility of Oversampling Goal:
Page 269 and 270:
First Order Noise Shaping Stephan H
Page 271 and 272:
First Order Noise Shaping Stephan H
Page 273 and 274:
Calculation of Signal-to-Noise Rati
Page 275 and 276:
SC Implementation of 1. Order ΣΔ
Page 277 and 278:
Comparison Nyquist Rate vs. SD AD N
Page 279 and 280:
Calculation of Transfer Functions S
Page 281 and 282:
Simulation with Matlab/Simulink Ste
Page 283 and 284:
Output Spectrum of ΣΔ-Modulator f
Page 285 and 286:
Input Level Dependent SNR 2. Order
Page 287 and 288:
Tones Stephan Henzler Mixed-Signal-
Page 289 and 290:
Dithering Reduce the risk of tones
Page 291 and 292:
maximum noise peak Tones input DC l
Page 293 and 294:
STF of 3. Order ΣΔ-Modulator Step
Page 295 and 296:
Cascaded ΣΔ-Modulator (Multi stAg
Page 297 and 298:
3. Order MASH Structure Stephan Hen
Page 299 and 300:
hist(S1) 12000 10000 8000 6000 4000
Page 301 and 302:
hist(S1) 2.5 2 1.5 1 0.5 0 -1 -0.8
Page 303 and 304:
ΣΔ-Analog-to-Digital Conversion S
Page 305 and 306:
Sinc-Filter Basic low-pass filter a
Page 307 and 308:
Sinc Filter Transfer Functions Step
Page 309 and 310:
Implementation of Sinc-Filter Steph
Page 311 and 312:
ΣΔ-Digital-to-Analog Conversion S
Page 313 and 314:
Continuous Time Sigma-Delta Convert
Page 315 and 316:
Comparison of Discrete- and Continu
Page 317:
Web References Murmann. VLSI Data
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