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Data converters
ID: 176601
Franco Maloberti
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A manual dedicated to modern analog-to-digital (A / C) and digital-to-analog (D / A) converters. It contains all the information necessary to fully understand the issues of sampling, quantization and noise in systems with sampled data, parameters characterizing individual transducers, methods used in transducers working according to Nyquist frequency and analysis of their properties, operation of over-samplers and sigma-delta transducers with examples, as well as methods for digital correction and calibration, testing and description of data processing methods for testing and measuring parameters.
Recipients of the book: students of electronics and information technology faculties of technical universities, electronic engineers and everyone interested in modern A / C and C / A converters.
Table of Contents:
List of selected English abbreviations 11
Foreword 13
Chapter 1
Basic information 17
1.1. The perfect data converter 17
1.2. Sampling 18
1.2.1. Subsampling 25
1.2.2. Jitter sampling time 27
1.3. Quantization of the signal value 30
1.3.1. The quantization noise 32
1.3.2. Quantizing noise properties 33
1.4. Noise kT / C 37
1.5. Discrete and fast Fourier transforms 40
1.6. Ways of writing 47
1.7. Converter f. 48
1.7.1. Perfect playback 49
1.7.2. Actual playback 49
1.8. Transformation Z 53
Tasks 57
Literature 59
Chapter 2
Parameters of data converters 60
2.1. Transducer type 60
2.2. Working conditions 61
2.3. Parameter distribution 63
2.4. General properties 63
2.5. Static parameters 64
2.6. Dynamic parameters 73
2.7. Parameters related to switching and digital signals 84
Tasks 85
Literature 86
Chapter 3
Digital-to-analogue converters operating in accordance with the Nyquist 88 frequency
3.1. Introduction 88
3.1.1. Applications of transducers c / a 90
3.1.2. Reference voltage and current sources 91
3.2. Types of transducers 93
3.3. Systems with resistor networks 93
3.3.1. Resistor divider 94
3.3.2. Choice of XY 96
3.3.3. Determining the output voltage 97
3.3.4. Segmented method 100
3.3.5. Impact of mismatch 102
3.3.6. Trim and calibration 105
3.3.7. Digital potentiometer 108
3.3.8. Converters c / a with resistor ladder R-2R 108
3.3.9. Correcting interference problems 116
3.4. Systems with capacitor networks 117
3.4.1. Transducer c / a with capacitive divider 118
3.4.2. Capacitive MDAC converter 121
3.4.3. Flop-around MDAC 122 transducers
3.4.4. Hybrid c / a capacitive resistors 124
3.5. Systems with current sources 125
3.5.1. The basics of activity 125
3.5.2. Individual current source 128
3.5.3. Random mismatch with unit selection 132
3.5.4. Selection of current sources 133
3.5.5. Current switching and segmentation 135
3.5.6. Switching current sources 139
3.6. Other solutions 142
Tasks 146
Literature 148
Chapter 4
Analog-digital converters operating in accordance with the Nyquist 151 frequency
4.1. Introduction 151
4.2. Accuracy of time dependencies 153
4.2.1. Time errors 153
4.2.2. Metastability error 156
4.3. Single-stage (full-wave) flash transmitters 157
4.3.1. Reference voltages 157
4.3.2. Unbalance of comparators 160
4.3.3. Autozero unbalance 162
4.3.4. Practical limitations 165
4.4. Split into sub-ranges and two-stage transducers 167
4.4.1. Accuracy requirements 169
4.4.2. Two-stage processing as a non-linear process 174
4.5. Signal composition and interpolation 175
4.5.1. Double folding 177
4.5.2. Interpolation 178
4.5.3. Application of interpolation in flash transmitters 179
4.5.4. Application of interpolation in transducers with signal assembly 180
4.5.5. Interpolation to improve linearity 181
4.6. Time interleaved transmitters 185
4.7. Transducer with parallel compensation 188
4.7.1. Errors and their correction 191
4.7.2. Redistribution of cargo 193
4.8. Piped transducers 194
4.8.1. Accuracy requirements 198
4.8.2. Digital correction 199
4.8.3. Dynamic parameters 205
4.8.4. A signal generating system for the rest of the data sampled 208
4.9. Other methods 209
4.9.1. Cyclic (or algorithmic) converter 210
4.9.2. Integral converter 211
4.9.3. Voltage-frequency converter 213
Tasks 214
Literature 216
Chapter 5
System elements of data converters 219
5.1. Sampling and recall systems 219
5.2. Layout p / p with diode bridge 220
5.2.1. Imperfections of the diode bridge 221
5.2.2. Improved diode bridge 222
5.3. Switchable emitter recirculation 223
5.3.1. Implementation of the system 224
5.3.2. Complementary bipolar system p / p 226
5.4. Properties of p / p systems with bipolar transistors 227
5.5. CMOS 232 sample and hold system
5.5.1. Penetration of the clock run 233
5.5.2. Clock wave permeation compensation 235
5.5.3. Two-stage OTA amplifier as tracking and memorizing system 237
5.5.4. The use of apparent weight in CMOS 238 p / p systems
5.5.5. Noise analysis 240
5.6. CMOS switch with low supply voltage 245
5.6.1. Principle of operation 245
5.6.2. "Bootstrapping" switch 247
5.7. Amplifiers consisting of 249 signal
5.7.1. Submission of current signals 250
5.7.2. Folding of voltage signals 251
5.8. Voltage-current converter 252
5.9. Generation of a clock wave 256
Tasks 257
Literature 259
Chapter 6
Oversampling and low order modulators ΣΔ 261
6.1. Input 261
6.1.1. Advantages of oversampling 261
6.1.2. Modulation of delta and sigma-delta 263
6.2. Noise shaping 264
6.3. First order modulator 265
6.3.1. Intuitive explanations 270
6.3.2. Application of one-bit quantization 271
6.4. Second order modulator 273
6.5. Designing the layout 275
6.5.1. Unbalance 276
6.5.2. Finite amplification value of the operational amplifier 276
6.5.3. The finite value of the frequency band of the operational amplifier 279
6.5.4. Finite value of the change rate of the output voltage of the operational amplifier 280
6.5.5. Non-ideal operation of the a / c converter 283
6.5.6. Non-perfect operation of the converter c / a 283
6.6. System design 284
6.6.1. Integrator dynamic range 284
6.6.2. Dynamic range optimization 289
6.6.3. Implementation of the sampled data modulator 295
6.6.4. Noise analysis 297
6.6.5. Quantization error and dithering 301
6.6.6. One-bit and multi-bit quantizers 303
Tasks 306
Literature 307
Chapter 7
ΣΔ transducers with continuous and high order time and c / a 310Δ 310 transducers
7.1. Increasing the signal-to-noise ratio 310
7.2. High-order noise shaping 312
7.2.1. One-stage solutions 315
7.2.2.Analysis of stability 316
7.2.3. Feedback with weighting summation 318
7.2.4. Modulator with local coupling 321
7.2.5. Integrator chain with unfolded feedback 323
7.2.6. Cascade modulator ΣΔ 324
7.2.7. Dynamic range MASH 328
7.3. Modulators ΣΔ
7.3.1. Limitations of the sampling and storage system 333
7.3.2. Implementations of continuous time (CT) systems 335
7.3.3. Designing of continuous time (CT) systems based on
their equivalent circuits with sampled data 339
7.4. Bandpass modulator ΣΔ 342
7.4.1. The N -torowy 345 interlaced
7.4.2. Synthesis of the noise transfer function (NTF) 350
7.5. Converters with over sampling 352
7.5.1. Encoder 1 / bit 353
7.5.2. Dual c / az converter back to zero 357
Tasks 358
Literature 361
Chapter 8
Improved digital methods 364
8.1. Introduction 364
8.2. Measurements of errors 365
8.3.Trying elements 367
8.4. Calibration with priority 369
8.5. Calibration in the background 372
8.5.1. Strengthening and image in 375 interlaced transducers
8.5.2. Calibration of imbalance without redundancy 375
8.6. Dynamic matching 378
8.6.1. Butterfly Randomization 381
8.6.2. Individual level averaging 386
8.6.3. Weighted data averaging 390
8.7. Decimation and interpolation 395
8.7.1. Decimation 395
8.7.2. Interpolation 399
Tasks 402
Literature 402
Chapter 9
Testing a / cic / a 405 transmitters
9.1. Introduction 405
9.2. Test card 407
9.3. Quality and reliability test 409
9.4. Processing of measurement data 411
9.4.1. Best matching chart 411
9.4.2. Adjusting the sine wave 413
9.4.3. Histogram method 414
9.5. Static testing of 4 / 4A transducers
9.5.1. Transfer characteristic test 418
9.5.2. Adding errors 419
9.5.3. Non-linearity errors 420
9.6. Dynamic testing of converters c / a 421
9.6.1. Spectral properties 422
9.6.2. Processing time 423
9.6.3. Pulse interference energy 424
9.7. Static testing of a / c converters 425
9.7.1. The purpose of static test 425
9.7.2. Measurement of the digital word output limit 427
9.8. Dynamic testing of a / c converters 429
9.8.1. Parameters in the time domain 429
9.8.2. Improving the purity of sine waves 431
9.8.3. Measurement of the aperture uncertainty 432
9.8.4. Measurement of setting time 434
9.8.5. Application of FFT for testing 435
Tasks 437
Literature 438
with continuous time 331 with continuous time, high order and d / 310 converters
Recipients of the book: students of electronics and information technology faculties of technical universities, electronic engineers and everyone interested in modern A / C and C / A converters.
Table of Contents:
List of selected English abbreviations 11
Foreword 13
Chapter 1
Basic information 17
1.1. The perfect data converter 17
1.2. Sampling 18
1.2.1. Subsampling 25
1.2.2. Jitter sampling time 27
1.3. Quantization of the signal value 30
1.3.1. The quantization noise 32
1.3.2. Quantizing noise properties 33
1.4. Noise kT / C 37
1.5. Discrete and fast Fourier transforms 40
1.6. Ways of writing 47
1.7. Converter f. 48
1.7.1. Perfect playback 49
1.7.2. Actual playback 49
1.8. Transformation Z 53
Tasks 57
Literature 59
Chapter 2
Parameters of data converters 60
2.1. Transducer type 60
2.2. Working conditions 61
2.3. Parameter distribution 63
2.4. General properties 63
2.5. Static parameters 64
2.6. Dynamic parameters 73
2.7. Parameters related to switching and digital signals 84
Tasks 85
Literature 86
Chapter 3
Digital-to-analogue converters operating in accordance with the Nyquist 88 frequency
3.1. Introduction 88
3.1.1. Applications of transducers c / a 90
3.1.2. Reference voltage and current sources 91
3.2. Types of transducers 93
3.3. Systems with resistor networks 93
3.3.1. Resistor divider 94
3.3.2. Choice of XY 96
3.3.3. Determining the output voltage 97
3.3.4. Segmented method 100
3.3.5. Impact of mismatch 102
3.3.6. Trim and calibration 105
3.3.7. Digital potentiometer 108
3.3.8. Converters c / a with resistor ladder R-2R 108
3.3.9. Correcting interference problems 116
3.4. Systems with capacitor networks 117
3.4.1. Transducer c / a with capacitive divider 118
3.4.2. Capacitive MDAC converter 121
3.4.3. Flop-around MDAC 122 transducers
3.4.4. Hybrid c / a capacitive resistors 124
3.5. Systems with current sources 125
3.5.1. The basics of activity 125
3.5.2. Individual current source 128
3.5.3. Random mismatch with unit selection 132
3.5.4. Selection of current sources 133
3.5.5. Current switching and segmentation 135
3.5.6. Switching current sources 139
3.6. Other solutions 142
Tasks 146
Literature 148
Chapter 4
Analog-digital converters operating in accordance with the Nyquist 151 frequency
4.1. Introduction 151
4.2. Accuracy of time dependencies 153
4.2.1. Time errors 153
4.2.2. Metastability error 156
4.3. Single-stage (full-wave) flash transmitters 157
4.3.1. Reference voltages 157
4.3.2. Unbalance of comparators 160
4.3.3. Autozero unbalance 162
4.3.4. Practical limitations 165
4.4. Split into sub-ranges and two-stage transducers 167
4.4.1. Accuracy requirements 169
4.4.2. Two-stage processing as a non-linear process 174
4.5. Signal composition and interpolation 175
4.5.1. Double folding 177
4.5.2. Interpolation 178
4.5.3. Application of interpolation in flash transmitters 179
4.5.4. Application of interpolation in transducers with signal assembly 180
4.5.5. Interpolation to improve linearity 181
4.6. Time interleaved transmitters 185
4.7. Transducer with parallel compensation 188
4.7.1. Errors and their correction 191
4.7.2. Redistribution of cargo 193
4.8. Piped transducers 194
4.8.1. Accuracy requirements 198
4.8.2. Digital correction 199
4.8.3. Dynamic parameters 205
4.8.4. A signal generating system for the rest of the data sampled 208
4.9. Other methods 209
4.9.1. Cyclic (or algorithmic) converter 210
4.9.2. Integral converter 211
4.9.3. Voltage-frequency converter 213
Tasks 214
Literature 216
Chapter 5
System elements of data converters 219
5.1. Sampling and recall systems 219
5.2. Layout p / p with diode bridge 220
5.2.1. Imperfections of the diode bridge 221
5.2.2. Improved diode bridge 222
5.3. Switchable emitter recirculation 223
5.3.1. Implementation of the system 224
5.3.2. Complementary bipolar system p / p 226
5.4. Properties of p / p systems with bipolar transistors 227
5.5. CMOS 232 sample and hold system
5.5.1. Penetration of the clock run 233
5.5.2. Clock wave permeation compensation 235
5.5.3. Two-stage OTA amplifier as tracking and memorizing system 237
5.5.4. The use of apparent weight in CMOS 238 p / p systems
5.5.5. Noise analysis 240
5.6. CMOS switch with low supply voltage 245
5.6.1. Principle of operation 245
5.6.2. "Bootstrapping" switch 247
5.7. Amplifiers consisting of 249 signal
5.7.1. Submission of current signals 250
5.7.2. Folding of voltage signals 251
5.8. Voltage-current converter 252
5.9. Generation of a clock wave 256
Tasks 257
Literature 259
Chapter 6
Oversampling and low order modulators ΣΔ 261
6.1. Input 261
6.1.1. Advantages of oversampling 261
6.1.2. Modulation of delta and sigma-delta 263
6.2. Noise shaping 264
6.3. First order modulator 265
6.3.1. Intuitive explanations 270
6.3.2. Application of one-bit quantization 271
6.4. Second order modulator 273
6.5. Designing the layout 275
6.5.1. Unbalance 276
6.5.2. Finite amplification value of the operational amplifier 276
6.5.3. The finite value of the frequency band of the operational amplifier 279
6.5.4. Finite value of the change rate of the output voltage of the operational amplifier 280
6.5.5. Non-ideal operation of the a / c converter 283
6.5.6. Non-perfect operation of the converter c / a 283
6.6. System design 284
6.6.1. Integrator dynamic range 284
6.6.2. Dynamic range optimization 289
6.6.3. Implementation of the sampled data modulator 295
6.6.4. Noise analysis 297
6.6.5. Quantization error and dithering 301
6.6.6. One-bit and multi-bit quantizers 303
Tasks 306
Literature 307
Chapter 7
ΣΔ transducers with continuous and high order time and c / a 310Δ 310 transducers
7.1. Increasing the signal-to-noise ratio 310
7.2. High-order noise shaping 312
7.2.1. One-stage solutions 315
7.2.2.Analysis of stability 316
7.2.3. Feedback with weighting summation 318
7.2.4. Modulator with local coupling 321
7.2.5. Integrator chain with unfolded feedback 323
7.2.6. Cascade modulator ΣΔ 324
7.2.7. Dynamic range MASH 328
7.3. Modulators ΣΔ
7.3.1. Limitations of the sampling and storage system 333
7.3.2. Implementations of continuous time (CT) systems 335
7.3.3. Designing of continuous time (CT) systems based on
their equivalent circuits with sampled data 339
7.4. Bandpass modulator ΣΔ 342
7.4.1. The N -torowy 345 interlaced
7.4.2. Synthesis of the noise transfer function (NTF) 350
7.5. Converters with over sampling 352
7.5.1. Encoder 1 / bit 353
7.5.2. Dual c / az converter back to zero 357
Tasks 358
Literature 361
Chapter 8
Improved digital methods 364
8.1. Introduction 364
8.2. Measurements of errors 365
8.3.Trying elements 367
8.4. Calibration with priority 369
8.5. Calibration in the background 372
8.5.1. Strengthening and image in 375 interlaced transducers
8.5.2. Calibration of imbalance without redundancy 375
8.6. Dynamic matching 378
8.6.1. Butterfly Randomization 381
8.6.2. Individual level averaging 386
8.6.3. Weighted data averaging 390
8.7. Decimation and interpolation 395
8.7.1. Decimation 395
8.7.2. Interpolation 399
Tasks 402
Literature 402
Chapter 9
Testing a / cic / a 405 transmitters
9.1. Introduction 405
9.2. Test card 407
9.3. Quality and reliability test 409
9.4. Processing of measurement data 411
9.4.1. Best matching chart 411
9.4.2. Adjusting the sine wave 413
9.4.3. Histogram method 414
9.5. Static testing of 4 / 4A transducers
9.5.1. Transfer characteristic test 418
9.5.2. Adding errors 419
9.5.3. Non-linearity errors 420
9.6. Dynamic testing of converters c / a 421
9.6.1. Spectral properties 422
9.6.2. Processing time 423
9.6.3. Pulse interference energy 424
9.7. Static testing of a / c converters 425
9.7.1. The purpose of static test 425
9.7.2. Measurement of the digital word output limit 427
9.8. Dynamic testing of a / c converters 429
9.8.1. Parameters in the time domain 429
9.8.2. Improving the purity of sine waves 431
9.8.3. Measurement of the aperture uncertainty 432
9.8.4. Measurement of setting time 434
9.8.5. Application of FFT for testing 435
Tasks 437
Literature 438
with continuous time 331 with continuous time, high order and d / 310 converters
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Franco Maloberti