Analog and Telecommunication Electronics

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1 Politecnico di Torino - ICT School Analog and Telecommunication Electronics D5 - Special A/D converters» Differential converters» Oversampling, noise shaping» Logarithmic conversion» Approximation, A and μ laws» Model encoding 17/04/ ATLCE - D DDC 2013 DDC 1

2 Lesson D5: special A/D converters Differential converters Adaptive converters, Sigma-delta converters Oversampling, Noise shaping Voice conversion, SNRq and dynamic range Logarithmic conversion Piecewise approximation, A and μ laws Waveform encoding and model encoding Voice LPC References: Elettronica per Telecom.: 4.5 Convertitori per usi speciali Design with Op Amp : 12.5 Oversampling Converters 17/04/ ATLCE - D DDC 2013 DDC 2

3 Radio systems: where are ADC/DAC? Services V battery, TX power,.. Baseband chain A/D e D/A for voice signals Receiver chain: A/D conversion of I/Q components in the IF channel Transmitter chain D/A conversion of synthesized I/Q components Software Defined Radio architectures Most functions by digital/programmable circuits A/D or D/A conversion very close to antenna 17/04/ ATLCE - D DDC 2013 DDC 3

4 A/D and D/A conversion: where? A/D and D/A converters for voice signal. 17/04/ ATLCE - D DDC 2013 DDC 4

5 ADC and DAC system goals Improve cost/performance figure Cost factors» Complexity, Bit rate,. Performance parameters» Bandwidth, Precision,. Signals with known features Amplitude distribution Statistic parameters Source model ADC/DAC optimized for specific applications Low cost (no high precision component) Low bit rate 17/04/ ATLCE - D DDC 2013 DDC 5

6 Tracking converter The tracking ADC is a differential converter The serial bit flow from the comparator output represents the sign of A - A (current value previous value) A A + - U/D counter SERIAL DATA CK DAC D 17/04/ ATLCE - D DDC 2013 DDC 6

7 Differential converters Quantization of difference between previous and current values Dynamic reduction 1-bit A/D conversion (comparator) Serial flow of uniform bits CODER DECODER counter counter 17/04/ ATLCE - D DDC 2013 DDC 7

8 (Delta/differential) converter Integrating differential converter Counter + DAC replaced by SW + integrator L is a sequence of + or pulses, with rate Fck = 1/Tck The recovered signal is R = Σ(L) On each pulse R changes of one step γ (posive or negative). 17/04/ ATLCE - D DDC 2013 DDC 8

9 Signals in the converter L is a sequence of positive or negative pulses, with rate Fck = 1/Tck The recovered signal is S(L) On each pulse R changes of one step (posive or negative). 17/04/ ATLCE - D DDC 2013 DDC 9

10 Delta ADC dynamic Minimum signal (IDLE state) Peak level γ/2; idle noise Maximum tracked signal Slew rate γ/tck overload 17/04/ ATLCE - D DDC 2013 DDC 10

11 Characteristic of Delta ( ) ADC A differential converter Does not require high precision devices Does not require formatting of serial output data Provides limited dynamic range Low bound: idle noise High bound: overload For a specific SNRq, generates a bit flow with high rate Operates in oversampling mode Sampling rate far higher than Nyquist limit Higher bit flow (compared with Nyquist minimum) 17/04/ ATLCE - D DDC 2013 DDC 11

12 Oversampling Sampling at a rate far higher than the Nyquist limit Example: 3 khz audio signal (Nyquist = 6 ks/s) 8 ks/s Nyquist sampling; 1 MS/s Oversampling Oversampling sends aliased spectra far from baseband Reduced aliasing noise, folded from first alias Relaxed specifications on the anti-alias input filter Quantization noise is spread over a wider band (0 - Fs) Reduced spectral density of quantization noise Higher bit rate (more samples/s) Can be reduced with digital filtering Move complexity from analog digital domain 17/04/ ATLCE - D DDC 2013 DDC 12

13 Oversampling vs. Nyquist Nyquist Main spectrum (baseband) First alias Second alias X(ω) f 0 F S1 2F S1 Quantization noise (0-Fs1 band) Oversampling X(ω) First alias f 0 Quantization noise (0-Fs2 band) F S2 17/04/ ATLCE - D DDC 2013 DDC 13

14 Filtering oversampled signals Nyquist X(ω) Steep filter f Oversampling F S1 0 2F S1 Different filters: same quantization noise power (after reconstruction filter) X(ω) Smooth filter 0 F S2 f 17/04/ ATLCE - D DDC 2013 DDC 14

15 Oversampling vs. Nyquist noise Nyquist X(ω) Steep filter f F S1 0 2F S1 Oversampling X(ω) Steep filter Same filter: reduced quantization noise power (after reconstruction filter) Removed quantization noise 0 F S2 f 17/04/ ATLCE - D DDC 2013 DDC 15

16 Which is the actual limit? Actual Nyquist rule: A signal must be sampled at least twice the signal BANDWIDTH Example: a 1 GHz carrier, 100 khz BW signal can be safely sampled at Fs > 200 ks/s Spectrum is folded around K Fs/2 Less stringent specs for RF A/D converters Sampling rate related with bandwidth, not carrier Tight specs for the S/H sampling jitter related with carrier, not bandwidth 17/04/ ATLCE - D DDC 2013 DDC 16

17 Filter for Nyquist sampling NYQUIST X(ω) Steep antialias filter, to limit aliasing noise Spectrum segment folded to baseband (aliasing noise) f F S 0 2F S F S /2 A/D Complex analog LP filter 17/04/ ATLCE - D DDC 2013 DDC 17

18 Oversampling: more simple filter Complex, steep digital filter: - reduce noise - reduce bit rate (decimation) Alias is far away; antialias analog filter can be simple X( ) 0 2 F S2 17/04/ ATLCE - D DDC 2013 DDC 18

19 Filters with oversampling NYQUIST Complex analog LP filter A/D OVERSAMPLING Simple analog filter A/D Move complexity from the analog to the digital domain Complex digital filter Can reduce the bit rate (decimation) 17/04/ ATLCE - D DDC 2013 DDC 19

20 converter input dynamic range Range of input signals correctly handled γ corresponds to The quantization step A D in a standard ADC Input dynamic range: Fck/ Fs» Does not depend on γ To increase input dynamic range constant need to change Tck (Fck) higher bit rate variable (adaptive converters)» Minimum in idle condition (output sequence )» Maximum near overload (output sequences 000 or ) Remove dependency from signal frequency (ω)» converters 17/04/ ATLCE - D DDC 2013 DDC 20

21 Numeric example Audio signal Fmax 3 khz, peak V Sampled 8 ks/s, 8 bit quantization» Which SNRq? 1 bit quantization (delta)» Which Fck to obtain the same SNRq?. 17/04/ ATLCE - D DDC 2013 DDC 21

22 Adaptive converters Two integrators in the loop Stability problems Integrator + predictor (pole/zero) Variable step, depending from Signal level (power estimation)» Syllabic adaptation Error sign sequences» Real-time adaptation Adaptation circuits must use the line signal idle: alternated sequence at output overload: continuous streams 0000 or /04/ ATLCE - D DDC 2013 DDC 22

23 Adaptive converters DAC uses only line signal Power estimation Power estimation 17/04/ ATLCE - D DDC 2013 DDC 23

24 Differential converter architectures The differential converter can operate on many bits The comparator is replaced by an ADC A DAC drives the integrator Integrator 17/04/ ATLCE - D DDC 2013 DDC 24

25 Digital differential converters Integration can occur in the digital domain Integrator becomes accumulator 17/04/ ATLCE - D DDC 2013 DDC 25

26 converters The input dynamic range is limited by signal slew rate For wider dynamic: limit slew rate Integrator on input signal» Decrease amplitude as frequency goes up (integrator) constant slew rate 17/04/ ATLCE - D DDC 2013 DDC 26

27 converters The input dynamic range is limited by signal slew rate For wider dynamic: limit slew rate Integrator on input signal» Decrease amplitude as frequency goes up (integrator) To correctly rebuild the signal: derive the output Standard differential chain 17/04/ ATLCE - D DDC 2013 DDC 27

28 Sigma-Delta ADC and DAC Move integrators on adder input single integrator at the output Remove the integrator-derivator in DAC ADC DAC Keep antialias input and reconstruction output filters (not shown) 17/04/ ATLCE - D DDC 2013 DDC 28

29 Quantization noise in In the ADC quantization noise εq is generated after integraton Y/N transfer function is highpass 17/04/ ATLCE - D DDC 2013 DDC 29

30 Noise shaping Noise is shifted towards high frequencies Noise power spectrum density is higher at high frequencies: Noise shaping Noise power spectrum density in baseband is reduced Further reduction to output noise power Or simpler reconstruction filter 17/04/ ATLCE - D DDC 2013 DDC 30

31 Oversampling vs. Nyquist noise Oversampling X(ω) Reconstruction filter Flat quantization noise 0 F S2 f Noise shaping X(ω) Shaped quantization noise 0 Noise power is moved to HF, lower power density in baseband F S2 f 17/04/ ATLCE - D DDC 2013 DDC 31

32 Complete conversion chain Anti aliasing filter» Oversampling allows simple filters ADC order 1, 2, N» Produces a high speed, non-weighted bit stream Decimator» Changes the high speed bit rate in low rate words ---- Channell Interpolator» Recreates the high speed serial flow DAC» Rebuilds analog signal Reconstruction filter 17/04/ ATLCE - D DDC 2013 DDC 32

33 Bit rate reduction A DECIMATOR A filtered D serial, High rate D parallel, Low rate INTERPOLATOR A 17/04/ ATLCE - D DDC 2013 DDC 33

34 Lesson D5: special A/D converters Differential converters Adaptive converters, Sigma-delta converters Oversampling, Noise shaping Voice conversion, SNRq and dynamic range Logarithmic conversion Piecewise approximation, A and μ laws Waveform encoding and model encoding Voice LPC 17/04/ ATLCE - D DDC 2013 DDC 34

35 Voice signal conversion Voice signal exponential amplitude distribution» more dense at lower levels wide dynamic range» SNRq low and variable with signal level ADC can exploit these characteristics Minimize noise for low-level signals Logarithmic analog to digital conversion constant SNRq over a wide signal dynamic range fewer bits for the same SNRq 17/04/ ATLCE - D DDC 2013 DDC 35

36 Linear and nonlinear A/D conversion Linear A/D conversion all A D intervals have same amplitude» quantization error does not depend on signal level poor results with signals at low levels for most time (voice)» high quantization noise power, low signal power Nonlinear A/D conversion different A D intervals» quantization error changes with signal level» the nonlinear relation can be chosen to optimize SNRq for a specific signal type (PDF, amplitude distribution) for voice signals (exponential distribution)» logarithmic law 17/04/ ATLCE - D DDC 2013 DDC 36

37 Linear quantization A D intervals with constant width Constant quantization noise power D SNRq varies with signal level (worse for low-level signals) A 17/04/ ATLCE - D DDC 2013 DDC 37

38 Nonlinear quantization A D intervals with variable width Quantization noise power related with signal level D SNRq independent from signal level A 17/04/ ATLCE - D DDC 2013 DDC 38

39 Standard conversion The A/D conversion adds q noise to analog signal D = A + q A D is constant, therefore» constant absolute error on D» % error (SNRq) is related with signal level A A D q 17/04/ ATLCE - D DDC 2013 DDC 39

40 Logarithmic conversion Conversion of signal logarithm: D = log A + q sum of logs log of product» D = log A + q = log K A ( q = log K)» multiplying error (1 - K)» constant % error, independent from signal level A A log D log A q 17/04/ ATLCE - D DDC 2013 DDC 40

41 Nominal SNRq Log quantization causes a constant relative error constant SNRq log SNRq lin Level Full scale 17/04/ ATLCE - D DDC 2013 DDC 41

42 A and approximation Audio signals are bipolar the log curve must be replicated in the III quadrant» symmetric curve from I quadrant Log 0 is undefined near 0 the log curve can be only approximated law» translate the positive and negative branches to get a continuous curve in (0,0) A law» replace the curves near 0 with a straight line (crossing 0,0) 17/04/ ATLCE - D DDC 2013 DDC 42

43 A and μ approximation - graphs Translation (μ law) Replacement (A law) 17/04/ ATLCE - D DDC 2013 DDC 43

44 SNRq near 0 A law: signals less than 1/A --> linear quantization SNRq depends from signal level (6 db/octave) μ law: almost linear quantization at low levels similar effect: SNRq drop SNRq Level 1/A Full scale (S) 17/04/ ATLCE - D DDC 2013 DDC 44

45 SNRq with A and μ law μ law A law linear Linear behavior Log behavior Overload 17/04/ ATLCE - D DDC 2013 DDC 45

46 Log A/D approximation Obtaining calibrated continuous nonlinear behavior requires complex and expensive analog circuits Piecewise approximation The log curve is divided in linear segments due to log scale, the same ratio of input signal corresponds to the same shift in horizontal axis slope and starting point of each segment are sequenced as 2 powers (2, 4, 8, 16,.) linear coding inside each segment 17/04/ ATLCE - D DDC 2013 DDC 46

47 Piecewise approximation Compressed signal Continuous log law slope slope slope slope Input signal 17/04/ ATLCE - D DDC 2013 DDC 47

48 Log PCM format Each sample is coded on 8 bit MSB (bit 7): sign bit 6, 5, 4: segment bit 3, 2, 1, 0: level within the segment /04/ ATLCE - D DDC 2013 DDC 48

49 Piecewise approximation: SNRq Within each segment quantization error q remains constant signal level changes signal power changes SNRq changes with unity slope From each segment to the next one (from S to 0) quantization error q is divided by 2 signal level is divided by 2 SNRq constant Near 0 same behavior as linear quantization constant q signal level changes 17/04/ ATLCE - D DDC 2013 DDC 49

50 SNRq with A and approximation μ 255 law A (87.6) law 17/04/ ATLCE - D DDC 2013 DDC 50

51 Log conversion techniques Analog log circuit, followed by A/D poor precision and stability in the analog circuit high cost High resolution A/D conversion, followed by digital log encoding makes available both the linear and log conversion Intrinsic log A/D converter nonlinear law A/D or D/A conversion suitable for any type of nonlinear transfer function (DAC for DDS) 17/04/ ATLCE - D DDC 2013 DDC 51

52 A/D logarithmic converter A logarithmic A/D converter can use the D/A feedback technique: comparator-approximation logic - D/A loop the D/A must have exponential transfer function How to build an exponential D/A (bipolar): sign bit: inverts the D/A reference voltage segment bits: provide a voltage with 2 N steps» segment bits are decoded into linear code (3-8 decoder)» the 8 bit feed a linear 8-bit D/A» each segment generates outputs with a ratio 2 towards adjacent ones level bits: fed directly to a linear D/A 17/04/ ATLCE - D DDC 2013 DDC 52

53 Logarithmic ADC Sign bit inverts the reference voltage Vr Segment bits voltage Vs scaled with 2 N steps (1, 2, 4, 8, ) Level bits fed directly to a linear DAC using Vs as reference Vs 17/04/ ATLCE - D DDC 2013 DDC 53

54 Nonlinear DAC Structure for nonlinear DAC and ADC with piecewise approximation Segment bit decoder Standard DAC + lookup table Decoded DAC uniform elements» To build starting point and slope of each segment Linear coding within each segment (level bits) Output adder» Shifts the segment starting point Technique used for DACs in DDS (sine generators) Sine conversion law (piecewise approximation) 17/04/ ATLCE - D DDC 2013 DDC 54

55 Nonlinear DAC block diagram Piecewise nonlinear characteristic Da: segment bits Db: level bits Da Db DECODER/LOOKUP +Vr -Vr SEGMENT SLOPE DAC LEVEL DAC + VO SEGMENT START DAC 17/04/ ATLCE - D DDC 2013 DDC 55

56 Lesson D5: special A/D converters Differential converters Sigma-delta converters Oversampling Noise shaping Logarithmic conversion Piecewise approximation A and μ laws Logarithmic converters Waveform encoding and model encoding Voice LPC Comparison quality/bit rate 17/04/ ATLCE - D DDC 2013 DDC 56

57 Model encoding vs waveform encoding Waveform encoding: Sequence of number which represent the sequence of values generated by sampling the time varying signal. Example: sine tone» Values of the sine signal at sampling times. Model encoding: Define a source model Model parameters are derived from the signal The signal is rebuilt from parameters using the model Example: sine tone» Model: sine generator» Parameters: amplitude, frequency, and phase» Rebuilt using a properly set signal generator. 17/04/ ATLCE - D DDC 2013 DDC 57

58 Waveform encoding Sequence of samples example: sine tone» Values of A sinωt for t = K Ts 10 V Ts = 0,2 ms 2 1 t (ms) Values: 8, -1, -10, -7, +2, +10, +5, -6, -10, -4,. 17/04/ ATLCE - D DDC 2013 DDC 58

59 Model and parameters Phase Period T Peak value V 1 2 t [ms] Model: v(t) = V sen ( t + ) Parameters: V = 10 V = 2 f = 2 /T = 5.2 krad/s = 0,3 = 0,9 rad 6 decimal digits 17/04/ ATLCE - D DDC 2013 DDC 59

60 SNR for model encoding Which factors influence SNR? Waveform encoding Sampling rate Resolution of samples (bit number) Model encoding Model accuracy Correctness and resolution of parameters 17/04/ ATLCE - D DDC 2013 DDC 60

61 Example of model encoding LPC (Linear Predictive Coding) for voice signals Based on a vocal segment model (larinx) Signal is divided in frames (10-30 ms) For each frame:» voiced/unvoiced decision» evaluation periodicity step (pitch)» Evaluation of adapted filter coefficients Voiced: complex waveforms repeated» Pulse generator at pitch rate» Filter to generate the waveform Unvoiced: filtered noise» Noise generator + filter 17/04/ ATLCE - D DDC 2013 DDC 61

62 Block diagram of LPC decoder PITCH PULSE GENERATOR VOICED FILTER PARAMETERS FILTER NOISE GENERATOR UNVOICED 17/04/ ATLCE - D DDC 2013 DDC 62

63 Model encoding: performance Standard criteria: speaker recognition (A) speech understanding (B) Waveform encoding speed (kbit/s) log PCM 64/32 Differential 32/16 Adaptive Differential (ADPCM) 4 (only B) Model encoding LPT (GSM phones) 9,6 Frequency slots vocoder 4,8 LPC 2,4 17/04/ ATLCE - D DDC 2013 DDC 63

64 Lesson D5 final test Which parameter controls the dynamic range of a differential ADC? Explain the structure of delta-sigma ADC. Which are benefits and drawbacks of oversampling? Describe techniques to reduce noise in differential converters. Explain noise shaping. Which are the benefits of logarithmic conversion? What happens for signals close to 0 in a log ADC? Which are the differences between A and μ log approximations? Which parameters influence S/N for model encoding? Describe features of waveform and model encoding techniques. 17/04/ ATLCE - D DDC 2013 DDC 64

Telecommunication Electronics

Politecnico di Torino ICT School Telecommunication Electronics C5 - Special A/D converters» Logarithmic conversion» Approximation, A and µ laws» Differential converters» Oversampling, noise shaping Logarithmic