29/06/2011 - 1 ATLCE - D5 - © 2010 DDC

Politecnico di Torino - ICT School

Analog and Telecommunication Electronics

D5 - Special A/D converters» Logarithmic conversion» Approximation, A and μ laws» Differential converters» Oversampling, noise shaping

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Lesson D5: special A/D converters

• Voice conversion, SNRq and dynamic range• Logarithmic conversion

– Piecewise approximation– A and μ laws

• Differential converters– Adaptive converters– Sigma-delta converters– Oversampling, Noise shaping

• Waveform encoding and model encoding– Voice LPC

• References sect. 4.5

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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

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A/D and D/A conversion: where ?

A/D and D/A convertersfor voice signal.

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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– Model encoding

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Voice signal conversion

• Voice signal– exponential amplitude distribution

» more dense at lower levels– wide dynamic range

» SNRq low and variable with signal level

• Logarithmic analog to digital conversion – constant SNRq over a wide signal dynamic range– fewer bits for the same SNRq

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Linear and nonlinear A/D conversion

• Linear A/D conversion– all AD 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 AD 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

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Linear quantization

• AD intervals with constant width

• Constant quantization noise power

• SNRq varies withsignal level(worse for low-levelsignals)

A

D

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Nonlinear quantization

• AD intervals with variable width

• Quantization noise power related with signal level

• SNRq independentfrom signal level

A

D

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Standard conversion

• The A/D conversion adds q noise to analog signal

– D = A + q– AD is constant, therefore

» constant absolute error on D » % error (SNRq) is related with signal level A

A

q

D

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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

q

Dlog

log A

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Nominal SNRq

• Log quantization causes a constant relative error– constant SNRq

SNRq

Level

Full scale

log

lin

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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)

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A and μ approximation - graphs

• Translation (μ law) Replacement (A law)

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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

Full scale (S)1/A

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SNRq with A and μ law

μ law

A law

linear

Linear behavior Log behavior Overload

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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

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Piecewise approximation

Compressed signal

Continuous log law

slope

slope

slope

slope

Input signal

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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

7 6 5 4 3 2 1 0

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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

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SNRq with A and approximation

μ 255 law

A (87.6) law

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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)

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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 2N 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

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Logarithmic ADC

• Sign bit inverts the reference voltage Vr• Segment bits voltage Vs scaled with 2N steps (1, 2, 4, 8, …)• Level bits fed directly to a linear DAC using Vs as reference

Vs

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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)

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Nonlinear DAC block diagram

• Piecewise nonlinear characteristic– Da: segment bits– Db: level bits

+Vr-Vr

Da

LEVELDAC

Db

SEGMENT SLOPE DAC

DECODER/LOOKUP

SEGMENTSTART DAC

+VO

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Lesson D5: special A/D converters

• Logarithmic conversion– Piecewise approximation– A and μ laws– Logarithmic converters

• Differential converters– Sigma-delta converters– Oversampling – Noise shaping

• Waveform encoding and model encoding– Voice LPC– Comparison quality/bit rate

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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

D

A’

DAC

U/D counter CK

SERIALDATA

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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

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Delta converter

• Integrating differential 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).

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Signal in the Delta 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).

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Delta ADC dynamic

• Minimum signal (IDLE state)– Peak level γ/2; idle noise

• Maximum tracked signal– Slew rate γ/Tck overload

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Characteristic of Delta (Δ) 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

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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

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Oversampling vs. Nyquist

X(ω)f

FS10

Main spectrum (baseband) First alias

2FS1

Second alias

X(ω)

f

FS20

First alias

Oversampling

Quantization noise (0-Fs1 band)

Nyquist

Quantization noise (0-Fs2 band)

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Oversampling vs. Nyquist filtering

X(ω)f

FS10 2FS1

X(ω)

f

FS20

Oversampling

Nyquist Steep filter

Smooth filter

Different filters:same quantization noise power (after reconstruction filter)

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Oversampling vs. Nyquist noise

X(ω)f

FS10 2FS1

Nyquist Steep filter

Same filter:reduced quantization noise power (after reconstruction filter)

X(ω)

f

FS20

Oversampling Steep filter

Removed quantization noise

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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

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Filter for Nyquist sampling

A/D

Complex analog LP filter

NYQUIST

X(ω)f

FS0 2FSFS/2

Spectrum segment folded to baseband (aliasing noise)

Steep antialias filter, to limit aliasing noise

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Oversampling: more simple filter

X()

2FS20

Complex, steep digital filter:- reduce noise- reduce bit rate (decimation)

Alias is far away; antialias analogfilter can be simple

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Filters with oversampling

A/D

Simple analog filter

Complex digital filterCan reduce the bit rate (decimation)

NYQUIST

OVERSAMPLING

Complex analog LP filter

A/D

Move complexity from the analog to the digital domain

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Δ converter input dynamic range

• Range of input signals correctly handled– γ corresponds to

the quantization stepAD in a standard ADC

– Input dynamic range: Fck/Fs» Does not depend on γ

• To increase input dynamic range– constant

» possible only to change Fck

– variable (adaptive converters)» Minimum in idle condition (output sequence 0-1-0-1-0-…)» Maximum near overload (output sequences 000… or 111... )

– Remove dependency from signal frequency (ω)» converters

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Numeric example

• Audio signal– Fmax 3 kHz– Sampled 8 ks/s, 8 bit quantization

» Which SNRq ?» Which Fck to obtain the same SNRq with a differential converter?

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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 0-1-0-1… sequence at output– overload: continuous streams 0000… or 1111...

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Adaptive converters

• DAC uses only line signal

Powerestimation

Powerestimation

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Differential converter architectures

• The differential converter can operate on many bits

– The comparator is replaced by an ADC

– A DAC drives the integrator

Integrator

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Digital differential converters

• Integration can occur in the digital domain

– Integrator becomes accumulator

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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

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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

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Sigma-Delta ADC and DAC

• Move integrators on adder input single integrator at the output

• Remove the integrator-derivator in DAC

• Keep antialias input and reconstruction output filters (not shown)

ADC DAC

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Quantization noise in

• In the ADC quantization noise εq is generated after integraton

• Y/N transfer function is highpass

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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

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Oversampling vs. Nyquist noise

Noise power is moved to HF, lower power density in baseband

X(ω)

f

FS20

Noise shaping

Shaped quantization noise

X(ω)

f

FS20

Oversampling Reconstruction filter

Flat quantization noise

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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

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Bit rate reduction

DECIMATOR

INTERPOLATOR

A

A filtered

D serial, High rate

D parallel, Low rate

A’

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Lesson D5: special A/D converters

• Logarithmic conversion– Piecewise approximation– A and μ laws– Logarithmic converters

• Differential converters– Sigma-delta converters– Oversampling – Noise shaping

• Waveform encoding and model encoding– Voice LPC– Comparison quality/bit rate

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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.

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Waveform encoding

• Sequence of samples– example: sine tone

» Values of A sinωt for t = K Ts

• Values: 8, -1, -10, -7, +2, +10, +5, -6, -10, -4, ….

Ts = 0,2 ms

t(ms)

10 V

1

2

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Model and parameters

Model: v(t) = V sen ( t + )

Parameters: V = 10 V = 2f = 2/T = 5.2 krad/s= 0,3 = 0,9 rad

6 decimal digits

Period TPhase

t[ms]1

2Peak value V

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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

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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

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Block diagram of LPC decoder

PULSE GENERATOR

NOISEGENERATOR

FILTER

PITCH

FILTER PARAMETERS

VOICED

UNVOICED

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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

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Lesson D5 – final test

• 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 parameter controls the dynamic range of a differential ADC?• Explain structure of delta-sigma ADC.

–

• Which are benefits and drawbacks of oversampling?

• Explain noise shaping.

• Which parameters influence S/N for model encoding?

• Describe features of waveform and model encoding techniques.