Download Software Defined Radio Course - Introduction

Software Defined Radio
Lec 12 – Data Converters –
ADC/DAC
Sajjad Hussain,
MCS-NUST.
Outline for Today’s Lecture
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A/D Converters for SDR
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Intro + parameters of interest
Sampling
Quantization
Parameters of practical data-converters
Impact of Interference and Noise on Dynamic
Range
 Techniques to improve performance
 Different structures for ADC/DAC
ADC and DAC
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Proper selection of DAC/ADC is one of the most challenging steps
in SDR design
Determining factor for the overall performance –> power,cost,BW
etc
System design ADC/DAC performance dependent  better
performance needed for broadband IF sampling than for
narrowband super-heterodyne receivers
Ideal SDR  data-conversion at RF requires
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Very high sampling-rate
High no. of quantization bits – high dynamic range
Large SFDR to recover small signals in presence of large interferers
High BW – dynamically varying range of freqs.
High power and price
Tradeoff b/w BW and Dynamic-range

Selection of data-converters has effects on multiple-aspects of
system-design
Parameters of Ideal Data-Coverters
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Conversion of a signal
(analog in time and value )
to a representation
(discrete in time and value)
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1.
Sampling (reversible
process subject to
constraints)
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2.
Sampling (Discretization in
time) and Quantization
(Discretization in Value)
Mathematical Analysis
Nyquist Zones
Sampling and Aliasing
Bandpass Sampling
Quantization
Data converters
Sampling
Sampling
Mathematical
analysis
Nyquist Zones
Band-pass sampling
Sampling
Sampling
Anti-aliasing Filter

For SDRs Anti-Aliasing filters creates additional
problems 
 Front-end
of SDR should be freq. and BW
independent
 Shifting of processing burden from flexible RF to
data-converters – filter limitations
 MEMs technology for flexible analog filters
Bandpass Sampling - Undersampling
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Frequency translation via sampling  bandpass
to baseband
Nyquist theorem – twice the BW vs. twice the
Fmax
Practical limits  BW of the data-converter,
which limits the highest input freqs. that can be
processed w/o significant distortion
When the relationship b/w Fc and Fs/2 is odd, an
inverted image if at the first image freq,
otherwise the same image
Down-conversion through Band-pass Sampling
Relationship between Fc and Fs/2
Usefulness of Band-pass Sampling
– Sampling two separated tones
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Along with the constraint that each signal
remains within a single Nyquist zone the
new-constraint that both the systems should
not overlap within a Nyquist Zone
Quantization
Quantization
Quantization
Noise + SQN ratio
Non Uniform Quantization
Quantization
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Mapping a continuous valued signal onto a
discrete set of levels
of quantization levels -> 2B
 Range of quantizable input voltages
 Step-size -> width of quantization level
 No.
Quantization error
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e(x) = xQ – x
Max (e(x)) = ±LSB/2 = ±Δ/2
Quantization error can be viewed as an additive
signal that distorts the input signal – random,
uncorrelated
Unavoidable but can be minimized –
oversampling
Another distortion linked with quantization 
overload distortion -> V exceeds Vmax
Improper placement of quantization levels due to
fabrication flaws
Quantization Error
Quantization Noise
For analysis of Quantization Noise, input
signal samples assumed to be random,
zero-mean, uniformly distributed over
quantization- range [-Δ/2 Δ/2]
 PDF of e(x) 
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Quantization noise power
Signal to Quantization Noise Ratio
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Useful metric to see how much distortion will be
introduced
For a uniformly distributed input –
Each additional quantization bit results in an SQNR
improvement of about 6 dB
Many signals are non-uniformly distributed across the
complete voltage range
Non-Uniform Quantization
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Min MSE for uniformly distributed input by using data-converter with
uniformly distributed quantization levels
For non-uniformly distributed  min MSE by concentrating
quantization level in voltage regions where signal more probable
Optimal non-uniform quantization-levels distribution??
Lloyd-Max algorithm
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Method for locating boundaries for quantization-levels based on pdf of
input signal
 Flexibility for dynamic changes in quantization levels for wireless SDR
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Instantaneous companding
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Pre-processing by non-linearity to alter quantizer response
Companding for speech-processing in SDR
µ-Law Companding
Over-sampling
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Increasing the sampling-rate can be used to improve system SNR
Total Quantization noise power remains same but Quantization-Noise
PSD decreases with increasing sampling-rate
If a filter is placed after the quantizer, so that filtered signal is tightly
limited to input signal BW, the quantization noise power in the band
of interest decreases with increasing sampling frequencies
Over-sampling
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Final SQNR
With every doubling of the over-sampling
rate, and thus every doubling of Fs, the
SQNR improves by 3dB
 Impact on processing requirements?
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 Any
solution to this?..
Overload distortion
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Occurs when the input signal exceeds the
max. quantizable range of ADC – Vmax
 Increased
 Totally
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MSE + severe harmonic distortion
eliminating overload is very difficult
Use of AGC
ADC Overload Characteristics
Parameters of practical data
converters
Parameters
of practical data-converters
Generic model
Dynamic Range
Timing considerations
Power consumption
Bandwidth
Parameters of practical data
converters
Performance of data-converters is
significantly influenced by data-converters
physical device characteristics
 Phase errors, bit-errors, non-linearities,
thermal noise, power-consumption etc.
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Physical Models for ADC/DACs
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Anti-aliasing filter
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Sample-and-Hold
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Band-limits the input signal so that no distortion of the images in the first Nyquist
zone
Provide quantizer a constant value for the sampling period
Simple RC circuit has dramatic impact on performance of ADC
Settling-time, clipping, filtering
Quantizer
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Collection of resistor and comparators to compare input value to quantized levels
Encoder circuit to be implemented in digital logic to give the digital word
Generic 1-bit Quantizer
DAC
DAC – conceptually reverse of the ADC
functionality
 Decoder
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 Maps
digital words onto discrete values
 Complex network of resistors and switches
2 -- Practical Transfer Characteristics
Considerations
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Transfer Characteristics -> relation
of data converter’s output-to-input
Ideally linear and monotonic outputs
from quantizer (ADC encoder) and
decoder (DAC) circuit
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Increase in output proportional to
input step-size
Relationship using linear eq.
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D = K + GA (ADC)
 A = K + GD (DAC)
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Practical data-converters because of
variations in resistor network values
deviate from this linear response
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Gain error
Offset Error
Non-Linear Transfer Characteristics Errors
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Integral Non-Linearity (INL) –
maximum deviation from the
ideal characteristics. For
calculating error
Differential Non-Linearity
(DNL)
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Variation in size of each
quantization-level w.r.t. each
desired step
These errors lead to
distortion -> reduced
dynamic range for the dataconverters
Dynamic Range Considerations
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Wireless scenario  desired signal +
interference
Extraction of ‘desired’ signal requires
information about the interference 
accomodating the interference  high
dynamic-range of the data converters
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Dynamic Range of an Ideal DataConverter
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Dynamic Range of a Practical DataConverter
Dynamic Range Considerations
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Important Aspects
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Full-scale range utilization
Thermal Noise
Harmonic Distortion and SFDR
Inter-modulation Distortion
SNDR
Full Scale Range Utilization :
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% of the full-scale range utilized by the input signals
When input signal occupies less than 100% FSR, resolution is lost
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FSR is dependent on the gain at the front-end
 Static gain and dynamic gain?
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Thermal Noise
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Electrons movement in front-end resistive components
 Adverse effect on wideband signals
 SDR with AMPS and WCDMA
Dynamic Range Considerations
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Harmonic Distortion and
SFDR :
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Data conversion is a non-linear
process  harmonic
distortions
Total harmonic distortion
SFDR using the strongest
spurs only
Dynamic Range Considerations
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Inter-Modulation Distortion :
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Cross-product of multiple tones into a non-liner device
SDR – simultaneous digitization of multiple signals
For two tone f0 and f1, harmonics are at mf0 – nf1
Difficulty in prediction for inter-modulation components amplitudes
(depend on device non-linearities), necessitates empirical means.
Data-converter datasheets with IMD measurements (for a particular
freq., temp., power)
For SDR – use worst case scenario
Noise Power Ratio Test
Signal to Noise-and-Distortion ratio (SINAD)
Effective No. of Bits
Noise Power Ratio Test
Variation of SNR and SINAD w.r.t
Freq.
Practical Timing Issues
Performance of data-converters depend
on accuracy and stability of the system
clock – high sampling-rates
 Aperture jitter and glitches (sample and
hold circuit (ADC) and decoder circuit
(DAC))
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Aperture Jitter
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Sample to sample
uncertainty in the
spacing b/w pulses –
aperture jitter
 Uncertainty
 ISI
of phase
SNR degradation due to aperture
jitter
SNR relation with Jitter
-If jitter time is large, increasing ADC specs from 2 to 16 bits only
improves the SNR by 2 dB.
-For low frequency signal, only sampling rate and resolution
required to measure noise but for high freq signals aperture noise
should also be included.
Glitches
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Glitches
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Transient incorrect voltage
levels because of timing
error in switches in DACs
Most severe when MSB
changes – most voltage
change
Methods to minimize
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Double buffering
Deglitching circuit
(functionally same as
Sample-and-Hold)
Other Parameters affected by
‘Practical’ Data-converters
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Analog Bandwidth
 RC
circuits in the data-converters (Sample and Hold
circuit) act as low-pass filters attenuating higher-freq
input signals
 Varies with input power – multiple specs given
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Power Consumption
 Important
parameter to consider when selecting data-
converter
 For the ADC to fully use the resolution available, its
quantization noise power should be less than the
thermal noise power at data-converter input
Power Consumption
Impact of Noise and Distortion on
Dynamic Range Requirements
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For SDR – highly dependent
on waveform and environment
used
Care so that interference
neither under-ranges or overranges ADC
Min. Quantization noise
desired
For a specific environment,
required dynamic range is a
function of signal power,
interference power, noise
Dynamic Range Requirements
GSM ADC Design
Pulse –Shaping & Receive/Matched Filtering
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For symbols-to-waveform conversions
Main reason – shaping the bandwidth
Pulse Requirements
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The value of the message at time k does not interfere with the value of
the message at other sample times (the pulse shape causes no intersymbol interference)
 The transmission makes efficient use of bandwidth
 The system is resilient to noise.
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The pulse shaping itself is carried out by the ‘filtering’ which
convolves the pulse shape with the data sequence.
Receive/Matched Filtering  Signal to Symbols
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Correlation
Choosing 1 out of M samples
Quantization to the nearest alphabet value
Pulse-Shaping
Sampling for waveform-to-symbols
Inter-Symbol Interference
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Two scenarios
 Pulse-shape
longer than Tsym
 Non-unity channel with delays
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Tradeoff between BW and Tpulse
Eye Diagrams – Different Pulses
Nyquist Pulses
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Ideal Sinc pulses
 No
interference and
band-limited but
infinitely long
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Other pulse –shapes
that are narrower in
time and only little
wider in frequency.
Raised Cosine
Raised Cosine Pulses
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The raised cosine pulse with nonzero β
has the following characteristics:
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Zero crossings at desired times,
 An envelope that falls of rapidly as compared
to sinc