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					    Software Defined Radio

Lec 12 – Data Converters –
ADC/DAC
                    Sajjad Hussain,
                       MCS-NUST.
Outline for Today’s Lecture
   A/D Converters for SDR
     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
   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
     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
    Conversion of a signal
     (analog in time and value )
     to a representation
     (discrete in time and value)
        Sampling (Discretization in
         time) and Quantization
         (Discretization in Value)
1.   Sampling (reversible
     process subject to
     constraints)
        Mathematical Analysis
        Nyquist Zones
        Sampling and Aliasing
        Bandpass Sampling
2.   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
   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




   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
   QuantizationNoise + SQN ratio
   Non Uniform Quantization
Quantization
   Mapping a continuous valued signal onto a
    discrete set of levels
     No. of quantization levels -> 2B
     Range of quantizable input voltages
     Step-size -> width of quantization level
Quantization error
   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) 


   Quantization noise power
Signal to Quantization Noise Ratio
   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
   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
      Method for locating boundaries for quantization-levels based on pdf of
       input signal
      Flexibility for dynamic changes in quantization levels for wireless SDR
   Instantaneous companding
      Pre-processing by non-linearity to alter quantizer response
      Companding for speech-processing in SDR
µ-Law Companding
Over-sampling
   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
   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?
     Any   solution to this?..
Overload distortion
   Occurs when the input signal exceeds the
    max. quantizable range of ADC – Vmax
     Increased    MSE + severe harmonic distortion




     Totally   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.
    Physical Models for ADC/DACs
   Anti-aliasing filter
        Band-limits the input signal so that no distortion of the images in the first Nyquist
         zone
   Sample-and-Hold
        Provide quantizer a constant value for the sampling period
        Simple RC circuit has dramatic impact on performance of ADC
        Settling-time, clipping, filtering
   Quantizer
        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
     Mapsdigital words onto discrete values
     Complex network of resistors and switches
2 -- Practical Transfer Characteristics
Considerations
   Transfer Characteristics -> relation
    of data converter’s output-to-input
   Ideally linear and monotonic outputs
    from quantizer (ADC encoder) and
    decoder (DAC) circuit
        Increase in output proportional to
         input step-size
   Relationship using linear eq.
      D = K + GA (ADC)
      A = K + GD (DAC)
   Practical data-converters because of
    variations in resistor network values
    deviate from this linear response
      Gain error
      Offset Error
Non-Linear Transfer Characteristics Errors

   Integral Non-Linearity (INL) –
    maximum deviation from the
    ideal characteristics. For
    calculating error
   Differential Non-Linearity
    (DNL)
       Variation in size of each
        quantization-level w.r.t. each
        desired step
   These errors lead to
    distortion -> reduced
    dynamic range for the data-
    converters
     Dynamic Range Considerations
   Wireless scenario  desired signal +
    interference
   Extraction of ‘desired’ signal requires
    information about the interference 
    accomodating the interference  high
    dynamic-range of the data converters




   Dynamic Range of an Ideal Data-
    Converter

   Dynamic Range of a Practical Data-
    Converter
Dynamic Range Considerations
   Important Aspects
       Full-scale range utilization
       Thermal Noise
       Harmonic Distortion and SFDR
       Inter-modulation Distortion
       SNDR
   Full Scale Range Utilization :
     % of the full-scale range utilized by the input signals
     When input signal occupies less than 100% FSR, resolution is lost




     FSR is dependent on the gain at the front-end
     Static gain and dynamic gain?
   Thermal Noise
     Electrons movement in front-end resistive components
     Adverse effect on wideband signals
     SDR with AMPS and WCDMA
Dynamic Range Considerations
   Harmonic Distortion and
    SFDR :
     Data conversion is a non-linear
      process  harmonic
      distortions
     Total harmonic distortion


       SFDR using the strongest
        spurs only
Dynamic Range Considerations
   Inter-Modulation Distortion :
       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))
Aperture Jitter
   Sample to sample
    uncertainty in the
    spacing b/w pulses –
    aperture jitter
     Uncertainty   of phase
     ISI
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
   Glitches
       Transient incorrect voltage
        levels because of timing
        error in switches in DACs
       Most severe when MSB
        changes – most voltage
        change
       Methods to minimize
            Double buffering
            Deglitching circuit
             (functionally same as
             Sample-and-Hold)
Other Parameters affected by
‘Practical’ Data-converters
   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
   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
   For SDR – highly dependent
    on waveform and environment
    used
   Care so that interference
    neither under-ranges or over-
    ranges 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

   For symbols-to-waveform conversions
   Main reason – shaping the bandwidth
   Pulse Requirements
      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 inter-
       symbol interference)
      The transmission makes efficient use of bandwidth
      The system is resilient to noise.
   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
      Correlation
      Choosing 1 out of M samples
      Quantization to the nearest alphabet value
Pulse-Shaping
Sampling for waveform-to-symbols
Inter-Symbol Interference
   Two scenarios
     Pulse-shape longer than Tsym
     Non-unity channel with delays


   Tradeoff between BW and Tpulse
Eye Diagrams – Different Pulses
Nyquist Pulses
   Ideal Sinc pulses
     No   interference and
      band-limited but
      infinitely long
   Other pulse –shapes
    that are narrower in
    time and only little
    wider in frequency.
   Raised Cosine
Raised Cosine Pulses
   The raised cosine pulse with nonzero β
    has the following characteristics:
      Zero crossings at desired times,
     An envelope that falls of rapidly as compared
      to sinc

				
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posted:11/3/2011
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