Software Defined Radio Course - Introduction_2_

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					         Software Defined Radio

Lec 6 – Digital Generation of Signals

                           Sajjad Hussain
Outline for Today’s Lecture
    Digital Generation of Signals
    1.   Introduction
    2.   Comparison to Analog generation
    3.   DDS Techniques
    4.   Analysis of Spurious Contents
    5.   Band-pass Signal Generation
    6.   Performance of DDS Systems
    7.   Generation of Random Numbers
    8.   ROM compression techniques
Digital Generation of Signals - Introduction
   Many of the traditional analog techniques of radio design
    have thus far proven to be inefficient and unsuitable for
   Development of increasingly fast and efficient digital ICs
    and better digital design techniques have made software
    radios a reality
   It is therefore important to understand the components of
    the underlying architecture, which actually define the SDR
    and its capabilities
   E.g. synthesis of waveforms – sinusoids (modulation,
    pulse-shaping, filtering etc.)– important part of comm. sys.
Digital Generation of Signals - Introduction
   Analog techniques have long dominated frequency
       Bulky analog devices – quartz crystals, inductors, capacitors,
        mechanical resonators
       Digital techniques – more accurate, easy to manufacture with
       Direct Digital Synthesis – DDS –generation of waveforms directly
        in discrete time
Direct Digital Synthesis - DDS
    History
         Earlier designs – 1970s – for audio signal applications – from
          sampled values of sine wave in ROM later driving DAC
         Modern approaches – much improved and mostly derivative of the
          classical approach
         Practical use in Comm. System by 1990s
         1980s – Highest freq. - < 10 MHz– limitation of DAC tech.
         Current DDS systems – 100s of MHz
    Advantages
         Preferred form of signal generation nowadays
         Precision
         Fast switching capability
         Generation of arbitrary wave-shapes
         Small low-powered devices – portability
         Fewer components per system – low costs
         Fewer assembly operations / reduced product reject rates
    Direct Digital Synthesis - DDS
   Allow carrier modulation in digital domain and then
    to DAC
   AM Modulation :
      Multiplyingsinusoidal output of ROM with modulating
       signal and then to DAC
   PM modulation :
      Changing instantaneous phase angle
      Using the modulating signal to alter the   input to the
       ROM (phase)
   FM
      Varyinginstantaneous frequency
      Using modulating signal to increment the phase
    Comparison of DDS with Analog Synthesis
   Common Approaches
      DAS – Direct Analog Synthesis
      PLLs – Phase Locked Loops

      DAS
           From crystals freq. and their harmonics combinations
           Advantages :
                 High purity and low spurious outputs -> -80 dB
                 Fast frequency switching till 0.1 μs
           Disadvantages
                 Limited by size, cost and power consumptions – improper for
                  portable applications
           Applications : medical and radar imaging, spectroscopy, radar
Comparison of DDS with Analog Synthesis
   PLLs
       Feedback mechanism for tracking a given freq.
       VCO, Phase detector and loop filter

       Advantages
            Very low level of spurious contents
            Comparatively low cost

         Disadvantages
            Relatively higher level of phase noise as compared to DAS
            Inherently slow freq. switching times due to loop filter
             settling delay
    Comparison of DDS with Analog Synthesis
   DDS overcomes most of the problems associated with DAS
    and PLLs
   Advantages
        Ease of implementation
             VLSI implementations are inexpensive and readily available
             Size of equipment is fraction of that of similar analog synthesizer
        Precision
             Use in systems demanding tight freq. control
                   Most of today’s DDS designs provide step sizes as fine as 1 mHz or
        Stability
        More stable response than analog versions
             Stray in freq. because of changes in temperature, humidity and other
              factors influencing analog components response
             Limited to use in less demanding applications w.r.t tight freq. control
DDS Advantages
   Advantages
       Flexibility - Easy to perform digital tuning (BW, resolution)
       Fast Switching : Output is smooth, transient-free and phase-
        continuous during freq. change – crucial in fast Frequency
        Hopping systems
       Spectral Purity Solution : Ability to consistently and precisely
        predict the performance of digital components of a DDS system
   Disadvantage
       Presence of spurious frequencies. in output signal – challenging
        problem to tackle
Approaches for Direct Digital
   Nyquist constraint
     Maximum    attainable output freq. limited to Fclk/2
     Exploitation of spectral replication, creation of a signal
      with center freq. higher than clock freq.
   Common Approaches
     ROM     Look-up table approach
          Phase-truncation distortion
          Analysis of Output Sequence
     Pulse-Output     DDS
Pulse-Output DDS
   Very simple implementation
   Used for generation of pulse, saw-tooth or rectangular
   Basic idea :
       Cycling through an accumulator, as a way to create an
        adjustable pulse-frequency from a stable high-frequency driving
       N bit adder and register to form an accumulator
       A freq. word Δr is added to the accumulator once every clock
        period Tclk
Pulse-Output DDS
   The output of the accumulator S(n), at time n is given by

   The accumulator will overflow, and the counter resets on
    average once every 2N/ Δr clock periods
   The average freq. for which the counter is reset is

   The output of this synthesizer could be the carry output of the
    accumulator for the pulse output or the MSB of the output for
    approx. square-wave output or S(n) for a saw-tooth output
ROM Look-Up Table Approach
   ROM LUT approach uses sampled
    values of a periodic function stored in a
   Every clock cycle, a value of the
    periodic function stored in the ROM is
    output through a DAC to generate the
    synthesized signal.
   Output from the DAC is often a
    distorted version, due to sample-and-
    hold nature of the waveform –
      use of LPFs and amplifiers
      Sometimes use of pre-DAC digital
       filtering to cater for analog distortion
ROM Look-Up Table Approach
   Structure :
      Based on a single crystal oscillator, which generates a reference clock
      Use of accumulator = Adder + Register
      ROM
   Function :
        The output of the accumulator takes the form of an address used by a
         ROM LUT that contains the waveform samples.
        The number of clock-cycles needed to step through the entire ROM LUT
         defines the time-period of the waveform along with the step-size Δr
        LUT contents – digital representation of the desired waveform – digital
         words describing the amplitude of the waveform as a function of phase
        Address generated by the adder represents the phase value of the
        Example of ROM LUT with 512 addresses

   Extensive pipe-lining can be used to speed-up the flow of data to
    achieve an output freq. in excess of hundreds of MHz
   Phase – Truncation distortion :
       As previously described, the step-size Δr determines the output
        frequency where Fout = ( Fclk * Δr ) / 2N

       Nyquist criterion limits the output freq. to half that of the input clock
            Taking the smallest possible change in Δr = 1, the freq. resolution can be
             found as ΔF = Fclk / 2N

       Example :
            Max. output freq. = 2.5 MHz with tuning-step = 1 Hz  Fclk should be 10 MHz
            Sufficient accumulator width  2N = Fclk / ΔF  smallest N = 24
            Size of LUT = 224 = 16 MB  having this size of memory on board is costly
            LUT size can be reduced by storing only one-fourth the period of the sine-
             wave and repeating it with necessary sign inversions  still 4 MB
            Solution – Phase truncation
DDS with ROM-LUT – Phase truncation
   In phase truncation, not all of the N bits
    of the phase accumulator are used to
    address the ROM
   If we choose any W such that W< N,
    for address of the ROM LUT, then the
    phase will be held for some time before
    moving ahead depending upon the
    value of W.

   Example :
        A 3-bit DDS accumulator, but only 2 of
         the MSBs (W=2) of the accumulator are
         used to address a 2*8 ROM
DDS with ROM-LUT – Phase truncation

   In phase truncation, not all of the N bits of the phase accumulator
    are used to address the ROM
A rudimentary DDS system
Analysis of Output Sequence
   Phase accumulator uses the modulo 2N property of an N
    bit accumulator to simulate the modulo 2π property of the
    sine function
   ROM serves as LUT, converting its Index (phase) into sine
    amplitude samples
   Output freq. = ( Fclk * Δr ) / 2N and phase-increment per
    clock-cycle = ( Δr * 2π ) / 2N
   Fastest output freq. – Nyquist vs. practical  Fclk / 2 ,
     Fclk / 4.5
       Slowest output freq.  Δr = 1  Fout = Fclk / 2N
   Use of LPF at the output of DAC for images removal
Analysis of Spurious Signals
   Purpose of output filters of DDS system  interpolate
    the discrete time signal and minimize spurious outputs.
       Cannot completely remove all non-linear distortions 
        modeling of noise at different points of system
   Three major sources of error :
       Amplitude truncation because of finite no. of bits  not the
        major source of error
       Phase truncation  use of truncated no. of bits to address
        ROM  major source of error
            Location of spurs due to phase-truncation alone occur at integral
             multiples of freq f given by

       Resolution of DAC  for periodic signals, harmonic spurious
        frequency components
Sources of Spurious Signals in a
DDS System
Phase-truncation errors
   For every output freq., a subset of the ROM LUT values
    are used to synthesize the signal, which impacts the
    spurious signals in the final output.
   No. of address-lines to ROM vs. no. of output bits
       Optimum no. of bits required  W-1or W-2 depending upon
        whether entire sine-wave or 1/4th of the values are stored
   Given that at least two samples are needed to represent
    a periodic waveform, the range of Δr is constrained from
    1 to 2N/2.
   No phase-quantization occurs when LSBs which are
    ignored by ROM are always 0. Thus there are 2w/2 freqs
    for which phase-quantization does not occur
   Total no. of frequencies generable ( Nyquist criteria ) vs.
    Freq. without phase-quantization effect. For N = 32 and
    W = 14…>>>Total combinations possible 231, but without
    phase quantization 213.
Effect of Large na and small W
Effect of having small na and large W
Spurious Components due to periodic jitter
   Signal periodicity controlled by Δr and size of accumulator N
   Depending upon how many periods (k) of the fundamental
    output period N are required to return to the original state 
    defines the mount of harmonic spurious signals at (1/k)th the
    original freq.
   Another periodicity is generated, denoted by P, for which the
    phase relation S(i)= S(i+P), for all i.
   While main output freq. given by Δr / (Tclk * 2N ), other
    periodicities will be determined by 2N / gcd (Δr , 2N )
   Only Δr = 2G (G<N) generated a solution gcd (Δr , 2N ) = Δr
   However, for the majority of Δr,, this is not the case , and the
    secondary periodicity will manifest itself as a spurious signal
Spurious periodicities
Spurious Components due to periodic jitter
    For N=4 and Δr = 6  period of the secondary term = 8
    Normalized main output freq. period is (16/6)Tclk = 2.666
    Hence the spectrum of a digital sine, at the output of a
     ROM (with no amplitude truncation) consists of principal
     (2.666 *Tclk ) and secondary (8 *Tclk) periodicities
    The ratio between them is 3, therefore a spurious signal at
     the fundamental frequency ± 1/3 and its harmonics will
    The output spectral lines, of which only one is the desired
     signal, will show all periodicities that are multiples of
     (2N *Tclk) / gcd (Δr , 2N )  this is the fundamental
     relationship for locating spurious signals
Band-pass Signal Generation
   Spectral images can be used to obtain higher freq. than the sampling
   Images will appear at n*Fsamp ± Fsine
   The roll-off in the amplitude of aliased images follows the sinc(x)
    function due to the non-ideal nature of the ADC
        Non-ideal ADC – pulses of finite width instead of infinitely narrow pulses
   Real signals – presence of spurious signals due to phase and
    amplitude truncation  SFDR of the signal
   Spurious energy due to non-linearities inherent in the DAC
   Higher output freqs. require higher order DACs and sometimes require
    a combination with PLLs or heterodyne mixers
Sinc effect for bandpass DDS
Performance of DDS Systems
   First limitation comes from the presence of spurious
        Sources of spurious signals
             Amplitude truncation
             Phase-truncation
             DAC- non linearities
   Other limitation comes from bandwidth – Nyquist Criterion –little a
    problem now in the presence of high-speed FPGAs and DSPs
   Relation of chosen output freq. with clock freq.  presence of spurs
   Possible to predict spurs in digital signals, however, the non-linearities
    added in the analog part of DDS (=DAC) are difficult to model
   This along with some errors introduced by ROM that are not
    analytically traceable -> use of empirical models
   Measurement based model
Use of Hybrid Systems
   DDS Systems make a trade-off between bandwidth and spectral purity
   In a DDS using ROM-LUT , freq. resolution is determined primarily by
    word-length of phase accumulator
        Greater resolution with more bits to accumulator but need to reduce
         phase-truncation for same spectral-purity (More ROM)
   PLLs
        High switching-times but good characteristics
   Hybrid structures that retain good qualities of both the systems
   Hybrid DDS-PLL system
        Using the output of DDS as a freq. reference for the PLL
        DDS can provide very high resolution and high switching speeds
             Possible to obtain very small increments of Fref and it can also be varied at very
              fast rate  not possible with traditional PLL
        Spectral purity of hybrid system largely defined by spectral purity of PLL
Hybrid DDS-PLL system
Applications of DDS Systems
   High freq. switching enablers
     Can  be as high as one clock-cycle plus delay added by
      output filter
     Generate signals for paging radios, mobile phones and
      multi-mode radios
     Use in FH-SS systems – fast switching with spectral
      purity required
     For testing equipment/electronics for different freqs +
      creating custom and arbitrary waveforms
     Capturing waveform with oscilloscopes/ data-recorders
      and reproducing using DDS

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