Frequency Domain Methods - PowerPoint

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					            Frequency Domain Methods




8/30/2010
            Time Domain  Frequency Domain
                   Vi  Ai sin( 2  f i  t  i )
Amplitude




                                      Amplitude
                             time                     frequency




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  Why go to the Frequency Domain
   • Frequency analysis can show characteristics
     of oscillator:
            – Noise processes
            – Side bands (modulation, parasitic)
   • Spectrum analyzer easy to use to show
     noise far from the nominal frequency.
            – Limited by the bandwidth of the measuring
              system.


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            Detection of parasitic signals
   • Parasitic signals simply adds to the signal
   • Parasitic signal modulates the signal

   • In either case, if the signal is far enough
     from the carrier (greater than the resolution
     of the spectrum analyser available) it can be
     resolved.


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                    Sideband detection

            Sy(f)




                                    frequency



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                    Line width problems

            Sy(f)




                                    frequency



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        Increase time of measurement

            Sy(f)




                             frequency



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            Solution to limited spectrum
                      analyzers
   • Record the data for a very long time using a
     time measurement system
   • Feed your data to a proper analyzer
     software.
   • Convert the time data into frequency data.
   • Interpret the results



8/30/2010
     Time Domain => Frequency Domain
x(t )  A sin( 2  v(t ))  signal in the time domain
                1 d t 
 t    0              " instantaneous" frequency;
               2 dt
               t
 t   0   2  t '  0 dt '
               0
                           
          t   0  t 
y t                      normalized frequency;
             0       2 0

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            Noise in frequency domain
  RMS      S  f  df
   2                                Spectral density of the phase fluctuations

            BW
                                                   2
                               2
                                  0                                Spectral
                 S  f         Sy  f 
                                    RMS

                            BW  f 
                                                                      density of the
                                                                    frequency
                                                                      fluctuations

  Lf   S  f , per IEEE S tandard 1139
         1
          2
  relationsh ip between noise in time domain
                            and frequency domain
                                                         
   y      yk 1  yk                S  f  sin 4 f  df
            1                        2
                                   0 2 
    2                        2

            2                               0

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            Noise in frequency domain
                                             
        yk 1  yk                S  f  sin 4 f  df
          1                        2
                                        2 
     2                     2
     y
          2                      0  0
   • Not very useful to calculate the Allan
     variance from the spectral density of the
     noise
   • Very useful to detect anomalies in the noise
     pattern of a device



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            Common types of noise S ( f )
                                         0
                                     f
                                         1
                                     f
                                         2
                                     f
                                         3
                                     f
                                         4
                                     f
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            Common types of noise

Type of noise          S ( f )       2
                                       0   Sy  f     
                                  0               2
white phase               h2 f             h2 f
                                 1               1
flicker phase             h1 f             h1 f
                                  2                  0
white frequency           h0 f             h0 f
                                   3                 1
flicker frequency         h1 f            h1 f
                                   4                     2
random walk frequency     h 2 f            h 2 f


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                          Types of phase noise
     S ( f )  0
                2


     L f    Log scale
                           random walk frequency : f 4



                               flicker frequency : f 3


                                     white frequency : f 2

                                                 flicker phase : f 1
                                                                      white phase : f 0


                                                          Log scale     frequency


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              Types of frequency noise
      Sy ( f )
                        random walk frequency : f 2
            Log scale


                                                    white phase : f 2



                                flicker frequency : f 1
                                                              flicker phase : f 1

                                      white frequency : f 0
                                                      Log scale   frequency


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                    Power Law Dependence of
                             y()
                     real noise
                              As measured by
            y()             Allan Deviation
                                                          1/f noise
1
   yt   yt 2                 -1
2                   -3/2                                 1/2
                                         -1/2
                                                   0
                                                                  
      Noise type: White     Flicker     White    Flicker Random
                  phase     phase       freq.     freq.  walk freq.


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                   Frequency Analysis
                using a spectrum analyser
   • Advantages of frequency analysis
            – Good detector of modulation/parasitic signals
            – Easier to look at high frequency noise
            – Can discriminate between white and flicker
              phase noise!
   • Disadvantages
            – Not very good for noise very close to the carrier



8/30/2010
            Some examples stressing the
       differences between time domain and
             frequency domain analysis




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            White vs flicker phase noise




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Time domain
             White vs Flicker phase noise
     ADev()                        ADev()

                                              Slope @ -1
                Slope = -1



                                    Not
                                   very
                                 different



                                                          

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Frequency domain
     White versus Flicker phase noise
                                    No
     S(f)             S(f)     ambiguity
                                   here!




                          f -1
         f0


                   f                  f

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            White and flicker phase noise
   • They are often present over the same time
     scale and are difficult to separate.
   • ADev is unable to do it.
   • FFT will tell quickly if white phase noise is
     present, which is very likely for most
     oscillators on short time interval.
   • This is true generally at high frequency
     offset from the nominal frequency.

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            Hydrogen maser example I
   • Case of a “sick” hydrogen maser
   • It has excess white or flicker phase noise.
   • ADev method of evaluation reveals higher
     than normal noise at short term. Unable to
     sort out white from flicker noise.
   • FFT of phase signal sorts out the type of
     noise


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            Hydrogen maser example II

              f0 or f-1




             Which
             one?




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              Hydrogen maser example III

                               f-3

                No f-4                    No flicker phase
  amplitude




                                              noise f-1

                                                             ??

                         f-2
                                     f0




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            Hydrogen maser example IV
   • Frequency analysis has resolved the type of
     noise affecting the performance of the
     maser.
   • Frequency analysis has also revealed the
     presence of parasitic signals.
            – Some of it is due to some 4 seconds cycle
              operation within the phase comparator itself



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            Another way of looking at data:
                   the moving FFT
   • Easy to implement
   • Can reveal intermittent problems




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            Moving FFT I




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                          Moving FFT II
        Moving FFT over sixty days of phase residuals of two hydrogen
        masers reveals strange parasitic signal.




                                                              Modulation
                                                               period =
                                                              one week




              Parasitic
             frequency
             not stable


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            Parasitic signal

                         It turns out that this signal
                         is generated in the path
                         between one maser and
                         the phase comparator.
                         There are three buffer
                         amplifiers and distribution
                         boxes along the path.
                         The one week amplitude
                         modulation tends to point
                         out to interference with
                         normal activities in the
                         building.




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                 Conclusion
   • Frequency domain methods should be used
     as well as time domain methods
   • Both methods are complement of each other
   • Never miss the opportunity to look at your
     data from all angles possible.




8/30/2010