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Harmonic Distortion of step-approximation to sine wave

Discussion in 'Electronic Design' started by Norm Dresner, May 16, 2004.

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  1. Norm Dresner

    Norm Dresner Guest

    Is there any www-resource which gives values (or simple ways to calculate
    the values) for the harmonic distortion of various step-approximations to
    sine waves, e.g. 8-bit, 10-bit,...

    TIA
    Norm
     
  2. John Jardine

    John Jardine Guest

    Simply as you find it ...
    8 bits can be no cleaner than one part in 256 parts. Therefore THD
    =1/256th or 1/2%
    12 bits is one part in 4096 parts = 0.025%
    ect ect
     
  3. Don Pearce

    Don Pearce Guest

    Except of course that you naturally generate only a properly dithered
    step approximation, in which case there is no harmonic distortion.

    d
     
  4. John Jardine

    John Jardine Guest

    Yes, a good point. Harmonic distortion can be usefully controlled by adding
    natural or man-made dither. But then one is forced to add a rider caveat
    and specify a particular range of frequencies that this new THD figure (or
    spectrum) is to be measured over. The noise floor grass grows higher and the
    S/N must reduce. Kind of spread-spectrummy, or swapping ac volts in exchange
    for noise bandwidth. The ultimate reduction to a limit, is dithering a
    single bit stream but this now becomes a technically expensive fast DSP
    operation rather than simple analogue processing.
    I much prefer the direct approach. Knowing beforehand which field my errant
    harmonics will choose to graze in and can there pick them off at will. If
    the THD is too high then I'll try for more 'real' bits. If my THD is still
    too high then tough!, I designed it badly in the first place :)
    regards
    john
     
  5. Don Pearce

    Don Pearce Guest

    What you say is true enough for the harmonics, but unfortunately most
    of the discrete product of quantisation is decidedly non-harmonic and
    distributed widely up and down the spectrum. From the point of view of
    measurement, dither noise is easier to deal with, and from the point
    of view of sound quality, dither noise is vastly preferable. Either
    way dither seems to win over non-dither.

    d
     
  6. legg

    legg Guest

    There are a couple of articles covering n-level power conversion
    harmonics, where the number of levels employed is ~ constant and the
    phase angle of the steps is considered. I think you are more
    interested in other things, if you are only starting to consider 8
    weighted levels as a minimum.

    I've always thought this 'full-scale' number pretty irrelevant in
    audio signals, where the program level is so seldom full scale, and
    the distortion is scarcely related to a harmonic, as such. I guess
    you've got to start somewhere, and that's how meaningful distortion
    measurements used to be made, so......

    RL
     
  7. Tim Shoppa

    Tim Shoppa Guest

    If you ignore D/A error... usually integrated D/A converters are specced
    to +/-1LSB linearity and +/- 0.9LSB differential linearity
    which makes it questionable why you're bothering to dither.

    Dithering does make a lot of sense if you have a D/A guaranteed to be
    monotonic (most are) and it's part of a feedback loop where you don't care
    about specs like THD at all. These are important and
    interesting applications but the thought of THD doesn't come up when
    you're talking about them.

    Now if you're building a D/A from scratch or can spec the innards
    of your D/A to be better than 0.5 or 1LSB then the story can be a little
    different.

    Tim.
     
  8. Tim Shoppa

    Tim Shoppa Guest

    If you ignore D/A error... usually integrated D/A converters are specced
    to +/-1LSB linearity and +/- 0.9LSB differential linearity
    which makes it questionable why you're bothering to dither.

    Dithering does make a lot of sense if you have a D/A guaranteed to be
    monotonic (most are) and it's part of a feedback loop where you don't care
    about specs like THD at all. These are important and
    interesting applications but the thought of THD doesn't come up when
    you're talking about them.

    Now if you're building a D/A from scratch or can spec the innards
    of your D/A to be better than 0.5 or 1LSB then the story can be a little
    different.

    Tim.
     
  9. Tim Shoppa

    Tim Shoppa Guest

    If you ignore D/A error... usually integrated D/A converters are specced
    to +/-1LSB linearity and +/- 0.9LSB differential linearity
    which makes it questionable why you're bothering to dither.

    Dithering does make a lot of sense if you have a D/A guaranteed to be
    monotonic (most are) and it's part of a feedback loop where you don't care
    about specs like THD at all. These are important and
    interesting applications but the thought of THD doesn't come up when
    you're talking about them.

    Now if you're building a D/A from scratch or can spec the innards
    of your D/A to be better than 0.5 or 1LSB then the story can be a little
    different.

    Tim.
     
  10. Don Pearce

    Don Pearce Guest

    I think the OP was talking about distortion inherent in the
    quantisation process, rather than simple non-linearities that any
    circuit might have. Having said that, it is very many years since I
    came across any D/A that exhibited non-monotonicity.

    And of course the reasons for dithering are quite unrelated to
    failings in linearity of the D/A, but are addressing the fundamental
    issue of quantisation distortion, which will otherwise occur in even a
    perfect D/A

    d
     
  11. The Phantom

    The Phantom Guest

    Can you post the references?

    where the number of levels employed is ~ constant and the
     
  12. legg

    legg Guest

    I can post links to the ones I've bothered to save.

    What is your specific interest?

    RL
     
  13. The Phantom

    The Phantom Guest

    The topic of this thread; n-level power conversion harmonics.
     
  14. legg

    legg Guest

    Don't forget to google on your own time, if you're really interested.

    The reasons to avoid or encourage specific kinds of harmonic
    distortion, outside of Standards conformance, are probably as
    important as the methods outlined to do so.

    These are the more obvious ones. Two recent references have lost their
    link - if anyone picks up a new link for either of these articles,
    posting it (the link) would be a service.

    RL

    "Opportunities for Harmonic Cancellation with Carrier Based
    PWM for Two-Level and Multi-Level Cascaded Inverters"
    D.Holmes, B.McGrath
    IAS'99
    http://www.peg.monash.edu.au/postgrads/ias99_bmcgrath.pdf

    "Minimization of Total Harmonic Distortion
    for Square Wave Voltage Source Inverters"
    C.Liu1, J.Zhu, V.Ramsden
    AUPEC'99
    http://www.itee.uq.edu.au/~aupec/aupec99/liu399.pdf

    "Optimum Harmonic Reduction with a Wide Range of
    Modulation Indexes for Multilevel Converters"
    S.Sirisukprasert, J.Lai, T.Liu
    IAS'00
    http://manuales.elo.utfsm.cl/conferences/seminarios/Eenergy/DATA/48_02.PDF

    "Multilevel PWM Methods at Low Modulation Indices"
    L.Tolbert, F.Peng, T.Habeytler.
    transPE'00
    http://www.ece.utk.edu/~tolbert/publications/trans_pe_july_2000.pdf

    "Investigation into the Harmonic Behaviour of Multipulse Converter
    Systems in an Aluminum Smelter."
    S Perera, V J Gosbell, D Mannix, N Gersch,
    AUPEC'00.
    http://www.itee.uq.edu.au/~aupec/aupec00/perera00.pdf

    "Voltage Harmonics Generated by 3-Level Converters
    Using PWM Natural Sampling"
    O.S‡daba, P.Gœrpide, J.Taberna, I.Morales, L.Palomo
    Universidad Pœblica de Navarra - **no link
    PESC'01

    "Harmonic Elimination in Multilevel Converters"
    J.Chiasson, L.Tolbert, K.Mckenzie, Z.Du.
    IASTED'03.
    http://www.ece.utk.edu/~tolbert/publications/iasted_2003_harm_elim.pdf

    "A Reduction of the AC Line Current Harmonics in a
    Multilevel-Voltage Source Rectifier"
    S.Brovanov, S.Kharitonov
    Novosibirsk State Technical of University - **no link
    KORUS'03
     
  15. The Phantom

    The Phantom Guest

    I am really interested, which is why I asked. In your first reply
    to the OP, you said, "There are a couple of articles covering n-level
    power conversion
    harmonics...", and it was because you said "article" rather than
    "link", that I made the unwarranted assumption that you weren't
    referring to papers you found on the web. I thought that you, like I,
    had a collection of xeroxes gotten from the library. :)

    I was already aware of Tolbert and Chiasson's interest in these
    topics. Did you notice the paper titled "A Complete Solution to the
    Harmonic Elimination Problem" on Tolbert's web site?
    http://www.ece.utk.edu/~tolbert/publications/trans_pe_mar_2004_complete.pdf

    He seems to have solved the same problem that Don Lancaster
    attacks with his Magic Sine Waves method.
     
  16. legg

    legg Guest

  17. The Phantom

    The Phantom Guest

    Quite so, which is why I followed what you have quoted above with

    " He seems to have solved the same problem that Don Lancaster
    attacks with his Magic Sine Waves method."

    because that is what Lancaster's Magic Sine Wave method does.

    I thought this would explain my digression. :)
     
  18. R.Legg

    R.Legg Guest

    This does not cover multi-level switching - it covers pulse-width
    I am unfamiliar with Lancaster's magic sinewave method. Chiasson, on
    the other hand, seems to have 're-discovered' hysteritic control,
    though how PWM symmetry is intended to be enforced, on a system that
    is variable in any way, is a mystery to me.

    RL
     
  19. The Phantom

    The Phantom Guest

    Go have a look at: http://www.tinaja.com/magsn01.asp

    There has been some previous discussion on this group, and Google
    has some discussion from other forums, but so far no one seems to have
    implemented an actual inverter

    Chiasson, on
     
  20. ddwyer

    ddwyer Guest

    As well as steps also beware transients between stweps out of D/A caught
    me out had to de-glitch with sample and hold.
     
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