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Does not have any harmonics

Discussion in 'Electronic Basics' started by karthikbalaguru, Jan 1, 2008.

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  1. Hi,
    Why does a sinusoidal waveform alone does not have any harmonics or
    distortion ?

    For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
    Sawtooth wave of constant period contains odd and even harmonics
    Square wave of constant period contains odd harmonics
    Triangle wave, (an integral of square wave) contains odd harmonics

    But, How is it possible that sinusoidal wave alone does not have any
    harmonics or distortion ?
    I searched the internet,but i did not find any link/pdf that talks in
    detail about these .
    Any ideas ?

    Thx in advans,
    Karthik Balaguru
     
  2. Joerg

    Joerg Guest

    Just calculate the FFT of a sine wave :)
     
  3. David Wright

    David Wright Guest

    A continuous sinewave with infinite duration in an ideal distortionless
    transmission medium would only have the fundamental in its spectrum.
    However, real-world finite duration sinewaves in distorted transmission
    system would have some harmonics. These harmonics would not be as
    pronounced as those of an impulse waveform. However, by running the impulse
    through an integrator circuit, the harmonics can be reduced. With a series
    of integrators, of course, you return to to something approaching a
    sinewave. Since most radio transmission are bandwidth limited with filters,
    many of the higher harmonics are hopefully missing.
     
  4. Mike Wahler

    Mike Wahler Guest


    As I understand it, a harmonic *is* a sine wave. So I suppose if
    you consider something to contain itself, a sine wave contains a
    (single) harmonic.

    From http://www.ethnomusic.ucla.edu/systematic/definiti.htm :
    Harmonic: Sine component of a complex signal. Thus, a complex
    signal is composed of harmonics. Its frequency is obtained as
    the integer multiple of the fundamental frequency

    Also see:
    http://www.its.bldrdoc.gov/fs-1037/dir-017/_2542.htm

    -Mike
     
  5. David Wright

    David Wright Guest

    Mike is correct. A frequency spectrum consists of a positive and negative
    mirror image of the waveform. This brings up all sorts of interesting
    possibilities - such a SSB or single-sided sideband and DSB or double-sided
    sideband.
     
  6. Don Bowey

    Don Bowey Guest

    (It's not nice to Top Post)

    YOU are talking of modulation products, which is not what the OP was asking.

    Whatever Mike had in mind, it is wrong WRT the OP's question.

    It could have some distortion. It depends on the quality of the signal
    generator. For practical purposes the distortion may not be significant,
    but may be measurable.

    Yes. Complex waveforms are constructed of various harmonics.

    A single frequency sinewave is not a "harmonic" (it is NOT a multiple
    frequency of itself)

    See above.
     
  7. Eeyore

    Eeyore Guest

    Because it doesn't. Read up 'simple harmonic motion'.

    Graham
     
  8. John Fields

    John Fields Guest

     
  9. John Fields

    John Fields Guest

    ---
    Because it's a single pure tone.
    ---
    ---
    Every waveform which isn't a perfect sine wave is made up of more
    than one sine wave, and when they combine they result in the shape
    of the final waveform.
     
  10. Guest

    You were badly brought up. My parents told me that fine dust particles
    suspended in the air scattered my short wavelength light - blue light
    - than longer-wavelength light - the other colours.

    It didn't make much sense to me at the time - I was around four - but
    at least I wasn't mis-informed.

    In fact Eeyore has done a litttle better than your parents did -
    "simple harmonic motion" as a search string does get you to this

    http://en.wikipedia.org/wiki/Simple_harmonic_motion

    which in turn points you to this

    http://en.wikipedia.org/wiki/Complex_harmonic_motion

    which gets you to

    http://en.wikipedia.org/wiki/Harmonic_analysis

    which is probably where the OP needs to go, though they may need a
    fair bit of education before they can get much out of it.
     
  11. Odd and even harmonics are themselves pure sine waves that are
    frequency multiples of a fundamental sine wave. Distortion of a sine
    wave produces odd and/or even harmonics. So, sine waves are
    irreducible pure signals that other signals can be analyzed into.
     
  12. john jardine

    john jardine Guest

    It's a good question.
    Myself I'd say a triangle waveform looks like it should be the one to have
    no harmonics.
    But it's all down to how smoothly the waveform voltage changes. The triangle
    and square have significant 'shape' discontinuities during each cycle and
    these have the effect of creating harmonics.
    The sine wave although a horrible looking non linear waveform, is the one
    with the absolutely smoothest rate of change over all its cycle.
    (DC is even smoother but isn't a frequency :)
     
  13. Eeyore

    Eeyore Guest

    Not QUITE correct.

    Distortion as caused typically by non-linearities in a transfer
    characteristic such as in an amplifier may be modelled and indeed measured
    as harmonic distortion but the mechanism producing it is typically
    producing a wide range of harmonic products of which typically only a few
    may usually be considered of interest.

    Graham,
     
  14. Eeyore

    Eeyore Guest

    Uh ? With those rapid discontinuities ?

    Exactly. Simple harmonic motion. As in a child's swing or a pendulum for
    example.

    Graham
     
  15. Fred Bartoli

    Fred Bartoli Guest

    john jardine a écrit :
    It's more a matter of definition. When you take the view of decomposing
    a waveform on a sine waves base, it is not abnormal that a sine wave has
    just one component on that base: itself. The contrary would be abnormal.

    If you were to decompose a sine wave on a triagular waveforms base
    (which is as valid as the sine waves case), it'd had lots of 'harmonics'
    and a triangular waveform would have just the fundamental.
     
  16. Sorry, but I think it's exactly correct.
    That's a different question.
     
  17. Phil Allison

    Phil Allison Guest

    "Fred Bartoli"

    ** No it is not - you posturing wanker.


    ** No it is not.

    A sine wave uniquely has the property of no harmonics.

    Unlike all other periodic waves, its shape is unaltered after passing
    though any kind of filter.



    ........ Phil
     
  18. Eeyore

    Eeyore Guest

    Phil's right too.

    Graham
     
  19. Eeyore

    Eeyore Guest

    The non-linearities that are/cause distortion *result* in the production of
    harmonics. They don't actually *make* harmonics.

    It's a subtle distinction.

    Graham
     

  20. Fourier analysis (http://en.wikipedia.org/wiki/Fourier_analysis)
    demonstrates that any periodic waveform can be expressed as the sum of a
    series of sine waves. The relationship between the waves frequencies of
    the series is that there is one, called the fundamental, which is a sine
    wave of frequency equal to that of the periodic waveform. All of the
    other waves of the series have frequencies that are integer multiples of
    the fundamental. These are called harmonics.

    If, for your periodic wave, you select a sine wave, then the fundamental
    of the series emulates it exactly. No other harmonics are needed.
    Distortion is a bit different. It is a broad term that refers to a
    change in a waveform between the input and output of some system.

    Used in the context you, it refers to the change in harmonic content
    introduced when driving a system with a pure sinusoidal input.
     
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