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Harmonic distortion

  1. Sep 4, 2015 #1
    A voltage amplifier ideally should have the input-output relationship of
    vo = 100vi but in practice the relationship is vo = vi(98 + 2vi).
    Calculate the %age second harmonic distortion present in the amplifier’s
    output for a sinusoidal input of 10 mV r.m.s

    % harmonic distortion = amplitude of nth harmonic / amplitude of fundnamental

    fundnamental
    98*0.01=0.98 v

    harmonic
    2*2*0.01^2 = 0.004 v


    %= 0.0408


    No frequency has been given. So in am unsure.

    All help is appreciated.

    Thanks
     
  2. jcsd
  3. Sep 5, 2015 #2
    I'm not sure what the question is.
     
  4. Sep 5, 2015 #3

    rude man

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    Calculate the %age second harmonic distortion present in the amplifier’s
    output for a sinusoidal input of 10 mV r.m.s
     
  5. Sep 5, 2015 #4

    rude man

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    That part is right.
    OK
    No no.
    Frequency is irrelevant. So is the 10mV input magnitude.
    You're not comparing fundamental and 2nd harmonic amplitudes. But you must.
    Hint: there is a relation in trig between sin2(x) and cos(2x). Use that ...
     
  6. Sep 5, 2015 #5
    Thanks for your reply.

    sin^2(x) = ½(1 - cos(2x))


    vo = 98vi + 2vi^2

    so vi = sin(x)

    vo = 98 sin(x) + 2 sin(x)^2

    vo = 98 sin(x) + 4 sin^2 (x)

    vo = 98 sin + 2(1 - cos(2x)) = 98 sin + 2 - 2 cos(2x)
     
  7. Sep 5, 2015 #6
    why have i been provided with the "output for a sinusoidal input of 10 mV r.m.s" if it is irrelevant?
     
  8. Sep 5, 2015 #7

    rude man

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    because your instructor wants to see if you're on your toes!
     
  9. Sep 5, 2015 #8

    rude man

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  10. Sep 5, 2015 #9
    I am a bit stuck

    vo=98 sin(x)+(2 sin(x)^2

    vo=98 sin(x)+4(1/2(1- cos(2x))

    Is this correct
     
  11. Sep 5, 2015 #10

    rude man

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    No. Why are you squaring the "2" in "vo=98 sin(x)+(2 sin(x)^2?
    BTW I assume you meant "vo=98 sin(x)+(2 sin(x))^2"
    which is vo=98 sin(x) + 4sin2(x)
    which is still wrong; see my first sentence.

    In case you need it,
    (sin(x))2 is commonly written as sin2(x).
     
  12. Sep 7, 2015 #11
    Looked again at my learning material and I don’t need to sq the 2. Don’t know where I got that one.

    Vo=98sin(x)+2sin^2(x) =98sin(x)+2(1/2(1-cos(2x))

    =1+98sin(x)-1cos(2x)

    fundamental = 98mV

    second harmonic = 1mV

    with a d.c. term of 1mV

    So "harmonic distortion = (amplitude of nth harmonic / amplitude of fundamental)x100".

    %harmonic distortion= (1/98)x100=1.02%
     
  13. Sep 7, 2015 #12

    rude man

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    Very good!
     
  14. Sep 8, 2015 #13
    Thank you for all your help..
     
  15. Sep 8, 2015 #14

    rude man

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    My pleasure!
     
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