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A.C. Voltage waveforms and harmonics?

  1. Sep 17, 2011 #1
    Hi, I have the following question:

    An A.C. voltage, V comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging.

    (1) Write down an expression for the voltage waveform

    (2) Given an ideal V = 100V rms, what is the percentage error at 20ms (milliseconds)?

    I have an idea for the first part (see below) but clueless as to the second, can anyone help please? I guess the first step would be to work out the voltage at 20ms but from there...?

    (1) Since V = Vrms x sqrt2 = 141.4V at 120Hz

    3rd harmonic = 20% of 141.4 = 28.3V at 360Hz

    5th harmonic = 10% of 141.4 = 14.1V at 600Hz

    v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)]
  2. jcsd
  3. Sep 17, 2011 #2

    rude man

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    You're comparing two voltages and so error should be obvious? If you get $0.38 in change and you should have gotten $0.40, what's the error in the change you got? :-)
  4. Sep 17, 2011 #3


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    Staff: Mentor

    Once you have the expression for voltage as a function of time, you can substitute any value of t to determine the instantaneous value at that time. Compare this with the value of an undistorted sinusoid at that time.
  5. Sep 18, 2011 #4
    Ok so using the equation in (1), V at 20ms = 36.8 + 20.1 + 13.7 = 70.6V

    Would this mean that the error is 29.4% !? That seems like a massive error, where has my equation gone wrong?
  6. Sep 19, 2011 #5


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    Staff: Mentor

    For many applications, providing the approximation to a sinusoid gives the same heating or average effect as would the ideal waveform, it will satisfy our need. To judge whether your answer is probably correct, or probably not, try graphing V(t). You could overlay it with a sinusoid and adjust its phase shift for best fit, to visualize the error. An online plotter may be convenient. http://rechneronline.de/function-graphs/" [Broken]
    Last edited by a moderator: May 5, 2017
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