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ttokoro
21-Topaz I
ttokoro21-Topaz I
21-Topaz I
May 6, 2025
Solved

Make equivarent sine waveform that has maximum value = 1 and RMS = 1/sqrt(2).

  • May 6, 2025
  • 3 replies
  • 1128 views

Show another waveform that is equivalent to a sine wave with a maximum value of 1 and an effective value of 1/sqrt(2), and find its Fourier series so that the effective value of the Fourier series is 1/sqrt(2).

 

Below is an exsample of the answers.

 

image.pngimage.pngimage.pngimage.png

Best answer by Werner_E

So here is the alternate signal:

Werner_E_0-1746582478732.png

 

 

3 replies

W
Werner_E25-Diamond I
25-Diamond I
May 6, 2025

I'd be really curious to see how you get from em(t) with m->infinity to the expression for E using the usual RMS definition (integral) and the symbolic calculation possibilities of Prime 😈

    W
    Werner_E25-Diamond IAnswer
    25-Diamond I
    May 7, 2025

    So here is the alternate signal:

    Werner_E_0-1746582478732.png

     

     

      ttokoro
      21-Topaz I
      ttokoro21-Topaz IAuthor
      21-Topaz I
      May 9, 2025

      Chopped DC can make 1/sqrt(n) RMS waveform by 1/n chopping.

      Another waveforms with same 1/sqrt(2) RMS are there. Red dotted lines are fundamental component of Fourier series.

      If anyone has another waveform with 1/sqrt(2) RMS, please share here your waveform and Fourier series.

      image.pngimage.pngimage.pngimage.pngimage.png

      t.t.
      ttokoro
      21-Topaz I
      ttokoro21-Topaz IAuthor
      21-Topaz I
      May 9, 2025

      My above answers have Average values

       image.png,.image.png

      So, they are not 2/pi of sine waveform.

      Therefore, the next probrem is find RMS=1/sqrt(2) and Average=2/pi but not sine waveform.

       

      t.t.
      ttokoro
      21-Topaz I
      ttokoro21-Topaz IAuthor
      21-Topaz I
      May 15, 2025

      image.pngimage.pngimage.png

      image.png

      t.t.
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