Integral of full-wave rectified sinewave, find equivalent sine waveform

  1. 1. The problem statement, all variables and given/known data
    I am given two waveforms (a square wave and DC) that define the maximum allowable operating parameters for an LED. I wish to derive the maximum allowable fully-rectified sine waveform (120hz).
    Square wave: 442mW peak, 0.1ms pulse width, 10% duty cycle
    DC: 87mW

    See attached PDF. Use the power on the right axis instead of current on the left. Also ignore the temperature stuff. I was trying to figure out why the energy for each waveform is different.

    Here is a link to the actual spec sheet:
    http://marktechopto.com/pdfs/Cree/LO566EBL3-70H-A3-MT 03DEC07.pdf

    This is a two-part question. First, how do I write the integral for the full-wave rectified sine? Note that the sinewave's x-axis intersection is advanced/delayed by ~1.12ms. Integrate from 0 to pi?

    Second, how do I deal with the fact that the total energy for the given waveforms is different? Or is this unsolvable?

    2. Relevant equations

    3. The attempt at a solution
    See PDF.
     

    Attached Files:

  2. jcsd
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