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

gfgray

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/LO...%2003DEC07.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

Pulse Width Calculations 09-30-2008.pdf (659.5 KB, 11 views)