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

In summary, the conversation involved deriving the maximum allowable fully-rectified sine waveform for an LED based on two given waveforms: a square wave and DC. The square wave had a peak power of 442mW, a pulse width of 0.1ms, and a duty cycle of 10%, while the DC had a power of 87mW. A link to the spec sheet for the LED was provided, and the question also asked about writing the integral for the full-wave rectified sine and dealing with the different total energies of the given waveforms.
  • #1
gfgray
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Homework Statement


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%2003DEC07.pdf [Broken]

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?

Homework Equations



The Attempt at a Solution


See PDF.
 

Attachments

  • Pulse Width Calculations 09-30-2008.pdf
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  • #2
I attempted to write the integral but it's probably wrong. I don't know how to deal with the energy differences.
 

1. What is the integral of full-wave rectified sinewave?

The integral of full-wave rectified sinewave is the mathematical process of finding the area under the curve of a full-wave rectified sine waveform. It is a measure of the total energy or power of the signal over a specific time period.

2. How is the integral of full-wave rectified sinewave calculated?

The integral of full-wave rectified sinewave can be calculated by taking the definite integral of the absolute value of the original sine waveform. This involves finding the area under the curve of the positive portion of the waveform and doubling it to account for the negative portion.

3. What is the purpose of finding the integral of full-wave rectified sinewave?

The integral of full-wave rectified sinewave is often used in engineering and physics to determine the average power or energy of a signal. It can also be used to analyze and compare different waveforms and signal processing techniques.

4. How is a full-wave rectified sinewave equivalent to a sine waveform?

A full-wave rectified sinewave is equivalent to a sine waveform in terms of its average power or energy. This means that the integral of a full-wave rectified sinewave will have the same value as the integral of a sine waveform with the same amplitude and frequency.

5. What are some real-world applications of the integral of full-wave rectified sinewave?

The integral of full-wave rectified sinewave has various applications in fields such as electrical engineering, signal processing, and physics. It is commonly used in power analysis and control systems, as well as in the design of electrical circuits and devices.

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