Fundamental Component of a square wave

Thread Starter

Christopher B Williams

Joined Jan 9, 2021
5
Hi Guys,
Thanks for a great site.
I have read in multiple sources that the equivalent sine wave of a square wave is (4/pi) * square wave peak.
This looks correct to me, but I am trying to find mathematical proof.
Appreciate any help.

Regards
ChrisW
 

Ian0

Joined Aug 7, 2020
1,121
It rather depends on that you mean by "equivalent", but . . .
The average voltage of a sinewave is found form
\(\dfrac{\int_{0}^{\pi}\sin\theta d\theta}{\pi}\)
The integral evaluates as 2.
\(\dfrac{2}{\pi}\) is therefore the positive-going voltage for the squarewave.
The negative half gives \(-\dfrac{2}{\pi}\)
So the peak-to-peak value is \(\dfrac{4}{\pi}\)
 
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Ian0

Joined Aug 7, 2020
1,121
What you are looking at there is the Fourier transform. Put it into a graph-plotting program such as Veusz and you'll see what they mean.
Start with \(y=\dfrac{4}{\pi}\sin x\)
then try \(y=\dfrac{4}{\pi}\sin x+\dfrac{4}{\pi}\dfrac{\sin 3x}{3} \)
then try \(y=\dfrac{4}{\pi}\sin x+\dfrac{4}{\pi}\dfrac{\sin 3x}{3}+\dfrac{4}{\pi}\dfrac{\sin 5x}{5} \)
 
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Thread Starter

Christopher B Williams

Joined Jan 9, 2021
5
What you are looking at there is the Fourier transform.
Hi Ian,
Correct, but I am trying to get my head around where the 4/pi bit comes from.

I am reading a text book with an interest in high power rectifiers., but mainly my interest is in high power inverters for solar farms.
The ones I have been playing with are generally around 5MW made up of 3 separate inverters.

The bit that got me interested in the 4/pi thing is highlighted in yellow below:

Regards
ChrisW

1610277564959.png
 
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