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> Equation With Sine Expressions, LLC resonant converter equations
treez
Posted: August 25, 2012 08:38 am
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Hello,

How do you derive the equation at the bottom left of page three of this.....

http://www.fairchildsemi.com/an/AN/AN-4151.pdf

...that is, how does the expression containg alll the w's come out from the expression containg a sine in the numerator and denominator?..

..is there some standard substitution you can do for the sine expressions?
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Sch3mat1c
Posted: August 25, 2012 05:25 pm
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Substitution, cancellation, substitution again.


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Village Idiot
Posted: August 25, 2012 07:28 pm
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The applicable substitution appears to be:

sin(x)/sin(x)=1
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treez
Posted: August 26, 2012 12:52 pm
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Thanks, i cant find them in maths book, do you just call them "sine substitutions"
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Village Idiot
Posted: August 26, 2012 08:35 pm
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Try looking for "trigonometric identities"

Lot's of info here:
http://en.wikipedia.org/wiki/Trigonometric_identities
Actually, it's a bit of information overload.

Generally, useful in electronics are the sum-to-product and product-to-sum transformations, which you can find on that page.

What I mentioned in my previous post doesn't even qualify as a trigonometric substitution. It was simply two identical terms in the numerator and denominator which automatically cancel out. It had nothing to do with the fact that it was a sine function.
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