# half wave rectified sine wave

#### Hiikaru

Joined May 25, 2010
8
Hey guys,

I am having trouble finding a source of information about rectified sine wave harmonics. The equation is in the attached file. I need to derive that question but don't know where to begin, can anyone link me to a few sites? or keywords to type into google?

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#### PRS

Joined Aug 24, 2008
989
I noticed no one answered you. You seem to be in a second electrical circuit course and that was a hard one. The equation you posted seems to be obtained by either a MacLaren or a Taylor infinite series, but it may be obtainable from Fourier or Laplace transforms. I think it is derived from the analysis of a sine wave from zero to pi. The other n terms are due to even n terms in order to exclude the bottom half of the sine wave. I'm not sure about this at all, but I hope this helps somewhat. It's been 20 years since I took the course.

#### Hiikaru

Joined May 25, 2010
8

#### Fraser_Integration

Joined Nov 28, 2009
142
yeah you can solve this by just applying the fourier series equations. you have to find a0, and bn. you do not need to find an because this function is an odd one.

it becomes simpler to find bn when you apply the trig identity sinAsinB = (cos(A-B)-cos(A+B))/2

#### Hiikaru

Joined May 25, 2010
8
thanks for the tips so far, its really got me going, but now im just stuck and confused

using the trig identity, i now have:

1/(2pi) int [ cos((k-1)t) - cos((k+1)t) dt ] from zero to pi

when i integrate that, i get sine terms, but integrating from zero to pie, will make all the sine terms become zero?

the answer should be: 1/2 when k=1 and zero k=2,3,4,..