What waveform does this Fourier series produce?

[suv79]

Homework Statement

what type of waveform would this make ?

Homework Equations

V(t)=2/π(sin(ωt)+1/2sin(2ωt)+1/3sin(3ωt)+1/4sin(4ωt)+...)

5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt)...

The Attempt at a Solution

 

[suv79]

all that I have read about Fourier series, it uses odd number for 'n' to make an sawtooth waveform,

5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt)... this is not add together as it is increasing the voltage ?

 

[cpscdave]

Where did you come up with

5sin(ωt)+5sin(2ωt)+5sin(3ωt)+5sin(4ωt)

 

[suv79]

that is from the input, see the 2nd attached.
i don't understand what waveform the input will be making.

 

[cpscdave]

Those inputs I don't think are valid, cause you are right as they stand they'd keep adding.
Generally with Fourier series as the frequency of the component goes up the scalar goes down.
Take a look at http://en.wikipedia.org/wiki/Fourier_series
example 1 is actually the sawtooth waveform. You'll notice that is not 5 as you have in your example but rather $$2*(-1)^{n+1}\over(\pi*n)$$

 

[suv79]

the 5 is Peak amplitude.

 

[cpscdave]

Well then it would be multiplied by 5. The peak amplitude is generally taken into account when you do the integral to calculate Bn & An