Fourier Analysis - Can someone check my answer!?

[Oracle]

If have a square periodic waveform where the period is 0.3 times the width of the pulse.

I understand this wavefore to be even therefore i'm going to derive an expression (An) in order to find the ampiltude of the fundamental and the harmonics

The voltage at the peak is 12v

So, let me see if I have this right sorry of for the long maths and or bad formatting

An = 1/Pi (integrale with pi/03 and -pi/0.3)12cos (ntheta)dtheta

An = 12/Pi [sin(ntheta)/n](integrale Pi/0.3 and -Pi/0.3

An = 12/nPi [ sin(nPi/0.3) - sin(-nPi/0.3)]

An = 12/nPi [ sin (nPi/0.3) + sin (nPi/0.3)] as sin(theta) = -sin(-theta)

An = 12/nPi [2sin (nPi/0.3)]

An = 24/nPi sin (nPi/0.3) volts

So taking the 2nd harmonic of this waveform would give

An = (24/2Pi)sin(2Pi/0.3) = 3.31 volts

God, I hope thats right, but please correct me if i'm wrong

Thanks

 

[Oracle]

So the period of the waveform is whats used as the pi/ -Pi/ in the integration

If the waveform was purely even i.e. had a period of 1ms, would you just use Pi or you would you alter it!?

Edit: - Its just that on one of my examples the period and pulse are both 0.5ms. Using these in the equation gives zero values for the fundamental and harmonics.

But in the example, the pulse marked by 2pi and -2pi and 2 has been used in the integration

 

[Oracle]

Edit: Actually, if I remember correctly then a square wave is only made up of odd harmonics - so you must be doing something wrong to get a nonzero amplitude for the second harmonic.

Can you explain what you mean when you say that "the period is 0.3 times the width of the pulse"? What do you mean when you say "period"?

Thats what i'm worried about

Right imagine a simple square wave - the peak lasts for 0.1ms (at 12v) and the trough lasts for 0.3ms (at 0v) - by saying the period is 0.3 times, i mean in length, not voltage, and yes you are right, only the odd harmonics should have voltage!

Dammit

 

[Oracle]

Ok, can we take this one:-

A voltage squarewave signal alternates between 0 and 10v with a period of 1ms (freq = 1kHz).

'An' Derivation as follows:- (Simplified)

An = 1/pi (Int: Pi/2 and -Pi/2)10 cos(ntheta)dthets

An = 10/Pi [sin (nPi/2) + sin (nPi/2)]

An = 10/Pi [2sin (nPi/s)]

An = 20/nPi sin (nPi/2) volts

So F = 6.37v
2 = 0
3 = -2.12v
4 = 0
5 = 1.27v
6 = 0

Firstly are these correct!?

Secondly - assuming a 1Ohm resistance can you calculate the average power in the wave form:-

10v(sqrd.) = 100v (Av = 50v(sqrd.)) so, Vrms = 7.071

Pav = Vrms2 / R or 7.071(sqrd)/1 = 50watts

How do I work out Pdc and Pac??

Is Pdc 25 watts!? If so, why!?

whats Pac and then I guess you add them together to get Pav

Thanks so far

 

[Oracle]

anyone!?