# Fourier coefficients

#### dirtyflare

Joined Dec 4, 2012
10
I have managed to find the rms value of the output voltage, but haven't a clue where to start with finding the Fourier coefficients requested in the question below:

A single-phase ac voltage regulator has a resistive load of R= 10 ohms, and the input voltage is Vs = 240 V, 50 Hz. The delay angle of each of the Thyristors is alpha = pi/2. Determine:

(a) The rms value of the output voltage.
(b) The Fourier coefficients of the fundamental, 11th and 13th current harmonics. #### dirtyflare

Joined Dec 4, 2012
10
So do I need to put n=11 and n=13 into the two equations below?  #### Georacer

Joined Nov 25, 2009
5,182
Don't forget n=1. You are required to find the amplitude of the fundamental frequency as well.

#### dirtyflare

Joined Dec 4, 2012
10

#### Georacer

Joined Nov 25, 2009
5,182
On inspection I get the feeling that the RMS value you came up with is wrong as well, so let's start from there.

What formula did you use to get that result? It should be this one: (from: http://en.wikipedia.org/wiki/Root_mean_square#Definition)
Where f(t) is your output waveform.

It would also be a good idea for you to sketch and post your output waveform, just to make sure we 're on the same page.

#### dirtyflare

Joined Dec 4, 2012
10
No i didnt use that equation, please could you advise as to how I would use it?

What values would I need to use for the variables T and f and t? and is it as simple of just pluging them into the equation for the various values of time (over a range of 360 degrees/2pi?)

#### Georacer

Joined Nov 25, 2009
5,182
I copied the wrong image, sorry for the headache. Here is the correct one: That last equation is the definition of the Root Mean Square value of a f, over the time interval [T1,T2].

Since f is periodic in your case, calculating over a period is the same as the overall RMS value.

Yes, f(t) is in your case a function of the phase (angle), so v(φ).
Yes, your time interval will be one period [0,2π).

Since you are having trouble with this, I urge you once again to sketch or plot v(φ), so that we can be sure that you understand the problem correctly.

#### dirtyflare

Joined Dec 4, 2012
10
Please see my attempted at plotting the voltage load diagram. Is this correct? #### Georacer

Joined Nov 25, 2009
5,182