# Very Lost! Square wave coefficienrs/duty cycle

Discussion in 'Homework Help' started by labhelp, Feb 11, 2010.

1. ### labhelp Thread Starter New Member

Jan 28, 2010
28
0   Like i said i'm totally lost, anyone have any insight on any of these? 2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
You might start by writing an expression which describes the time function [the pulse train] in a form which could be used to derive the Fourier series coefficients.

Remember the a0 term is simply the average value of the pulse train and it is written formally as

So how would you write the function f(t) over the interval t=0 to T

Looking at the waveform you will have to break it into several parts -

from t=0 to αT0/2,
from t=αT0/2 to (T0-αT0/2)
and from t=(T0-αT0/2) to T

The same will be true for finding the other Fourier coefficients.

If you think carefully about the average value case [a0] you don't need to do any integration ......

3. ### labhelp Thread Starter New Member

Jan 28, 2010
28
0
Okay i have,
x(t)= A from t=0 to αT0/2,
x(t)= 0 from t=αT0/2 to (T0-αT0/2)
x(t)= A from t=(T0-αT0/2) to T

then would the average be (A*αT0)/T ?

4. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
Correct.

So if you make T=T0 (which is reasonable) what do you have for the average.