# 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
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Like i said i'm totally lost, anyone have any insight on any of these?

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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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

$a_{0}=\frac{1}{T}\int^{T}_{0}f(t)dt$

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
783
Correct.

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