Finding Impulse and Convolution Integral

Discussion in 'Homework Help' started by IronMod, Mar 8, 2012.

  1. IronMod

    Thread Starter New Member

    Jun 14, 2011
    15
    3
    The method I am using for the impulse, h(t), is finding my H(s), and taking the inverse laplace. So assuming I am correct on my work there, I get to the convolution part and I can not seem to get it to work correctly. I think my error is the step where I actually integrate the convolution. From what I understand, we only care about the function from 0 to t, because the function after that just goes to zero since there is no overlap in the responses. I think I am messing up from the multiplication of [δ(τ)-10,000e^(-10000τ)]δ(t-τ).

    The last part of the problem I believe is correct, that is what i am using my convolution to check towards. If anyone could help it would be greatly appreciated. I believe it is something very elementary I am missing. Thank you.
     
  2. Vahe

    Member

    Mar 3, 2011
    75
    9
    Don't mix time functions and s-domain functions -- you can't write v_o(t) = H(s) v_i(t).
    Your H(s) can be found by voltage division,

    <br />
H(s) = \frac{V_o(s)}{V_i(s)}= \frac{s L_2}{R+s L_1+s L_2} = \frac{s L_2}{R+s (L_1+ L_2)}<br />

    where L_1=4 \, \text{mH}, L_2=16\, \text{mH} and R=200\Omega.

    <br />
H(s) = \frac{s \frac{L_2}{L_1+L_2}}{s + \frac{R}{L_1+s L_2}} = \frac{0.8 s}{s + 10}<br />

    Vahe
     
    Last edited: Mar 10, 2012
  3. Vahe

    Member

    Mar 3, 2011
    75
    9
    One way to proceed is by using partial fraction expansion,

    <br />
H(s) = \frac{0.8s}{s+10000} = 0.8 - \frac{8000}{s+10000}<br />

    Therefore,

    <br />
h(t) = 0.8 \delta (t) - 8000 e^{-10000t} u(t)<br />
     
    Last edited: Mar 10, 2012
  4. IronMod

    Thread Starter New Member

    Jun 14, 2011
    15
    3
    Thank you for your reply. Even after doing it that way, I still end up with:

    .8δ(t)-8,0000e^(-10,000t) u(t)

    I am assuming this was just because the 0's were left off on accident when you did it?

    I had a friend help me, and he was able to figure out how to solve part b where I was going wrong.
     
  5. Vahe

    Member

    Mar 3, 2011
    75
    9
    I think you are correct --- I had 10^3 missing.
     
    Last edited: Mar 10, 2012
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