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Inverse Laplace Transform Square Wave

  1. Mar 20, 2006 #1
    Is the following correct?

    I have a simple series RL circuit with a square wave input (periodic) defined by:

    Code (Text):

    e(t) = {10 0 <= t < 2
           { 0 2 <= t < 4
    With a period of 4

    E(s) = 1/(1-exp(-2as) * int (0 -> 2) exp(-st) f(t) dt
     
    Here the period = 2a thus a = 2

    E(s) = 1/(1-exp(-4s) * int (0->2) exp(-st) (10) dt
    E(s) = 1/(1-exp(-4s) * 10 * exp(-st)/-s | 0 -> 2
    E(s) = 10/s * (1-exp(-2s)/(1-exp(-4s)


    Since this is an RL circuit, the equation is

    E(s) = I(s) (R + sL)
    thus,
    I(s) = E(s) / (R+sL)
    = 10/s * (1-exp(-2s)/(1-exp(-4s)(R+sL)
    = 10 / (s * (R+sL) * (1+exp(-2s))


    Now, I don't have a transform where the exponent is on the bottom - how do I get the inverse laplace transform?
     
  2. jcsd
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