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Inverse Laplace Transform

Inverse Laplace Transform. Chairul Hudaya, ST, M.Sc. Electric Power & Energy Studies (EPES) Department of Electrical Engineering University of Indonesia http://www.ee.ui.ac.id/epes.

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Inverse Laplace Transform

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  1. Inverse Laplace Transform Chairul Hudaya, ST, M.Sc Electric Power & Energy Studies (EPES) Department of Electrical Engineering University of Indonesia http://www.ee.ui.ac.id/epes Depok, October, 2009 Electric Circuit

  2. Inverse Laplace transform (ILT) • The inverse Laplace transform of F(s) is f(t), i.e. where L−1 is the inverse Laplace transform operator.

  3. Example 4 Find the inverse Laplace transform of (a) (b) (c) (d) (e) (f)

  4. Solution From the table of Laplace transform, (a) (b) (c)

  5. (d) Write (e)

  6. Since the ILT of the term cannot be found directly from the table, we need to rewrite it as the following (f)

  7. Example 5 Find the inverse Laplace transform of (a) (b) (c) (d) (e)

  8. Solution We use the partial fractions technique: (a) L =L (b) L =L =L

  9. (c) L =L =L where, if we let , then Hence, L =L

  10. (d) L =L =L =L =L

  11. (e) L =L =L =L =L

  12. The convolution theorem where is called as the convolution of f(t) and g(t), defined by Convolution property: Therefore, Sometimes, denoted as or simply

  13. Example 6 Use the convolution theorem to find the inverse Laplace transforms of the following: (a) (b) (c)

  14. Solution (a)

  15. (b)

  16. (c)

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