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Unformatted text preview: Boise State University Department of Electrical and Computer Engineering ECE225 Circuit Analysis and Design The Laplace Transform I Reading Assignment : Read Sections 15.215.3 Lecture Objectives : 1. To define the Laplace transform. 2. To review some properties of Laplace transforms. 3. To derive the Laplace transforms of elementary time functions. Example of a Transform: The Logarithm Transform Real Domain Real Domain a ln x = ln a b ln y = ln b c = ab = e ln z e = ln 1  z = x + y = ln a + ln b = ln ab Definition of the (OneSided) Laplace Transform : L{ f ( t ) } = Z  f ( t ) e st dt = F ( s ) Notes : 1. The Laplace integral is integrated over time starting shortly time t = 0. (This is indicated by the notation 0 which means 0 , being an arbitrarily small number.) The reason for using 0 instead of 0 will become apparent later on. 2. The variable s is a complex variable. Thus the Laplace domain (or sdomain) represents functions of a complex number s = + j . 3. The Laplace integral defined above will converge for a particular s if Z   f ( t ) e st  dt = Z   f ( t )  e t dt < 4. In particular, a function that does not grow faster than an exponential,4....
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This document was uploaded on 11/01/2011 for the course ECE 212 at Boise State.
 Fall '08
 AhmedZaid

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