lt1 - Boise State University Department of Electrical and...

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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 15.2-15.3 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 (One-Sided) 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 s-domain) 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.

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lt1 - Boise State University Department of Electrical and...

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