laplace transforms and circuit analysis

Laplace Transforms and Circuit Analysis

Laplace transform as a means of signal representation

Example 1 - unit step

Example 2 - sinusoid

Other Examples

Table of Laplace transforms of common wave formsTable of Laplace transforms of basic functionsTable of Laplace transforms of trigonometric functionsTable of Laplace transform pairs

Laplace Transforms and Circuit Analysis http://people.seas.harvard.edu/~jones/es154/lectures/lecture_0/Laplace/la...

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Laplace transform in circuit analysis

Property 1 - derivative

Integrate by parts

Property 2 - integral

Integrate by parts

Other Properties

Table of Laplace transform properties

RLC CircuitsAn Example of the Application of Laplace

Transforms


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Kirchoff's voltage law

Kirchoff's voltage law transformed

where

Example 1 - A series RLC circuit excited by a unit impulsefunction - that is to say

(The unit impulse always gives the "natural response" of any circuit. Natural ascompared to "forced" response.)

This is to be compared to the transform pair

See the table of Laplace transform pairs

Therefore, if


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where

Comparison - A series RC circuit excited by a unit impulsefunction - that is to say

In general

and in particular


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Example 2 - A series RLC circuit excited by a unit cosinefunction - that is to say

We need more methodology so go see Partial FractionExpansions

See Symbolic Inverse Laplace Transform Applet

This page was prepared and is maintained by R. Victor Jones

Comments to: [email protected].


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Last updated September 28, 2001


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laplace transforms and circuit analysis

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