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Laplace transform as a means of signal representation

Example 1 - unit step

Example 2 - sinusoid

Other ExamplesTable of Laplace transforms of common wave formsTable of Laplace transforms of basic functionsTable of Laplace transforms of trigonometric functionsTable of Laplace transform pairs

Laplace transform in circuit analysisProperty 1 - derivativeIntegrate by partsProperty 2 - integralIntegrate by partsOther PropertiesTable of Laplace transform properties

RLC CircuitsAn Example of the Application of Laplace TransformsKirchoff's voltage law

Kirchoff's voltage law transformed

where

Example 1 - A series RLC circuit excited by a unit impulse function - that is to say(The unit impulse always gives the "natural response" of any circuit. Natural as compared to "forced" response.)This is to be compared to the transform pairSee the table of Laplace transform pairsTherefore, if

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

In general

and in particular

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

We need more methodology so go see Partial Fraction Expansions

Last updated September 28, 2001