Electronic Devices and Circuits
Engineering Sciences 154

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 forms
Table of Laplace transforms of basic functions
Table of Laplace transforms of trigonometric functions
Table of Laplace transform pairs

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 Circuits
An Example of the Application of Laplace Transforms

Kirchoff'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 pair

See the table of Laplace transform pairs
Therefore, if

where 
 


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
 
 
 
 
 
 

See Symbolic Inverse Laplace Transform Applet
 
 

 
 

This page was prepared and is maintained by R. Victor Jones
Comments to: jones@deas.harvard.edu.

Last updated September 28,  2001