Electronic Devices and Circuits Engineering Sciences 154

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