Our frequency-domain analysis has been limited to circuits with sinusoidal inputs. In other words, we have assumed sinusoidal time-varying excitations in all our non-dc circuits. This chapter introduces this transformation method, a very powerful tool for analyzing circuits with sinusoidal or non-sinusoidal inputs.

## The Laplace Transform Overview

The idea of transformation should be familiar by now. When using phasors for the analysis of circuits, we transform the circuit from the time domain to the frequency or phasor domain. Once we obtain the phasor result, we transform it back to the time domain.

This transformation method follows the same process: we use this transformation to transform the circuit from the time domain to the frequency domain, obtain the solution, and apply the inverse of this transformation to the result to transform it back to the time domain.

This transformation is significant for a number of reasons.

First, it can be applied to a wider variety of inputs than phasor analysis.

Second, it provides an easy way to solve circuit problems involving initial conditions, because it allows us to work with algebraic equations instead of differential equations.

Third, this transformation is capable of providing us, in one single operation, the total response of the circuit comprising both the natural and forced responses.

We begin with the definition of this transformation and use it to derive the transforms of some basic, important functions. We consider some properties of this transformation that are very helpful in circuit analysis.

We then consider the inverse Laplace transformation, transfer functions, and convolution.

Finally, we examine how this transformation is applied in circuit analysis, network stability, and network synthesis.

## Laplace Transform Summary

So, we will learn the transformation introduction topics below:

- Laplace Transform Definition
- Laplace Transform Properties
- Laplace Transform Inverse
- Laplace Transform Convolution Integral
- Application to Intergrodifferential Equation

After learning the introduction above, we will absolutely learn about Laplace application.