الاثنين، 5 أكتوبر 2020

Laplace transform

 

Laplace transform.

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 so The Laplace transform 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, the Laplace transform is capable of providing us, in one single operation, the total response of the circuit comprising both the natural and forced responses

Given a function f (t), its Laplace transform, denoted by F(s) or L [f (t)], is given by

                                              

Where s is a complex variable given by s = σ +jω.

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