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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