Transfer Function
Using voltage divider law, we can write
where
is the transfer function of the circuit, defined as the ratio of the
output to the input.
We can have other quantities as either the input or output. For example, if
we specify the input and
The Laplace Transform
The Laplace transform can be used to solve a system of differential
equations. It converts integral and differential equations into algebraic
equations, and hence, simplifies the solution for an unknown quantity to the
manipulation o
Given the initial condition,
analysis to be
,
. Hence,
can be determined using transient
.
Both
and
can also be determined using Laplace transform. Using
KVL, we can write
1
Taking the Laplace transform yields
Taking the inverse Laplace transform yields
S
Fourier Transform
The application of Fourier series is limited to periodic signals. There are
many aperiodic signals of interest in science and engineering. Therefore, an
alternative method is desired. This method is a generalization of Fourier
series and
Fourier Series
Periodic functions are common in many electrical engineering applications.
A periodic function can be represented by the sum of an infinite number of
sine and cosine functions that are harmonically related.
The steady-state response to a si
Discrete-Time Signal
A discrete-time signal can be expressed using graphical, functional or
sequence representations.
Given the functional representation of
as
for
0
= 2 for 3
0 otherwise
the sequence representation is
4
1
= ,0,2,2,2,0,1,2,3,4,0,
and t
Resistor in the Frequency Domain
In the time domain, Ohms Law specifies that
.
Taking the Laplace Transform of both sides yields
The quantity
unit ohms
.
is the impedance in the frequency domain, , with the
Inductor in the Frequency Domain
In the time dom