FOCUS ON MATH
Linear and Nonlinear Circuit Elements
An
element or device is defined as
linear in terms of the excitation
and response. In the case of electric circuits,
the excitation is the input current (I)
and the response is the voltage (V).
A linear element satisfies
the properties of superposition and homogeneity.
In general, a necessary condition for a
linear system can be determined in terms
of an excitation x
and a response y.
When a system at rest is subjected to an
excitation x1,
it provides a response y1.
Moreover, when the system is subjected to
an excitation x2,
it provides a corresponding response y2.
For a linear system, it is necessary that
the excitation x1
+ x2
result in a response y1
+ y2.
This is usually called the principle
of superposition. It is expressed
as
It
is also necessary that the magnitude scale
factor be preserved in a linear system.
Again, consider a system with an input x
that results in an output y.
Then it is important that the response of
a linear system to a constant multiple k
of an input x
be equal to the response to the input multiplied
by the same constant so that the output
is equal to ky.
This is called the property of homogeneity.
An element or device that does not satisfy
both the superposition and homogeneity principles
is said to be nonlinear.
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