ECE103
Spring 2008
Lecture 6
Circuit Theorems
Linearity Property
Linearity is the property of one element describing a linear relationship between
cause and effect. The linearity property is a combination of the scaling property and the
additivity property
The homogeneity property requires that if the input or excitation is multiplied by
a constant factor, the output or response will be multiplied by the same constant factor.
For a resistor in an electric circuit, we can easily check that Ohm’s law relates the
current through and the voltage across a resistor linearly. To corroborate that we observe
that the scaling property applies:
v
R i
kv
R k i
=
→
=
When we increase the current by a constant factor
k
the voltage increases by the same
factor.
The other property is the additivity: the voltage across a resistor is related to the
current by the Ohm’s law
1
1
2
2
v
i R
v
i R
=
=
If we apply a current
1
2
i
i
+
, the voltage is calculated
(
)
1
2
1
2
1
2
v
i
i
R
i R
i R
v
v
=
+
=
+
=
+
So we can conclude that a resistor is a linear element because the voltagecurrent
relationship fulfills both the homogeneity and additivity properties.
A linear circuit is one whose output is linearly related (or directly proportional) to its
input
Superposition
The superposition principle rests on the linearity property. In a circuit with two or more
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 Spring '08
 MARCONI
 ohm, Thévenin's theorem, Voltage source, Norton's theorem, Current Source

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