EECS 215
Circuit Theorems
J. Phillips
EECS 215
Linearity
A circuit is linear if output is proportional to input
•
A function f(x) is linear if f(ax)=af(x)
•
All Circuit Elements In 215 are Linear
–
Resistors V=IR
•
V(I) is linear, I(V) is linear
–
Linearly Dependent Sources
–
Capacitors
–
Inductors
We will examine theorems and principles that apply to
linear circuits to simplify analysis
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View Full DocumentJ. Phillips
EECS 215
Linearity – Additive property
The output current or voltage of a linear circuit can be
expressed as a linear combination of inputs (current or voltage)
•
y=f(x
1
+x
2
+x
3
)=k
1
x
1
+ k
2
x
2
+k
3
x
3
•
y is output current or voltage
•
x
i
are input current or voltage
•
k
i
are proportionality constants, depending on circuit elements
•
Note: k
i
can be unitless, in
Ω
, or in
S
, depending on y, x
i
units
x
1
x
3
x
2
Inputs
k
1
k
2
k
3
y=k
1
x
1
+k
2
x
2
+k
3
x
3
J. Phillips
EECS 215
Linearity – Additive property Illustration
Examine dependence of
v
0
on inputs
v
s
and
i
s
v
s
v
0
+

R
1
R
2
i
s
Relate v
0
to v
s
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 Winter '08
 Phillips
 Thévenin's theorem, Norton's theorem, J. Phillips EECS

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