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INTRODUCTION
A large
complex circuits

Simplify
circuit analysis

Circuit Theorems
‧Thevenin’s theorem
‧Circuit linearity
‧source transformation

‧
‧
‧

Norton theorem
Superposition
max. power transfer
Source Transformation
A

source transformation is the process of
replacing a voltage source vs in series with a
resistor R by a current source is in parallel
with a resistor R, or vice versa
Source Transformation

vs
vs = is R or is =
R
Source Transformation

Vs = Rs I s

Vs
Is =
Rs
Source Transformation
 Equivalent

sources can be used to simplify
the analysis of some circuits.
 A voltage source in series with a resistor is
transformed into a current source in parallel
with a resistor.
 A current source in parallel with a resistor is
transformed into a voltage source in series
with a resistor.
Example
 Use

source transformation to find vo in the
circuit.
Example
Example
we use current division to get

and

2
i=
(2) = 0.4A
2+8

vo = 8i = 8(0.4) = 3.2V
Superposition
 The

superposition principle states that the
voltage across (or current through) an
element in a linear circuit is the algebraic
sum of the voltages across (or currents
through) that element due to each
independent source acting alone.
Steps to apply superposition principle

1.

Turn off all independent sources except one source. Find
the output (voltage or current) due to that active source
using nodal or mesh analysis.




1.
2.



Turn off voltages sources = short voltage sources; make it
equal to zero voltage
Turn off current sources = open current sources; make it
equal to zero current

Repeat step 1 for each of the other independent sources.
Find the total contribution by adding algebraically all the
contributions due to the independent sources.

Dependent sources are left intact.
Superposition - Problem

2kΩ

4mA

12V
– +

2mA

1kΩ
I0

2kΩ
2mA Source Contribution

2kΩ

2mA

1kΩ
I’0

I’0 = -4/3 mA

2kΩ
4mA Source Contribution

2kΩ

4mA

1kΩ
I’’0

I’’0 = 0

2kΩ
12V Source Contribution

12V

2kΩ

– +
1kΩ
I’’’0

I’’’0 = -4 mA

2kΩ
Final Result
I’0 = -4/3 mA
I’’0 = 0
I’’’0 = -4 mA
I0 = I’0+ I’’0+ I’’’0 = -16/3 mA

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