Techniques of Circuit
Analysis (Part B)
Ch. 4 – Techniques of Circuit Analysis (Part-B)
2
 Linearity
Linearity implies two properties
 Scaling (proportionality)
 Addition (superposition)
Example of scaling
Now scale the applied voltage to kV.
The output current becomes:
ELEC 250 – Summer 2015

V
R
kV

 kI1
R
I1 
Assume a voltage V is applied on a resistor 
I new
Ch. 4 – Techniques of Circuit Analysis (Part-B)
Superposition Method:

If a linear system is excited by more than one
independent sources of energy, then its response is the
sum of its responses to the individual sources of energy
Steps:
Points:
(1) Connect each source separately
(2) Obtain the individual response
(3) The response to all connected sources is the sum of
the individual responses
(1) A voltage source is disabled by replacing it with a short-circuit
(2) A current source is disabled by replacing it with an open-circuit
(3) Dependent sources are left intact because they are controlled by
circuit variables
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
4
Superposition Method:
Final solution
i1  i1  i1
i3  i3  i3
i2  i2  i2
i4  i4  i4
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
5
Source Transformation:
Note that the arrow of the current source is directed toward the positive
terminal of the voltage source
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is 
vs
R
is 
vs
R
Ch. 4 – Techniques of Circuit Analysis (Part-B)
Example – (superposition):
Example – (source transformation):
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
Thevenin’s Theorem
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
8
Thevenin equivalent

For Thevenin equivalent, we need to obtain two components:

Thevenin Voltage: Replace the load resistor with a open circuit and
calculate the open circuit voltage voc
[

Thevenin Resistance: Replace the load resistor with a short circuit. Then,
the ratio of open circuit voltage (voc) and short circuit current (isc) gives the
Thevenin Resistance
RTh 
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voc
isc
Ch. 4 – Techniques of Circuit Analysis (Part-B)
9
Important point about Thevenin resistance

The Thevenin resistance in the circuits without the independent sources
can simply be obtained as equivalent resistance.
Example:
Rab  RTh  (5 || 20)  4
Thevenin
Resistance
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
10
More Examples (Thevenin equivalent):
Fig. (a)
Fig. (b)
Fig. (c)
Fig. (d)
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
Norton’s Theorem
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
12
Norton equivalent

For Norton equivalent, we need to obtain two components:

Norton Current: Replace the load resistor with a short circuit and calculate
the short circuit current isc
[

Norton Resistance: Replace the load resistor with a open circuit. Then, the
ratio of open circuit voltage (voc) and short circuit current (isc) gives the
Norton Resistance
RTh 
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voc
isc
Ch. 4 – Techniques of Circuit Analysis (Part-B)
13
More Examples (Norton equivalent):
Fig. (a)
Fig. (b)
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
Maximum Power Transfer

Find the load that will receive (consume) the maximum power
2
 VTh 
P
 RL
R

R
L 
 Th
2


dP
2  RTh  RL   2 RL  RTh  RL 
 VTh 
0
4


dRL
R

R


Th
L


 RTh  RL 
2
 2 RL  RTh  RL   0
RL  RTh
Pmax
VTh2

4 RTh
This load will receive the maximum power
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Ch. 4 – Techniques of Circuit Analysis (Part-B)
Example:



(a) For the circuit shown in the following, find the value of load
resistance that results in maximum power being transferred to the
load resistance.
(b) Calculate the maximum power that can be delivered to the load
resistance.
(c) When load resistance is adjusted for maximum power transfer,
what percentage of the power delivered by the 360v source reaches
load resistance?
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