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•
•
An equivalent circuit is one whose v-i
characteristics are identical with the original circuit.
It 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.
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(a) Independent source transform
(b) Dependent source transform
• The arrow of the
current source is
directed toward
the positive
terminal of the
voltage source.
• The source
transformation is
not possible when
R = 0 for voltage
source and R = ∞
for current source.
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Example 4.6
Use source transformation to find v0
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Example 4.7
Find vx using Source Transformation
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Practice Problem 4.6
Find i0 in the circuit below using source transformation
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Practice Problem 4.7
Find ix in the circuit below using source transformation
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
It states that a linear two-terminal circuit can be
replaced by an equivalent circuit consisting of a
voltage source VTH in series with a resistor RTH,
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•
VTH is the open-circuit voltage at the terminals.
•
RTH is the input or equivalent resistance at the terminals
when the independent sources are turned off.
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Finding Thevenin resistance, RTH:
CASE 1 (If network has NO dependent sources)
•
Turn off all independent sources. RTH is the input resistance of the
network looking between its two terminals
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Finding Thevenin resistance, RTH:
CASE 2 (If network has dependent sources)
•
•
Turn off all independent sources BUT leave dependent sources
intact (similar to superposition theorem)
Two approaches:
 Approach 1 – Apply a voltage source v0 at the terminals and determine the
resulting current i0. Then RTH = v0/i0 (figure a)
 Approach 2 – Insert a current source i0 at the network terminal and find the
terminal voltage v0 (figure b)
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A Thevenin-equivalent circuit is a simple voltage divider, VL by mere
inspection
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Example 4.8
Find the Thevenin equivalent circuit of the circuit below to the
left of the terminals a-b. Also find the current when RL is 6, 16
and 36 ohms.
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Example 4.8
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Example 4.9
Find the Thevenin equivalent circuit of the circuit below at
terminals a-b.
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Example 4.9
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Practice Problem 4.8
Using Thevenin’s Theorem, find the equivalent circuit to the left
of the terminals in the circuit below. Then find I
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Practice Problem 4.9
Find the Thevenin equivalent circuit of the circuit below
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Practice Problem 4.10
Using Thevenin’s Theorem, find the equivalent circuit to the left
of the terminals in the circuit below
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Problem 4.27
Apply source transformation to find vx in the circuit below
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Problem 4.32
Use source transformation to find ix in the circuit below
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Problem 4.33
Determine RTH and VTH at terminals 1-2 of each of the circuit
below:
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Problem 4.38
Apply thevenin’s theorem to find Vo in the circuit below:
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Problem 4.39
Obtain the thevenin equivalent at terminals a-b of the circuit
below:
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Problem 4.44
For the circuit below, obtain the thevenin’s equivalent as seen
from terminals (a) a-b (b) b-c
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Problem 4.40
Find the thevenin equivalent at terminals a-b of the circuit
below:
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Problem 4.42
Find the thevenin equivalent between terminals a-b of the
circuit below:
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Problem 4.43
Find the thevenin equivalent looking into terminals a-b of the
circuit below:
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Problem 4.36
Solve for the current i in the circuit below (Hint: find thevenin
equivalent seen by the 12 ohm resistor)
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
It states that a linear two-terminal circuit can be
replaced by an equivalent circuit of a current
source IN in parallel with a resistor RN,
The Thevenin’s and Norton equivalent circuits are related
by a source transformation.
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Where
IN is the short circuit current through the terminals.
RN is the input or equivalent resistance at the terminals when
the independent sources are turned off.
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𝑉𝑇𝐻
𝐼𝑁 =
𝑅𝑇𝐻
𝑉𝑇𝐻 = 𝑣𝑜𝑐
𝐼𝑁 = 𝑖𝑠𝑐
𝑅𝑇𝐻
𝑣𝑜𝑐
=
= 𝑅𝑁
𝑖𝑠𝑐
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Example 4.11
Find the Norton equivalent of the circuit in the figure below
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1st approach
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2nd approach
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Example 4.12
Find the Norton equivalent of the circuit at terminals a-b in the figure
below
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Practice Problem 4.11
Find the Norton equivalent of the circuit at terminals a-b in the figure
below
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Practice Problem 4.12
Find the Norton equivalent of the circuit at terminals a-b in the figure
below
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Problem 4.50
Obtain the Norton equivalent of the circuit below to the left of
the terminals a-b. Use the result to find current i
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Problem 4.51
Obtain the norton equivalent as viewed from terminals:
a) a-b
b) c-d
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Problem 4.53
Find the Norton equivalent at terminals a-b of the circuit below:
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Try these problems:
1.
Problem 4.57, ans: RTH = 10 ohm, VTH = 166.67 V, IN =
16.667 A
2.
Problem 4.56, ans: V0 = -2.857 V
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