Transcript CSCI 2980: Introduction to Circuits, CAD, and Instrumentation

EENG 2610: Circuits Analysis
Class 9: Thevenin’s and Norton’s Theorems,
Maximum Power Transfer
Oluwayomi Adamo
Department of Electrical Engineering
College of Engineering, University of North Texas
Example 5.9: Determine Thevenin’s equivalent of the network at terminals A-B.
Circuits containing only dependent sources
V2
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EENG 2610, Class 9
V3
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Example 5.10: Determine RTh at terminals A-B.
Circuits containing only dependent sources
V3
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EENG 2610, Class 9
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Example 5.11: Use Thevenin’s theorem to find Vo
Circuits containing both independent and dependent sources
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EENG 2610, Class 9
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Example 5.12: Use Thevenin’s theorem to find Vo
Circuits containing both independent and dependent sources
© Dr. Xinrong Li
EENG 2610, Class 9
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Source Transformation/Source Exchange
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If we have embedded within a network a current source i(t) in parallel with a
resistor R, we can replace this combination with a voltage source of value
v(t) = i(t)R in series with the resistor R.
The reverse is also true; that is, a voltage source v(t) in series with a
resistor R can be replaced with a current source of value i(t) = v(t)/R in
parallel with the resistor R.
Parameters within the circuit are unchanged under these transformations.
We can use source transformations back and forth to simplify circuits.
Important: the two equivalent circuits are equivalent only at the two
external nodes.
RTh
voc
i
A
vo
voc  RTh isc
isc
B
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Circuit B
(Load) EENG 2610, Class 9
i
RTh
A
vo
B
Circuit B
(Load)
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Example 5.14: Use source transformation to find Vo
3 k
12 V
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2 k
6 k
4 k
2 mA
8 k
VO
EENG 2610, Class 9
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General Rules for Circuit Analysis
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Try to select a simple technique for a given problem,
 First, count the number of nodes and loops.
 Next, examine the type and number of sources.
 Select a technique based on this information, your objective, and
your experiences.
Loop analysis and nodal analysis are straightforward and as
good as any technique that you have learned.
What about other techniques?
 Equivalency, Linearity, Superposition,
Thevenin’s and Norton’s Theorems
 The real value of these techniques is the insight and
understanding that they provide about the physical nature of the
network.
© Dr. Xinrong Li
EENG 2610, Class 9
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Maximum Power Transfer
i
v
R
PL  i 2 RL  (
RL
v
) 2 RL
R  RL
d PL
0
d RL
RL  R
Maximum power transfer takes place
when the load resistance RL  R .
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Thevenin’s theorem provides a way to determine the maximum
power that a circuit can supply; that is, RL  RTh .
© Dr. Xinrong Li
EENG 2610, Class 9
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Example 5.16: Find out RL for maximum power transfer and
the maximum power that can be transferred to this load.
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EENG 2610, Class 9
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Example 5.17: Find out RL for maximum power transfer and
the maximum power that can be transferred to this load.
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EENG 2610, Class 9
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Example 5.18: Plots
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EENG 2610, Class 9
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