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Chapter 18

AC application of Chapter 9
◦ Superposition theorem for independent and dependent
sources.
◦ Thévenin’s theorem for independent and dependent
sources.
◦ Norton’s theorem for independent and dependent sources.
◦ Maximum power transfer to a load in an ac network with
independent or dependent sources.
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18.1-18.2
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“The current through, or voltage across,
any element of a network is equal to
the algebraic sum of the currents or
voltages produced independently by
each source”
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
In general, the theorem can be used to do
the following:
◦ Analyze networks that have two or more sources
that are not in series or parallel.
◦ Reveal the effect of each source on a particular
quantity of interest.
◦ Solve networks with AC and DC sources
◦ Solve for multi-frequency networks

NOT used directly for finding power
FIG. 9.1 Removing a voltage source and a current source to
permit the application of the superposition theorem.
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FIG. 18.1 Example
18.1.
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FIG. 18.3 Determining the effect of the voltage source E1 on
the current I of the network in Fig. 18.1.
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FIG. 18.4 Determining the effect of the voltage source E2 on
the current I of the network in Fig. 18.1.
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FIG. 18.5
Determining the
resultant current
for the network in
Fig. 18.1.
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FIG. 18.6 Example
18.2.
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FIG. 18.8 Determining the
effect of the current
source I1 on the current I
of the network in Fig.
18.6.
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FIG. 18.9 Determining the effect of
the voltage source E1 on the
current I of the network in Fig.
18.6.
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FIG. 18.10 Determining the
resultant current I for the
network in Fig. 18.6.
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
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Mixed sources require
careful approach
In DC
◦ Capacitors are ______
◦ Inductors are _______
FIG. 18.12 Example 18.4.
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DC
FIG. 18.13 Determining the effect of
the dc voltage source E1 on the
voltage v3 of the network in Fig.
18.12.
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AC
FIG. 18.14 Redrawing the network in Fig. 18.12 to determine
the effect of the ac voltage source E2.
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FIG. 18.15 Assigning the subscripted
impedances to the network in Fig. 18.14.
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FIG. 18.17 The resultant voltage v3 for the network in
Fig. 18.12.
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18.3
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
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Simplify VOLTAGE
source from the load’s
perspective
ONE FREQUENCY PER
EQUIVALENT
FIG. 18.23 Thévenin
equivalent circuit for ac
networks.
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Find VR
FIG. 18.25 Assigning the subscripted
impedances to the network in Fig. 18.24.
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FIG. 18.26 Determining the
Thévenin impedance for the
network in Fig. 18.24.
FIG. 18.27 Determining the
open-circuit Thévenin voltage
for the network in Fig. 18.24.
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Load returned
to circuit
FIG. 18.28 The Thévenin equivalent circuit for the network in Fig. 18.24.
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
Find Thevenin
equivalent
FIG. 18.29
Example 18.8.
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FIG. 18.31 Determining the Thévenin impedance for
the network in Fig. 18.29.
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FIG. 18.32 Determining the open-circuit Thévenin voltage
for the network in Fig. 18.29.
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FIG. 18.33 The Thévenin equivalent circuit for the network in Fig.
18.29.
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
For any circuit
◦
◦
◦
=
=
=
◦ Dependent Sources
 Same formulas, controller
values used as placeholders
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18.4-18.5
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

Simplify CURRENT
source from the load’s
perspective
ONE FREQUENCY PER
EQUIVALENT
FIG. 18.60 The Norton equivalent
circuit for ac networks.
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FIG. 18.61 Conversion between the Thévenin and Norton
equivalent circuits.
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Find Norton equivalent
FIG. 18.62 Example
18.14.
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FIG. 18.63 Assigning the
subscripted impedances to the
network in Fig. 18.62.
FIG. 18.64 Determining the
Norton impedance for the
network in Fig. 18.62.
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FIG. 18.65 Determining IN for the
network in Fig. 18.62.
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Must be converted to real
components
Load returned
to circuit
FIG. 18.66 The Norton equivalent circuit for the network in Fig.
18.62.
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FIG. 18.67 Example
18.15.
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FIG. 18.68 Assigning the subscripted
impedances to the network in Fig. 18.67.
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FIG. 18.69 Finding the Norton impedance for the
network in Fig. 18.67.
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FIG. 18.71 Determining IN for the network
in Fig. 18.67.
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FIG. 18.72 The Norton equivalent circuit for the network in Fig.
18.67.
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FIG. 18.73
Determining the
Thévenin equivalent
circuit for the Norton
equivalent in Fig.
18.72.
FIG. 18.74 The Thévenin
equivalent circuit for the network
in Fig. 18.67.
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“When applied to ac circuits, the
maximum power transfer theorem
states that maximum power will be
delivered to a load when the load
impedance is the conjugate of the
Thévenin impedance across its
terminals.”
=
=−
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will be purely resistive

◦

=1
Fixed load resistance
◦
=
FIG. 18.81 Defining the conditions for maximum
power transfer to a load.
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FIG. 18.83 Example
18.19.
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FIG. 18.84 Determining (a) ZTh and (b) ETh for the network
external to the load in Fig. 18.83.
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Find
where max
power is available
◦
=
ℎ +
◦
=
◦
=
◦
+
=
FIG. 18.90 Example 18.21.
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
No questions covering dependent sources
are assigned
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