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3.4. Superposition Theorem
3.4. Superposition Theorem
 Since AC circuits are linear, the superposition theorem applies to AC circuits the same way it applies to dc circuits.
 The theorem becomes important if the circuit has sources operating different frequencies.
 In this case, we must have a different frequency‐domain circuits for each frequency.
 The total response must be obtained by adding the individual responses in the time domain.
 İts incorrect to try to add the responses in the phasor or frequency domain.
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Example 3.7.
Use the superposition theorem to
find ‫ܫ‬଴ in the circuit.
Solution: For two sources
Example 3.7.
When current source is closed the
circuit…
Z
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Example 3.7.
Example 3.7.
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Total response;
Example 3.8.
Fin ݅଴ in the circuit shown in Fig
using superposisiton.
Solution: dc source
ac source
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Example 3.8.
Example 3.8.
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Example 3.9.
 The circuit operates at three different frequencies
 For this reason superposition the best way.
Example 3.9.
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Example 3.9.
Example 3.9.
To find ‫ݒ‬ଶ we set zero both 5‐V soruce and the 2sin5t current
source.
Transform the circuit to the frequency domain.
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Example 3.9.
Z
Example 3.9.
To obtain ‫ݒ‬ଷ we set the voltage sources zero
Transform what is left to the frequency domain.
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Example 3.9.
Example 3.9.
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3.5. Source
Transformation
3.5. Source Transformation
Source transformation in the frequency domain involves transforming a voltage source in series with an impedance to a current source in parallel with an impedance, or vice versa.
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Example 3.10.
Calculate ܸ௫ in the circuit of Fig. using the method of source transformation.
Solution:
We transform the voltage source to a current source obtain
the circuit in Fig.
Example 3.10.
ࢆ૚
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Example 3.10.
Example 3.11.
Use the method of source transformation
to find ‫ܫ‬௫ in the
circuit of Fig.
Solution:
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Example 3.11.
ࢆ࢙
Example 3.11.
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Example 3.11.
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