1. Useful Circuit Analysis Techniques
Chapter 5:
Useful Circuit Analysis Techniques 1
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2. Objectives : Superposition Source transformation
the Thevenin equivalent of any network
the Norton equivalent of any network
the load resistance that will result in maximum
power transfer 2
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3. Linearity and Superposition :
Linear Elements and Linear Circuits
a linear element is a passive element that has a linear voltage-current relationship.
a linear dependent source is a dependent current or voltage source whose output current or voltage is proportional only to the first power of a specified current or voltage variable in the circuit (or to the sum of such quantities).
a linear circuit is a circuit composed entirely of independent sources, linear dependent sources, and linear elements. 3
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4. The principle of superposition :
The response in a linear circuit having more than one independent source can be obtained by adding the responses caused by the separate independent sources acting alone.
(a) A voltage source set to zero acts like a short circuit.
(b) A current source set to zero acts like an open circuit. 4
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5. Example 5.1: Use superposition to find the current ix. 5
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6. Practice: 5.1 Use superposition to find the current Ix. 6
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7. Example 5.3 : Use superposition to find the current Ix. 7
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8. Example 5.3 : Use superposition to find the current Ix. 8
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9. Practice: 5.2 Use superposition to obtain the voltage
across each current source. 9
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10. Source Transformation:
(a) A general practical voltage source connected to a load resistor RL. (b) The terminal characteristics compared to an ideal source.
(a) A general practical current source connected to a load resistor RL. (b) The terminal characteristics compared to an ideal source. 10
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11. Equivalent Sources: 11
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12. Equivalent Sources: 12
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13. Example 5.4:
Compute the current through the 4.7 k resistor after transforming the 9 mA source into an equivalent voltage source. 13
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14. Practice: 5.3 compute the current ix after performing a source
transformation on the voltage source 14
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15. Example 5.5: Calculate the current through the 2Ω resistor 15
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16. Practice: 5.4
Compute the voltage V 16
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17. Thevenin and Norton Equivalent:
A complex network including a load resistor RL.
A Thévenin equivalent network connected to RL.
A Norton equivalent network connected to RL. 17
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18. Thevenin’s theorem: Given any linear circuit, rearrange it in the form
of two networks A and B connected by two wires.
Define a voltage voc as the open-circuit voltage
which appears across the terminals of A when B
is disconnected. Then all currents and voltages
in B will remain unchanged if all independent
voltage and current sources in A are “killed” or
“zeroed out,” and an independent voltage source
voc is connected, with proper polarity, in series
with the dead (inactive) A network. 18
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19. Example 5.6:
Determine the Thevenin equivalent. 19
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20. Example 5.7: Determine the Thevenin equivalent. (use Theory) 20
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21. Practice: 5.5 Using repeated source transformations,
determine the Thevenin equivalent of the
highlighted network 21
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22. Practice: 5.6 Use Thevenin’s theorem to find the current
through the 2-c resistor 22
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23. Example 5.8:
Determine the Thevenin equivalent for the network faced by 1-kohm . 23
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24. “killed” or “zeroed out,” and an independent current
Norton’s theorem:
Given any linear circuit, rearrange it in the form of
two networks A and B connected by two wires. If
either network contains a dependent source, its
control variable must be in that same network.
Define a current isc as the short circuit current that
appears when B is disconnected and the terminals
of A are short-circuited. Then all currents and
voltages in B will remain unchanged if all
independent voltage and current sources in A are
“killed” or “zeroed out,” and an independent current
source isc is connected, with proper polarity, in
parallel with the dead (inactive) A network 24
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25. Example: Determine the Norton equivalent for the network
faced by 1-kohm . 25
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26. Thevenin and Norton equivalents26
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27. Determine the Thevenin and Norton equivalents
Practice: 5.7
Determine the Thevenin and Norton equivalents 27
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28. Example 5.9:
Determine the Thevenin equivalent. 28
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29. Example 5.9:
Determine the Thevenin equivalent. 29
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30. Practice: 5.8
Determine the Thevenin equivalent 30
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31. Example 5.10: Find the Thévenin equivalent of the circuit shown. 31
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32. Practice: 5.9 Page 52 Determine the Thevenin equivalent 32
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33. Example 5.9: Determine the Thevenin equivalent resistance (RTH). 33
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34. Maximum Power Transfer:34
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35. Maximum Power Transfer:35
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36. Example:
Select R1 so that maximum power is transferred from stage 1 to stage 2 and find the maximum power 36
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37. Example 5.11:
The circuit shown is a model for a common-emitter bipolar junction transistor amplifier. Choose a load resistance so that maximum power is transferred to it from the amplifier, and calculate the actual power absorbed. 37
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38. Practice: 5.10 If Rout = 3kΩ, find the power delivered to it
What is the maximum power that can be delivered to any Rout 38
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