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Chapter 5: Useful Circuit Analysis Techniques

Chapter 5: Useful Circuit Analysis Techniques. 1. 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. Linearity and Superposition : .

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Chapter 5: Useful Circuit Analysis Techniques

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  1. Chapter 5: Useful Circuit Analysis Techniques 1

  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

  3. Linearity and Superposition : Linear Elements and Linear Circuits • a linear element is a passive element that has a linearvoltage-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

  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

  5. Example 5.1: Use superposition to find the current ix. 5

  6. Practice: 5.1 Use superposition to find the current Ix. 6

  7. Example 5.3 : Use superposition to find the current Ix. 7

  8. Use superposition to find the current Ix. Example 5.3 : 8

  9. Practice: 5.2 Use superposition to obtain the voltage across each current source. 9

  10. 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.

  11. Equivalent Sources: 11

  12. Equivalent Sources: 12

  13. Compute the current through the 4.7 k resistor after transforming the 9 mA source into an equivalent voltage source. 13 Example 5.4:

  14. Practice: 5.3 compute the current ix after performing a source transformation on the voltage source 14

  15. Example 5.5: Calculate the current through the 2Ωresistor 15

  16. Practice: 5.4 Compute the voltage V 16

  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

  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

  19. Example 5.6: Determine the Thevenin equivalent. 19

  20. 20 Determine the Thevenin equivalent. (use Theory) Example 5.7:

  21. Practice: 5.5 Using repeated source transformations, determine the Thevenin equivalent of the highlighted network 21

  22. Practice: 5.6 Use Thevenin’s theorem to find the current through the 2-c resistor 22

  23. Example 5.8: Determine theThevenin equivalent for the network faced by 1-kohm . 23

  24. 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

  25. Example: Determine the Norton equivalent for the network faced by 1-kohm . 25

  26. Thevenin and Norton equivalents 26

  27. Practice: 5.7 Determine the Thevenin and Norton equivalents 27

  28. Example 5.9: Determine the Thevenin equivalent. 28

  29. Example 5.9: Determine the Thevenin equivalent. 29

  30. Practice: 5.8 Determine the Thevenin equivalent 30

  31. Example 5.10: Find the Thévenin equivalent of the circuit shown. 31

  32. Practice: 5.9 Page 52 Determine the Thevenin equivalent 32

  33. Example 5.9: Determine the Theveninequivalent resistance (RTH). 33

  34. Maximum Power Transfer: 34

  35. Maximum Power Transfer: 35

  36. Example: Select R1 so that maximum power is transferredfrom stage 1 to stage 2 and find the maximum power 36

  37. 37 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. Example 5.11:

  38. 38 If Rout = 3kΩ, find the power delivered to it What is the maximum power that can be delivered to any Rout Practice: 5.10

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