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# Circuit Theorem

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### Circuit Theorem

1. 1. Chapter 4 : Circuit Theorem <ul><li>4.1 Superposition Theorem </li></ul><ul><li>4.2 Source Transformation, </li></ul><ul><li>Thevenin’s and Norton’s </li></ul><ul><li>Theorem </li></ul><ul><li>4.3 Maximum Power Transfer </li></ul>BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
2. 2. Learning Outcomes <ul><li>Discuss the Superposition Principles </li></ul><ul><li>Solve circuit problems using Superposition theorem </li></ul><ul><li>Apply the Source Transformation in the circuits </li></ul><ul><li>Carry out the Thevenin's and Norton's Theorem in the circuits </li></ul><ul><li>Describe Maximum Power Transfer </li></ul>BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
3. 3. SUPERPOSITION THEOREM BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
4. 4. Superposition Theorem <ul><li>Superposition : the voltage across (or current through) an element in a linear circuits is the algebraic sum of the voltage across (or current through) that element due to each independent source acting alone. </li></ul>BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA Current Source  open circuit(0 A) Voltage Source  short circuit (0 V)
5. 5. <ul><li>Step to apply: </li></ul><ul><ul><li>Turn off all independent sources except one source. Find the output (voltage or current) due to that active source. </li></ul></ul><ul><ul><li>Repeat step 1 for each other independent sources. </li></ul></ul><ul><ul><li>Find the total contribution by adding algebraically all the contribution due to the independent source. </li></ul></ul>Superposition Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
6. 6. <ul><li>Determine I 0 using superposition </li></ul>Example 1 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (-0.4706 A)
7. 7. <ul><li>Determine v x using superposition </li></ul>Exercise 1 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (12.5 V)
8. 8. SOURCE TRANSFORMATION BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
9. 9. Source Transformation <ul><li>Source transformation : replacing a voltage source v s in series with a impedance Z by a current source i s in parallel with a impedance Z, or vice versa. </li></ul>BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
10. 10. Source Transformation BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
11. 11. <ul><li>Determine v 0 using source transformation </li></ul>Example 2 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (3.2 V)
12. 12. <ul><li>Determine I x using source transformation </li></ul>Exercise 2 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (1.176 A)
13. 13. THEVENIN’S THEOREM BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
14. 14. Thevenin’s Theorem <ul><li>Thevenin’s theorem : a linear two terminal circuit can be replaced by an equivalent circuit consisting of a voltage V Th in series with an impedance Z Th , where V Th is the open circuit voltage at the terminals and Z Th is the input or equivalent impedance at the terminals when the independent source are turned off. </li></ul>BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
15. 15. Thevenin’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
16. 16. Thevenin’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA Finding V Th and Z Th
17. 17. Thevenin’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA Finding Z Th when circuit has dependent sources Z
18. 18. Thevenin’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA Circuit with load
19. 19. <ul><li>Determine the Thevenin equivalent at terminals a-b </li></ul>Example 3 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (R Th =6 Ω , V Th =20 V)
20. 20. <ul><li>Determine the Thevenin equivalent at terminals a-b </li></ul>Exercise 3 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (R Th =0.44 Ω , V Th =5.33 V)
21. 21. NORTON’S THEOREM BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
22. 22. <ul><li>Norton’s Theorem : a linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source I N in parallel with an impendence Z N , where I N is the short circuit current through the terminals and Z N is the input or equivalent impedance at the terminals when the independent source are turned off. </li></ul>Norton’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
23. 23. Norton’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
24. 24. Norton’s Theorem BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA Finding Norton current I N .
25. 25. Thevenin and Norton Equivalent BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
26. 26. <ul><li>Determine the Norton equivalent at terminals a-b </li></ul>Example 4 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (R N =5 Ω , I N =7 A)
27. 27. <ul><li>Determine the Norton equivalent at terminals a-b </li></ul>Exercise 4 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (R N =1 Ω , I N =10 A)
28. 28. MAXIMUM POWER TRANSFER BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
29. 29. <ul><li>Maximum power : transferred to the load when the load resistance equals the Thevenin resistance as seen from the load (R L = R Th ) </li></ul>Maximum Power Transfer BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
30. 30. Maximum Power Transfer BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA
31. 31. <ul><li>Determine </li></ul><ul><li>a) The value or R L for maximum power transfer </li></ul><ul><li>b) The maximum power transfer </li></ul>Example 5 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (R L =9 Ω , p max =13.44 W)
32. 32. <ul><li>Determine </li></ul><ul><li>a) The value or R L for maximum power transfer </li></ul><ul><li>b) The maximum power transfer </li></ul>Exercise 5 BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA (R L =4.22 Ω , p max =2.901 W)
33. 33. BEE1113 Chapter 4 : Circuit Theorem NH-credit to NHA <ul><li>Q & A </li></ul><ul><li>Outcomes : </li></ul><ul><ul><li>Discuss the Superposition Principles </li></ul></ul><ul><ul><li>Solve circuit problems using Superposition theorem </li></ul></ul><ul><ul><li>Apply the Source Transformation in the circuits </li></ul></ul><ul><ul><li>Carry out the Thevenin's and Norton's Theorem in the circuits </li></ul></ul><ul><ul><li>Describe Maximum Power Transfer </li></ul></ul><ul><li>Reflection </li></ul>