INC 112 Basic Circuit Analysis

1. INC 112 Basic Circuit Analysis Week 5 Thevenin’s Theorem

2. Special Techniques • Superposition Theorem • Thevenin’s Theorem • Norton’s Theorem • Source Transformation

3. Linearity Characteristic If RL change its value , how will it effect the current and voltage across it?

4. I Voc = Voltage open-circuit Isc = Current short-circuit ISC V VOC For any circuit constructed from only linear components Not just RL, all resistors have this property.

5. Thevenin’s Theorem When we are interested in current and voltage across RL, we can simplify other parts in the circuit. Equivalent circuit

6. I ISC Slope = 1/R V VOC Voc = Voltage open-circuit Isc = Current short-circuit R = R equivalent

7. Thevenin’s Equivalent Circuit Thevenin’s equivalent circuit VTH = Voc (by removing RL and find the voltage difference between 2 pins) RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

8. Why do we needequivalent circuit? • To analyze a circuit with several values of RL • For circuit simplification(source transformation) • To find RL that gives maximum power (maximum power transfer theorem)

9. Procedure • Remove RL from the circuit • Find voltage difference of the 2 opened connections. Let it equal VTH. • From step 2 findRTH by • 3.1 short-circuit voltage sources • 3.2 open-circuit current sources • 3.3 Look into the 2 opened connections. Find equivalent resistance.

10. Example Find Thevenin’s equivalent circuit and find the current that passes through RL when RL = 1Ω

11. 6V 10V 6V 0V 0V 0V Find VTH

12. Find RTH Short voltage source RTH

13. Thevenin’s equivalent circuit If RL = 1Ω, the current is

14. Example Find Thevenin’s equivalent circuit

15. 3V 5V 3V 0V 0V 0V Find VTH

16. Find RTH Open circuit current source RTH

17. Thevenin’s equivalent circuit

18. Example: Bridge circuit Find Thevenin’s equivalent circuit

19. 10V Find VTH 8V 2V 0V VTH = 8-2 = 6V

20. Find RTH RTH

22. Thevenin’s equivalent circuit

23. Special Techniques • Superposition Theorem • Thevenin’s Theorem • Norton’s Theorem • Source Transformation

24. I ISC V VOC For any point in linear circuit

25. Thevenin’s Equivalent Circuit

26. Norton’s Equivalent Circuit In= Isc from replacing RL with an electric wire(resistance = 0) and find the current Rn = RTH (by looking into the opened connections that we remove RL, see how much resistance from the connections. If we see a voltage source, we short circuit. If we see a current source, we open circuit.)

27. Example Find Norton’s equivalent circuit and find the current that passes through RL when RL = 1Ω

28. Find R total Find I total Current divider Find In

29. Find Rn Short voltage source RTH

30. Norton’s equivalent circuit IfRL = 1Ω, the current is

31. Relationship BetweenThevenin’s and Norton’s Circuit I ISC Slope = - 1/Rth V VOC

32. Norton’s equivalent circuit Thevenin’s equivalent circuit Same R value

33. Example Find Norton’s equivalent circuit

34. Current divider Find In

35. Find RTH Open circuit current source RTH

36. Norton’s equivalent circuit

37. Thevenin’s equivalent circuit Norton’s equivalent circuit 0.2 x 15 = 3

38. Equivalent Circuits withDependent Sources We cannot find Rth in circuits with dependent sources using the total resistance method. But we can use

39. Example Find Thevenin and Norton’s equivalent circuit

40. I2 I1 KVL loop1 KVL loop2 Find Voc

41. I2 I1 Solve equations I1 = 3.697mA I2 = 3.678mA

42. I2 I1 I3 KVL loop1 KVL loop2 KVL loop3 Find Isc

43. I2 I1 I3 Find Isc I1 = 0.632mA I2 = 0.421mA I3 = -1.052 A Isc = I3 = -1.052 A

44. Norton’s equivalent circuit Thevenin’s equivalent circuit