1. Lecture Chapter 4C Thevenin Equivalent Circuits

2. Problem 1Problem 1 Two measurements are made on the same "linear mystery circuit" as shown. What would be the measured current Im if the 50-ohm resistor is replaced by a short circuit? ( 96 Amps)

3. Thevenin: simple model for complex circuit To find Thevenin Equivalent at a terminal a-b: 1.Find V open circuit 2.Find I short circuit 3.Vth = Voc 4.Rth = Voc/Isc Vth = Voc = 30V; Rth = 120Ω

4. "Lookback" resistance Another way to find Rth – Turn off all sources Replace Voltage source with short Replace Current source with open Calculate Rab, equivalent resistance

5. Find Thevenin Eq at a-b note how R4 does not affect Voc! [Vth=__Rth=8]

6. Problem 3Problem 3 Find the Thèvenin equivalent circuit at the terminals A-B. Rt = 25Ω;Vt = 160V

7. Norton Equivalent Norton vs Thevenin Equivalents – same at a-b

8. Thevenin and Norton Equivalents would be indistinguishable at a-b To find Norton Equivalent, find Thevenin, set In = Vth/Rth, and Rn = Rth this is the basis of the "source transform" method, which can help simplify circuits

9. Given Thevenin Equivalent, What is the Norton Equivalent?

10. Find Thevenin by "Source Transform"

11. Another Way to Look at Thevenin Equivalents All our circuit elements and laws are linear – Vs = 9V, Is = 10A, V=IR, sum of v= 0, sum of i=0 We can model the V-I curve of any linear circuit – define equation of line: slope and a y-offset Rth and Vth

12. Do Handouts Problem 1/2

13. More Thevenin Equivalents Dependent Sources – Find Voc the same (use NV, MC, Source Xform, etc) – For Rth: You can always find Isc, then Rth = Voc/Isc OR Turn off Independent sources, – hook up a “Test Voltage Source” Vt (not Vth!!) – Find current produced by test source It, » Then Rth = Vt/It

14. Find Thevenin at a-b (Vth=8, Rth=1) Option 1) Find Voc, Isc 24

15. Option 2, Rth by Test Source 24

16. Problem 2Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V. (Rt = 9.74) Circuits with only dependent sources are resistive. MUST hook up external test source

18. One More (if time permits)

20. Do Handout problems 3 and 4

21. Max Power Transfer Q: What is the most power we can deliver to RL?

22. RL gets Max Power when RL = Rth Thevenin Eq of circuit in previous slide:

23. Example: Max power RL can get?

24. Find io by Superposition Fundamental theorem in physics, – applies to ccts too.

25. Superposition continued Activate each source separately, add results

26. Handouts

27. 1) (ans: 48V, 16 Ohms)

28. 2) Find Thevenin Equivalent to left of 8 ohm R This can be simplified with Source Xform, OR Solved with NV [72V, 4 Ohm]

29. 3) Problem 1 Find the Thèvenin equivalent circuit at the terminals G-H. (Vth=12, Rth=34)Problem 1

30. 4) Problem 14) Problem 1 Find the Thèvenin equivalent circuit at the terminals S-T. Rt = 50Ω

32. Find Thevenin at a-b. Use "Lookback" to find Rth, Superposition to find Vth

33. Problem 2Problem 2 Find the Thèvenin equivalent circuit to the left of the terminals A-B. (1V, 0 Ohm)

34. Find Thevenin at a-b (Vth=8, Rth=1) Option 1) Find Voc, Isc 24

35. Option 2, Rth by Test Source 24

36. Problem 2Problem 2 Find the Thèvenin equivalent circuit at the terminals U-V. (Rt = 9.74) Circuits with only dependent sources are resistive. MUST hook up external test source

38. One More (if time permits)

40. Do Handout problems 3 and 4

41. Max Power Transfer Q: What is the most power we can deliver to RL?

42. RL gets Max Power when RL = Rth Thevenin Eq of circuit in previous slide:

43. Example: Max power RL can get?

44. Find io by Superposition Fundamental theorem in physics, – applies to ccts too.

45. Superposition continued Activate each source separately, add results

46. Handouts

47. 1) (ans: 48V, 16 Ohms)

48. 2) Find Thevenin Equivalent to left of 8 ohm R This can be simplified with Source Xform, OR Solved with NV [72V, 4 Ohm]

49. 3) Problem 1 Find the Thèvenin equivalent circuit at the terminals G-H. (Vth=12, Rth=34)Problem 1

50. 4) Problem 14) Problem 1 Find the Thèvenin equivalent circuit at the terminals S-T. Rt = 50Ω

52. Find Thevenin at a-b. Use "Lookback" to find Rth, Superposition to find Vth

53. Problem 2Problem 2 Find the Thèvenin equivalent circuit to the left of the terminals A-B. (1V, 0 Ohm)