1. ELECTRICAL TECHNOLOGY EET 103/4
Explain and analyze series and parallel circuits
Explain, derive and analyze Ohm’s Law, Kirchhoff Current Law, Kirchhoff Voltage Law, Source Transformation, Thevenin theorem.

2. NETWORK THEOREM
(CHAPTER 9)

3. 9.2 Superposition Theorem
Used to find the solution to networks with two or more sources that are not in series or parallel.
The current through, or voltage across, an element in a network is equal to the algebraic sum of the currents or voltages produced independently by each source.
Since the effect of each source will be determined independently, the number of networks to be analyzed will equal the number of sources.

4. 9.2 Superposition Theorem
When removing a voltage source from a network schematic, replace it with a direct connection (short circuit) of zero ohm. Any internal resistance associated with the source must remain in the network.

5. 9.2 Superposition Theorem
When removing a current source from a network schematic, replace it with an open circuit of infinite ohms. Any internal resistance associated with the source must remain in the network.

6. 9.2 Superposition Theorem
The total power delivered to a resistive element must be determined using the total current through or the total voltage across the element and cannot be determined by a simple sum of the power levels established by each source.

7. 9.2 Superposition Theorem
Example 9.1
Using superposition theorem, find I1:

8. 9.2 Superposition Theorem
Example solution
Open the current source:

9. 9.2 Superposition Theorem
Example 9.1 – solution (cont’d)
Replace the current source and short the voltage source:

10. 9.2 Superposition Theorem
Example 9.1 – solution (cont’d)
With both sources in the circuit, the total current is therefore;

11. 9.2 Superposition Theorem
Example 9.2
Use superposition theorem to find I2:

12. 9.2 Superposition Theorem
Example 9.2 – solution
Short the voltage source E2:

13. 9.2 Superposition Theorem
Example 9.2 – solution (cont’d)
Redraw the circuit:

14. 9.2 Superposition Theorem
Example 9.2 – solution (cont’d)

15. 9.2 Superposition Theorem
Example 9.2 – solution (cont’d)
Replace E2 and short the voltage source E1:

16. 9.2 Superposition Theorem
Example 9.2 – solution (cont’d)
Redraw the circuit:

17. 9.2 Superposition Theorem
Example 9.2 – solution (cont’d)

18. 9.2 Superposition Theorem
Example 9.2 – solution (cont’d)
With both sources in the circuit, the total current is therefore;

19. 9.2 Superposition Theorem
Example 9.3
(a) Use superposition theorem to find I2
(b) Demonstrate that the superposition theorem is not applicable to power level

20. 9.2 Superposition Theorem
Example 9.3 – solution
(a)
Replace the current source with an open circuit:

21. 9.2 Superposition Theorem
Example 9.3 – solution (cont’d)
Reconnect the current source and replace the voltage source with a short circuit:

22. 9.2 Superposition Theorem
Example 9.3 – solution (cont’d)
With both sources in the circuit, the current through R2 is;

23. 9.2 Superposition Theorem
Example 9.3 – solution (cont’d)
which is not equal to:
Hence, the superposition is not applicable to power level

24. 9.3 Thevenin’s Theorem
Any two-terminal dc network can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

25. 9.3 Thevenin’s Theorem Thévenin’s theorem can be used to:
Analyze networks with sources that are not in series or parallel.
Reduce the number of components required to establish the same characteristics at the output terminals.
Investigate the effect of changing a particular component on the behavior of a network without having to analyze the entire network after each change.

26. 9.3 Thevenin’s Theorem
Procedure to determine the proper values of RTh and ETh

27. 9.3 Thevenin’s Theorem Preliminary
Remove that portion of the network across which the Thévenin equation circuit is to be found. In the figure below, this requires that the load resistor RL be temporarily removed from the network.

28. 9.3 Thevenin’s Theorem
2. Mark the terminals of the remaining two-terminal network. (The importance of this step will become obvious as we progress through some complex networks.)

29. 9.3 Thevenin’s Theorem
3. Calculate RTh by first setting all sources to zero (voltage sources are replaced by short circuits, and current sources by open circuits) and then finding the resultant resistance between the two marked terminals. (If the internal resistance of the voltage and/or current sources is included in the original network, it must remain when the sources are set to zero.)

30. 9.3 Thevenin’s Theorem
In a laboratory, RTh may be measured:

31. 9.3 Thevenin’s Theorem
4. Calculate ETh by first returning all sources to their original position and finding the open-circuit voltage between the marked terminals. (This step is invariably the one that will lead to the most confusion and errors. In all cases, keep in mind that it is the open-circuit potential between the two terminals marked in step 2.)

32. 9.3 Thevenin’s Theorem
In a laboratory, ETh may be measured:

33. 9.3 Thevenin’s Theorem
5. Draw the Thévenin equivalent circuit:

34. 9.3 Thevenin’s Theorem
6. If required, reconnect the portion which had been removed previously:

35. 9.3 Thevenin’s Theorem Example 9.7
Find the Thevenin equivalent circuit for the network in the shaded area:

36. 9.3 Thevenin’s Theorem Example 9.7 – solution
Remove the component external to the relevant network i.e. R3.

37. 9.3 Thevenin’s Theorem Example 9.7 – solution (cont’d)
Replace the current source with an open circuit and calculate RTh:

38. 9.3 Thevenin’s Theorem Example 9.7 – solution (cont’d)
Reconnect the current source and calculate ETh:

39. 9.3 Thevenin’s Theorem Example 9.7 – solution (cont’d)
Draw the Thevenin equivalent circuit:

40. 9.3 Thevenin’s Theorem Example 9.7 – solution (cont’d)
The original circuit
The corresponding Thevenin equivalent circuit

41. 9.3 Thevenin’s Theorem Example 9.7 – solution (cont’d)
If required, reconnect the external component which had been removed previously:

42. 9.3 Thevenin’s Theorem Example 9.8
Find the Thevenin equivalent circuit for the network in the shaded area:

43. 9.3 Thevenin’s Theorem Example 9.8 – solution
Remove the component external to the relevant network i.e. R3.

44. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Replace the voltage source with a short circuit:

45. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Redraw the circuit and calculate RTh:

46. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Reconnect the voltage source:

47. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Redraw the circuit:

48. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Redraw the circuit further and calculate ETh:

49. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Draw the corresponding Thevenin equivalent circuit:

50. 9.3 Thevenin’s Theorem Example 9.8 – solution (cont’d)
Reconnect R3 which had been removed previously:

51. 9.3 Thevenin’s Theorem Example 9.10
Find the Thevenin circuit for network within the shaded area.

52. 9.3 Thevenin’s Theorem
Example 9.10 – solution
Redraw the circuit:

53. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Disconnect the component(s) external to the network:

54. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Replace the voltage sources with short circuits and find RTh:

55. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Replace R2 and R3 with Ra:

56. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Replace R1 and Ra with Rb:

57. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Use superposition theorem to find ETh:

58. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Replace E2 with a short circuit and find E’Th:

59. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Reconnect E2 and replace E1 with a short circuit and find E”Th:

60. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Since E’Th and E”Th are of opposite polarities:

61. 9.3 Thevenin’s Theorem Example 9.10 – solution (cont’d)
Draw the corresponding Thevenin equivalent circuit and reconnect RL.