1. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Introductory Circuit Analysis, 12/e Boylestad Chapter 17 Methods of Analysis and Selected Topics (AC)

2. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] OBJECTIVES Understand the differences between independent and dependent sources and how the magnitude and angle of a controlled source is determined by the dependent variable. Be able to convert between voltage and current sources and vice versa in the ac domain. Become proficient in the application of mesh and nodal analysis to ac networks with independent and controlled sources. Be able to define the relationship between the elements of an ac bridge network that will establish a balance condition.

3. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION For networks with two or more sources that are not in series or parallel, the methods described in the last two chapters cannot be applied. Rather, methods such as mesh analysis or nodal analysis must be used.

4. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INDEPENDENT VERSUS DEPENDENT (CONTROLLED) SOURCES In the previous chapters, each source appearing in the analysis of dc or ac networks was an independent source, such as E and I (or E and I) in Fig. 17.1. The term independent specifies that the magnitude of the source is independent of the network to which it is applied and that the source displays its terminal characteristics even if completely isolated. A dependent or controlled source is one whose magnitude is determined (or controlled) by a current or voltage of the system in which it appears.

5. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INDEPENDENT VERSUS DEPENDENT (CONTROLLED) SOURCES FIG. 17.1 Independent sources.

6. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INDEPENDENT VERSUS DEPENDENT (CONTROLLED) SOURCES FIG. 17.2 Controlled or dependent sources. FIG. 17.3 Special notation for controlled or dependent sources.

7. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INDEPENDENT VERSUS DEPENDENT (CONTROLLED) SOURCES FIG. 17.4 Conditions of V = 0 V and I = 0 A for a controlled source.

8. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SOURCE CONVERSIONS When applying the methods to be discussed, it may be necessary to convert a current source to a voltage source or a voltage source to a current source. This source conversion can be accomplished in much the same manner as for dc circuits, except that now we shall be dealing with phasors and impedances instead of just real numbers and resistors.

9. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SOURCE CONVERSIONS Independent Sources FIG. 17.5 Source Conversion.

10. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SOURCE CONVERSIONS Independent Sources FIG. 17.6 Example 17.1.

11. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SOURCE CONVERSIONS Independent Sources FIG. 17.7 Example 17.2.

12. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SOURCE CONVERSIONS Dependent Sources FIG. 17.8 Source conversion with a voltage-controlled voltage source.

13. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] SOURCE CONVERSIONS Dependent Sources FIG. 17.9 Source conversion with a current-controlled current source.

14. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS General Approach Independent Voltage Sources FIG. 17.10 Example 17.5.

15. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS General Approach Independent Voltage Sources FIG. 17.11 Assigning the mesh currents and subscripted impedances for the network in Fig. 17.10.

16. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS General Approach FIG. 17.12 Applying mesh analysis to a network with a voltage-controlled voltage source.

17. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS General Approach FIG. 17.13 Applying mesh analysis to a network with an independent current source.

18. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS General Approach FIG. 17.14 Applying mesh analysis to a network with a currentcontrolled current source.

19. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS Format Approach FIG. 17.15 Example 17.9.

20. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS Format Approach FIG. 17.16 Assigning the mesh currents and subscripted impedances for the network in Fig. 17.15.

21. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS Format Approach FIG. 17.18 Example 17.10.

22. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS Format Approach FIG. 17.19 Assigning the mesh currents and subscripted impedances for the network in Fig. 17.18.

23. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] MESH ANALYSIS Format Approach FIG. 17.20 Example 17.11. FIG. 17.21 Assigning the mesh currents and subscripted impedances for the network in Fig. 17.20.

24. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach Independent Sources FIG. 17.22 Example 17.12.

25. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach Independent Sources FIG. 17.23 Assigning the nodal voltages and subscripted impedances to the network in Fig. 17.22.

26. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach Independent Sources FIG. 17.24 Applying Kirchhoff ’s current law to the node V 1 in Fig. 17.23.

27. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach Independent Sources FIG. 17.25 Applying Kirchhoff ’s current law to the node V 2 in Fig. 17.23.

28. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach FIG. 17.26 Applying nodal analysis to a network with a current-controlled current source.

29. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach FIG. 17.27 Applying nodal analysis to a network with an independent voltage source between defined nodes.

30. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS General Approach FIG. 17.28 Applying nodal analysis to a network with a voltage-controlled voltage source.

31. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.29 Example 17.16.

32. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.30 Assigning the nodal voltages and subscripted impedances for the network in Fig. 17.29.

33. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.32 Example 17.17.

34. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.33 Assigning the subscripted impedances for the network in Fig. 17.32.

35. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.34 Converting the voltage source in Fig. 17.33 to a current source and defining the nodal voltages.

36. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.35 Example 17.18.

37. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.36 Assigning the nodal voltages and subscripted impedances for the network in Fig. 17.35.

38. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.37 Example 17.19

39. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] NODAL ANALYSIS Format Approach FIG. 17.38 Assigning the nodal voltage and subscripted impedances for the network in Fig. 17.37.

40. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BRIDGE NETWORKS (ac) FIG. 17.39 Maxwell bridge. FIG. 17.40 Assigning the mesh currents and subscripted impedances for the network in Fig. 17.39.

41. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BRIDGE NETWORKS (ac) FIG. 17.41 Hay bridge. FIG. 17.42 Assigning the nodal voltages and subscripted impedances for the network in Fig. 17.41.

42. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BRIDGE NETWORKS (ac) FIG. 17.43 Investigating the balance criteria for an ac bridge configuration.

43. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BRIDGE NETWORKS (ac) FIG. 17.44 Capacitance comparison bridge.

44. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS The Δ-Y, Y-Δ (or p- T, T-p as defined in Section 8.12) conversions for ac circuits are not derived here since the development corresponds exactly with that for dc circuits. FIG. 17.45 Δ-Y configuration.

45. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.46 The T and π configurations.

46. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.47 Converting the upper Δ of a bridge configuration to a Y.

47. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.48 The network in Fig. 17.47 following the substitution of the Y configuration.

48. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.49 Example 17.21.

49. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.50 Converting a Δ configuration to a Y configuration.

50. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.51 Substituting the Y configuration in Fig. 17.50 into the network in Fig. 17.49.

51. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.52 Converting the Y configuration in Fig. 17.49 to a Δ.

52. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] Δ-Y, Y-Δ CONVERSIONS FIG. 17.53 Substituting the Δ configuration in Fig. 17.54 into the network in Fig. 17.49.