1. ELL100: INTRODUCTION TO ELECTRICAL ENGG.
Lecture 9
Course Instructors:
J.-B. Seo, S. Srirangarajan, S.-D. Roy, and S. Janardhanan
Department of Electrical Engineering, IITD

2. Impedance

3. Analysis with Impedance
the ratio of voltage to current for exponential waveform
extends the concept of resistance to AC circuits
It has both magnitude and phase; unlike resistance, which has only magnitude.
Impedances can be combined in Series and Parallel just like Resistances

4. Example

5. Example

6. Example

7. Example

8. Example

9. Example

10. Example

11. Example

12. Example

13. Equivalent Impedance
 Impedance in series
In parallel

14. Equivalent Impedance
 Impedance in series
In parallel

15. Equivalent Impedance
 Impedance in series
 Impedance in parallel

16. Equivalent Impedance
 Impedance in series
 Impedance in parallel

17. Example – 1

18. Example – 1

19. Example – 1

20. Example – 1

21. Example – 1

22. Poles and Zeros (1/2)
Zero impedance implies that a current can exist with no external forcing voltage

23. Poles and Zeros (1/2)
Zero impedance implies that a current can exist with no external forcing voltage

24. Poles and Zeros (1/2)
Zero impedance implies that a current can exist with no external forcing voltage

25. Poles and Zeros (1/2)
Zero impedance implies that a current can exist with no external forcing voltage

26. Poles and Zeros (1/2) - + + -

27. Poles and Zeros (1/2) - + + -

28. Poles and Zeros (1/2) - + + -

29. Poles and Zeros (1/2) - + + -

30. Poles and Zeros (2/2)

31. Poles and Zeros
Example:

32. Poles and Zeros
Example:

33. Natural response using impedance
Write the impedance or admittance function for the terminals of interest
Determine the poles and zeros
For the terminals short-circuited, the natural behavior current is
For the terminals open-circuited, the natural behavior voltage is
Evaluate the coefficients from the initial conditions

34. Natural response using impedance
Write the impedance or admittance function for the terminals of interest
Determine the poles and zeros
For the terminals short-circuited, the natural behavior current is
For the terminals open-circuited, the natural behavior voltage is
Evaluate the coefficients from the initial conditions

35. Example – 1
Switch is open at t=0. Find the open-circuit voltage across terminals ab

36. Example – 1
Switch is open at t=0. Find the open-circuit voltage across terminals ab

37. Example – 1
Switch is open at t=0. Find the open-circuit voltage across terminals ab

38. Example – 1
Switch is open at t=0. Find the open-circuit voltage across terminals ab

39. Example – 1
Switch is open at t=0. Find the open-circuit voltage across terminals ab

40. Example – 2
If terminals ab is short-circuited, find the current

41. Example – 2
If terminals ab is short-circuited, find the current

42. Example – 2
If terminals ab is short-circuited, find the current

43. Example – 2
If terminals ab is short-circuited, find the current

44. Forced response using Impedance

45. Forced response using Impedance

46. Forced response using Impedance

47. Forced response using Impedance

48. Forced response using Impedance

49. Forced response using Impedance

50. General solution method
Transform time functions to phasor and convert element values to impedance/admittance
Combine impedance/admittance to simplify circuit
Determine the desired response in phasor form
Draw phasor diagram to check calculation and display result
Transform phase result to time function

51. Example

52. Example

53. Example

54. Example

55. Example

56. Example

57. Example

58. General solution method
Transform time functions to phasor and convert element values to impedance/admittance
Combine impedance/admittance to simplify circuit
Determine the desired response in phasor form
Draw phasor diagram to check calculation and display result
Transform phase result to time function

59. Admittance

60. Admittance

61. Admittance

62. Admittance

63. Admittance

64. Admittance

65. Example

66. Example

67. Example

68. Example

69. Example

70. Example

71. Example

72. Example

73. Example

74. Example

75. Example

76. Example

77. Example

78. Dual circuit
Duals ?
When the set of transforms that converts one system into another also converts the second into the first, the systems are said to be duals.

79. Dual circuit
Duals ?
When the set of transforms that converts one system into another also converts the second into the first, the systems are said to be duals.

80. Dual circuit
Duals ?
When the set of transforms that converts one system into another also converts the second into the first, the systems are said to be duals.

81. Example

82. Example