1. ELL100: INTRODUCTION TO ELECTRICAL ENGG.
Lecture 10
Course Instructors:
J.-B. Seo, S. Srirangarajan, S.-D. Roy, and S. Janardhanan
Department of Electrical Engineering, IITD

2. Complete Response Natural response Forced response
Energy storage elements
The form of natural response is governed by circuit itself
Use poles and zeros of the impedance function
Forced response
External sources, e.g., batteries or generators
The amplitude of forced response is determined by
the magnitude of the forcing function and impedance
Complete response = Natural response + Forced response

3. Complete Response Natural response Forced response
Energy storage elements
The form of natural response is governed by circuit itself
Use poles and zeros of the impedance function
Forced response
External sources, e.g., batteries or generators
The amplitude of forced response is determined by
the magnitude of the forcing function and impedance
Complete response = Natural response + Forced response

4. Complete Response Natural response Forced response
Energy storage elements
The form of natural response is governed by circuit itself
Use poles and zeros of the impedance function
Forced response
External sources, e.g., batteries or generators
The amplitude of forced response is determined by
the magnitude of the forcing function and impedance
Complete response = Natural response + Forced response

5. Complete Response Natural response Forced response
Energy storage elements
The form of natural response is governed by circuit itself
Use poles and zeros of the impedance function
Forced response
External sources, e.g., batteries or generators
The amplitude of forced response is determined by
the magnitude of the forcing function and impedance
Complete response = Natural response + Forced response

6. Complete Response Natural response Forced response
Energy storage elements
The form of natural response is governed by circuit itself
Use poles and zeros of the impedance function
Forced response
External sources, e.g., batteries or generators
The amplitude of forced response is determined by
the magnitude of the forcing function and impedance
Complete response = Natural response + Forced response

7. Complete Response

8. Complete Response

9. Complete Response

10. Complete Response

11. Complete Response Write the impedance function (or admittance)
Determine the forced response from the forcing func.
Identify the natural response from poles and zeros with undetermined constants
Add the forced and natural responses and evaluate the undetermined constants

12. Complete Response Write the impedance function (or admittance)
Determine the forced response from the forcing func.
Identify the natural response from poles and zeros with undetermined constants
Add the forced and natural responses and evaluate the undetermined constants

13. Complete Response Write the impedance function (or admittance)
Determine the forced response from the forcing func.
Identify the natural response from poles and zeros with undetermined constants
Add the forced and natural responses and evaluate the undetermined constants

14. Complete Response Write the impedance function (or admittance)
Determine the forced response from the forcing func.
Identify the natural response from poles and zeros with undetermined constants
Add the forced and natural responses and evaluate the undetermined constants

15. Step response of RL circuit

16. Step response of RL circuit

17. Step response of RL circuit

18. Step response of RL circuit

19. Step response of RL circuit

20. Step response of RL circuit

21. Example

22. Example

23. Example

24. Example

25. Example
Previous solution

26. Example
Previous solution

27. Example
Previous solution

28. Example
Previous solution

29. Example
Previous solution

30. Example

31. Example

32. Example

33. Example

34. Example

35. Step response of RLC circuit

36. Step response of RLC circuit

37. Step response of RLC circuit

38. Step response of RLC circuit

39. Step response of RLC circuit

40. Step response of RLC circuit

41. Step response of RLC circuit

42. Example – 1

43. Example – 1

44. Example – 1

45. Example – 1

46. Example – 1

47. Example – 1

48. Example – 1

49. Example – 1

50. Example – 1

51. Example – 1

52. Example – 2

53. Example – 2

54. Example – 2

55. Example – 2

56. Example – 2

57. Example – 2

58. Example – 2

59. Example – 2

60. Example – 2

61. Example – 2

62. Example – 2

63. Example – 2

64. Example – 3

65. KCL/KVL, Supermesh, Supernode, Superposition
Thevenin and Norton theorem, Source transformation
Phasor representation & Impedance function
KCL, KVL, Thevenin and Norton theorem work with impedance function
First-order & Second order circuit
Natural response: exponentially decaying
Forced response: DC and Sinusoidal forcing function
Complete response