1. ELL100: INTRODUCTION TO ELECTRICAL ENGG.
Lecture 4
Course Instructors:
J.-B. Seo, S. Srirangarajan, S.-D. Roy, and S. Janardhanan
Department of Electrical Engineering, IITD

2. Common Signal Waveforms

3. Common Signal Waveforms

4. Common Signal Waveforms
Battery, Ideal sources
Switch
Oscillating Switch
AC current, many places
Caps

5. Signal Waveforms (2)
Exponential Signals

6. Signal Waveforms (2) Exponential Signals
a : Instantaneous value of function
A : Maximum Amplitude
t : time variable
Tau : time constant

7. Signal Waveforms (2) Exponential Signals e = 2.718
a : Instantaneous value of function
A : Maximum Amplitude
t : time variable
Tau : time constant

8. Signal Waveforms (2) Exponential Signals
a : Instantaneous value of function
A : Maximum Amplitude
t : time variable
Tau : time constant
So, after ‘tau’ time an exponential function reduces by ~ 63 %

9. Signal Waveforms (2) Exponential Signals
a : Instantaneous value of function
A : Maximum Amplitude
t : time variable
Tau : time constant
So, after ‘tau’ time an exponential function reduces by ~ 63 %

10. Signal Waveforms (2) Exponential Signals
a : Instantaneous value of function
A : Maximum Amplitude
t : time variable
Tau : time constant
So, after ‘tau’ time an exponential function reduces by ~ 63 %

11. Example 1

12. Example 1

13. Example 1
Solution
Step 1: Calculate VR
Step 2: Calculate VL

14. Example 1
Solution
Step 1: Calculate VR
Step 2: Calculate VL

15. Example 1
Solution
Step 1: Calculate VR
Step 2: Calculate VL

16. Example 1
Solution
Step 1: Calculate VR
Step 2: Calculate VL

17. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC

18. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC

19. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC

20. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC

21. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC

22. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC
Solution

23. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC
Solution

24. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC
Solution

25. Example 1
Solution
Step 3: Calculate VRL
Step 4: Calculate VC
Solution

27. Signal Waveforms (3) a : Instantaneous value of function
A : Maximum Amplitude
t : time variable in seconds
T : time for 1 full cycle  Period
f : frequency  cycles/sec or Hertz
ω : frequency in radians/sec  2πf
α : phase angle/offset angle (radians)

28. Signal Waveforms (3) a : Instantaneous value of function
A : Maximum Amplitude
t : time variable in seconds
T : time for 1 full cycle  Period
f : frequency  cycles/sec or Hertz
ω : frequency in radians/sec  2πf
α : phase angle/offset angle (radians)

29. Signal Waveforms (3) a : Instantaneous value of function
A : Maximum Amplitude
t : time variable in seconds
T : time for 1 full cycle  Period
f : frequency  cycles/sec or Hertz
ω : frequency in radians/sec  2πf
α : phase angle/offset angle (radians)

30. Example 2
A Sinusoidal current with a frequency of 60 Hz reaches a positive maximum of 20 A at t = 2 ms. Write the equation of current as a function of time.

31. Example 2
A Sinusoidal current with a frequency of 60 Hz reaches a positive maximum of 20 A at t = 2 ms. Write the equation of current as a function of time.

32. Example 2
A Sinusoidal current with a frequency of 60 Hz reaches a positive maximum of 20 A at t = 2 ms. Write the equation of current as a function of time.
As per Sine wave equation,
A = 20 A
ω = 2πf = 2π (60) = 377 rad/s
The positive maximum is reached when (ωt + α) = 0
or any multiple of 2π. Letting (ωt + α) = 0,
α = - ωt
= -377 * 2 * 10-3
= (-) rad Or
α = * (360°/ 2π)
= °

33. Example 2
A Sinusoidal current with a frequency of 60 Hz reaches a positive maximum of 20 A at t = 2 ms. Write the equation of current as a function of time.
As per Sine wave equation,
A = 20 A
ω = 2πf = 2π (60) = 377 rad/s
The positive maximum is reached when (ωt + α) = 0
or any multiple of 2π. Letting (ωt + α) = 0,
α = - ωt
= -377 * 2 * 10-3
= (-) rad Or
α = * (360°/ 2π)
= °
i = 20 cos (377t – 43.2°)

34. Signal Waveforms (4)

35. Periodic Waveforms

36. Periodic Waveforms (2)

37. Periodic Waveforms (2)

38. Periodic Waveforms (2)

39. Periodic Waveforms (2)

40. Periodic Waveforms (2)
For sinusoidal wave total Q over full cycle = 0

41. Periodic Waveforms (3)

42. Periodic Waveforms (3)

43. Periodic Waveforms (3)

44. Periodic Waveforms (3)

45. Periodic Waveforms (3)

46. Periodic Waveforms (3)

47. Periodic Waveforms (4)
Delivering equivalent Energy

48. Periodic Waveforms (4)
Delivering equivalent Energy +
= Ieff

49. Periodic Waveforms (4)
Delivering equivalent Energy +
= Ieff

50. Periodic Waveforms (4) = Ieff + Delivering equivalent Energy

51. Periodic Waveforms (4) = Ieff + Delivering equivalent Energy

52. Periodic Waveforms (5)

53. Periodic Waveforms (5)

54. Periodic Waveforms (5)

55. Periodic Waveforms (5)

56. Periodic Waveforms (5)
Delivering equivalent Energy +
= Ieff

57. Periodic Waveforms (5) = Ieff +
Delivering equivalent Energy +
= Ieff
So for sinosoidal current, the Ieff/DC equivalent = Im = Irms