1. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance CHAPTER 6 Frequency Response, Bode Plots, and Resonance 1.State the fundamental concepts of Fourier analysis. 2. Determine the output of a filter for a given input consisting of sinusoidal components using the filter’s transfer function.

2. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance 3. Use circuit analysis to determine the transfer functions of simple circuits. 4. Draw first-order lowpass or highpass filter circuits and sketch their transfer functions. 5. Understand decibels, logarithmic frequency scales, and Bode plots.

3. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance 6. Draw the Bode plots for transfer functions of first-order filters.

4. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

5. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Fourier Analysis All real-world signals are sums of sinusoidal components having various frequencies, amplitudes, and phases.

6. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

7. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

8. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Filters Filters process the sinusoid components of an input signal differently depending of the frequency of each component. Often, the goal of the filter is to retain the components in certain frequency ranges and to reject components in other ranges.

9. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

10. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Transfer Functions The transfer function H(f ) of the two-port filter is defined to be the ratio of the phasor output voltage to the phasor input voltage as a function of frequency:

11. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance The magnitude of the transfer function shows how the amplitude of each frequency component is affected by the filter. Similarly, the phase of the transfer function shows how the phase of each frequency component is affected by the filter.

12. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

13. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Determining the output of a filter for an input with multiple components: 1. Determine the frequency and phasor representation for each input component. 2. Determine the (complex) value of the transfer function for each component.

14. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance 3. Obtain the phasor for each output component by multiplying the phasor for each input component by the corresponding transfer-function value. 4. Convert the phasors for the output components into time functions of various frequencies. Add these time functions to produce the output.

15. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Linear circuits behave as if they: 1.Separate the input signal into components having various frequencies. 2. Alter the amplitude and phase of each component depending on its frequency. 3. Add the altered components to produce the output signal.

16. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

17. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

18. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

19. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

20. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance FIRST-ORDER LOWPASS FILTERS

21. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

22. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

23. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

24. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

25. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

26. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance DECIBELS, THE CASCADE CONNECTION, AND LOGARITHMIC FREQUENCY SCALES

27. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

28. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

29. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

30. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Cascaded Two-Port Networks

31. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

32. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Logarithmic Frequency Scales On a logarithmic scale, the variable is multiplied by a given factor for equal increments of length along the axis.

33. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance A decade is a range of frequencies for which the ratio of the highest frequency to the lowest is 10. An octave is a two-to-one change in frequency.

34. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

35. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance BODE PLOTS A Bode plot shows the magnitude of a network function in decibels versus frequency using a logarithmic scale for frequency.

36. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

37. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance 1.A horizontal line at zero for f < f B /10. 2. A sloping line from zero phase at f B /10 to –90° at 10f B. 3. A horizontal line at –90° for f > 10f B.

38. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

39. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

40. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

41. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance FIRST-ORDER HIGHPASS FILTERS

42. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

43. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

44. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

45. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

46. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance SERIES RESONANCE Resonance is a phenomenon that can be observed in mechanical systems and electrical circuits.

47. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

48. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

49. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

50. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Series Resonant Circuit as a Bandpass Filter

51. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

52. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

53. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

54. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

55. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

56. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance PARALLEL RESONANCE

57. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

58. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

59. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

60. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Ideal Filters

61. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

62. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

63. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Second-Order Lowpass Filter

64. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

65. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

66. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

67. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

68. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

69. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

70. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

71. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance DIGITAL SIGNAL PROCESSING

72. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

73. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Conversion of Signals from Analog to Digital Form If a signal contains no components with frequencies higher than f H, the signal can be exactly reconstructed from its samples, provided that the sampling rate f s is selected to be more than twice f H.

74. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

75. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

76. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance Digital Lowpass Filter

77. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

78. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

79. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

80. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance

81. ELECTRICA L ENGINEERING Principles and Applications SECOND EDITION ALLAN R. HAMBLEY ©2002 Prentice-Hall, Inc. Chapter 6 Frequency Response, Bode Plots, and Resonance