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Angle (Exponential) Modulation

Angle (Exponential) Modulation. Dr. Amit Mishra. Historical Background. 1/2/2020. 2. 1/2/2020. 3. Concept of Instantaneous Frequency. If we rewrite, Eq. (5.1) as,. Note that when. 1/2/2020. 4. The function. are known as the instantaneous phase.

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Angle (Exponential) Modulation

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  1. Angle (Exponential) Modulation Dr. Amit Mishra

  2. Historical Background 1/2/2020 2

  3. 1/2/2020 3

  4. Concept of Instantaneous Frequency If we rewrite, Eq. (5.1) as, Note that when 1/2/2020 4

  5. The function are known as the instantaneous phase deviation and instantaneous radian frequency deviation of is called the maximum (or peak) radian frequency deviation of the angle-modulated signal. 1/2/2020 5

  6. Phase and Frequency Modulation 1/2/2020 6

  7. We have: 1/2/2020 7

  8. We know that: Instantaneous radian frequency: 1/2/2020 8

  9. Waveforms: 1/2/2020 9

  10. Phase Modulation 1/2/2020 10

  11. Frequency Modulation 1/2/2020 11

  12. Generalized Concept of Angle Modulation Fig. 5.2 1/2/2020 12

  13. Fig. Generalized exponential modulation 1/2/2020 13

  14. 1/2/2020 14

  15. Example Fig. 5.4 1/2/2020 15

  16. Solution Given: 1/2/2020 16

  17. m(t) Derivative of m(t) 1/2/2020 17

  18. 1/2/2020 18

  19. Example Fig. 5.5 1/2/2020 19

  20. Solution Given: For- FM 1/2/2020 20

  21. For- PM Given: 1/2/2020 21

  22. 1/2/2020 22

  23. 1/2/2020 23

  24. Power of an Angle-Modulated Wave 1/2/2020 24

  25. Bandwidth of Angle-Modulated Waves We have: We know that: 1/2/2020 25

  26. 1/2/2020 26

  27. Narrow-Band and Wide-Band Angle Modulation Angle modulation: Nonlinear 1/2/2020 27

  28. How to make FM linear: 1/2/2020 28

  29. We have: Similarly : 1/2/2020 29

  30. Narrow-Band PM generation Fig 5.6 1/2/2020 30

  31. Narrow-Band FM generation Fig 5.6 1/2/2020 31

  32. Wide-band FM (WBFM) : The Fallacy Exposed Explanation: Fig 5.7 1/2/2020 32

  33. 1/2/2020 33

  34. 1/2/2020 34

  35. We know this: We have 1/2/2020 35

  36. where: 1/2/2020 36

  37. In AM: 1/2/2020 37

  38. 1/2/2020 38

  39. Bandwidth (Wide-band FM (WBFM)) 1/2/2020 39

  40. BW seems large due to approximation involved in analysis: Adjustment in BW: We have: 1/2/2020 40

  41. Carson’s rule: 1/2/2020 41

  42. Phase Modulation 1/2/2020 42

  43. 1/2/2020 43

  44. Example Fig 5.4 a 1/2/2020 44

  45. Solution: Band width is not given. How to evaluate?: 1/2/2020 45

  46. We have: 1/2/2020 46

  47. We have: 1/2/2020 47

  48. 1/2/2020 48

  49. 1/2/2020 49

  50. Example 1/2/2020 50

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