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

4. 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

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

6. We have: 1/2/2020 7

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

8. Waveforms: 1/2/2020 9

9. Phase Modulation 1/2/2020 10

10. Frequency Modulation 1/2/2020 11

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

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

13. 1/2/2020 14

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

15. Solution Given: 1/2/2020 16

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

17. 1/2/2020 18

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

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

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

21. 1/2/2020 22

22. 1/2/2020 23

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

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

25. 1/2/2020 26

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

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

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

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

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

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

32. 1/2/2020 33

33. 1/2/2020 34

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

35. where: 1/2/2020 36

36. In AM: 1/2/2020 37

37. 1/2/2020 38

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

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

40. Carson’s rule: 1/2/2020 41

41. Phase Modulation 1/2/2020 42

42. 1/2/2020 43

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

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

45. We have: 1/2/2020 46

46. We have: 1/2/2020 47

47. 1/2/2020 48

48. 1/2/2020 49

49. Example 1/2/2020 50

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