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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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**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 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**Phase and Frequency Modulation**1/2/2020 6**We have:**1/2/2020 7**We know that:**Instantaneous radian frequency: 1/2/2020 8**Waveforms:**1/2/2020 9**Phase Modulation**1/2/2020 10**Frequency Modulation**1/2/2020 11**Generalized Concept of Angle Modulation**Fig. 5.2 1/2/2020 12**Fig. Generalized exponential modulation**1/2/2020 13**1/2/2020**14**Example**Fig. 5.4 1/2/2020 15**Solution**Given: 1/2/2020 16**m(t)**Derivative of m(t) 1/2/2020 17**1/2/2020**18**Example**Fig. 5.5 1/2/2020 19**Solution**Given: For- FM 1/2/2020 20**For- PM**Given: 1/2/2020 21**1/2/2020**22**1/2/2020**23**Power of an Angle-Modulated Wave**1/2/2020 24**Bandwidth of Angle-Modulated Waves**We have: We know that: 1/2/2020 25**1/2/2020**26**Narrow-Band and Wide-Band Angle Modulation**Angle modulation: Nonlinear 1/2/2020 27**How to make FM linear:**1/2/2020 28**We have:**Similarly : 1/2/2020 29**Narrow-Band PM generation**Fig 5.6 1/2/2020 30**Narrow-Band FM generation**Fig 5.6 1/2/2020 31**Wide-band FM (WBFM) : The Fallacy Exposed**Explanation: Fig 5.7 1/2/2020 32**1/2/2020**33**1/2/2020**34**We know this:**We have 1/2/2020 35**where:**1/2/2020 36**In AM:**1/2/2020 37**1/2/2020**38**Bandwidth (Wide-band FM (WBFM))**1/2/2020 39**BW seems large due to approximation involved in analysis:**Adjustment in BW: We have: 1/2/2020 40**Carson’s rule:**1/2/2020 41**Phase Modulation**1/2/2020 42**1/2/2020**43**Example**Fig 5.4 a 1/2/2020 44**Solution:**Band width is not given. How to evaluate?: 1/2/2020 45**We have:**1/2/2020 46**We have:**1/2/2020 47**1/2/2020**48**1/2/2020**49**Example**1/2/2020 50

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