1. Angle modulation varies the angle of the carrier signal based on the message signal. This includes phase modulation, which varies the phase, and frequency modulation, which varies the frequency. 2. In phase modulation, the phase is varied linearly with the message signal. In frequency modulation, the frequency is varied linearly with the message signal. 3. For a single frequency message signal, frequency modulation results in a carrier signal with its frequency modulated above and below the center frequency by an amount proportional to the amplitude of the message signal.

1. Module 4
Angle Modulation

2. Angle Modulation
• Angle Modulation is the process of varying angle of the high frequency
carrier signal inaccordance with the instantaneous amplitude of the low
frequency message signal
• Amplitude of the carrier signal is maintained constant
• Advantages:
• Noise immunity
• Improved SNR
• Improved system fidelity
• Efficient use of transmitted power
• Disadvantages:
• High bandwidth
• Less coverage area
• Transmitting and receiving circuits are complex

3. Definition of angle Modulation
• Angle – Frequency and phase
• The angle modulated wave is mathematically expressed as
s(t)  Ac cos[i (t)]    (1)
• AC - Amplitude of the carrier signal
• θi(t) – Angle of modulated sinusoidal carrier
• If θi(t) increases monotonically with time over an interval range from t to
(t+Δt), the average frequency is given as
(t) 
i (t  t) i (t)
    (2)
2t
ff

4. Definition of angle Modulation
• The instantaneous frequency of the angle modulated signal is
• The angle modulated signal is interpreted as a rotating phasor of length
Ac and angle θi(t)
• The angular velocity of phasor is dθi(t)/dt rad/s
• The angle θi(t) of an unmodulated carrier is
i (t)  2fct c     (4)
• The corresponding phasor rotates with a constant angular velocity of
2πfc and the constant Фc is the value of θi(t) at t=0
     (3)
f (t)  i
1 d (t)
2 dt
i

5. Types of Angle modulation

6. Phase Modulation (PM)
• Phase Modulation is the process of varying phase angle of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• θi(t) is varied linearly with respect to the message signal m(t)
i (t)  2fct  kpm(t)      (5)
• Where kp is the phase sensitivity of the modulator (rad/v)
• The phase modulated signal is given as

7. Phase Modulation (PM)
• Phase Modulation is the process of varying phase angle of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• θi(t) is varied linearly with respect to the message signal m(t)
i (t)  2fct  kpm(t)      (5)
• Where kp is the phase sensitivity of the modulator (rad/v)
• The phase modulated signal is given as
s(t)  Ac cos[2fct  kpm(t)]     (6)

8. Phase Modulation (PM)
• Phase Modulation is the process of varying phase angle of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• θi(t) is varied linearly with respect to the message signal m(t)
i (t)  2fct  kpm(t)      (5)
• Where kp is the phase sensitivity of the modulator (rad/v)
• The phase modulated signal is given as
s(t)  Ac cos[2fct  kpm(t)]     (6)
s(t)  Ac cos[2fct  mp cosmt]     (7)
• Modulation index(mp) or Phase deviation(Δθ) mp k pAm (rad)

9. Frequency Modulation (FM)
• Frequency Modulation is the process of varying frequency of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• fi(t) is varied linearly with respect to the message signal m(t)
fi (t)  fc  kf m(t)      (8)
• Where kf is the frequency sensitivity of the modulator (Hz/v)

10. Frequency Modulation (FM)
• Frequency Modulation is the process of varying frequency of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• fi(t) is varied linearly with respect to the message signal m(t)
fi (t)  fc  kf m(t)      (8)
• Where kf is the frequency sensitivity of the modulator (Hz/v)
• Integrating Eq.(8) w.r.t to time and multiplying the result by 2π, we get
i (t)  2  fi (t)dt

11. Frequency Modulation (FM)
• Frequency Modulation is the process of varying frequency of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• fi(t) is varied linearly with respect to the message signal m(t)
fi (t)  fc  kf m(t)      (8)
• Where kf is the frequency sensitivity of the modulator (Hz/v)
• Integrating Eq.(8) w.r.t to time and multiplying the result by 2π, we get
i (t)  2  fi (t)dt
t
i (t)  2fct  2kf m()d      (9)
0
• The frequency modulated signal in time domain is given as

12. Frequency Modulation (FM)
• Frequency Modulation is the process of varying frequency of the high
frequency carrier signal inaccordance with the instantaneous amplitude
of the low frequency message signal
• fi(t) is varied linearly with respect to the message signal m(t)
fi (t)  fc  kf m(t)      (8)
• Where kf is the frequency sensitivity of the modulator (Hz/v)
• Integrating Eq.(8) w.r.t to time and multiplying the result by 2π, we get
i (t)  2  fi (t)dt
t
i (t)  2fct  2kf m()d      (9)
0
• The frequency modulated signal in time domain is given as
t
s(t)  Ac cos[2fct  2kf m()d]     (10)
0

13. Frequency modulation by single frequency message
signal
• The frequency modulated signal in time domain is given as
t
s(t)  Ac cos[2fct  2k f m()d]     (1)
0
• The above equation is nonlinear function of message signal
• The analysis of FM signal is much more difficult than AM signal
• Consider a sinusoidal message signal defined as

14. Frequency modulation by single frequency message
signal
• The frequency modulated signal in time domain is given as
t
s(t)  Ac cos[2fct  2k f m()d]     (1)
0
• The above equation is nonlinear function of message signal
• The analysis of FM signal is much more difficult than AM signal
• Consider a sinusoidal message signal defined as
m(t)  Am cos2fmt     (2)
• The instantaneous frequency of the FM signal is given as

15. Frequency modulation by single frequency message
signal
• The frequency modulated signal in time domain is given as
t
s(t)  Ac cos[2fct  2k f m()d]     (1)
0
• The above equation is nonlinear function of message signal
• The analysis of FM signal is much more difficult than AM signal
• Consider a sinusoidal message signal defined as
m(t)  Am cos2fmt     (2)
• The instantaneous frequency of the FM signal is given as
fi (t)  fc  kf Am cos2fmt
fi (t)  fc  f cos2fmt      (3)
FrequencyDeviation f  k f Am (Hz)

16. Frequency modulation by single frequency message
signal
• Using Eq.(3), the angle θi(t) of the FM signal is given as

17. Frequency modulation by single frequency message
signal
• Using Eq.(3), the angle θi(t) of the FM signal is given as
i (t)  2  fi (t)dt

18. Frequency modulation by single frequency message
signal
• Using Eq.(3), the angle θi(t) of the FM signal is given as
i (t)  2  fi (t)dt
f
m
m
i c
 (t)  2f t 
f
sin 2f t      (4)

19. Frequency modulation by single frequency message
signal
• Using Eq.(3), the angle θi(t) of the FM signal is given as
i (t)  2  fi (t)dt
f
m
m
i c
 (t)  2f t 
f
sin 2f t      (4)
• The modulation index is defined as
 
f
fm
i (t)  2fct   sin 2fmt      (5)
• The FM signal is given as

20. Frequency modulation by single frequency message
signal
• Using Eq.(3), the angle θi(t) of the FM signal is given as
i (t)  2  fi (t)dt
f
m
m
i c
 (t)  2f t 
f
sin 2f t      (4)
• The modulation index is defined as
 
f
fm
i (t)  2fct   sin 2fmt      (5)
• The FM signal is given as
VFM (t)  Ac cos[2fct   sin 2fmt]     (6)

21. Generation of FM using phase modulator

22. Generation of PM using frequency modulator

23. Waveform of FM and PM signal