1. ANGLE MODULATION CHAPTER 3 Review on Part 1 Part 2
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
ANGLE MODULATION
CHAPTER 3
Review on Part 1
Part 2

2. Review on Part 1 ANGLE MODULATION
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Review on Part 1 ANGLE MODULATION

3. Amplitude modulation (AM) Angle modulation (FM,PM)
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Define the following…..
Modulation
Demodulation
Amplitude modulation (AM)
Angle modulation (FM,PM)
Modulating signal
Carrier signal
Bandwidth

4. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Introduction
Angle modulation is the process by which the angle (frequency or Phase) of the carrier signal is changed in accordance with the instantaneous amplitude of modulating or message signal.
also known as “Exponential modulation"

5. Cont’d… Classified into two types ; Used for :
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Cont’d…
Classified into two types ;
Frequency modulation (FM)
Phase modulation (PM)
Used for :
Commercial radio broadcasting
Television sound transmission
Two way mobile radio
Cellular radio
Microwave and satellite communication system

6. Cont’d… Advantages over AM:
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Cont’d…
Advantages over AM:
Freedom from interference: all natural and external noise consist of amplitude variations, thus receiver usually cannot distinguish between amplitude of noise or desired signal. AM is noisy than FM.
Operate in very high frequency band(VHF):88M-108MHz
Can transmit musical programs with higher degree of fidelity.

7. FREQUENCY MODULATION PRINCIPLES
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FREQUENCY MODULATION PRINCIPLES
In FM the carrier amplitude remains constant, the carrier frequency varies with the amplitude of modulating signal.
The amount of change (the relative displacement of carrier frequency in hertz in respect to it un-modulated value) in carrier frequency produced by the modulating signal is known as frequency deviation.

8. PHASE MODULATION (PM) PRINCIPLES
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
PHASE MODULATION (PM) PRINCIPLES
The process by which changing the phase of carrier signal in accordance with the instantaneous of message signal. The amplitude and frequency remains constant after the modulation process.
Mathematical analysis:
Let message signal:
And carrier signal:

9. PM (cont’d) After phase modulation, with
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
PM (cont’d)
After phase modulation, with
the instantaneous voltage will be
where
= Modulation index of phase modulation
K = a constant and called deviation sensitivities of the phase
= phase angle of carrier signal .It is changed in accordance with the amplitude of the message signal

10. FREQUENCY MODULATION(FM)
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FREQUENCY MODULATION(FM)
A process where the frequency of the carrier wave varies with the magnitude variations of the modulating or audio signal.
The amplitude of the carrier wave is kept constant.

11. FM(cont’d) Mathematical analysis: Let message signal:
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
Mathematical analysis:
Let message signal:
And carrier signal:

12. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM (cont’d)
During the process of frequency modulations the frequency of carrier signal is changed in accordance with the instantaneous amplitude of the message signal .Therefore the frequency of carrier after modulation is written as
To find the instantaneous phase angle of modulated signal, integrate equation above w.r.t. t

13. FM(cont’d) Thus, we get the FM wave as: Where
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
Thus, we get the FM wave as:
Where
Known as the modulation index for the FM

14. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
Frequency deviation: ∆f is the relative displacement of carrier frequency (Hz) w.r.t its unmodulated value. Given as:
Where K is the deviation sensitivity in Hz/V

15. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM(cont’d)
The peak to peak frequency deviation (2Δf) is called the carrier swing.
Therefore:
The modulation index is

16. Example 3.1 An FM modulator with Determine
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.1
An FM modulator with
Deviation sensitivity, K1=5kHz/V
Modulating signal Vm(t)=2cos(2π2000t)
Determine
The peak frequency deviation(Δf) : Ans:10kHz.
The modulation index (m) : 5 (unitless)
Hint:

17. Angle-modulated wave in the frequency domain.
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Angle-modulated wave in the frequency domain.

18. Example 3.2 A PM modulator with Determine
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.2
A PM modulator with
Deviation sensitivity, K=2.5rad/V
Modulating signal Vm(t)=2cos(2π2000t)
Determine
The peak phase deviation(m) : Ans: 5 rad
Hint: Peak phase shift for modulated wave is the modulation index itself.

19. Phase and frequency modulation of a sine-wave carrier by a sine-wave signal: (a) unmodulated carrier; (b) modulating signal; (c) frequency-modulated wave; (d) phase-modulated wave

20. FM&PM (Bessel function)
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM&PM (Bessel function)
Thus, for general equation:

21. Bessel function EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Bessel function

22. Representation of frequency spectrum
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Representation of frequency spectrum

23. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Bessel Functions of the First Kind, Jn(m) for some value of modulation index

24. Example 3.2 An FM modulator with
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.2
An FM modulator with
m=1
Modulating signal Vm(t)=Vmsin(2π1000t)
Unmodulated carrier V c(t)=10sin(2π500kt)
Determine
Number of sets of significant side frequencies
(Ans: 1 carrier + 3 sets sides freq.)
Their amplitudes
Draw the frequency spectrum
Hint: (i), (ii), (iii) use table of Bessel functions of the First Kind, Jnm

25. Solution (ii) Their amplitude J0=0.77(10) ; Carrier
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Solution
(ii) Their amplitude
J0=0.77(10) ; Carrier
J1=0.44(10), ; 1st sideband pairs
J2=0.11(10) ; 2nd sideband pairs
J3=0.02(10) ; 3rd side band pairs

26. (iii) Draw the frequency spectrum.
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Solution (cont’d)
(iii) Draw the frequency spectrum.
6kHz

27. Angle Modulation Part 2 FM Bandwidth Power distribution of FM
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Angle Modulation Part 2
FM Bandwidth
Power distribution of FM
Generation & Detection of FM
Application of FM

28. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Bandwidth
Theoretically, the generation and transmission of FM requires infinite bandwidth. Practically, FM system have finite bandwidth and they perform well.
The value of modulation index determine the number of sidebands that have the significant relative amplitudes
If n is the number of sideband pairs, and line of frequency spectrum are spaced by fm, thus the actual minimum bandwidth using Bessel table:
With n = number of significant sidebands
= modulating signal frequency

29. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Bandwidth (cont’d)
Carson’s rule also can be used to estimate the bandwidth regardless of modulation index

30. Example 3.3 An FM modulator has the following information; Determine
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.3
An FM modulator has the following information;
Determine
Actual minimum bandwidth from the B.F table : Ans=60kHz.
Approximate minimum bandwidth using Carson’s rule.
Plot the output frequency spectrum for the Bessel approximation
Hint:

31. Solution Given; Actual minimum bandwidth from the B.F table.
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Solution
Given;
Actual minimum bandwidth from the B.F table.
m=10kHz/10kHz=1, from B.F table, B=2(3x10kHz)=60kHz.
(b) Approximate minimum bandwidth using Carson’s rule.

32. (c) Plot the output frequency spectrum for the Bessel approximation
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
(c) Plot the output frequency spectrum for the Bessel approximation

33. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Deviation Ratio (DR)
The worse case modulation index which produces the widest output frequency spectrum.
Where
∆f(max) = max. peak frequency deviation
fm(max) = max. modulating signal frequency

34. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.4
An FM broadcast-band transmitter has a maximum frequency deviation of 75kHz and a maximum modulating signal frequency of 15kHz. Determine the deviation ratio bandwidth.
Solution
The deviation ratio (i.e the worst case modulation index).
From the B.F table, a modulation index of 5 gives 8 significant sidebands.
Then B=2(8x15kHz)=240kHz.

35. EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Power Distribution
As seen in Bessel function table, it shows that as the sideband relative amplitude increases, the carrier amplitude,J0 decreases.
This is because, in FM, the total transmitted power is always constant and the total average power is equal to the unmodulated carrier power, that is the amplitude of the FM remains constant whether it is modulated or not.
The total power in angle-modulated wave is equal to the power of the un-modulated wave.

36. FM Power Distribution (cont’d)
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
FM Power Distribution (cont’d)
In effect, in FM, the total power that is originally in the carrier is redistributed between all components of the spectrum, in an amount determined by the modulation index, mf, and the corresponding Bessel functions.
At certain value of modulation index, the carrier component goes to zero, where in this condition, the power is carried by the sidebands only.

37. Average Power EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Average Power
The average power in unmodulated carrier
The total power in the angle modulated carrier.
The modulated carrier power is the sum of the powers of the carrier and the side frequency components as follow;
Vc=peak unmodulated carrier voltage (volts), Vn= sidebands voltage (volts), Pc=Carrier power, R=Resisitive load (ohms)

38. Example 3.5 An FM modulator has the following information; Determine;
EKT 231 : COMMUNICATION SYSTEM
CHAPTER 3 : ANGLE MODULATION
Example 3.5
An FM modulator has the following information;
Determine;
The unmodulated carrier power for the FM modulator (Assume RL=50Ω)
The total power in the angle modulated wave.