1. Part 1 Principles of Frequency Modulation (FM)
ANGLE MODULATION (AM)
Part 1
Principles of Frequency Modulation (FM)

2. Objectives
To define and explain frequency modulation (FM) and phase modulation (PM)
To analyze the FM in terms of Mathematical analysis
To analyze the Bessel function for FM and PM
To analyze the FM bandwidth and FM power distribution

3. Lecture overview Frequency modulation (FM) and phase modulation (PM)
Analysis of FM
Bessel function for FM and PM
FM bandwidth
Power distribution of FM

4. 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.
Advantage: noise reduction, improved system fidelity and more efficient use of power
Disadvantage: required a wider bandwidth and more complex circuits in both transmitter and receiver.

5. Cont’d… Angle modulation is classified into two types such as
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. Frequency Modulation (FM) Introduction
FM is the process of varying the frequency of a carrier wave in proportion to a modulating signal.
The amplitude of the carrier wave is kept constant while its frequency and a rate of change are varied by the modulating signal.

7. FM :Introduction (cont…)
Fig 3.1 : Frequency Modulated signal

8. FM :Introduction (cont…)
The important features about FM waveforms are :
The frequency varies.
The rate of change of carrier frequency changes is the same as the frequency of the information signal.
The amount of carrier frequency changes is proportional to the amplitude of the information signal.
The amplitude is constant.

9. FM :Introduction (cont…)
The FM modulator receives two signals, the information signal from an external source and the carrier signal from a built in oscillator.
The modulator circuit combines the two signals producing a FM signal which passed on to the transmission medium.
The demodulator receives the FM signal and separates it, passing the information signal on and eliminating the carrier signal.

10. FM :Introduction (cont…)

11. Analysis of FM Mathematical analysis: Let the message signal:
And carrier signal:
Where carrier frequency is very much higher than message frequency.

12. Analysis of FM
In FM, frequency changes with the change of the amplitude of the information signal. So the instantaneous frequency of the FM wave is;
K is the deviation sensitivity.

13. Analysis of FM Thus, we get the FM wave as:
Modulation index for FM is given by
Where,
K = deviation sensitivity (hertz per volt)
Vm = peak modulating signal amplitude (volts)
= cyclic frequency (hertz)
(Eq. 1)

14. Analysis of FM
Frequency deviation: ∆f is the relative placement of carrier frequency (Hz) with respect to its unmodulated value. Given as:
For FM, the deviation sensitivity, K is often given in hertz per volt. Therefore, the peak frequency deviation is
(Eq. 2)

15. Therefore, Eq. 2 can be substituted into Eq
Therefore, Eq. 2 can be substituted into Eq. 1, and the expression for the modulation index in FM can be rewritten as:

16. Example 1
FM broadcast station is allowed to have a frequency deviation of 75 kHz. If a 4 kHz (highest voice frequency) audio signal causes full deviation (i.e. at maximun amplitude of information signal) , calculate the modulation index.

17. Example 2
Determine the peak frequency deviation, ∆f and the modulation index, mf, for an FM modulator with a deviation sensitivity K = 5 kHz/V and a modulating signal Vm(t) = 2 cos (2π2000t).

18. Equations for Phase- and Frequency-Modulated Carriers

19. FM & PM (Bessel function)
The general equation for FM modulated wave:

20. Bessel function

21. Bessel Function
It is seen that each pair of side band is preceded by J coefficients. The order of the coefficient is denoted by subscript m. The Bessel function can be written as
N=number of the side frequency
M=modulation index

22. Bessel Functions of the First Kind, Jn(m) for some value of modulation index

23. Bessel Functions

24. Representation of frequency spectrum

25. Example 3
For an FM modulator with a modulation index m=1, a modulating signal Vm(t)=Vm sin(2π1000t), and an unmodulated carrier Vc(t) = 10sin(2π500kt), determine :
a)Number of sets of significant side frequencies
b)Their amplitudes
c)Draw the frequency spectrum showing their relative amplitudes.

26. 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 bandwidth is:
For n=>1

27. Cont’d… Estimation of transmission bandwidth;
Assume mf is large and n is approximate mf +2; thus
Bfm=2(mf +2)fm =
(1) is called Carson’s rule

28. Example 4
An FM modulator is operating with a peak frequency deviation ∆f = 20 kHz. The modulating signal frequency, fm is 10 kHz, and the 100 kHz carrier signal has an amplitude of 10 V. Determine :
a)The minimum bandwidth using Bessel Function table (actual minimum bandwidth).
b)The minimum bandwidth using Carson’s Rule (approximate minimum bandwidth).
c)Sketch the frequency spectrum for (a), with actual amplitudes.

29. 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

30. Example 5
Determine the deviation ratio and bandwidth for the worst-case (widest-bandwidth) modulation index for an FM broadcast-band transmitter with a maximum frequency deviation of 75 kHz and a maximum modulating signal frequency of 15 kHz
Determine the deviation ratio and maximum bandwidth for an equal modulation index with only half the peak frequency deviation and modulating signal frequency.

31. 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 or not it is modulated.

32. Cont…
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.

33. Average Power The average power in unmodulated carrier
The total instantaneous power in the angle modulated carrier.
The total modulated power

34. Example 6
a) Determine the unmodulated carrier power for the FM modulator and condition given in Example 3, (assume a load resistance RL = 50 Ώ)
b) Determine the total power in the angle modulated wave.

35. At the end of this chapter, you should be able,
To define and explain frequency modulation (FM) and phase modulation (PM)
To analyze the FM in terms of Mathematical analysis
To analyze the Bessel function for FM and PM
To analyze the FM bandwidth and FM power distribution

36. END OF CHAPTER 3 PART 1