1. CHAPTER 3 Frequency Modulation
Objectives: After completing this chapter, you will be able to;
1. Calculate the modulation index given the maximum deviation and the maximum modulating frequency and use the modulation index and Bessel coefficient to determine the number of significant sideband in an FM signal.
2. Calculate the bandwidth of an FM signal using (1) the modulation index and Bessel functions and (2) Carson’s rule, and explain the practical significance of the difference between two methods.
3. Explain how pre-emphasis is used to solve the problem of the interference of high-frequency components by noise.
4. List the advantages of and disadvantages of FM as compared to AM.
5. Give reasons for FM’s superior immunity to noise.

2. Introduction
The same person who developed the superheterodyne receiver was also responsible for the development of an alternative to AM that is Major E.H Armstrong.
Standard FM broadcast band from 88 MHz to 108 MHz.
Although AM broadcast was dominant type for many years, FM has been the most popular since 1970s because it provides;
- Much clearer signals, much lower distortion, less noise and static.

3. Introduction
There are only three (3) parameters of a carrier wave that can be changed or modulated in order for it to carry information – amplitude, frequency and phase.
Frequency and phase are closely related and can be group together in the term angle modulation.
Phase modulation produces frequency modulation. Since the amount of phase shift is varying, the effect is as if the carrier frequency is changed.
PM is often referred to as indirect FM. PM used extensively in data communication.

4. FM Principles
Maximum frequency deviation occurs at the maximum amplitude of the modulating signal.
If the modulation system is properly designed, it is said that this deviation is proportional to the amplitude of modulating signal – referred as linear modulation.
The frequency of modulating signal determines “how many times per second the carrier freq deviates above and below its nominal center freq.”
Eg: If the modulating signal is a 100 Hz sine wave, then the carrier frequency will shift above and below the center frequency 100 times per second.
This is called the frequency deviation rate.

6. FM Principles
In FM, the carrier amplitude remains constant while the carrier frequency is changed by the modulating signal.
As the amplitude of the information signal varies, the carrier frequency shifts in proportion.
As the modulating signal amplitude varies, the carrier frequency varies above and below its normal center frequency with no modulation.
The amount of change in carrier frequency produced by the modulating signal is known as the frequency deviation

7. Sidebands and Modulation Index
Any modulation process produces sidebands.
In FM, sum and difference sideband frequencies are produced.
Spectrum of FM signal is usually wider than an equivalent AM signal.
Although FM process produces an infinite number of upper and lower sidebands, only those with the largest amplitudes are significant in carrying the information.
Typically any sideband with an amplitude less than 1 percent of the unmodulated carrier is considered insignificant.

8. Modulation Index and Deviation Ratio
As indicated earlier, the number of significant sidebands and their amplitudes are dependent upon the amount of frequency deviation and the modulating frequency.
The ratio of the frequency deviation to the modulating frequency is known as the modulation index, m.
m = fd = frequency deviation
fm modulating frequency
In most communications systems using FM, maximum limits are put on both the frequency deviation and the modulating frequency.
Eg: The max permitted freq deviation = 75 kHz and the max permitted modulating freq = 15 kHz.

9. Spectrum Frequency of FM signal

10. Determining the number of Significant Sidebands
Knowing the modulation index, you can compute the number and amplitudes of the significant sidebands.
This is done through a complex mathematical process (beyond the scope of this text) known as the Bessel functions.
The spectrum of an FM signal varies considerably in bandwidth depending upon the modulation index.
The higher the modulation index, the wider the bandwidth of the FM signal.

11. Bessel Functions

12. Bandwidth BW = 2 (fd(max) + fm(max) )
The total bandwidth can be determine by knowing the modulation index and using the Bessel table.
The bandwidth can be determined using simple formula,
BW = 2 x N x fm(max)
An alternative way to calculate the bandwidth of an FM signal is to use Carson’s rule.
BW = 2 (fd(max) + fm(max) )
Number of significant sidebands
Maximum modulating freq
Max freq deviation

14. Given fm = 10 kHz and frequency deviation= 20 kHz
Given fm = 10 kHz and frequency deviation= 20 kHz. Draw the spectrum frequency

15. FM versus AM In general, FM is considered to be superior to AM.
Although both modulation types are suitable for transmitting information from one place to another, capable of equivalent fidelity and intelligibility.
FM offers some significant benefits over AM:
Better noise immunity – it rejects interfering signals because of the capture effects .
Provides better transmitter efficiency.
Its disadvantage – uses an excessive amount of spectrum space.

16. Capture Effect
If the signal of one is more than twice the amplitude of the other, the stronger signal ‘capture’ the channel and will totally eliminate the weaker, interfering signal.
This is known as capture effect in FM.
As long as the desired signal is considerably stronger than the interfering signal, that will be ok.
In FM, the capture effect allows the stronger signal to dominate while the weaker signal is eliminated.

17. Pre-emphasis & De-emphasis
Despite the fact that FM has superior noise rejection qualities, noise still interferes with an FM signal.
This is true for high-freq components in the modulating signal. Eg: music.
High-freq components are of a lower amplitudes.
20 kHz
70 kHz

18. Pre-emphasis & De-emphasis
To overcome this, most FM systems use a technique known as pre-emphasis – helps to offset high-freq noise interference.
To return the frequency response to its normal level, a de-emphasis circuit is used at the receiver.
As a result, the pre-emphasis at the transmitter is exactly offset by the de-emphasis circuit in the receiver, providing a normal frequency response.
The combined effect of pre-emphasis and de-emphasis is to increase the high-freq components during the transmission so that they will be stronger and not masked by noise.

19. Pre-emphasis

20. De-emphasis

21. Frequency response combination
f1=1/2R1C
Where =R1C

22. Frequency Modulators
A frequency modulators is a circuit that varies carrier frequency in accordance with the modulating signal.
The carrier is generated by either an LC or a crystal oscillator circuit, and so a way must be found to change the frequency of oscillation.
In an LC oscillator, the carrier freq is fixed by the values of the inductance and capacitance in a tuned circuit.
The carrier freq, therefore can be changed by varying either inductance or capacitance.

23. Tuned Circuit XL XC R
Series Tuned Circuit
Parallel Tuned Circuit

24. Varactor Modulators
The main problem with the circuit is that most LC oscillators are simply not stable enough to provide a carrier signal.
The frequency of LC oscillators will vary because of temperature changes, variations in circuit voltage and other factors.
Such instabilities cannot be tolerated in most modern electronic communication systems, where a transmitter must stay on freq. as precisely as possible.
As a result, crystal oscillators are normally used to set carrier frequency. IT is stable in wide temperature range.

25. Voltage Variable Capacitor

26. Freq-Modulating a Crystal Oscillator
It is possible to vary the frequency of a crystal oscillator by changing the value of capacitance in series or in parallel with the crystal.
When a small value of capacitance is connected in series with the crystal, the crystal frequency can be pulled slightly from its natural resonant frequency.
By making the series capacitance a varactor diode, frequency modulation of the crystal can be achieved.
The modulating signal is applied to varactor diode D1, which changes the oscillator frequency.

28. Frequency Demodulators
Any circuit that will convert a frequency variation in the carrier back into a proportional voltage can be used to demodulate or detect FM signals.
Circuit used to recover the original modulating signal from an FM transmission are called demodulators, detectors or discriminators.
The earliest demodulator:
Foster-Seeley Discriminators
Ratio Detector

29. Foster-Seeley Discriminators

30. Ratio Detector