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CHAPTER 3

- Frequency Modulation (fm)

- Before we begin the class, please seat according

to your group

By the end of this chapter you should be able to

- Describe angle modulation FM and PM and the

advantage of FM over AM - Describe the types of FM narrowband and wide

band, advantage and applications - Solve problems involving Bessel function,

bandwidth, frequency deviation, power

calculation, index modulation - Describe FM modulator and demodulator
- Describe Applications of FM commercial

broadcasting - Describe Pre-emphasize and de-emphasize
- Describe FM stereo

Introductions

- Describe what is frequency?
- What is phase?

Frequency

- Frequency is the measurement of the number of

times that a repeated event occurs per unit of

time. - It is also defined as the rate of change of phase

of a sinusoidal waveform.

Phase

- The phase of an oscillation or wave is the

fraction of a complete cycle corresponding to an

offset in the displacement from a specified

reference point at time t 0.

a phase-shift

Instantaneous phase

Phase

- Phase is the offset of the wave from a reference

point f0

Phase Shift

- A phase shift is a difference or change in the

initial phase.

Phase

- In phase waves
- Out of phase waves

Angle Modulation

- ANGLE MODULATION is often called as FM. Frequency

Phase Modulation (FM PM) are both forms of

ANGLE MODULATION. - Because of its superior performance than AM, it

is used extensively for commercial broadcasting,

radio broadcasting, television sound

transmission, 2-way mobile radio, cellular radio,

microwave and satellite communications systems.

Angle Modulation

- The angle modulation can be expressed

mathematically as

m(t) angle modulated wave Vc peak carrier

amplitude (Volt) ?c carrier radian frequency

(rad/sec) fc carrier frequency (hertz) ?(t )

instantaneous phase deviation (radians)

Angle Modulation

?(t ) is a function of the modulating signal

Where

Is the modulating signal

Frequency Modulation

Angle Modulation

Phase Modulation

Angle Modulation

The choice between frequency modulation and phase

modulation depends on which one is directly

varied by the modulating signal

Direct FM varying the frequency of a

constant-amplitude carrier signal directly

proportional to the amplitude of a modulating

signal

Direct PM varying the phase of a

constant-amplitude carrier signal directly

proportional to the amplitude of a modulating

signal

Whichever property is directly varied will cause

the other property to varied as well

PM and FM of sine-wave signal

Carrier

Modulating signal

FM

PM

Angle Modulation

- To show how much the frequency or phase is

changed compared to the original carrier signal,

we use

Frequency deviation (?f)

Phase deviation (??)

Relative displacement of the carrier frequency

compared to the original carrier signal frequency

in hertz.

How much phase shifts the carrier signal undergo

compared to the original carrier signal phase in

radians.

Phase modulation

The instantaneous phase of a harmonic carrier

signal is varied in such a way that the

instantaneous phase deviation i.e. the difference

between the instantaneous phase and that of the

carrier signal is linearly related to the size of

the modulating signal at a given instant of time.

Instantaneous phase deviation

Instantaneous phase

Phase modulation

17

Phase modulation

Instantaneous phase deviation, ? is given by

Where K is deviation sensitivity for phase

modulation

Thus

Remember this equation!

Phase modulation

? can also be written as

Where m is phase modulation index or also known

as peak phase deviation.

Phase modulation

Phase modulation index, m is defined by

- Where K deviation sensitivity (rad per volt)
- Vm peak modulating signal amplitude

(volt)

m KVm (radians)

Remember this equation!

Thus

Frequency Modulation (FM)

- Frequency Modulation is the process of changing

carrier frequency by the modulating signal while

the carrier amplitude remains constant. - As the modulating signal amplitude increases, the

carrier frequency increases and vice versa. - The amount of change in carrier frequency

produced by the modulating signal is called

Frequency Deviation (?f). - Sometimes frequency deviation can also be

expressed as maximum carrier swing which is equal

to 2?f - The deviation is proportional to the amplitude of

the modulating signal.

Frequency Modulation

FM vs AM

PM vs FM

CAN YOU SEE THE DIFFERENCE?

Carrier

Modulating signal

FM

PM

Frequency Modulation (FM)

- FM produces pairs of sidebands spaced from the

carrier in multiples of the modulating frequency. - The modulation index m of FM signal is the ratio

of the frequency deviation ?f (or can also be

written as fd ) to the modulating frequency, fm , - The modulation index determines the number of

significant pairs of sidebands in FM signals.

Remember sidebands??

- Its a product of any modulation.
- Angle modulation (FM PM) produce more bandwidth

compared to amplitude modulation - This is the distinct feature of angle modulation
- More sidebands means more immune to noise
- But it also causes angle modulation sideband to

be wider.

Advantage of FM over AM

- The primary advantage of FM over AM is its

immunity to noise. Noise is short-duration

amplitude variations caused by lightning, motors,

auto ignitions, power transients and other

sources. - Another advantage of FM over AM is the capture

effect that allows the strongest signal on

frequency to dominate without interference from

the other signal. - FM has greater transmitter efficiency since class

C Amplifier may be used

Disadvantage of FM over AM

- FM has wide bandwidth compared to AM. The

spectrum space taken up by FM signal may be

limited by carefully controlling the deviation

ratio. - The circuits used in FM to produce and demodulate

FM is more complex and expensive than AM circuits.

Frequency modulation index

- Frequency modulation index is defined as
- Frequency deviation which is the change in

carrier when acted on by a modulating signal

frequency is given by - Peak frequency shift in hertz
- Peak-to-peak frequency deviation of carrier swing
- Therefore m can be rewritten as

Percent Modulation

FM Group task

- Within 30 minutes, read through the handouts

given and produce a note on FM - How sidebands are produced in FM
- What is the FM equation
- What is Bessel function and how it is applied in

FM equation - What is narrow band FM (NBFM) and wideband FM

(WBFM) - The effects of varying the frequency deviation

and modulating frequency - How to calculate FM bandwidth
- Understand the examples given

FM equation

When a modulating signal is a single sine wave,

the FM equation is

Or

To expand the equation into complete FM equation,

including its sidebands is difficult. Thus Bessel

function is used to solve the equation

Bessel Function

- Expanding the equation, becomes

Bessel Function

- Expanding the equation, becomes

Bessel Function

- Where m modulation index
- Vc peak amplitude of the unmodulated carrier
- J0(m) carrier component
- J1(m)first set of side frequencies displaced

from the carrier by ?m - J2(m)second set of side frequencies displaced

from the carrier by 2?m - Jn(m)nth set of side frequencies displaced from

the carrier by n?m

Bessel function of the first kind

Bessel function of the first kind

Bandwidth of angle modulation

- The Bandwidth of angle modulation can be

determined by using Bessel Table and defined as- - Where n number of significant sidebands
- fm modulating signal frequency (Hz)
- By using Carsons rule, the bandwidth of angle

modulation is defined as - Where ?f peak frequency deviation (Hz)
- fm modulating signal frequency (Hz)

EXAMPLE 2

- For FM Modulator with frequency deviation of

10 kHz, modulating signal frequency of 10 kHz,

Carrier amplitude voltage of 50V and Carrier

frequency of 500 kHz, determine the following - (a) Minimum Bandwidth using Bessel table
- (b) Minimum Bandwidth using Carsons rule
- (c) Amplitudes of the side frequencies and

plot the output frequency spectrum

Solution

- a)
- From Bessel function table, m1 yields three sets

of significant sidebands. Thus bandwidth is - b) Approx. minimum bandwidth is given by Carsons

rule. So

Solution (cont)

Solution (cont)

- c)

EXAMPLE 3

- Determine the deviation ratio and bandwidth for

FM transmitter with frequency deviation of 75 kHz

and maximum modulating signal of 15 kHz.

Group Exercise 1

- For an FM modulator with modulation index m 2,

modulating signal and an

unmodulated carrier - (a) Determine the number of sets of significant

sidebands - (b) Determine the amplitudes
- (c) Draw the frequency spectrum showing the

relative amplitudes of the side frequencies - (d) Determine the bandwidth
- (e) Determine the bandwidth if the amplitude of

the modulating signal increases by a factor of 2.5

Question 2

- For an FM modulator with 40 kHz frequency

deviation and a modulationg signal frequency 10

kHz, determine the bandwidth using both the

Bessel table and Carsons rule

SUBMIT YOUR ANSWERS (PER GROUP) ON MONDAY

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