Frequency Modulation fm

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CHAPTER 3

• Frequency Modulation (fm)

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• Before we begin the class, please seat according
  to your group

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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

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Introductions

• Describe what is frequency?
• What is phase?

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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.

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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
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Phase

• Phase is the offset of the wave from a reference
  point f0

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Phase Shift

• A phase shift is a difference or change in the
  initial phase.

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Phase

• In phase waves
• Out of phase waves

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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.

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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)
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Angle Modulation
?(t ) is a function of the modulating signal
Where
Is the modulating signal
Frequency Modulation
Angle Modulation
Phase Modulation
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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
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PM and FM of sine-wave signal
Carrier
Modulating signal
FM
PM
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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.
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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
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Phase modulation
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Phase modulation
Instantaneous phase deviation, ? is given by
Where K is deviation sensitivity for phase
modulation
Thus
Remember this equation!
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Phase modulation
? can also be written as
Where m is phase modulation index or also known
as peak phase deviation.
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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
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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.

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Frequency Modulation
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FM vs AM
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PM vs FM
CAN YOU SEE THE DIFFERENCE?
Carrier
Modulating signal
FM
PM
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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.

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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.

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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

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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.

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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
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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

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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
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Bessel Function

• Expanding the equation, becomes

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Bessel Function

• Expanding the equation, becomes

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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

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Bessel function of the first kind
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Bessel function of the first kind
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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)

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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

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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

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Solution (cont)
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Solution (cont)

• c)

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EXAMPLE 3

• Determine the deviation ratio and bandwidth for
  FM transmitter with frequency deviation of 75 kHz
  and maximum modulating signal of 15 kHz.

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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

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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

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