Chapter03 fm modulation

© 2008 The McGraw-Hill Companies
1
Frequency ModulationFrequency Modulation
Phase ModulationPhase Modulation
Fundamentals of Angle Modulation

2
Frequency shift KeyingFrequency shift Keying
 When the modulating signal has only two amplitudes,
the modulated signal has only two values.
 The Carrier frequency and a higher frequency.
 No need to multiple frequencies.

3
Topics Covered in Chapter 5Topics Covered in Chapter 5
 5-1: Basic Principles of Frequency Modulation
 5-2: Principles of Phase Modulation
 5-3: Modulation Index and Sidebands
 5-4: Noise-Suppression Effects of FM
 5-5: Frequency Modulation Versus Amplitude
Modulation

4
5-1: Basic Principles5-1: Basic Principles
of Frequency Modulationof Frequency Modulation
 A sine wave carrier can be modified for the purpose of
transmitting information from one place to another by
varying its frequency. This is known as frequency
modulation (FM).
 In FM, the carrier amplitude remains constant and the
carrier frequency is changed by the modulating signal.

5
 As the amplitude of the information signal varies, the
carrier frequency shifts proportionately.
 As the modulating signal amplitude increases, the
carrier frequency increases.
 With no modulation the carrier is at its normal center
or resting frequency.

6
Figure 5-1: FM and PM
signals. The carrier is drawn
as a triangular wave for
simplicity, but in practice it is
a sine wave. (a) Carrier. (b)
Modulating signal. (c) FM
signal. (d) PM signal.

7
 Frequency deviation (fd) is the amount of change in
carrier frequency produced by the modulating signal.
 The frequency deviation rate is how many times per
second the carrier frequency deviates above or below
its center frequency.
 The frequency of the modulating signal determines the
frequency deviation rate.
 A type of modulation called frequency-shift keying
(FSK) is used in transmission of binary data in digital
cell phones and low-speed computer modems.

8
Frequency DeviationFrequency Deviation
 The level of deviation determines the bandwidth of the
overall signal.
 The deviation used for FM is different between
different applications.
 Broadcast stations in the VHF portion of the frequency
spectrum between 88.5 and 108 MHz use large
values of deviation, typically ±75 kHz. This is known
as wideband FM (WBFM).
 These signals are capable of supporting high quality
transmissions, but occupy a large amount of
bandwidth. Usually 200 kHz is allowed for each
wideband FM transmission(BW = 2(∆f + fs).)

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 For radio communications purposes less bandwidth is
used. Narrowband FM (NBFM) often uses deviations
of around ±3 kHz or possibly slightly more. Narrower
bandwidth has advantages in terms of radio spectrum
efficiency.

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 By now it should be clear to you that …….
 Frequency of the modulating wave has no effect on
the amount of deviation, rather it defines the rate of
deviation.

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ExampleExample

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Modulation IndexModulation Index
 The ratio of the frequency deviation to the modulating
frequency is known as the modulation index (mf)
μ or mf = fd / fm
fd denoted as ∆f
 In most communication systems using FM, maximum
limits are put on both the frequency deviation and the
modulating frequency.
 In standard FM broadcasting, the maximum permitted
frequency deviation is 75 kHz and the maximum
permitted modulating frequency is 15 kHz.
 The modulation index for standard FM broadcasting is
therefore 5.

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Side FrequenciesSide Frequencies
 Any modulation process produces side frequencies.
 In FM, when a carrier with frequency fc modulates a
signal with frequency fm, theoretically an infinite
number of side frequencies on both sides of fc are
generated.
 The distance between each of the side frequencies is
equal to the frequency of the modulating frequency.

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 The amplitude of each side frequency does not follow
any simple pattern and is dependent upon the
modulation index (μ) or deviation ratio.
 At a certain distance from the carrier (fc) the power in
the side frequencies will decrease to a level where
they can be considered insignificant.
 A side frequency is considered insignificant if its
voltage amplitude is less than 10% of the un-
modulated carrier amplitude.

15
 The number of significant side frequencies is directly
proportional to the modulation index and can be found
from Significant side frequencies = 2 (μ+ 1)
where μ= modulation index.
A table presents the relation of different side
frequencies amplitudes

16

17

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FM Signal BandwidthFM Signal Bandwidth
 The higher the modulation index in FM, the greater the
number of significant side frequencies and the wider
the bandwidth of the signal.
BW = 2fmN
or BW = 2(∆f + fm).
 When spectrum conservation is necessary, the
bandwidth of an FM signal can be restricted by
putting an upper limit on the modulation index.

19
ExampleExample
If the highest modulating frequency is 3 kHz and the
maximum deviation is 6 kHz, calculate the
modulation index and BW
mf = 6 kHz/3 kHz = 2
BW = 2fmN
Where N is the number of significant* sidebands
BW = 2(3 kHz)(4) = 24 kHz

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FM BWFM BW
 FM radio has a significantly larger bandwidth than AM
radio.
 In FM, both the modulation index and the modulating
frequency affect the bandwidth. As the information is
made stronger, the bandwidth also grows

21
SNRSNR
 An FM system provides a better signal-to-noise ratio
than an AM system.
 During its transmission (propagation), a frequency
modulated wave will be subject to noise and
interference voltages. The effect of these unwanted
voltages is to vary the amplitude of the modulated
signal.

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SNRSNR
 The noise amplitude variations have no effect on the
performance of the system. Information is not carried
in the amplitude of an FM wave.
 Amplitude variations are removed in the FM receiver
stage called the limiter.
 Signal-to-noise ratio of FM is primarily dependent
upon the system deviation ratio (D). .
Signal-to-noise ratio = 20 log (D sqrt 3) dB

23
EfficiencyEfficiency
 The efficiency of a signal is the power in the side-
bands as a fraction of the total.
 In FM signals, because of the considerable side-
bands produced, the efficiency is generally high.
 Recall that conventional AM is limited to about 33 %
efficiency when the modulation index was greater than
1.
 FM has no analogous problem.

24
EfficiencyEfficiency
 Efficiency is generally improved by making the
modulation index larger. i.e the bandwidth larger.
 A compromise between efficiency and SNR.
 The modulation index is normally limited to a value
between 1 and 5, depending on the application

25
Frequency shift KeyingFrequency shift Keying
 When the modulating signal has only two amplitudes,
the modulated signal has only two values.
 The Carrier frequency and a higher frequency.
 No need to multiple frequencies.

26
5-2: Principles of Phase Modulation5-2: Principles of Phase Modulation
Figure 5-6: Phase modulation of a carrier by binary data produces PSK.

27
 When the amount of phase shift of a constant-
frequency carrier is varied in accordance with a
modulating signal, the resulting output is a phase-
modulation (PM) signal.
 Phase modulators produce a phase shift which is a
time separation between two sine waves of the same
frequency.
 The greater the amplitude of the modulating signal,
the greater the phase shift.

28
Principles of Phase ModulationPrinciples of Phase Modulation
As the modulating signal goes positive, the amount
of phase lag, and thus the delay of the carrier output,
increases with the amplitude of the modulating
signal. The result at the output is the same as if the
constant-frequency carrier signal had been stretched
out, or had its frequency lowered.

29
Principles of Phase ModulationPrinciples of Phase Modulation
 When the modulating signal goes negative, the phase shift
becomes leading. This causes the carrier sine wave to be
effectively speeded up or compressed. The result is the
same as if the carrier frequency had been increased.

30
 In PM. the amount of carrier deviation is proportional
to the rate of change of the modulating signal, i.e. the
calculus derivative. With a sine wave modulating
signal. The PM carrier appears to be frequency-
modulated by the cosine of the modulating signal.

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 The maximum frequency deviation produced by a
phase modulator occurs during the time that the
modulating signal is changing at its most rapid rate.

32
Figure 5-3: A frequency shift
occurs in PM only when the
modulating signal amplitude
varies. (a) Modulating
signal. (b) FM signal. (c) PM
signal.

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Relationship between the Modulating Signal and Carrier
Deviation
 In FM and in PM, the frequency deviation is directly
proportional to the amplitude of the modulating signal.
 In PM, the maximum amount of leading or lagging
phase shift occurs at the peak amplitudes of the
modulating signal.
 In PM the carrier deviation is proportional to both the
modulating frequency and the amplitude.

34
Figure 5-4: Frequency deviation as a function of (a) modulating signal amplitude and
(b) modulating signal frequency.

35
 The higher the modulating signal frequency. the
shorter is its period and the faster the voltage
changes.
 Higher modulating voltages results in greater phase
shift and this in turn produces greater frequency
deviation.
 However higher modulating frequencies produce a
faster rate of change of the modulating voltage and
thus greater frequency deviation.

36
 In PM then the carrier frequency deviation is
proportional to both the modulating frequency (slope
of modulating voltage) and the amplitude. In FM,
frequency deviation is proportional only to the
amplitude of the modulating signal regardless of its
frequency.

37
Converting PM into FM
 In order to make PM compatible with FM, the deviation
produced by frequency variations in the modulating
signal must be compensated for.
 This compensation can be accomplished by passing the
intelligence signal through a low-pass RC network.
 This RC low-pass filter is called a frequency-
correcting network, predistorter, or 1/f filter and
causes the higher modulating frequencies to be
attenuated.
 The FM produced by a phase modulator is called
indirect FM.

38
Phase-Shift Keying
 The process of phase modulating a carrier with binary
data is called phase-shift keying (PSK) or binary
phase-shift keying (BPSK).
 The PSK signal has a constant frequency, but the
phase of the signal from some reference changes as
the binary modulating signal occurs.

39
Figure 5-6: Phase modulation of a carrier by binary data produces PSK.

40
5-3: Modulation Index5-3: Modulation Index
and Sidebandsand Sidebands
 Any modulation process produces sidebands.
 When a constant-frequency sine wave modulates a
carrier, side frequencies on both sides are produced.
 Side frequencies are the sum and difference of the
carrier and modulating frequency.
 The bandwidth of an FM signal is usually much wider
than that of an AM signal with the same modulating
signal.

41

42
 For the above figure, Note that the sidebands are
spaced from the carrier fc and from one another by a
frequency equal to the modulating frequency fm.
 If the modulating frequency is 1 kHz, the first pair of
sidebands is above and below the carrier by 1000 Hz.
The second pair of sidebands is above and below the
carrier by 2x 1000= 2000 Hz and so on.
 Amplitudes of side bands vary.
 Side frequencies with amplitude less than 1 percent of
the carrier are considered insignificant.

43
Modulation Index
 The ratio of the frequency deviation to the modulating
frequency is known as the modulation index (mf).
mf = fd / fm
 In most communication systems using FM, maximum
limits are put on both the frequency deviation and the
modulating frequency.
 In standard FM broadcasting, the maximum permitted
frequency deviation is 75 kHz and the maximum
permitted modulating frequency is 15 kHz.
 The modulation index for standard FM broadcasting is
therefore 5.

44
Bessel Functions
 The equation that expresses the phase angle in terms
of the sine wave modulating signal is solved with a
complex mathematical process known as Bessel
functions.
 Bessel coefficients are widely available and it is not
necessary to memorize or calculate them.

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Figure 5-8: Carrier and sideband amplitudes for different modulation indexes of FM
signals based on the Bessel functions.

46
Figure 5-9: Plot of the Bessel function data from Fig. 5-8.

47
Bessel Functions
 The symbol ! means factorial. This tells you to multiply
all integers from 1 through the number to which the
symbol is attached. (e.g. 5! Means 1 × 2 × 3 × 4 × 5 =
120)
 Narrowband FM (NBFM) is any FM system in which
the modulation index is less than π/2 = 1.57, or
mf < π /2.
 NBFM is widely used in communication. It conserves
spectrum space at the expense of the signal-to-noise
ratio.

48
FM Signal Bandwidth
 The higher the modulation index in FM, the greater the
number of significant sidebands and the wider the
bandwidth of the signal.
 When spectrum conservation is necessary, the
bandwidth of an FM signal can be restricted by putting
an upper limit on the modulation index.

49
FM Signal Bandwidth
 Example:
If the highest modulating frequency is 3 kHz and the
maximum deviation is 6 kHz, what is the modulation
index?
mf = 6 kHz/3 kHz = 2
What is the bandwidth?
BW = 2fmN
Where N is the number of significant*
sidebands
BW = 2(3 kHz)(4) = 24 kHz
*
Significant sidebands are those that have an amplitude of greater than 1% (.01)
in the Bessel table.

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5-4: Noise-Suppression Effects of FM5-4: Noise-Suppression Effects of FM
 Noise is interference generated by lightning, motors,
automotive ignition systems, and power line switching
that produces transient signals.
 Noise is typically narrow spikes of voltage with high
frequencies.
 Noise (voltage spikes) add to a signal and interfere
with it.
 Some noise completely obliterates signal information.

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 FM signals have a constant modulated carrier
amplitude.
 FM receivers contain limiter circuits that deliberately
restrict the amplitude of the received signal.
 Any amplitude variations occurring on the FM signal
are effectively clipped by limiter circuits.
 This amplitude clipping does not affect the information
content of the FM signal, since it is contained solely
within the frequency variations of the carrier.

52
Figure 5-11: An FM signal with noise.

53
Preemphasis
 Noise can interfere with an FM signal and particularly
with the high-frequency components of the modulating
signal.
 Noise is primarily sharp spikes of energy and contains a
lot of harmonics and other high-frequency components.
 To overcome high-frequency noise, a technique known
as preemphasis is used.
 A simple high-pass filter can serve as a transmitter’s
pre-emphasis circuit.
 Pre-emphasis provides more amplification of only high-
frequency components.

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Figure 5-13 Preemphasis and deemphasis. (a) Preemphasis circuit.

55
Preemphasis
 A simple low-pass filter can operate as a deemphasis
circuit in a receiver.
 A deemphasis circuit returns the frequency response to
its normal flat level.
 The combined effect of preemphasis and deemphasis is
to increase the signal-to-noise ratio for the high-
frequency components during transmission so that they
will be stronger and not masked by noise.

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Figure 5-13 Preemphasis and deemphasis. (c) Deemphasis circuit.

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5-5: Frequency Modulation Versus5-5: Frequency Modulation Versus
Amplitude ModulationAmplitude Modulation
Advantages of FM
 FM typically offers some significant benefits over AM.
 FM has superior immunity to noise, made possible by
clipper limiter circuits in the receiver.
 In FM, interfering signals on the same frequency are
rejected. This is known as the capture effect.
 FM signals have a constant amplitude and there is
no need to use linear amplifiers to increase power
levels. This increases transmitter efficiency.

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Disadvantages of FM
 FM uses considerably more frequency spectrum space.
 FM has used more complex circuitry for modulation and
demodulation.
 In the past, the circuits used for frequency modulation
and demodulation involved were complex. With the
proliferation of ICs, complex circuitry used in FM has all
but disappeared. ICs are inexpensive and easy to use.
FM and PM have become the most widely used
modulation method in electronic communication today.

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Major applications of AM and FM

Chapter03 fm modulation

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