Elements Of
Telecommunication
CHAPTER 7
FREQUENCY MODULATION
Aim
To equip participants with the fundamental knowledge of
modulation and its applications in telecommunication
equipment.
Objectives
At the end of the chapter participants should be able to:
• Define frequency modulation
• Give reasons why modulation is necessary in telecommunication.
• State advantages and disadvantages of FM over AM
• Calculate modulation frequency deviation, swing, modulation index
and bandwidth
• Explain the functionality of frequency modulator and demodulator
circuits
Introduction
• Frequency modulation, FM is widely used for a variety of
radio communications applications.
• FM broadcasts on the VHF bands still provide
exceptionally high quality audio, and FM is also used for
a variety of forms of two way radio communications, and
it is especially useful for mobile radio communications.
• The information to be transmitted is added to the carrier
with the help of a process called modulation.
• In this process a certain parameter of the carrier (e.g.
amplitude, frequency, phase) is varied by the signal to be
transmitted, the so called modulating signal.
Frequency Modulation
• It is the variation of the carrier frequency in accordance with the amplitude of
the modulating signal voltage.
• During modulation, the carrier frequency increases when the modulating voltage
increases and it decreases. When the modulating voltage decreases.
• The amplitude of a frequency-modulated wave does not vary
• The total power contained in the wave is constant and equal to the unmodulated
carrier power.
Advantages of FM over AM
• Improved signal to noise ratio (about 25dB) w.r.t. to man made
interference.
• Smaller geographical interference between neighboring
stations.
• Less radiated power.
• Well defined service areas for given transmitter power.
Disadvantages of FM:
• Much more Bandwidth (as much as 20 times as much).
• More complicated receiver and transmitter.
FM CARRIER WAVE
• The unmodulated carrier wave frequency is 3MHz.
• Three complete cycles of the unmodulated carrier wave will occur in 1 microsecond.
• When, at t = 0 to t = 1
• V = 0V
• The frequency remains at 3MHz
• When, at t = 1 to t = 2
• The voltage of the modulating signal increases to +1V,
• The instantaneous carrier frequency increases to 4MHz (for modulator sensitivity =1 MHz/V)
• There are now four complete cycles of the carrier voltage.
• At t = 2 to t=3
• The modulating signal returns to 0V
• The frequency falls to its original 3MHz.
• At t = 3 to t = 4
• The modulating signal voltage is -I V
• The carrier frequency is reduced to.
• When, at t = 4
• The signal voltage is 0V and frequency is 3MHz
• And so on
Frequency Modulated Waves
FM of a Sine wave
• The carrier frequency is made to vary in accordance with the
instantaneous value of the modulating signal.
• The amount by which the carrier deviates from its nominal
value is proportional to the amplitude of the modulating signal
• The number of times per second the carrier deviates is equal to
the modulating frequency.
• It should be noted that the minimum and maximum values of
the modulated carrier frequency are determined when the
modulating voltage is at its peak value.
• The amplitude of the carrier is not changed when frequency
modulation takes place
• There is no change in the amount of power carried by the wave.
Frequency Deviation
• The magnitude of frequency variation to either side of
the nominal carrier frequency is known as the frequency
deviation of an FM carrier wave
• It is proportional to the amplitude of the modulating
signal voltage.
• There is no inherent maximum value to the frequency
deviation that can be obtained in a FM system,
• Compared with amplitude modulation where the
maximum amplitude deviation possible corresponds to
m=1 (defined by the modulation index)
Rated System Deviation (Fd)
• Is the maximum value of frequency deviation which is
permitted to occur in a particular FM system.
• A maximum allowable frequency deviation must be
specified since the bandwidth occupied by an FM wave
increases with increase in the frequency deviation.
• Frequency deviation is directly proportional to the
modulating signal voltage
• The choice of rated system deviation sets the maximum
allowable modulating signal voltage that can be applied
to the frequency modulator.
Example 1
A frequency modulated system has a rated system
deviation of 30KHz. If the sensitivity of the frequency
modulator is 4KHz/V, what is the maximum allowable
modulating signal voltage?
Frequency Swing
Is the maximum carrier frequency minus the minimum carrier frequency and it
is equal to twice the frequency deviation i.e. 2fd.
Modulating Signal Factor (K)
• Most of the time the amplitude of the modulating signal
voltage will be less than its maximum allowable value.
• Then the frequency deviation of the carrier will be smaller
than the rated system deviation.
• This can be accounted for by introducing a factor k where:
• The frequency deviation of the carrier frequency is then given
by the product k.fd where fd is the rated system deviation.
• The factor k can have any value between 0 (modulating signal)
and 1 (maximum modulating signal).
Example 2
An FM system has a rated system deviation of 75 KHz and
this is produced by a modulating signal voltage of 10V.
Determine
• The sensitivity of the modulator, and
• The frequency deviation produced by a 2V modulating
signal.
• The frequency deviation of the carrier is proportional to
the amplitude of the modulating signal
• The modulation index will continually vary as the
amplitude and/or frequency of the modulating signal
changes.
Modulation Index
• When a carrier voltage is frequency modulated, its phase
is also caused to vary.
• The peak phase deviation is equal to the ratio of the
frequency deviation to the modulating frequency and is
called the modulation index of the modulated
Modulation Index M Is Equal
To Zero
• With no modulating signal present
• the frequency deviation will be zero and so the modulation index.
• Only the carrier wave with stable frequency fc is left.
Modulation Index M Not Equal To Zero
• With a modulation signal present, the modulation index
mf actually determines the peak phase deviation of the
carrier wave.
• The value of the cosine function in (1) (varies between +1
and -1, so the phase change of the carrier wave varies
between +mf and -mf radians.
• A change in phase of the carrier wave equals at the same
time a change in frequency of this wave.
EXAMPLE 3
A 100MHz carrier wave is frequency modulated by a 10V,
10 KHz sinusoidal voltage using a linear modulator. The
instantaneous carrier frequency varies between 99.95 and
100.05MHz. Calculate:
• The sensitivity of the modulator
• The modulation index,
• The peak phase deviation of the carrier
EXAMPLE 4
What will be the new values of the peak frequency and
phase deviation in the system of Exercise 3 if the
amplitude an the frequency of the modulating signal are
changed to 20V and 5 KHz respectively?
THE FM SPECTRUM AND BANDWIDTH
• The bandwidth, spectrum and sidebands are of great
importance when using frequency modulation.
• The sidebands of a frequency modulated signal extend
out either side of the main carrier, and cause the
bandwidth of the overall signal to increase well beyond
that of the unmodulated carrier.
• As the modulation of the carrier varies, so do the
sidebands and hence the bandwidth and overall
spectrum of the signal.
Mathematical Expression
• It can be seen that besides the carrier frequency fc, a set
of side frequencies are generated on a repeated distance
of fm .
• The amplitudes of the side frequencies just as the carrier
frequency depend on the modulation index mf and are
determined by the coefficients Jn (mf) , the so called
Bessel functions of the first kind and order.
• It is enough to know that these functions exist and that
their values for different modulation indices are known.
Bessel Function
• The total spectrum can be seen to consist of the carrier plus
an infinite number of sidebands spreading out on either side
of the carrier at integral multiples of the modulating
frequency.
• The relative levels of the sidebands can be obtained by
referring to a table of Bessel functions.
• It can be seen from the image below that the relative levels
rise and fall according to the different values of modulation
index.
• With increasing modulation index mf more side
frequencies are generated.
• The carrier energy decreases and even vanishes at
modulation index mf= 2.4.
• As the modulation index increases it is found that other
sidebands at twice the modulation frequency start to appear.
• As the index is increased further other sidebands can also be
seen.
Frequencies Contained In An FM Wave
• When a carrier of frequency fc is modulated by a
sinusoidal wave of frequency fm; the resultant waveform
contains components at a number of different frequencies
as follows:-
• The carrier frequency fc
• First-order side frequencies fc ± fm
• Second-order; side frequencies fc ± 2fm
• Third-order side frequencies fc ± 3fm
• etc.
• The number of side frequencies present in a particular
wave depends upon the modulation index;
• The larger the modulation index value the greater the
number of side frequencies generated.
• The amplitudes of the various components including the
carrier itself vary in a complicated manner as the
modulation index increases.
• Any component; again including the carrier; may have
zero amplitude at a particular value of modulation index.
Narrowband And Broadband FM
• For small values of mf (mf < l) there are only one or two
pairs of significant side frequencies.
• These cases correspond to so called narrow band FM. For
values of mf>>1 the side frequencies cover a wide
spectrum.
• They show clearly that an increase in the modulation
index of an FM wave will result in an increase in the
number of side frequencies generated.
• When the number of side frequencies is greater than
about 10, the number of significant side frequencies
does not depend very much on mf.
Frequency modulation
bandwidth
• In the case of an amplitude modulated signal the bandwidth
required is twice the maximum frequency of the modulation.
• Whilst the same is true for a narrowband FM signal, the situation
is not true for a wideband FM signal.
• The required bandwidth can be very much larger, with detectable
sidebands spreading out over large amounts of the frequency
spectrum.
• Usually it is necessary to limit the bandwidth of a signal so that it
does not unduly interfere with stations either side.
• As a frequency modulated signal has sidebands that extend out to
infinity, it is normal accepted practice to determine the bandwidth
as that which contains approximately 98% of the signal power.
• For the case of fd = 75 KHz and fm(max) = 15 KHz, which
is typical for a normal FM broadcast system, we obtain a
bandwidth of 180KHz.
• A corresponding AM system (2 x fm(max) = 30 KHz and
accounts for the inherent wideband nature of FM.
• The use of a large bandwidth leads to a considerable
improvement in signal-to-noise ratio, which is one of the
main advantage of FM compared to AM.
• Narrowband PM does not possess this property due to
its small frequency deviation.
Key points for frequency modulation
bandwidth and sidebands
• There are a few interesting points of summary relative to frequency modulation
bandwidth:
• The bandwidth of a frequency modulated signal varies with both deviation and
modulating frequency.
• Increasing modulating frequency reduces modulation index - it reduces the number of
sidebands with significant amplitude and hence the bandwidth.
• Increasing modulating frequency increases the frequency separation between sidebands.
• The frequency modulation bandwidth increases with modulation frequency but it is not
directly proportional to it.
• Frequency modulation bandwidth is of importance as it is with any other form of
signal.
• With band occupancy growing, and pressure on spectrum space, it is necessary to
ensure the bandwidth of a frequency modulated signal falls within its specified
allowance.
• Any undue signal spread outside this is likely to cause interference to other users.
Frequency Demodulators
• The function of frequency demodulator is to produce an
output voltage whose magnitude is directly proportional
to the frequency deviation of the input signal.
• The frequency should be equal to the number of times
per second the input signal frequency is varied about its
mean value.
• In simple terms in order to extract the modulation from
an FM wave; changes in frequency must be converted to
corresponding amplitude changes.
Advantage of FM over AM
• The range of modulating signal amplitudes from lowest to highest provided is
much higher.
• Selective fading is not a problem in f.m receivers since they do not respond to
any amplitude variations of the input signal.
• An increased output SIN for wideband ~ because of the use of greater than
unity deviation ratio.
• The FM transmitter is more efficient because:-
• Class C amplifiers can be used throughout the r.f section of the transmitter.
• The f.m wave bas a constant amplitude and this allows each r.f stage to be
operated in an optimum manner.
• An f.m receiver has the ability to suppress the weaker of two signals which are
simultaneously present at its antenna terminals at or near the same
frequency.
• The main disadvantage of f.m is the much wider bandwidth required if the
possible S/N improvement is to be realized.
Any questions?
Thank you!
