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By Ihsan UlHaq
Fundamentals of Frequency Modulation
© 2008 The McGraw-Hill Companies
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Learning Outcomes
Compare and contrast frequency modulation and phase
modulation.
Calculate the modulation index given the maximum deviation
and the maximum modulating frequency and use the
modulation index and Bessel coefficients to determine the
number of significant sidebands in an FM signal.
Calculate the bandwidth of an FM signal by using two methods
and explain the difference between the two.
Explain how pre-emphasis is used to solve the problem of the
interference of high-frequency components by noise.
List the advantages and disadvantages of FM as compared to
AM.
Give the reasons for FM’s superior immunity to noise.
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Topics Covered
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
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Introduction
There are three parameters of a carrier that
may carry information:
Amplitude
Frequency
Phase
Frequency and Phase modulation are
closely related and grouped together as
angle modulation
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Angle Modulation
The Angle of the carrier signal is varied with the
modulating signal m(t)
Two Cases:
Frequency Modulation
The instantaneous frequency of the carrier signal is
changed with respect to the message signal
Phase Modulation
The phase of the carrier signal is changed according
to the variations in the message signal
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Angle modulation
Nonlinear modulation
Requires high bandwidth
Good performance in the presence of noise
Used in situations where BW is not a major concern and
high SNR is required
FM is used in
High fidelity FM broadcasting
TV audio broadcasting
Microwave carrier modulation
Point-to-Point communications system
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Frequency Modulation
Power in an FM signal does not vary with
modulation
FM signals do not have an envelope that
reproduces the modulation
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1
FM
0.8 message
0.6
0.4
0.2
-0.2
-0.4
-0.6
-0.8
-1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
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5-1: Basic Principles
of 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.
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Basic Principles
of Frequency Modulation
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.
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Basic Principles
of Frequency Modulation
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.
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Basic Principles
of Frequency Modulation
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.
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FSK
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.
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The concept of Instantaneous
Frequency
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The concept of Instantaneous
Frequency (…cont)
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Phase Modulation
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Frequency Modulation
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Generalized Concept
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Representation of PM and FM
PM
Phase is directly proportional to m(t)
(t ) k p m(t )
k p : deviation constants of PM
Or Phase sensitivity of PM
FM
Phase is proportional to the integral of m(t)
t
(t ) 2 k f m( )d
k f : deviation constants of FM
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Principles of Phase Modulation
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.
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Principles of Phase Modulation
The maximum frequency deviation produced by a
phase modulator occurs during the time that the
modulating signal is changing at its most rapid rate.
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5-2: Principles of Phase Modulation
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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Principles of Phase Modulation
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.
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5-2: Principles of Phase Modulation
Figure 5-4: Frequency deviation as a function of (a) modulating signal amplitude and
(b) modulating signal frequency.
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5-2: Principles of Phase Modulation
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.
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5-2: Principles of Phase Modulation
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.
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5-2: Principles of Phase Modulation
Figure 5-6: Phase modulation of a carrier by binary data produces PSK.
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Frequency Modulation Index
Another term common to FM is
the modulation index, as
determined by the formula:
mf
fm
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5-3: Modulation Index
and Sidebands
Any modulation process produces sidebands.
When a constant-frequency sine wave modulates a
carrier, two side frequencies 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.
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5-3: Modulation Index
and Sidebands
Modulation Index
The ratio of the frequency deviation to the modulating
frequency is known as the modulation index (mf).
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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5-3: Modulation Index
and Sidebands
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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Bessel Functions
FM and PM signals have similar equations
regarding composition
Bessel functions represent normalized
voltages for the various components of an FM
or PM signal
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Sidebands
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5-3: Modulation Index
and Sidebands
Figure 5-8: Carrier and sideband amplitudes for different modulation indexes of FM
signals based on the Bessel functions.
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5-3: Modulation Index
and Sidebands
Figure 5-9: Plot of the Bessel function data from Fig. 5-8.
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5-3: Modulation Index
and Sidebands
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.
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5-3: Modulation Index
and Sidebands
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.
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Bandwidth
For FM, the bandwidth varies with both
deviation and modulating frequency
Increasing modulating frequency reduces
modulation index so it reduces the number of
sidebands with significant amplitude
On the other hand, increasing modulating
frequency increases the frequency separation
between sidebands
Bandwidth increases with modulation frequency
but is not directly proportional to it
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Carson’s Rule
Calculating the bandwidth of an FM signal is
simple, but tedious using Bessel functions
Carson’s Rule provides an adequate
approximation for determining FM signal
bandwidth:
B 2 max f m (max)
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5-3: Modulation Index
and Sidebands
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 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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5-4: Noise-Suppression Effects of FM
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.
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5-4: Noise-Suppression Effects of FM
Figure 5-11: An FM signal with noise.
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5-4: Noise-Suppression Effects of FM
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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5-4: Noise-Suppression Effects of FM
Figure 5-13 Preemphasis and deemphasis. (a) Preemphasis circuit.
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5-4: Noise-Suppression Effects of FM
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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5-4: Noise-Suppression Effects of FM
Figure 5-13 Preemphasis and deemphasis. (c) Deemphasis circuit.
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5-5: Frequency Modulation Versus
Amplitude 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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5-5: Frequency Modulation Versus
Amplitude Modulation
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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5-5: Frequency Modulation Versus
Amplitude Modulation
Major applications of AM and FM
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