PRINCIPLES OF COMMUNICATION
SYSTEMS
ECE 407 | THIRD YEAR, FIRST SEMESTER
CARCABUSO, C.L.C.
MODULATION INDEX AND PERCENTAGE OF
MODULATION
AMPLITUDE MODULATION FUNDAMENTALS
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AM CONCEPTS
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In the modulation process, the voice, video, or digital
signal modifies another signal called the carrier.
In amplitude modulation (AM) the information
signal varies the amplitude of the carrier sine wave.
The instantaneous value of the carrier amplitude
changes in accordance with the amplitude and
frequency variations of the modulating signal.
An imaginary line called the envelope connects the
positive and negative peaks of the carrier waveform.
•
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The modulation index (m) is a value that describes
the relationship between the amplitude of the
modulating signal and the amplitude of the carrier
signal.
m = Vm / Vc
This index is also known as the modulating factor or
coefficient, or the degree of modulation.
Multiplying the modulation index by 100 gives the
percentage of modulation.
OVERMODULATION AND DISTORTION
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The modulation index should be a number between
0 and 1.
If the amplitude of the modulating voltage is higher
than the carrier voltage, m will be greater than 1,
causing distortion.
If the distortion is great enough, the intelligence
signal becomes unintelligible.
Distortion of voice transmissions produces garbled,
harsh, or unnatural sounds in the speaker.
Distortion of video signals produces a scrambled and
inaccurate picture on a TV screen.
Figure 3-1: Amplitude Modulation. (a) the modulating
or information signal. (b) the modulated carrier.
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In AM, it is particularly important that the peak value
of the modulating signal be less than the peak value
of the carrier.
Vm < Vc
Distortion occurs when the amplitude of the
modulating signal is greater than the amplitude of
the carrier.
A modulator is a circuit used to produce AM.
Amplitude modulators compute the product of the
carrier and modulating signals.
Figure 3-3. Distortion of the envelope caused by
overmodulation where the modulating signal
amplitude Vm is greater than the carrier signal Vc.
PERCENTAGE OF MODULATION
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•
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Figure 3-2. Amplitude modulator showing input and
output signals.
The modulation index is commonly computed from
measurements taken on the composite modulated
waveform.
Using oscilloscope voltage values:
The amount, or depth, of AM is then expressed as the
percentage of modulation (100 × m) rather than as a
fraction.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
1
AMPLITUDE MODULATION FUNDAMENTALS
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A spectrum analyzer is used to display the frequency
domain as a signal.
Bandwidth is the difference between the upper and
lower sideband frequencies.
BW = fUSB−fLSB
Figure 3-4. AM wave showing peaks (Vmax) and troughs
(Vmin).
SIDEBANDS AND THE FREQUENCY DOMAIN
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Side frequencies, or sidebands are generated as
part of the modulation process and occur in the
frequency spectrum directly above and below the
carrier frequency.
SIDEBAND CALCULATIONS
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Single-frequency sine-wave modulation generates
two sidebands.
Complex wave (e.g. voice or video) modulation
generates a range of sidebands.
The upper sideband (fUSB) and the lower sideband
(fLSB) are calculated:
fUSB = fc + fm
and
Figure 3-6. The relationship between the time and
frequency domains.
EXAMPLE
A standard AM broadcast station is allowed to transmit
modulating frequencies up to 5 kHz. If the AM station is
transmitting on a frequency of 980 kHz, what are
sideband frequencies and total bandwidth?
fUSB = 980 + 5 = 985 kHz
fLSB = 980 – 5 = 975 kHz
BW = fUSB – fLSB = 985 – 975 = 10 kHz
BW = 2 (5 kHz) = 10 kHz
fLSB = fc − fm
Suppose that on an AM signal, the Vmax(p-p) value read
from the graticule on the oscilloscope screen is 5.9
divisions and Vmin(p-p) is 1.2 divisions.
What is the modulation index?
𝑚=
𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛
5.9 − 1.2
4.7
=
=
= 𝟎. 𝟔𝟔𝟐
𝑉𝑚𝑎𝑥 + 𝑉𝑚𝑖𝑛
5.9 + 1.2
7.1
Calculate Vc, Vm, and m if the vertical scale is 2 V per
division.
Figure 3-5. The AM wave is the algebraic sum of the
carrier and upper and lower sideband sine waves. (a)
Intelligence or modulating signal. (b) Lower sideband.
(c) Carrier. (d) Upper sideband. (e) Composite AM wave.
•
Observing an AM signal on an oscilloscope, you see
only amplitude variations of the carrier with respect
to time.
A plot of signal amplitude versus frequency is
referred to as frequency-domain display.
𝑉𝑚𝑎𝑥 + 𝑉𝑚𝑖𝑛
5.9 + 1.2
7.1
2𝑉
=
=
= 3.55 @
2
2
2
𝑑𝑖𝑣
𝑉𝑐 = 3.55 × 2 𝑉 = 7.1 𝑉
𝑉𝑚 =
𝑉𝑚𝑎𝑥 − 𝑉𝑚𝑖𝑛
5.9 − 1.2
4.7
2𝑉
=
=
= 2.35 @
2
2
2
𝑑𝑖𝑣
𝑉𝑚 = 2.35 × 2 𝑉 = 4.7 𝑉
𝑚=
FREQUENCY-DOMAIN REPRESENTATION OF AM
•
𝑉𝑐 =
𝑉𝑚
4.7
=
= 𝟎. 𝟔𝟔𝟐
𝑉𝑐
7.1
PULSE MODULATION
•
When complex signals such as pulses or rectangular
waves modulate a carrier, a broad spectrum of
sidebands is produced.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
2
AMPLITUDE MODULATION FUNDAMENTALS
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A modulating square wave will produce sidebands
based on the fundamental sine wave as well as the
third, fifth, seventh, etc. harmonics.
Amplitude modulation by square waves or
rectangular pulses is referred to as amplitude shift
keying (ASK).
ASK is used in some types of data communications.
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Total transmitted power (PT) is the sum of carrier
power (Pc ) and power of the two sidebands (PUSB and
PLSB).
When the percentage of modulation is less than the
optimum 100, there is much less power in the
sidebands.
Output power can be calculated by using the
formula
PT = (IT)2R
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where IT is measured RF current and R is antenna
impedance
The greater the percentage of modulation, the
higher the sideband power and the higher the total
power transmitted.
Power in each sideband is calculated
PSB = PLSB = PUSB = Pcm2 / 4
Figure 3-7. Frequency spectrum of an AM signal
modulated by a square wave.
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Maximum power appears in the sidebands when the
carrier is 100 percent modulated.
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In amplitude modulation, two-thirds of the
transmitted power is in the carrier, which conveys no
information.
Signal information is contained within the
sidebands.
Single-sideband (SSB) is a form of AM where the
carrier is suppressed and one sideband is eliminated.
SINGLE-SIDEBAND MODULATION
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DBS SIGNALS
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Figure 3-8. Amplitude modulation of a sine wave
carrier by a pulse or rectangular wave is called
amplitude-shift keying. (a) Fifty percent modulation. (b)
One hundred percent modulation.
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Continuous-wave (CW) transmission can be
achieved by turning the carrier off and on, as in
Morse code transmission.
Continuous wave (CW) transmission is sometimes
referred to as On-Off keying (OOK).
Splatter is a term used to describe harmonic
sideband interference.
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The first step in generating an SSB signal is to
suppress the carrier, leaving the upper and lower
sidebands.
This type of signal is called a double-sideband
suppressed carrier (DSSC) signal. No power is
wasted on the carrier.
A balanced modulator is a circuit used to produce
the sum and difference frequencies of a DSSC signal
but to cancel or balance out the carrier.
DSB is not widely used because the signal is difficult
to demodulate (recover) at the receiver.
AM POWER
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In radio transmission, the AM signal is amplified by a
power amplifier.
A radio antenna has a characteristic impedance that
is ideally almost pure resistance.
The AM signal is a composite of the carrier and
sideband signal voltages.
Each signal produces power in the antenna.
Figure 3-9. A frequency-domain display of DSB signal.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
3
AMPLITUDE MODULATION FUNDAMENTALS
SSB SIGNALS
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One sideband is all that is necessary to convey
information in a signal.
A single-sideband suppressed carrier (SSSC) signal
is generated by suppressing the carrier and one
sideband.
SSB signals offer four major benefits:
o Spectrum space is conserved and allows
more signals to be transmitted in the same
frequency range.
o All power is channeled into a single
sideband. This produces a stronger signal
that will carry farther and will be more
reliably received at greater distances.
o Occupied bandwidth space is narrower and
noise in the signal is reduced.
o There is less selective fading over long
distances.
DISADVANTAGES OF DSB AND SSB
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Single and double-sideband are not widely used
because the signals are difficult to recover (i.e.
demodulate) at the receiver.
A low power, pilot carrier is sometimes transmitted
along with sidebands in order to more easily recover
the signal at the receiver.
Figure 3-10. Radio emission code designations.
SIGNAL POWER CONSIDERATIONS
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In SSB, the transmitter output is expressed in terms
of peak envelope power (PEP), the maximum
power produced on voice amplitude peaks.
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A vestigial sideband signal (VSB) is produced by
partially suppressing the lower sideband. This kind of
signal is used in TV transmission.
•
A code is used to designate the types of signals that
can be transmitted by radio and wire.
The code is made up of a capital letter and a number.
Lowercase subscript letters are used for more
specific definition.
Examples of codes:
o DSB two sidebands, full carrier = A3
o DSB two sidebands, suppressed carrier = A3b
o OOK and ASK = A1
The International Telecommunications Union
(ITU), a standards organization, uses a code to
describe signals.
Examples are:
o A3F
amplitude-modulated analog TV
o J3E
SSB voice
o F2D
FSK data
o G7E
phase-modulated voice, multiple
signals
APPLICATIONS OF DSB AND SSB
CLASSIFICATION OF RADIO EMISSIONS
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Figure 3-11. ITU emissions designations.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
4
PRINCIPLES OF COMMUNICATION
SYSTEMS
ECE 407 | THIRD YEAR, FIRST SEMESTER
CARCABUSO, C.L.C.
AMPLITUDE MODULATOR AND DEMODULATOR
CIRCUITS
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BASIC PRINCIPLES
OF AMPLITUDE MODULATION
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Intermodulation products are easy to filter out.
Tuned circuits filter out the modulating signal and
carrier harmonics, leaving only carrier and
sidebands.
Modulator circuits cause carrier amplitude to be
varied in accordance with modulating signals.
Circuits produce AM, DSB, and SSB transmission
methods.
The basic equation for an AM signal is
νAM = Vcsin 2πfct + (Vmsin 2πfmt)(sin 2πfct)
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The first term is the sine wave carrier
The second term is the product of the sine wave
carrier and modulating signals.
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Amplitude modulation voltage is produced by a
circuit that can multiply the carrier by the
modulating signal and then add the carrier.
If a circuit’s gain is a function of 1+ m sin 2πfmt, the
expression for the AM signal is
Figure 4-2. A square-law circuit for producing AM.
AM IN THE TIME DOMAIN
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Figure 4-3. AM signal containing not only the carrier
and sidebands but also the modulating signal.
νAM = A(νc)
Where A is the gain or attenuation factor.
Figure 4-1. Block diagram of a circuit to produce AM.
Figure 4-4. The tuned circuit filters out the modulating
signal and carrier harmonics, leaving only the carrier
and sidebands.
AM IN THE FREQUENCY DOMAIN
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The product of the carrier and modulating signal can
be generated by applying both signals to a nonlinear
component such as a diode.
A square-law function is one that varies in
proportion to the square of the input signals. A diode
gives a good approximation of a square-law
response. Bipolar and field-effect transistors (FETs)
can also be biased to give a square-law response.
Diodes and transistors whose function is not a pure
square-law function produce third-, fourth-, and
higher-order harmonics, which are sometimes
referred to as intermodulation products.
AMPLITUDE MODULATORS
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There are two types of amplitude modulators. They
are low-level and high-level modulators.
Low-level modulators generate AM with small
signals and must be amplified before transmission.
High-level modulators produce AM at high power
levels, usually in the final amplifier stage of a
transmitter.
LOW-LEVEL AM: DIODE MODULATOR
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Diode modulation consists of a resistive mixing
network, a diode rectifier, and an LC tuned circuit.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
1
AMPLITUDE MODULATOR AND DEMODULATOR CIRCUITS
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The carrier is applied to one input resistor and the
modulating signal to another input resistor.
This resistive network causes the two signals to be
linearly mixed (i.e. algebraically added).
A diode passes half cycles when forward biased.
The coil and capacitor repeatedly exchange energy,
causing an oscillation or ringing at the resonant
frequency.
Figure 4-7. High-frequency amplitude modulators
using PIN diodes.
LOW-LEVEL AM: DIFFERENTIAL AMPLIFIER
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Figure 4-5. Amplitude modulation with a diode.
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LOW-LEVEL AM: TRANSISTOR MODULATOR
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Transistor modulation consists of a resistive mixing
network, a transistor, and an LC tuned circuit.
The emitter-base junction of the transistor serves as
a diode and nonlinear device.
Modulation and amplification occur as base current
controls a larger collector current.
The LC tuned circuit oscillates (rings) to generate the
missing half cycle.
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Figure 4-8. (a) Basic differential amplifier. (b)
Differential amplifier modulator.
Figure 4-6. Simple transistor modulator.
LOW-LEVEL AM: PIN DIODE MODULATOR
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Differential amplifier modulators make excellent
amplitude modulators because they have a high
gain, good linearity and can be 100 percent
modulated.
The output voltage can be taken between two
collectors, producing a balanced, or differential,
output.
The output can also be taken from the output of
either collector to ground, producing a singleended output.
The modulating signal is applied to the base of a
constant-current source transistor.
The modulating signal varies the emitter current
and therefore the gain of the circuit.
The result is AM in the output.
Variable attenuator circuits using PIN diodes
produce AM at VHF, UHF, and microwave
frequencies.
PIN diodes are special type silicon junction diodes
designed for use at frequencies above 100 MHz.
When PIN diodes are forward-biased, they operate
as variable resistors.
Attenuation caused by PIN diode circuits varies with
the amplitude of the modulating signal.
HIGH-LEVEL AM
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In high-level modulation, the modulator varies the
voltage and power in the final RF amplifier stage of
the transmitter.
The result is high efficiency in the RF amplifier and
overall high-quality performance.
COLLECTOR MODULATOR
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The collector modulator is a linear power amplifier
that takes the low-level modulating signals and
amplifies them to a high-power level.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
2
AMPLITUDE MODULATOR AND DEMODULATOR CIRCUITS
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A modulating output signal is coupled through a
modulation transformer to a class C amplifier.
The secondary winding of the modulation
transformer is connected in series with the collector
supply voltage of the class C amplifier.
AMPLITUDE DEMODULATORS
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Demodulators, or detectors, are circuits that accept
modulated signals and recover the original
modulating information.
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On positive alternations of the AM signal, the
capacitor charges quickly to the peak value of pulses
passed by the diode.
When the pulse voltage drops to zero, the capacitor
discharges into the resistor.
The time constant of the capacitor and resistor is
long compared to the period of the carrier.
The capacitor discharges only slightly when the
diode is not conducting.
The resulting waveform across the capacitor is a
close approximation to the original modulating
signal.
Because the diode detector recovers the envelope of
the AM (modulating) signal, the circuit is sometimes
called an envelope detector.
If the RC time constant in a diode detector is too
long, the capacitor discharge will be too slow to
follow the faster changes in the modulating signal.
This is referred to as diagonal distortion.
DIODE DETECTOR
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Figure 4-9. A high-level collector modulator.
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SERIES MODULATOR
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A series modulator produces high-level modulation
without a large and expensive modulation
transformer used in collector modulators.
It improves frequency response.
It is, however, very inefficient.
A series modulator replaces the modulation
transformer with an emitter follower.
The modulating signal is applied to the emitter
follower.
The emitter follower is in series with the collector
supply voltage.
The collector voltage changes with variations in the
amplified audio modulating signal.
•
Figure 4-11. A diode detector AM demodulator.
SYNCHRONOUS DETECTION
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Synchronous detectors use an internal clock signal
at the carrier frequency in the receiver to switch the
AM signal off and on, producing rectification similar
to that in a standard diode detector.
Synchronous detectors or coherent detectors have
less distortion and a better signal-to-noise ratio than
standard diode detectors.
The key to making the synchronous detector work is
to ensure that the signal producing the switching
action is perfectly in phase with the received AM
carrier.
An internally generated carrier signal from an
oscillator will not work.
Figure 4-10. Series modulation. Transistors may also be
MOSFETs with appropriate biasing.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
3
AMPLITUDE MODULATOR AND DEMODULATOR CIRCUITS
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The carrier turns the diodes off and on at a high rate
of speed.
The diodes act like switches that connect the
modulating signal at the secondary of T1 to the
primary of T2.
IC BALANCED MODULATORS
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Figure 4-12. A practical synchronous detector.
BALANCED MODULATOR
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A balanced modulator is a circuit that generates a
DSB signal, suppressing the carrier and leaving only
the sum and difference frequencies at the output.
The output of a balanced modulator can be further
processed by filters or phase-shifting circuitry to
eliminate one of the sidebands, resulting in a SSB
signal.
Types of balanced modulators include lattice,
1496/1596 IC, and the analog multiplier.
LATTICE MODULATOR
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A popular and widely used balanced modulator is
the diode ring or lattice modulator.
The lattice modulator consists of an input
transformer, an output transformer and four diodes
connected in a bridge circuit.
The carrier signal is applied to the center taps of the
input and output transformers.
The modulating signal is applied to the input
transformer.
The output appears across the output transformer.
The 1496/1596 IC is a versatile circuit available for
communication applications.
It can work at carrier frequencies up to 100 MHz.
It can achieve a carrier suppression of 50 to 65 dB.
The 1496/1596 IC can operate as a balanced
modulator or configured to perform as an amplitude
modulator, a product detector, or a synchronous
detector.
ANALOG MULTIPLIER
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An analog multiplier is a type of integrated circuit
that can be used as a balanced modulator.
Analog multipliers are often used to generate DSB
signals.
The analog multiplier is not a switching circuit like
the balanced modulator.
The analog multiplier uses differential amplifiers
operating in the linear mode.
The carrier must be a sine wave and the multiplier
produces the true product of two analog inputs.
GENERATING SSB SIGNALS
THE FILTER METHOD
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The filter method is the simplest and most widely
used method of generating SSB signals.
The modulating signal is applied to the audio
amplifier.
The amplifier’s output is fed to one input of a
balanced modulator.
A crystal oscillator provides the carrier signal which
is also applied to the balanced modulator.
The output of the balanced modulator is a doublesideband (DSB) signal.
An SSB signal is produced by passing the DSB signal
through a highly selective bandpass filter.
With the filter method, it is necessary to select either
the upper or the lower sideband.
Figure 4-13. Lattice-type balanced modulator.
•
•
The carrier sine wave is considerably higher in
frequency and amplitude than the modulating
signal.
The carrier sine wave is used as a source of forward
and reverse bias for the diodes.
Figure 4-14. An SSB transmitter using the filter
method.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
4
AMPLITUDE MODULATOR AND DEMODULATOR CIRCUITS
PHASING METHOD
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The phasing method of SSB generation uses a
phase-shift technique that causes one of the
sidebands to be canceled out.
The phasing method uses two balanced modulators
which eliminate the carrier.
The carrier oscillator is applied to the upper balanced
modulator along with the modulating signal.
The carrier and modulating signals are both shifted
in phase by 90 degrees and applied to another
balanced modulator.
Phase-shifting causes one sideband to be canceled
out when the two modulator outputs are added
together.
Figure 4-15. An SSB generator using the phasing
method.
DSB AND SSB DEMODULATION
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•
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To recover the intelligence in a DSB or SSB signal, the
carrier that was suppressed at the receiver must be
reinserted.
A product detector is a balanced modulator used in
a receiver to recover the modulating signal.
Any balanced modulator can be used as a product
detector to demodulate SSB signals.
Figure 4-16. A balanced modulator used as a product
detector to demodulate an SSB signal.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
5
PRINCIPLES OF COMMUNICATION
SYSTEMS
ECE 407 | THIRD YEAR, FIRST SEMESTER
CARCABUSO, C.L.C.
FUNDAMENTALS OF FREQUENCY MODULATION
BASIC PRINCIPLES
OF FREQUENCY MODULATION
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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.
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.
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.
EXAMPLE
A transmitter operates on a frequency of 915 MHz. The
maximum FM deviation is ±12.5 kHz. What are the
maximum and minimum frequencies that occur during
modulation?
915 MHz = 915,000 kHz
Maximum deviation = 915,000 + 12.5 = 915,012.5 kHz
Minimum deviation = 915,000 – 12.5 = 914,987.5 kHz
PRINCIPLES OF PHASE MODULATION
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When the amount of phase shift of a constantfrequency carrier is varied in accordance with a
modulating signal, the resulting output is a phasemodulation (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.
The maximum frequency deviation produced by a
phase modulator occurs during the time that the
modulating signal is changing at its most rapid rate.
Figure 5-2. A frequency shift occurs in PM only when
the modulating signal amplitude varies. (a)
Modulating signal. (b) FM signal. (c) PM signal.
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.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
1
FUNDAMENTALS OF FREQUENCY MODULATION
RELATIONSHIP BETWEEN THE MODULATING
SIGNAL AND CARRIER DEVIATION
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•
•
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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.
The PSK signal has a constant frequency, but the
phase of the signal from some reference changes as
the binary modulating signal occurs.
Figure 5-5. Phase modulation of a carrier by binary
data produces PSK.
MODULATION INDEX AND SIDEBANDS
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Figure 5-3. Frequency deviation as a function of (a)
modulating signal amplitude and (b) modulating
signal frequency.
CONVERTING PM INTO FM
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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 frequencycorrecting 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.
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.
MODULATION INDEX
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•
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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.
BESSEL FUNCTIONS
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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.
Figure 5-4. Using a low-pass filter to roll off the audio
modulating signal amplitude with frequency.
PHASE-SHIFT KEYING
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The process of phase modulating a carrier with
binary data is called phase-shift keying (PSK) or
binary phase-shift keying (BPSK).
Figure 5-6. Carrier and sideband amplitudes for
different modulation indexes of FM signals based on
the Bessel functions.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
2
FUNDAMENTALS OF FREQUENCY MODULATION
What is the maximum bandwidth of an FM signal with a
deviation of 30 kHz and a maximum modulating signal
of 5 kHz as determined by (a) Figure 5-6 and (b) Carson’s
rule?
a.
𝑚𝑓 =
𝑓𝑑
30 𝑘𝐻𝑧
=
=6
𝑓𝑚
5 𝑘𝐻𝑧
Figure 5-6 shows 9 significant sidebands spaced 5 kHz
apart for mf = 6
BW = 2fmN = 2(5 kHz) 9 = 90 kHz
b.
BW = 2[fd (max) + fm (max)]
= 2(30 kHz + 5 kHz)
=2(35 kHz)
BW = 70 kHz
Figure 5-7. Plot of the Bessel function data from Fig. 56.
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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.
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NBFM is widely used in communication. It conserves
spectrum space at the expense of the signal-tonoise ratio.
FM SIGNAL BANDWIDTH
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NOISE-SUPPRESSION EFFECTS OF FM
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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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EXAMPLE
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.
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.
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
Figure 5-8. An FM signal with noise.
Where N is the number of significant* sidebands
PREEMPHASIS
BW = 2(3 kHz)(4) = 24 kHz
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Significant sidebands are those that have an
amplitude of greater than 1% (.01) in the Bessel table.
*
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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 highfrequency components.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
3
FUNDAMENTALS OF FREQUENCY MODULATION
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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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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.
Figure 5-9. Preemphasis circuit.
DEEMPHASIS
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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.
Figure 5-11. Major applications of AM and FM
Figure 5-10. Deemphasis circuit.
FREQUENCY MODULATION VERSUS AMPLITUDE
MODULATION
ADVANTAGES OF FM
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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.
DISADVANTAGES OF FM
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FM uses considerably more frequency spectrum
space.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
4
PRINCIPLES OF COMMUNICATION
SYSTEMS
ECE 407 | THIRD YEAR, FIRST SEMESTER
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CARCABUSO, C.L.C.
VARACTOR MODULATOR
FM CIRCUITS
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FREQUENCY MODULATORS
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There are many circuits used to produce FM and PM
signals. There are two types of frequency modulator
circuits: direct circuits and phase modulation
circuits.
A frequency modulator is a circuit that varies carrier
frequency in accordance with the modulating
signal.
The carrier is generated by LC or crystal oscillator
circuits.
In LC oscillators, the carrier frequency can be
changed by varying either the inductance or
capacitance.
The idea is to find a circuit or component that
converts a modulating voltage to a corresponding
change in capacitance or inductance.
In crystal oscillators, the frequency is fixed by the
crystal.
A varactor is a variable capacitance diode used to
change oscillator frequencies.
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In Figure 6-2, the capacitance of varactor diode D1
and L1 form the parallel tuned circuit of the oscillator.
The value of C1 is made very large so its reactance is
very low.
C1 connects the tuned circuit to the oscillator and
blocks the dc bias on the base of Q1 from being
shorted to ground through L1.
The values of L1 and D1 fix the center carrier
frequency.
The modulating signal varies the effective voltage
applied to D1 and its capacitance varies.
Most LC oscillators are not stable enough to provide
a carrier signal.
The frequency of LC oscillators will vary with
temperature changes, variations in circuit voltage,
and other factors.
As a result, crystal oscillators are normally used to set
carrier frequency.
VARACTOR OPERATION
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A junction diode is created when P- and N-type
semiconductors
are
formed
during
the
manufacturing process.
A depletion region, where there are no free carriers,
holes, or electrons, is formed in the process.
This region acts like a thin insulator that prevents
current from flowing through the device.
A forward bias will cause the diode to conduct.
A reverse bias will prevent current flow.
A reverse-biased diode acts like a small capacitor.
The P- and N-type materials act as the two plates of
the capacitor.
The depletion region acts as the dielectric material.
The width of the depletion layer determines the
width of the dielectric and, therefore the amount of
capacitance.
All diodes exhibit variable capacitance.
Varactors
are
designed
to
optimize
this
characteristic.
Figure 6-2. A direct-frequency-modulated carrier
oscillator using a varactor diode.
FREQUENCY-MODULATING A CRYSTAL
OSCILLATOR
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Crystal oscillators provide highly accurate carrier
frequencies and their stability is superior to LC
oscillators.
The frequency of a crystal oscillator can be varied by
changing the value of capacitance in series or
parallel with the crystal.
By making the series capacitance a varactor diode,
frequency modulation can be achieved.
The modulating signal is applied to the varactor
diode which changes the oscillator frequency.
Figure 6-1. Schematic symbols of a varactor diode.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
1
FM CIRCUITS
Figure 6-5. A reactance modulator.
PHASE MODULATORS
Figure 6-3. Frequency modulation of a crystal oscillator
with a VVC.
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Varactors are made with a wide range of capacitance
values, most units having a nominal capacitance in
the 1- to 200-pF range.
A frequency multiplier circuit is one whose output
frequency is some integer multiple of the input
frequency.
A frequency multiplier that multiplies a frequency by
two is called a doubler.
A frequency multiplier that multiplies a frequency by
three is called a tripler.
Frequency multipliers can also be cascaded.
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Most modern FM transmitters use some form of
phase modulation (PM) to produce indirect FM.
In PM the carrier oscillator can be optimized for
frequency accuracy and stability.
Crystal oscillators or crystal-controlled frequency
synthesizers can be used to set the carrier frequency
accurately and maintain stability.
The output of the carrier oscillator is fed to a phase
modulator where the phase shift is made to vary in
accordance with the modulating signal.
Simple phase shifters do not produce a linear
response over a large range of phase shift.
To compensate for this, restrict the total allowable
phase shift to maximize linearity.
Multipliers must also be used to achieve the desired
deviation.
Figure 6-4. How frequency multipliers increase carrier
frequency and deviation.
VOLTAGE-CONTROLLED OSCILLATORS
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Oscillators whose frequencies are controlled by an
external input voltage are generally referred to as
voltage-controlled oscillators (VCOs).
Voltage-controlled crystal oscillators are generally
referred to as VXOs.
VCOs are primarily used in FM.
VCOs are also used in voltage-to-frequency
conversion applications.
REACTANCE MODULATOR
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A reactance modulator is a circuit that uses a
transistor amplifier that acts like either a variable
capacitor or an inductor.
When the circuit is connected across the tuned
circuit of an oscillator, the oscillator frequency can be
varied by applying the modulating signal to the
amplifier.
Reactance modulators can produce frequency
deviation over a wide range.
Reactance modulators are highly linear, so distortion
is minimal.
Figure 6-6. RC phase-shifter basics.
VARACTOR PHASE MODULATORS
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A simple phase-shift circuit can be used as a phase
modulator if the resistance or capacitance can be
made to vary with the modulating signal.
A varactor can be used to vary capacitance and
achieve phase shift modulation.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
2
FM CIRCUITS
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Circuits used to recover the original modulating
signal from an FM transmission are called:
o Demodulators
o Detectors
o Discriminators
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The slope detector makes use of a tuned circuit and
a diode detector to convert frequency variations into
voltage variations.
The main difficulty with slope detectors lies in tuning
them.
SLOPE DETECTOR
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Figure 6-7. A varactor phase modulator.
TRANSISTOR PHASE MODULATOR
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A transistor can be used as a variable resistor to
create a phase modulator.
A standard common emitter class A amplifier biased
into the linear region is used in PM.
The transistor from collector to ground acts like a
resistor.
The transistor’s resistance forms part of the phase
shifting circuit.
Figure 6-9. Slope detector operation.
PULSE-AVERAGING DISCRIMINATORS
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Figure 6-8. A transistor phase shifter.
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TUNED-CIRCUIT PHASE MODULATORS
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Most phase modulators are capable of producing a
small amount of phase shift. The limited phase shift,
therefore, produces a limited frequency shift.
Phase and frequency shift can be increased by using
a parallel tuned circuit.
At resonance, a parallel resonant circuit acts like a
large resistor.
Off resonance, the circuit acts inductively or
capacitively and produces a phase shift.
Phase modulators are easy to implement, but they
have two main disadvantages.
o The amount of phase shift they produce and
the resulting frequency deviation are
relatively low.
o All the phase-shift circuits produce
amplitude variations as well as phase
changes.
FREQUENCY DEMODULATORS
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A pulse-averaging discriminator uses a zero
crossing detector, a one shot multivibrator and a
low-pass filter in order to recover the original
modulating signal.
The pulse-averaging discriminator is a very highquality frequency demodulator.
Originally this discriminator was limited to expensive
telemetry and industrial control applications.
With availability of low-cost ICs, this discriminator is
used in many electronic products.
Figure 6-10. Pulse-averaging discriminator.
QUADRATURE DETECTOR
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The quadrature detector is probably the single
most widely used FM demodulator.
The quadrature detector is primarily used in TV
demodulation.
This detector is used in some FM radio stations.
The quadrature detector uses a phase-shift circuit to
produce a phase shift of 90 degrees at the
unmodulated carrier frequency.
Any circuit that will convert a frequency variation in
the carrier back into a proportional voltage variation
can be used to demodulate or detect FM signals.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
3
FM CIRCUITS
Figure 6-11. A quadrature FM detector.
PHASE-LOCKED LOOPS
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A phase-locked loop (PLL) is a frequency- or phasesensitive feedback control circuit used in frequency
demodulation, frequency synthesizers, and various
filtering and signal-detection applications. PLLs
have three basic elements. They are:
o Phase detector
o Low-pass filter
o Voltage-controlled oscillator
Figure 6-12. Block diagram of a PLL.
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The primary job of the phase detector is to compare
the two input signals and generate an output signal
that, when filtered, will control the VCO.
If there is a phase or frequency difference between
the FM input and VCO signals, the phase detector
output varies in proportion to the difference.
The filtered output adjusts the VCO frequency in an
attempt to correct for the original frequency or
phase difference.
This dc control voltage, called the error signal, is also
the feedback in this circuit.
When no input signal is applied, the phase detector
and low-pass filter outputs are zero.
The VCO then operates at what is called the freerunning frequency, its normal operating frequency
as determined by internal frequency-determining
components.
ECE 407 | PRINCIPLES OF COMMUNICATION SYSTEMS
4