Republic of the Philippines
Tarlac State University
COLLEGE OF ENGINEERING AND TECHNOLOGY
Department of Electrical and Electronics Engineering
Tarlac City
A353 –
FUNDAMENTALS OF
ELECTRONIC
COMMUNICATIONS
Prepared by:
Idris Jeffrey M. Manguera
June 2020
Fundamentals of Electronic Communications
Chapter 3: Amplitude Modulation
Intended Learning Outcomes
1. To describe how an Amplitude Modulated signal is generated.
2. To be able to calculate and analyze the time, frequency and power of Double Sideband
(DSBFC) and Single Sideband (SSB) AM Systems.
Activities
Tune in to an AM radio station. Imagine how does a signal from a broadcast studio travel
through the airwaves and then detected by an AM receiver.
Processing
Modulation is the process of altering a characteristic of the carrier in accordance with
the instantaneous value of the intelligence signal. The characteristics of the carrier that can be
varied are amplitude, frequency and phase.
Demodulation is the process of recovering the intelligence signal from a modulated
carrier signal.
Consider a sine wave carrier;
Carrier signal
Mathematically,
𝑒! = 𝐸! sin(𝜔! 𝑡 + θ)
where:
𝑒! = 𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑝𝑒𝑎𝑘 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒
𝐸! = 𝑝𝑒𝑎𝑘 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒
𝜔! = 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑟𝑎𝑑𝑖𝑎𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
𝜃 = 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑝ℎ𝑎𝑠𝑒
Reasons for Modulation
• For minimizing interference
• For frequency assignment
• For making antenna sizes practical
• For multiplexing
FCC Emission Designation
• In FCC emission designation, the first symbol signifies the type of modulation of the
main carrier; the second symbol signifies the nature of the modulation; and the third
symbol signifies the type of information being transmitted.
Abstraction
Amplitude Modulation (AM)
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•
Chapter 3: Amplitude Modulation
It is the simplest way of superimposing the characteristic of the intelligence signal onto
a carrier. The AM signal is produced by varying the amplitude of the carrier signal in
proportion to the instantaneous amplitude of the intelligence signal.
The trace of the peaks in the AM wave is called the envelope which has the same shape
as the modulating signal.
Mathematically, the instantaneous value of the AM signal is
𝑒"# = 𝐴 sin 𝜔! 𝑡
Where: 𝐴 = 𝐸$ + 𝑒%
𝑒"# = (𝐸$ + 𝑒% ) sin 𝜔! 𝑡
Where: 𝑒% = 𝑖𝑛𝑠𝑡𝑎𝑛𝑡𝑎𝑛𝑒𝑜𝑢𝑠 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑙𝑙𝑖𝑔𝑒𝑛𝑐𝑒 𝑠𝑖𝑔𝑛𝑎𝑙
𝑒% = 𝐸% sin 𝜔% 𝑡
Substituting,
𝑒"# = (𝐸$ + 𝐸% sin 𝜔% 𝑡) sin 𝜔! 𝑡
𝑒"# = 𝐸$ sin 𝜔! 𝑡 + 𝐸% sin 𝜔% 𝑡 sin 𝜔! 𝑡
The complete AM expression is
𝐸%
{cos(𝜔! − 𝜔% )𝑡 − cos(𝜔! + 𝜔% )𝑡 }
𝑒"# = 𝐸$ sin 𝜔! 𝑡 +
2
𝐸%
{cos 2𝜋(𝑓! − 𝑓% )𝑡 − cos2𝜋(𝑓! + 𝑓% )𝑡}
𝑒"# = 𝐸$ sin 𝜔! 𝑡 +
2
The expression is composed of three signals, the carrier, lower sideband and upper sideband.
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Chapter 3: Amplitude Modulation
Modulation Index
• The term that describes the amount of amplitude change in an FM waveform is called
the index of modulation.
• It is also called the Coefficient of Modulation, Modulation Factor, or Modulation Depth
𝑚=
𝐸%
𝐸$
The graph shows that
𝑉%&' = 𝐸! + 𝐸% and 𝑉%() = 𝐸! − 𝐸%
Thus the modulation index can be expressed as
𝑚=
𝐸% 𝑉%&' − 𝑉%()
=
𝐸$ 𝑉%&' + 𝑉%()
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Chapter 3: Amplitude Modulation
Percentage of Modulation
%𝑀 = 𝑚 × 100%
Classification According to the Degree of Modulation
AM Frequency Spectrum
Bandwidth for AM
𝐵𝑊 = 𝑓*+, − 𝑓-+,
𝐵𝑊 = (𝑓! + 𝑓% ) − (𝑓! − 𝑓% )
𝐵𝑊 = (2𝑓% )
Power Calculations
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Chapter 3: Amplitude Modulation
Unmodulated carrier power
𝑃! =
•
Lower Sideband Power, PLSB and Upper Sideband Power, PUSB
𝑃-+, = 𝑃*+,
•
𝑉$!"# . 𝐸! .
=
𝑅
2𝑅
𝑉-+,!"# . 𝑃$ 𝑚.
=
=
𝑅
4
Total Transmitted Power, PT
𝑃/ = 𝑃! + 𝑃-+, + 𝑃*+,
𝑚.
𝑃/ = 𝑃! (1 +
)
2
Where:
𝐸! = 𝑝𝑒𝑎𝑘 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑎𝑟𝑟𝑖𝑒𝑟
𝑅 = 𝑙𝑜𝑎𝑑 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒, Ω
𝑚 = 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑑𝑒𝑥
𝑃! = 𝑢𝑛𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑎𝑟𝑟𝑖𝑒𝑟 𝑝𝑜𝑤𝑒𝑟, 𝑊
𝑃/ = 𝑡𝑜𝑡𝑎𝑙 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟, 𝑊
𝑃*+, = 𝑢𝑝𝑝𝑒𝑟 𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑 𝑝𝑜𝑤𝑒𝑟, 𝑊
𝑃-+, = 𝑙𝑜𝑤𝑒𝑟 𝑠𝑖𝑑𝑒𝑏𝑎𝑛𝑑 𝑝𝑜𝑤𝑒𝑟, 𝑊
AM Power Spectrum for DSBFC Wave
Percent Power in the carrier, %PC
%𝑃$ =
𝑃!
=
𝑃/
1
𝑚.
(1 +
)
2
Percent Power in the sidebands, %PSB
%𝑃+,
𝑃+,
=
=
𝑃/
𝑚.
2
𝑚.
(1 +
)
2
Among the three signals comprising AM, only the sidebands contain the information. The
information found in the upper sideband is identical to the lower sideband. Notice that at 100%
modulation, 66.67% of the total power is in the carrier and 33.33% for the sidebands. Thus, it is
wasteful to transmit the carrier and it is redundant to transmit both sidebands.
Voltage Calculations
• Peak voltage of the Modulated Carrier, ET
𝐸/ = 𝐸! Z1 +
𝑚.
2
Current Calculations
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•
Chapter 3: Amplitude Modulation
Peak current of the Modulated Carrier, IT
𝐼/ = 𝐼! Z1 +
𝑚.
2
Where:
𝐼! = 𝑝𝑒𝑎𝑘 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑎𝑟𝑟𝑖𝑒𝑟, 𝑉
𝐼/ = 𝑝𝑒𝑎𝑘 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑠𝑖𝑔𝑛𝑎𝑙, 𝑉
𝐸! = 𝑝𝑒𝑎𝑘 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑢𝑛𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑐𝑎𝑟𝑟𝑖𝑒𝑟, 𝑉
𝐸/ = 𝑝𝑒𝑎𝑘 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑒𝑑 𝑠𝑖𝑔𝑛𝑎𝑙, 𝑉
Simultaneous Modulation
When several frequencies simultaneously amplitude modulate a carrier, the combined
coefficient of modulation is defined as:
𝑚 / = \𝑚0 . + 𝑚. . +𝑚1 . + ⋯ + 𝑚)
where:
.
𝑚 / = 𝑡𝑜𝑡𝑎𝑙 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑑𝑒𝑥
𝑚0 , 𝑚. , 𝑚1 , 𝑚) = 𝑖𝑛𝑑𝑒𝑥 𝑜𝑓 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑖𝑛𝑝𝑢𝑡 1,2,3, 𝑛
Double Sideband Suppressed Carrier AM
• In conventional AM, transmitting the carrier the whole time is a waste of power.
Moreover, chances of interference with other signals is very likely. Information is present
only in the sidebands so it is sensible to transmit only the sideband and to reinsert the
carrier at the receiver using an oscillator. This is called “Double Sideband Transmission
with Suppressed Carrier (DSBSC).
• Balanced modulators are circuits used to produce double sidebands by effectively
cancelling the carrier at the output.
• The DSBSC is not much used in practice since it is not easy to reinsert the carrier correctly.
The difficulty of transmission using two sidebands is that there is a tendency that the
reinserted signals could cancel each other out if the phase of the reinserted carrier is
incorrect. Either one of the sidebands, together with the replacement carrier, can recover
the original modulating signal.
Balanced Ring Modulator
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Chapter 3: Amplitude Modulation
Frequency Spectrum of DSBSC AM
Single Sideband System
Single Sideband Full Carrier, H3E
•
•
A form of amplitude modulation in which the carrier is transmitted at full power but only one of
the sidebands is transmitted.
The SSBFC requires less bandwidth than the conventional double sideband AM, but also
produces a demodulated signal with a lower amplitude.
Power Spectrum of SSBFC
In a perfectly modulated SSBFC, the carrier power constitutes 80% of the total power and
only 20% is in the sidebands. Although the SSBFC requires less total power than the DSBFC, it
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Chapter 3: Amplitude Modulation
actually utilizes a smaller percentage of that power for the information-carrying portion of the
signal.
At 100% modulation, 116.67% of power is saved by suppressing one of the sidebands.
Single Sideband Suppressed Carrier, J3E
•
•
A form of amplitude modulation in which the carrier is totally suppressed and one of the
sidebands is removed.
The SSBSC requires half as much bandwidth as the conventional double sideband AM and less
transmitted power.
Power Spectrum of SSBSC
In SSBSC, the sideband power constitutes 100% of the total power. The SSBSC requires
less total power than the conventional AM. At 100% modulation, 83.3% of power is saved by
suppressing the carrier and one of the sidebands.
Comparison of Common AM Transmission Systems
Single Sideband Reduced Carrier, R3E
•
A form of amplitude modulation in which one of the sidebands is totally removed and the carrier
voltage is reduced to approximately 10% of its unmodulated amplitude
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Chapter 3: Amplitude Modulation
To produce a reduced carrier component, the carrier is totally suppressed during modulation and
then reinserted at reduced amplitude.
Independent Sideband, B8E
•
•
A form of amplitude modulation in which a single carrier frequency is independently modulated
by two different modulating signals.
The ISB is a form of double sideband transmission in which the transmitter consists of two
independent single-sideband suppressed carrier modulators. The outputs of the two modulators
are combined to form a double sideband signal.
AM Vestigial Sideband, C3F
•
•
A form of amplitude modulation in which the carrier frequency and one complete sideband is
transmitted, but only part of the second sideband is transmitted.
The most widely known VSB is the picture portion of an analog commercial television broadcasting
signal.
Single Sideband Generation
•
Filter Method
•
Phase Shift Method
Single Sideband Transmitter Rating
_
𝑉23
𝑃𝐸𝑃 = √2
𝑅
.
a
Where:
𝑃𝐸𝑃 = 𝑝𝑒𝑎𝑘 𝑒𝑛𝑣𝑒𝑙𝑜𝑝𝑒 𝑝𝑜𝑤𝑒𝑟, 𝑊
𝑉23 = 𝑝𝑒𝑎𝑘 𝑣𝑜𝑙𝑡𝑎𝑔𝑒, 𝑉
𝑅 = 𝑙𝑜𝑎𝑑 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 𝑅
Reading Assignment
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Chapter 3: Amplitude Modulation
Research on the different symbols of FCC Emission Designation
Assessment Tasks
Practice Problems
1. An AM signal has the equation:
𝑒"# = (25 + 5 sin(44 × 101 𝑡)) sin(46.5 × 104 𝑡) 𝑉
a. Find the carrier frequency.
b. Find the frequency of the modulating signal.
c. Find the value of m.
d. What are the frequencies comprising the AM signal?
e. Sketch the signal in the time domain and the frequency domain.
2. An AM transmitter is modulated by two audio tones at 1 kHz and 2.5 kHz, with modulation
depths of 0.25 and 0.50 respectively. Find the effective modulation index.
3. A 1000-W carrier is to be modulated to a 95% level. Determine the total transmitted
power.
4. An AM broadcast station operates at its maximum allowed total output of 50 kW and at
85% modulation. How much of the transmitted power contains the intelligence?
5. The antenna current of an AM transmitter is 11 A when unmodulated but increases to 14
A when modulated. Find the percent modulation.
6. Calculate the percentage power saving when the carrier and one of the sidebands is
suppressed in an AM signal if the modulation is a) 100% and b) 25%.
7. For a 500-W carrier modulated toa depth of 80%, find the total power and %P.S. in each
of the following forms of AM.
a. J3E
b. H3E
c. DSB
8. An AM transmission 1000W is fully modulated. Calculate the power transmitted if it is
transmitted as SSB signal.
9. A SSB transmission drives 110-Vpk into a 75-W antenna. Calculate the PEP.
10. An SSB transmitter has a PEP of 10 kW, what is the average power?
References:
1. Tomasi W. Electronic Communications Systems – Fundamentals through Advanced 5th
Edition, New Jersey, Prentice Hall
2. Roddy J., Coolen E., Electronic Communications 5th Edition, New Jersey, Prentice Hall
3. Frenzel L., Principles of Electronic Communication Systems, New York, Mc Graw Hill
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