ENSC327
Communications Systems
3. Amplitude Modulation
Jie Liang
School of Engineering Science
Simon Fraser University
1
Outline
Overview
of Modulation
What is modulation?
Why modulation?
Overview of analog modulation
History
of AM & FM Radio Broadcast
Linear Modulation:
Amplitude modulation
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Overview of Modulation
What is modulation?
The process of varying a carrier signal in order to use that
signal to convey information.
Why
1.
modulation?
Reducing the size of the antennas:
The
optimal antenna size is related to wavelength:
Voice signal: 3 kHz
3
Overview of Modulation
Why
modulation?
2. Allowing transmission of more than one signal
in the same channel (multiplexing)
3. Allowing better trade-off between bandwidth
and signal-to-noise ratio (SNR)
4
Analog modulation
The input message is continuous in time and value
Continuous-wave modulation (focus of this course)
A parameter of a high-freq carrier is varied in accordance with the
message signal
If
a sinusoidal carrier is used, the modulated carrier is:
Linear
modulation: A(t) is linearly related to the message.
AM, DSB, SSB
Angle modulation:
Phase modulation: Φ(t) is linearly related the message.
Freq. modulation: dΦ(t)/dt is linearly related to the message.
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Analog modulation
Linear modulation
(Amplitude modulation)
Angle modulation:
Message
Carrier
Phase modulation
Freq modulation
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Problems to be studied
For each modulation scheme, we will study the
following topics:
How
does the modulator work?
How does the demodulator work?
What is the required bandwidth?
What is the power efficiency?
What is the performance in the presence of
noise?
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Outline
Overview of Modulation
What is modulation?
Why modulation?
Overview of analog modulation
History of AM & FM Radio Broadcast
Linear Modulation:
Amplitude modulation
8
History of Radio
Spark-gap transmitter
AM
1895 by Marconi
1906 by Fessenden
(Canadian)
Marconi in Newfoundland.
FM
1931 by Armstrong
9
Early History of Radio
1887: Heinrich Hertz first detected radio waves.
1894: Guglielmo Marconi invented spark transmitter with antenna in Bologna,
Italy.
1897: Marconi formed his company in Britain at age 23, awarded patent for
“wireless telegraph”.
1905-06: Reginald Fessenden (A Canadian) invented a continuous-wave voice
transmitter, first voice broadcast in Christmas Eve 1906.
1906: Lee de Forest patented his audion tube, had visited the Fessenden lab in 1903
and stole the design for a "spade detector" (de Forest sued Armstrong over the basic
regenerative patent from 1915 to 1930, and was finally awarded the basic radio
patent, causing him to become known as the "father of radio."
1912-1933: Edwin Armstrong invented the Regenerative Circuit (1912), the
Superheterodyne Circuit (1918), the Superregenerative Circuit (1922) and the
complete FM System (1933). He spent almost his entire adult life in litigation over
his patents and ultimately committed suicide by jumping to his death from a highrise in New York City in 1954.
1912: Due to Titanic disaster, all ships were required to have radios with 2
operators and auxiliary power and all transmitters must be licensed.
1920: The first licensed commercial AM radio services.
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AM and FM Radio
AM
The bandwidth of each station is 10 kHz.
The
We
radio ranges from 535 to 1605 kHz
FM radio band goes from 88 to 108 MHz
The bandwidth of each FM station is 200 kHz
FM has much better quality than AM
will learn in this course how these numbers are chosen.
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Other Usages of Spectrum
TV Band:
Channel 2 to 6.
Channel 7 to 13
Ultra-high frequency (UHF) TV
GSM:
400, 800, 900, 1800, 1900MHz
IEEE 802.11b/g (Wi-Fi): 2.4 - 2.4835 GHz
54-88 MHz:
174-216MHz:
450-800MHz
Also used by microwave ovens, cordless phones, medical and scientific
equipment, as well as Bluetooth devices.
UWB (Ultra Wideband):
3.1 - 10.6GHz
Opened up by FCC in 2002.
Signal bandwidth > 500MHz
Extremely low emission level
Many potential applications
Currently a hot research topic
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Outline
Overview of Modulation
History of AM & FM Radio Broadcast
Linear Modulation:
Amplitude modulation:
AM wave
Demodulation
Spectrum
Power Efficiency
Single tone modulation
Measure of modulation factor in time domain and freq domain
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Amplitude Modulation (AM)
An amplitude-modulated (AM) wave is given by:
s (t ) = Ac [1 + k a m(t )]cos(2πf c t )
m(t ) :
Message signal to be transmitted.
M(t) usually has zero mean.
ka :
Amplitude sensitivity (system parameter).
Ac :
Amplitude of the carrier.
fc :
Carrier frequency.
The amplitude of the carrier is a function of m(t).
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s(t ) = Ac [1 + k a m(t )]cos(2πf c t )
AM Percentage Modulation
The Percentage Modulation of an AM system is max k a m(t ) ×100
Example: m(t ) = cos(2πf 0t )
s(t)
max k a m(t ) = 0.5 or 50%
Observation:
Over-modulation: when
s(t)
max k a m(t ) = 1 or 100%
max k a m(t ) > 1
max k a m(t ) = 1.5 or 150%.
Observation:
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Amplitude Modulation (AM)
The Most Attractive Feature of AM: The message can be recovered from
the envelope of the AM wave if the following conditions are satisfied:
1. max k a m(t ) < 1 for all t.
2. f c >> W (W : message bandwidth)
Non-sinusoidal messages:
AM wave if
If max k a m(t ) > 1
Message signal
AM wave if
max k a m(t ) < 1
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Demodulation of AM: Envelope Detector
The following simple circuit can be used to recovered
the message from the AM envelope:
The diode: only allows the positive part to pass.
The lowpass RC circuit: tracks the envelope
The carrier freq. must be large enough
The RC time constant must be set carefully
Good RC
too large: discharge too slow, won’t track
too small: discharge too fast, too much distortion
RC too large
RC too small
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Spectrum of AM
Let M(f) be the FT of m(t), then the FT of the AM signal is
S( f ) =
Ac
[δ ( f − f c ) + δ ( f + f c )] + ka Ac [M ( f − f c ) + M ( f + f c )]
2
2
Proof:
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Spectrum of AM
Assume the message is a lowpass signal:
AM
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Bandwidth of AM
Assuming the bandwidth of the original lowpass signal is W
In AM, the low-pass signal M(f) is shifted to both fc and –fc:
Bandwidth of the AM signal is
Upper sideband (USB):
Lower sideband (LSB):
Disadvantages of AM:
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s (t ) = Ac [1 + k a m(t )]cos(2πf c t )
Power Efficiency of AM
1 T 2
m (t ) dt is message power,
∫
T
−
T → ∞ 2T
k a2 Pm
total sideband power
=
then the power efficiency of AM system is:
total power
1 + k a2 Pm
Assuming m(t) has zero average , and Pm = lim
Proof:
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Power Efficiency of AM
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Power Efficiency of AM
1 2 2
Psb = Ac k a Pm
2
PT =
1 2
Ac 1 + k a2 Pm .
2
[
]
The power efficiency is:
If ka approaches ∞,
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A Special Case: Single Tone Modulation
If the message is a single frequency signal:
m(t ) = Am cos(2πf mt )
The AM wave: s(t ) = Ac [1 + k a m(t )]cos(2πf c t )
To use envelope detector, need µ < 1.
2
µ
The power efficiency becomes:
2
2
+
µ
Proof:
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A Special Case: Single Tone Modulation
Power Efficiency =
µ2
2 + µ2
µ ∞: Eff 1 (leads to DSB, studied later)
If envelope detector is used, µ < 1:
For sinusoidal signals, the max power efficiency of AM is
0.35
0.3
0.25
Efficiency
0.2
0.15
0.1
0.05
0
0
0.1
0.2
0.3
0.4
0.5
0.6
Modulation Index
0.7
0.8
0.9
1
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Modulation factor
µ
Time-Domain Measurement of
Modulation Factor
How to measure the modulation factor
from oscilloscope display? (Part of Lab 2)
s (t ) = Ac [1 + µm(t )]cos(2πf c t )
If m(t) is chosen in [-1, 1], then
Emax − Emin
µ=
Emax + Emin
Proof:
-Emin
-Emax
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Frequency Domain Measurement of
Modulation Factor
Spectrum analyzer (SA): a device to examine
the spectral composition of a signals:
Can be used to measure the power at each frequency.
dBm: SA usually measures power in dBm unit (w.r.t. 1mW):
x = 10 log10
P
1mW
(See Page 459 of book)
P1 : carrier power (dBm)
P2 : sideband power of each side (dBm)
How to measure the modulation factor from Spectrum
Analyzer screen? (Part of Lab 2)
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Frequency Domain Measurement of
Modulation Factor
The modulation factor from Spectrum Analyzer screen:
If m(t ) = Am cos(2πf mt ), then µ = 2 ×10
−
P1 − P2
20
.
Proof:
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Summary of AM
s (t ) = Ac [1 + k a m(t )]cos(2πf c t )
Advantage: Simple demodulation
Envelope detector
Disadvantages:
Low power efficiency:
Waste of bandwidth:
Carrier power is wasted
Bandwidth is twice of the message.
USB and LSB has same information
Measurement of modulation factor
Concepts:
Percentage Modulation
Modulation factor (index): for single tone messages only.
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