ensc327 communications systems 3. amplitude modulation
TRANSCRIPT
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ENSC327 Communications Systems3. Amplitude Modulation
School of Engineering ScienceSimon Fraser University
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Outline
Some Required BackgroundOverview of Modulation What is modulation? Why modulation? Overview of analog modulation
History of AM & FM Radio BroadcastLinear Modulation: Amplitude modulation
Some Required Background Basics of sinusoidal signals: amplitude, frequency, phase.
RC Circuits, Natural Response. Assume initial voltage to be ππππ (π‘π‘0). Recall from ENSC-220, what is ππππ (π‘π‘)?
Fourier Transform of cos 2πππππππ‘π‘ or a complex exponential. Properties of FT, e.g., shift in frequency, Parsevalβs theorem. Definition of Bandwidth (BW) (see Lecture 2) 3
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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 modulation?1. Reducing the size of the antennas:The optimal antenna size is related to wavelength:Voice signal: 3 kHz
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Overview of Modulation
Why modulation? 2. Allowing transmission of more than one signal
in the same channel (multiplexing)
3. Allowing better trade-off between bandwidthand signal-to-noise ratio (SNR)
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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
Angle modulation:
Message
Carrier
Phase modulation
Freq modulation
Linear modulation
Message
(Amplitude 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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History of Radio
Spark-gap transmitter AM FM1895 by Marconi 1906 by Fessenden 1931 by Armstrong
(Canadian)
Marconi in Newfoundland.
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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
βwireless telegraphβ. 1905-06: Reginald Fessenden invented a continuous-wave voice transmitter, first
voice broadcast in Christmas Eve 1906. (See the attachment). 1906: Lee de Forest patented his audion tube (a triode device that could detect and
amplify electric signals).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 high-rise 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 radio ranges from 535 to 1605 kHz The bandwidth of each station is 10 kHz.
The 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
We will learn in this course how these numbers are chosen.
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Other Usages of Spectrum
TV Band: 54-88 MHz: Channel 2 to 6. 174-216MHz: Channel 7 to 13 450-800MHz Ultra-high frequency (UHF) TV
GSM: 400, 800, 900, 1800, 1900MHz (primary band used in Canada) IEEE 802.11b/g (Wi-Fi): 2.4 - 2.4835 GHz
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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Amplitude Modulation (AM) An amplitude-modulated (AM) wave is given by:
[ ] )2cos()(1)( tftmkAts cac Ο+=
: :
c
c
fA
:akππ ππ = π¨π¨ππ cos(ππ π π ππππππ): Carrier signal
:)(tm
In AM modulation, the amplitude of the modulated signal varies as a function of m(t).
Modulation Sensitivity
Carrier Amplitude
Carrier Frequency
Message signal (Usually has zero mean)
Example:
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Amplitude Modulation (Cont.) The Most Attractive Feature of AM: The message can be recovered from
the envelope of the AM wave if the following conditions are satisfied:
bandwidth) message :(W .2 t.allfor 1)(max .1
Wftmk
c
a
>>
<
Message signal
AM signal if 1)(max <tmka1)(max >tmka
AM wave if
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Examplem π‘π‘ = 2 cos(200 ππ π‘π‘), c π‘π‘ = cos(2000 ππ π‘π‘), ππππ = 0.5. Plot the AM modulated signal, s(t).
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Percentage Modulation[ ] )2cos()(1)( tftmkAts cac Ο+=
)2cos()( 0tftm Ο=s(t) s(t)
50%or 5.0)(max =tmka 100%or 1)(max =tmka
150%.or 5.1)(max =tmka
%100)(max Γtmka The Percentage Modulation of an AM system Example:
Over-modulation: When for some values of t. 1)(max >tmka
Observation: The positive envelope is different from the message.
Observation: The message can be recovered from the positive envelope.
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ExampleA message, m(t), and the AM modulated signal s(t) are given below. Find the percentage modulation and the value of βxβ shown on the graph of s(t). Assume π΄π΄ππ = 1.
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Demodulation of AM: Envelope Detector
RC too large RC too small
The diode: only allows the positive part of the signal to pass.
The lowpass RC circuit: tracks the envelope The carrier freq. must be large enough The RC time constant must be set carefully
too large: discharge too slow, wonβt track too small: discharge too fast, too much distortion
Good RC
The following simple circuit can be used to recover the message from the AM envelope (big advantage of AM):
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Spectrum of AM
[ ] [ ])()(2
)()(2
)( cccc ffMffMAkffffAfS cac ++β+++β= δδ
Let M(f) be the FT of m(t), then the FT of the AM signal is
Proof:
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Example
AM
Assume the message is a lowpass signal the spectrum below. Plot the spectrum of the AM signal:
[ ] [ ])()(2
)()(2
)( cccc ffMffMAkffffAfS cac ++β+++β= δδ
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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 βfc:
Bandwidth of the AM signal is Upper sideband (USB): Lower sideband (LSB):
Disadvantages of AM:
AM
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Power Efficiency of AM
Proof:
[ ] )2cos()(1)( tftmkAts cac Ο+=
power, message is )(21 2lim β«β
ββ
=T
TTm dttm
TP
then the power efficiency of AM system is:
ma
ma
PkPk2
2
1power totalpower sideband total
+=
Assuming m(t) has zero average , and
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ExampleFor the special case of single tone modulation, i.e., when the message is a single sinusoidal ( ), we have:
In this case, we define : Find the power efficiency of the AM modulated signal in terms of ΞΌ.
)2cos()( tfAtm mm Ο=
[ ] )2cos()(1)( tftmkAts cac Ο+=
modulation factor or modulation index. ma Ak=Β΅
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Efficiency of Single Tone Modulation (cont.)
Β΅ β: Eff 1 (leads to DSB, studied later) In order to use envelope detector, we need Β΅ < 1: Maximal power efficiency of AM?
2
2
2EfficiencyPower
¡¡+
=
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Modulation Index
Effi
cien
cy
Modulation factor Β΅
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Summary of AM
Advantage: Simple demodulation Envelope detector
Disadvantages: Low power efficiency:
Carrier power is wasted Waste of bandwidth:
Bandwidth is twice of the BW of the message. USB and LSB have the same information
Measurement of modulation factor Concepts:
Percentage Modulation Modulation factor (index): for single tone messages only.
[ ] )2cos()(1)( tftmkAts cac Ο+=
ma Ak=Β΅