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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 𝑒𝑒𝑜𝑜 (𝑡𝑡0). Recall from ENSC-220, what is 𝑒𝑒𝑜𝑜 (𝑡𝑡)?

Fourier Transform of cos 2𝜋𝜋𝑓𝑓𝑐𝑐𝑡𝑡 or a complex exponential. Properties of FT, e.g., shift in frequency, Parseval’s 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

“wireless telegraph”. 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 π+=

: :

c

c

fA

:ak𝒄𝒄 𝒕𝒕 = 𝑨𝑨𝒄𝒄 cos(𝟐𝟐 𝝅𝝅 𝒇𝒇𝒄𝒄𝒕𝒕): 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 𝑡𝑡 = 2 cos(200 𝜋𝜋 𝑡𝑡), c 𝑡𝑡 = cos(2000 𝜋𝜋 𝑡𝑡), 𝑘𝑘𝑎𝑎 = 0.5. Plot the AM modulated signal, s(t).

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Percentage Modulation[ ] )2cos()(1)( tftmkAts cac π+=

)2cos()( 0tftm π=s(t) s(t)

50%or 5.0)(max =tmka 100%or 1)(max =tmka

150%.or 5.1)(max =tmka

%100)(max ×tmka 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 “x” shown on the graph of s(t). Assume 𝐴𝐴𝑐𝑐 = 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, won’t 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 ++−+++−= 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 ++−+++−= 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 –fc:

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 π+=

power, message is )(21 2lim ∫−

∞→

=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 μ.

)2cos()( tfAtm mm π=

[ ] )2cos()(1)( tftmkAts cac π+=

modulation factor or modulation index. ma Ak=µ

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Efficiency of Single Tone Modulation (cont.)

µ ∞: Eff 1 (leads to DSB, studied later) In order to use envelope detector, we need µ < 1: Maximal power efficiency of AM?

2

2

2EfficiencyPower

µµ+

=

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 µ

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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 π+=

ma Ak=µ