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ENSC327

Communications Systems

3. Amplitude Modulation

Jie Liang

School of Engineering Science

Simon Fraser University

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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

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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 bandwidth

and 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

(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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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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History of Radio

Spark-gap transmitter AM FM

1895 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 (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 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

� 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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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:

[ ] )2cos()(1)( tftmkAtscacπ+=

frequency.Carrier :

carrier. theof Amplitude :

c

c

f

A

.parameter) (systemy sensitivit Amplitude :ak

M(t) usually has zero mean.

ed. transmittbe tosignal Message :)(tm

� The amplitude of the carrier is a function of m(t).

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AM Percentage Modulation[ ] )2cos()(1)( tftmkAts

cacπ+=

)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 is

� Example:

� Over-modulation: when 1)(max >tmka

Observation:

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:

bandwidth) message :(W .2

t.allfor 1)(max .1

Wf

tmk

c

a

>>

<

Message signal

AM wave if

� Non-sinusoidal messages:

1)(max <tmka

1)(max If >tmka

AM wave if

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Demodulation of AM: Envelope Detector

RC too large RC too small

� 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

� 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 recovered the message from the AM envelope:

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Spectrum of AM

[ ] [ ])()(2

)()(2

)(ccccffMffM

Akffff

AfS cac

++−+++−= δδ

� Let M(f) be the FT of m(t), then the FT of the AM signal is

� Proof:

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Spectrum of AM

AM

� Assume the message is a lowpass signal:

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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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Power Efficiency of AM

� Proof:

[ ] )2cos()(1)( tftmkAtscacπ+=

power, message is )(2

1 2

lim ∫−

∞→

=

T

TT

mdttm

TP

then the power efficiency of AM system is:ma

ma

Pk

Pk

2

2

1power total

power sideband total

+

=

Assuming m(t) has zero average , and

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Power Efficiency of AM

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Power Efficiency of AM

� � The power efficiency is:

� If ka approaches ∞,

[ ].12

1 22

macTPkAP +=

macsbPkAP22

2

1=

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A Special Case: Single Tone Modulation

� If the message is a single frequency signal:

)2cos()( tfAtmmmπ=

[ ] )2cos()(1)( tftmkAtscacπ+=� The AM wave:

� To use envelope detector, need µ < 1.

� The power efficiency becomes:

� Proof:2

2

2 µ

µ

+

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A Special Case: Single Tone Modulation

� 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

2

2

2EfficiencyPower

µ

µ

+

=

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

Efficiency

Modulation factor µ

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Time-Domain Measurement of

Modulation Factor

� How to measure the modulation factor

from oscilloscope display? (Part of Lab 2)

-Emin

-EmaxProof:

If m(t) is chosen in [-1, 1], then

[ ] )2cos()(1)( tftmAtscc

πµ+=

minmax

minmax

EE

EE

+

−=µ

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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):

1010 log

1mW

Px =

P1

P2

: carrier power (dBm)

: sideband power of each side (dBm)

� How to measure the modulation factor from Spectrum

Analyzer screen? (Part of Lab 2)

(See Page 459 of book)

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Frequency Domain Measurement of

Modulation Factor

Proof:

. 102 then ),2cos()( If 20

21PP

mmtfAtm

−

−

×== µπ

� The modulation factor from Spectrum Analyzer screen:

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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 message.

� USB and LSB has same information

� Measurement of modulation factor

� Concepts: � Percentage Modulation

� Modulation factor (index): for single tone messages only.

[ ] )2cos()(1)( tftmkAtscacπ+=