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TELE3113 Analogue and DigitalCommunications

Amplitude Modulation

Wei Zhang

[email protected]

School of Electrical Engineering and Telecommunications

The University of New South Wales

Modulation

Modulation is defined as the process by which some

characteristics of a carrier wave is varied in accordance with an

information-bearing signal.

amplitude modulation (AM) (varying amplitude)

angle modulation (varying phase or frequency)

AM family:

amplitude modulation

double sideband-suppressed carrier (DSB-SC)

single sideband (SSB)

vestigial sideband (VSB)

TELE3113 - Amplitude Modulation. August 4, 2009. – p.1/14

Amplitude Modulation (1)

Consider a sinusoidal carrier wave c(t) defined by

c(t) = Ac cos(2πfct),

where Ac is the carrier amplitude and fc is the carrier

frequency.

Amplitude modulation (AM) is a process in which the

amplitude of the carrier wave c(t) is varied linearly with the

message signal m(t). An AM wave is:

s(t) = Ac[1 + kam(t)] cos(2πfct).

where ka is a constant called the amplitude sensitivity.


Amplitude Modulation (2)

In AM, information resides solely in the envelop, i.e.,

Ac|1 + kam(t)|, which has the same shape as the message

signal m(t).

In order to properly detect the information, the shape of the

envelop of the modulated signal should be unchanged in the

modulation. Specifically,

1. The amplitude of kam(t) < 1 for all t;

2. The carrier frequency fc >> W , where W is the

message bandwidth.


Amplitude Modulation (3)AM wave for kam(t) < 1.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−20

0

20Carrier Wave c(t)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−1

0

1Message Signal m(t)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−40

−20

0

20

40Amplitude Modulated Wave s(t)


Amplitude Modulation (4)AM wave for |kam(t)| > 1. Over modulated.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8−20

−10

0

10

20Carrier Wave c(t)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8−0.5

0

0.5

1Message Signal m(t)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8−200

−100

0

100

200Amplitude Modualted Signal s(t)

Phase reversal


FT of AM (1)

Consider the AM signal,

s(t) = Ac[1 + kam(t)] cos(2πfct).

The Fourier transform of s(t) is given by

S(f) =Ac

2[δ(f − fc) + δ(f + fc)] +

kaAc

2[M(f − fc) + M(f + fc)].

We used the relations:

exp(j2πfct) ⇔ δ(f − fc)

m(t) exp(j2πfct) ⇔ M(f − fc) (Shifting Property)


FT of AM (2)

)( fS

)( fM

W W− 0

0 Wfc −− Wfc +− cf− Wfc − Wfc + cf

)(2 c

c ffA −δ )(

2 cc ff

A +δ )0(

2M

Ak ca

)0(M

f

f

Upper sideband

Lower sideband

Spectrum of message signal

Spectrum of AM wave signal


Example: Single-Tone AM (1)

Consider a message signal with a single tone,

m(t) = Am cos(2πfmt).

The corresponding AM wave is therefore given by

s(t) = Ac[1 + µ cos(2πfmt)] cos(2πfct),

where µ is called the modulation factor or percentage

modulation, as

µ = kaAm.



Let Amax and Amin denote the maximum and minimum values of

the envelope of the modulated wave, respectively. Then,

Amax = Ac(1 + µ),

Amin = Ac(1 − µ).

Rearranging the equation, we may express the modulation factor

as

µ =Amax − Amin

Amax + Amin

.



0 0.5 1 1.5−20

0

20Carrier wave

0 0.5 1 1.5−1

0

1Message signal

0 0.5 1 1.5−50

0

50µ=0.5

0 0.5 1 1.5−50

0

50µ=1

0 0.5 1 1.5−50

0

50µ=1.5



For the single-tone signal, we may express it as

s(t) = Ac cos(2πfct)+µAc

2cos[2π(fc+fm)t]+

µAc

2cos[2π(fc−fm)t].

The Fourier transform of s(t) is therefore

S(f) =Ac

2[δ(f − fc) + δ(f + fc)]

+µAc

4[δ(f − fc − fm) + δ(f + fc + fm)]

+µAc

4[δ(f − fc + fm) + δ(f + fc − fm)].



Carrier power = 12A2

c

Upper sideband power = 18µ2A2

c

Lower sideband power = 18µ2A2

c

Total sideband powerTotal sideband power+Carrier power

= µ2

2+µ2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Percentage modulation factor µ

Rat

io o

f tot

al tr

ansm

itted

pow

er

Sidebands

Carrier


Envelop Detection

Envelope detection is a demodulation process which is

responsible for extracting the message signal m(t) from the

modulated signal s(t).

Output

AM wave )(ts

sR

C lR


Pros and Cons of AM

Pros:

Easily generated and inexpensive to build.

Cons:

Waste of transmitted power. The carrier power is useless.

Waste of channel bandwidth. Due to the symmetry, only

upper or lower sideband is needed.

Modifications of AM:

Double sideband-suppressed carrier (DSB-SC) modulation

Single sideband (SSB) modulation

Vestigial sideband (VSB) modulationTELE3113 - Amplitude Modulation. August 4, 2009. – p.14/14

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