1. TELE3113 Analogue and Digital
Communications
Amplitude Modulation
Wei Zhang
w.zhang@unsw.edu.au
School of Electrical Engineering and Telecommunications
The University of New South Wales

2. 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.1/1

3. 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.
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4. 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.
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5. 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
20
Carrier Wave c(t)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−1
0
1
Message 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
40
Amplitude Modulated Wave s(t)
TELE3113 - Amplitude Modulation. August 4, 2009. – p.4/1

6. 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
20
Carrier 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
1
Message 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
200
Amplitude Modualted Signal s(t)
Phase reversal
TELE3113 - Amplitude Modulation. August 4, 2009. – p.5/1

7. 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)
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8. FT of AM (2)
)( fS
)( fM
WW− 0
0
Wfc −− Wfc +−cf− Wfc − Wfc +cf
)(
2
c
c
ff
A
−δ)(
2
c
c
ff
A
+δ
)0(
2
M
Ak ca
)0(M
f
f
Upper
sideband
Lower
sideband
Spectrum of message signal
Spectrum of AM wave signal
TELE3113 - Amplitude Modulation. August 4, 2009. – p.7/1

9. 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.
TELE3113 - Amplitude Modulation. August 4, 2009. – p.8/1

10. Example: Single-Tone AM (2)
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
.
TELE3113 - Amplitude Modulation. August 4, 2009. – p.9/1

11. Example: Single-Tone AM (3)
0 0.5 1 1.5
−20
0
20
Carrier wave
0 0.5 1 1.5
−1
0
1
Message signal
0 0.5 1 1.5
−50
0
50
µ=0.5
0 0.5 1 1.5
−50
0
50
µ=1
0 0.5 1 1.5
−50
0
50
µ=1.5
TELE3113 - Amplitude Modulation. August 4, 2009. – p.10/1

12. Example: Single-Tone AM (4)
For the single-tone signal, we may express it as
s(t) = Ac cos(2πfct)+
µAc
2
cos[2π(fc+fm)t]+
µAc
2
cos[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)].
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13. Example: Single-Tone AM (5)
Carrier power = 1
2 A2
c
Upper sideband power = 1
8 µ2A2
c
Lower sideband power = 1
8 µ2
A2
c
Total sideband power
Total sideband power+Carrier power = µ2
2+µ2
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Percentage modulation factor µ
Ratiooftotaltransmittedpower
Sidebands
Carrier
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14. 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
TELE3113 - Amplitude Modulation. August 4, 2009. – p.13/1

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