T 7.2.1.3 Amplitude Modulation

TPS 7.2.1.3
Review
3 Review of amplitude modulation
In amplitude modulation (AM) the momentary
value of the message signal s M (t) has an
immediate effect on the amplitude of the carrier
oscillation s C (t). This takes place in a modulator,
see Fig.3-1.
Here it would be:
s C
(t) = A C
cos (2 π f C
t) (3-1)
for the high-frequency carrier and:
1. s M
(t) = A M
cos (2 π f M
t) (3-2)
for the low frequency message signal. The combining
of the carrier and message signal in the
modulator then provides the following modulation
product:
s AM
(t) = [A C
+ α s M
(t)] cos (2 π f C
t) (3-3)
= [A C
+ α A M
cos (2 π f M
t)]
cos (2 π f C
t).
Where α stands for the modulator constant, which
expresses the affect of the message signal s M (t)
on the amplitude A C of the carrier. Normally (3-3)
is described in more general terms. For this you
need the following definitions:
∆A C
= α A M
Amplitude deviation (3-4)
A
m = ∆ C
A
C
Modulation index (3-5)
Amplitude deviation ∆A C describes the maximum
change away from the original value A C in the carrier
amplitude. The modulation index m reproduces
the ratio of the amplitude deviation to the carrier
Fig. 3-1: Generation of amplitude modulation
amplitude. Thus it is possible to convert (3-3) as
follows:
⎡ ∆A
⎤
C
sAM
( t) = A ⎢
C 1+ cos( 2π
fMt)
⎥cos
2π
fCt
⎢
⎣
A
⎥
C
⎦
A 1 mcos
2π
f t cos 2π
f t
C M C
( )
[ ] ( )
= + ( )
(3-6)
Fig. 3-2 shows the amplitude modulated signal according
to (3-6). The modulating signal s M (t) can
be recognized in the envelope curve.
Normally the following holds true: 0 < m < 1.
The following limiting cases for m are interesting:
m = 0 : no modulation effect
m = 1 : full modulation, the envelopes bordering
the modulating signal just touch at their
minimum values
m > 1 : overmodulation, the envelopes permeate
each other, modulation distortion arises.
m = 0%
A C
s AM
T C
Envelope
∆A C
∆A C
m = 100%
T M
Envelope
m > 100%
Fig. 3-2: The amplitude modulated signal
Fig. 3-3: Limiting cases for the modulation factor
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