Amplitude Modulation
Cuthbert Nyack
This was the first type of modulation used for communicating signals
from one point to another and is still the simplest to understand.
The signal can be written as:-
v = ac (1 +
m cos wmt)
cos wct
This represents a signal at frequency
wc
whose amplitude is modulated by another frequency
wm.
m = am/ac is the modulation index.
To find the frequency spectrum of the am signal the
above expression can be rewritten as a sum of signals
of constant amplitude:-
v(t) = ac{cos wct
+ m/2(cos(wc
+ wm)t
+ cos(wc
- wm)t)}
Above expression shows that the frequency spectrum consists of
3 components at frequencies
wc,
wc
+ wm and
wc
- wm.
The percent of the power transmitted which is in the carrier
is given by
Pc = 100/(1 + m * m/2) and varies from 100% for m = 0
to 66.66% for m = 1. This is considered to be one of the
disadvantages of AM since the carrier is a sine wave and
contains no information.
The applet below shows an amplitude modulated signal in red and
how it depends on m and wm.
The modulating signal is shown in orange and the frequency
spectrum in green.
If the modulating index becomes greater than 1 then the expression
for the AM signal amplitude (1 + m cos wmt)
can go negative. In practical AM systems The amplitude will be limited to
zero and the modulating index to one.
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COPYRIGHT © 1996 Cuthbert Nyack.