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Amplitude modulation uses the
instantaneous amplitude of a modulating signal (voice, music,
data, etc.) to directly vary the amplitude of a carrier signal.
Modulation index, m, is used to describe the ratio of
maximum voltage to minimum voltage in the modulated signal. If
the modulating signal is equal in magnitude to the carrier, then
m = 1 and the modulated signal varies from a scaled
maximum of unity down to zero (see figure below). When m = 0, no
modulation of the carrier is performed. If m is greater
than 1, the carrier is actually cut off for some period of time,
and unwanted harmonics are created at the transmitter output.
In the frequency
domain, the carrier frequency is flanked on both sides by mirror
image copies of the modulating signal.
wM1
= wc
± wm1,
wM2
= wc
± wm2
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AM
General Equation
|
Let the
carrier be xc(t) = Xc·cos
(wct),
and the modulating signal be
xm(t) = Xm·cos (wmt) |
Then x(t)
= Xc·[1+m·cos (wmt)]·cos
(wct) |
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Modulation
Index
|
|
m
=
|
Vmax
- Vmin
Vmax
+ Vmin |
|
|
| In the following
examples, the carrier frequency is eleven time the
modulation frequency. Red (dashed) lines represent the
modulation envelope. Blue (solid) lines represent the
modulated carrier. |
|
100%
Modulation
|
 |
Here,
the maximum voltage (Vmax) is 2 V and the minimum (Vmin)
is 0 V. From the modulation index formula:
|
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50%
Modulation
|
|
Here,
the maximum voltage (Vmax) is 3 V and the minimum (Vmin)
is 1 V. From the modulation index formula:
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25%
Modulation
|
 |
Here,
the maximum voltage (Vmax) is 1.25 V and the minimum (Vmin)
is 0.75 V. From the modulation index formula:
|
m
=
|
1.25
- 0.75
1.25
+ 0.75
|
=
0.25 |
|
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150%
Modulation
|
 |
Here,
the maximum voltage (Vmax) is 2.5 V and the minimum (Vmin)
is -0.5 V. From the modulation index formula:
|
m
=
|
2.5
- (-0.5)
2.5
+ (-0.5)
|
=
1.5 |
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