GW Instek GRF-1300A - Manual (Page 63)

RF Communication and Signals Experiments
This experiment begins with AM to learn some modulation
theory. AM uses the modulating signal to control the amplitude
of the high-frequency carrier signal. The modulating signal is
used to alter the amplitude of the carrier in proportion to the
amplitude of the modulating signal. A high frequency carrier
signal that is amplitude modulated is called an AM wave. AM
waves are divided into ordinary AM waves, double-sideband
AM waves with suppressed carrier transmission and single-
sideband AM waves with suppressed carrier transmission.
1. The formula to express the modulated waveform is as follows:
Assuming that the modulating signal is a sine wave of a single
frequency (Ω=2πf
Ω
)
And
u
Ω
(t) = U
Ωm
cosΩ t = U
Ωm
cos2πf
Ω
t (5.1)
then the carrier signal is
u
c
(t) = U
cm
cosω
c
t = U
cm
cos2πf
c
t (5.2)
Because the carrier frequency remains unchanged after
amplitude modulation and the amplitude of an AM wave is
proportional to the modulating signal, therefore, the modulated
wave can be expressed as below:
u
AM
(t) = U
AM
(t)cosω
c
t = U
cm
(1+m
a
cosΩt) cosω
c
t (5.3)
To simplify the analysis, we set the initial phase angle of both
waveforms to zero. In formula (5.3), m
a
is known as the degree of
AM modulation or the AM modulation index.
Namely,
a m
a
cm
k U
m
U
Ω
=
This equation indicates to what degree the carrier amplitude
is controlled by the modulating signal. The constant k
a
is a
proportional constant determined by the modulation circuit. The
AM modulation index should be less than or equal to 1. When
the AM modulation index is greater than 1, it is called over
modulation and will distort the modulated signal.
We can see from this that the AM wave also oscillates at a
high frequency. Its amplitude varies regularly (envelope
changes) and is proportional to the modulating signal. Therefore,
the information in a modulating signal is carried in the
amplitude of an amplitude modulated wave. The following
figure shows how a signal changes from a carrier signal
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