DIT, Kevin St,
Communications Engineering Laboratory Manual FT221/3
Lab 2: Amplitude Modulation
Objective:
To investigate the principles of amplitude modulation using a hp generator
and to simulate using Pspice.
Theory:
The instantaneous amplitude value of the carrier modulated by a
sinusoidal signal is:
vc (t ) = [ E c + E m cos 2πf m t ] cos 2πf c t Volts
We may consider the part in the square brackets as modifying the
amplitude of the carrier. Expand this equation by multiplying out and
getting the following result:
vc (t ) = E c cos 2πf c t + E m cos 2πf m t cos 2πf c t Volts
Apply to this equation, the well-known expansion formula:
cosAcosB = 1/2[cos(A - B) + cos(A + B)]
We see that the AM signal contains three components.
v c (t ) = E c cos 2πf c t +
Em
E
cos 2π ( f c − f m )t + m cos 2π ( f c + f m )t volts
2
2
In terms of the modulation index m
v c (t ) = E c cos 2πf c t +
mE c
mE c
cos 2π ( f c − f m )t +
cos 2π ( f c + f m )]t
2
2
Create the schematic circuit in Pspice as shown in figure 2.2. To
generate an amplitude modulated signal, three generators are connected
to the summing circuit. Set up the three generators with parameters as
shown in figure 2.2 (The carrier generator). Create two more but set
the frequency and amplitude to a value, which will create an AM with
50% modulation (you figure it out).
Copyright Paul Tobin School of Electronic and Communications Engineering
11
DIT, Kevin St,
Communications Engineering Laboratory Manual FT221/3
Figure 2.1: Amplitude modulator.
Figure 2.2: Generator parameters.
Figure 2.3: The AM signal.
The outline of the signal is called the envelope shown in figure 2.3, and
the upper or lower portion of the envelope has the same shape as the
modulating signal.
Copyright Paul Tobin School of Electronic and Communications Engineering
12
DIT, Kevin St,
Communications Engineering Laboratory Manual FT221/3
Use the FFT icon to display the signal in the frequency domain. The
resolution in this domain is determined by the parameters set in the
transient set-up. The greater the time axis the better the frequency
resolution. We can see the spectral components in figure 2.4 for the
100 kHz carrier modulated by a 2kHz modulating signal. The components
are located at the locations given by the above expression i.e. spectral
components at 98 kHz, 100 kHz and 102 kHz. Another point to notice
from the expression is that the side-bands are not equal in magnitude
to the carrier component. The bandwidth for this signal is obtained by
subtracting the lowest frequency component from the highest
frequency component.
Bandwidth = BW = ( f c + f m ) − ( f c − f m ) = 2 f m
The bandwidth is 2 kHz.
Figure 2.4: The AM spectrum.
Copyright Paul Tobin School of Electronic and Communications Engineering
13