Tutorial 3: Amplitude Modulation
Problem 1 A bandpass signal is given as
Obtain the inphase and quadrature components of this signal. Then simplify the expressions by assuming
Problem 2 Find the complex envelope. inphase. and quadrature components of the following band pass
signal
Xbp(J) =
I, 900 ~
{ 0,
If I ~ 1300
otherwise
The carrier frequency fe= 1200 Hz.
Problem 3 Do Problem 2 with
1,
Xbp(J) =
1100~
1/2, 1200L if I ~1350
0,
Problem 4 Let xbp(t)
If I~ 1200
= 2z(t)cos(wet ± wot + a).
otherwise
Find inphase and quadrature phase components and
then find the complex envelope of x(t).
Problem 5 Use complex envelope representation to find the band pass output Ybp(t). when the bandpass
input xbp(t) = Acoswetu(t) is applied to a bandpass system hbp(t) = 1/[1
+ J2(J - fe)/ B]
for f > O.
Problem 6 Consider a radio transmitter rated for 4 kW peak envelope power. Find the maximum value
of the modulation index for the I kW average transmitted power of the AM signal.
Problem 1 A signal x(t)
= 4sin~t is transmitted by using AM transmitter with unity modulation index.
Draw its phasor diagram. What is the minimum amplitude of the carrier frequency such that the phase
reversal does not occur?
2
Problem 8 A signal x(t) = ~cos(140t)
following characteristic
Vout
+ ~cos(240t)
is applied to the square-law modulator with the
= alVin + a2V;n' The carrier waveform cos (wet) has frequency Ie = 10 kHz.
(a) Give the center frequency and the bandwidth of the channel such that desired AM signal is obtained.
(b) Determine the values of al and
a2
such that A e the carrier power is 10 and the modulation index is
0.5.
Problem 9 Find the SSE envelope when x(t) = coswmt+~cos(3wmt). Sketch the envelope for A e = 81.