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# sm9_15

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Problem 9.15 The average noise power per unit bandwidth measured at the front end of
an AM receiver is 10-6 watts per Hz. The modulating signal is sinusoidal, with a carrier
power of 80 watts and a sideband power of 10 watts per sideband. The message
bandwidth is 4 kHz. Assuming the use of an envelope detector in the receiver, determine
the output signal-to-noise ratio of the system. By how many decibels is this system
inferior to DSB-SC modulation system?

Solution
For this AM system, the carrier power is 80 watts, that is,

watts80
2
2
=CA (1)

and the total sideband power is 20 watts, that is,
watts20
2
2
2
=PkA aC (2)

Comparing Eq.s (1) and (2), we determine that 412 =Pka . Consequently, that post-
detection SNR of the AM system is

dB
WN
PkASNR aCAMpost
37~
5000
400010
20
2
6
0
22
=
×=
=
\u2212

For the corresponding DSB system the post detection SNR is given by

higher7~
SNR5
1
SNR
1
SNR
AM
post
4
1
4
1
AM
post2
2
DSB
post
dB
Pk
Pk
a
a
×=
+=
+=

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