Compen/EE 362
Asst. 3 Solution
Spring 2011
Problem 1
. A radio signal in free space has its power reduced in
proportion to the inverse of the square of the distance from the
antenna. Note that this is not the same attenuation behavior as
propagation over a transmission line.
If a radio signal has been reduced to 20 dB below some
reference value after it propagates 2 kilometers, what would its
dB loss be relative to the same reference after a) 8 kilometers; b)
20 kilometers?
Solution. a) At 4 times the distance, the
10
power is reduced by a 1/16 factor. 10 log
16
= 12, so down 20+12 =32 dB. b)
At 10 times the distance, the power is
reduced by a 1/100 factor.
10
10 log
100 = 20, so down 20+20 = 40 dB.
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Problem 2
.
It is desired to have full duplex communication over a cable
between A and B such that they can simultaneously transmit 56
kilobits/second to each other. They must share a total bandwidth of 60
khz, which can be divided between them by band pass filters, assumed
with no guard band waste. Assume a pulse rate D pulses/second requires
a bandwidth of W = 1.5D herz. Multiple phase shift keying is to be used,
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 Spring '11
 Unknow
 pulse rate, radio signal, lightly loaded packet, maximum pulse rate

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