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20
5.12
From Equation 2.2, the ratio of transmitted power to received power is
P
t
/P
r
= (4
π
d/
λ
)
2
If we double the frequency, we halve
λ
, or if we double the distance, we double d,
so the new ratio for either of these events is:
P
t
/P
r2
= (8
π
d/
λ
)
2
Therefore:
10 log (P
r
/P
r2
) = 10 log (2
2
) = 6 dB
5.13
By the Pythagorean theorem:
d
2
+
r
2
= (
r
+
h
)
2
Or,
d
2
= 2
rh
+
h
2
. The
h
2
term is negligible with respect to 2
rh
, so we use
d
2
= 2
rh
.
Then,
d
km
=
2
r
km
h
km
=
2
r
km
h
m
/1000
=
2
×
6.37
×
h
m
=
3.57
h
m
5.14
For radio line of sight, we use
d
=
3.57
h
, with
K
= 4/3, we have
80
2
= (3.57)
2
×
1.33
×
h
. Solving for h, we get h = 378 m.
5.15
N
= –228.6 dBW + 10 log
T
+ 10 log
B
We have
T
= 273.15 + 50 = 323.15
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This note was uploaded on 02/20/2012 for the course ENC 3250 taught by Professor Dr.timothycerner during the Fall '11 term at UNF.
 Fall '11
 Dr.TimothyCerner
 Frequency

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