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ECET 512 Winter 2007 : Homework #4
Midterm Practice Problems
March 11, 2007
1
25.4.3
a)For the Friis’ law to hold, the separation of the two antennas should be at least one Rayleigh distance
apart. Rayleigh distance is calculated as:
d
R
=
2
L
2
a
λ
, where
L
a
is tha largest dimension of the antenna. In our case,
L
a
= 15
m
, and
λ
= 0
.
3
m
(1 GHz
carrier frequency), so Rayleigh distance is
d
R
= 1500
m >
90
m
, so for the speciﬁed distance, the Friis’ law
cannot be used.
b) The eﬀective area of a parabolic antenna is
A
eff
= 0
.
55
A
, where A is the physical area. So, in our
case,
A
eff
= 0
.
55
πr
2
= 97
.
193
m
2
. The antenna gain is then given as:
G
=
4
πA
eff
λ
2
= 13570
.
70
∼
= 41
.
33
dB
. If the Friis’ law was used for the link budget, then the received power
would be calculated as:
P
RX
=
P
TX
G
TX
G
RX
λ
2
(4
πd
)
2
⇒
P
RX
dB
=
P
TX
dB
+
G
RX
dB
+
G
RX
dB
+ 20 log(
lambda
4
πd
⇒
P
RX
dB
=
P
TX
dB
+ 82
.
66

71
.
53
⇒
P
RX
dB
=
P
TX
dB
+ 11
.
13
dB
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This note was uploaded on 02/09/2010 for the course ECET 512 taught by Professor Dand during the Spring '09 term at Drexel.
 Spring '09
 Dand

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