Graphics Programs Reference
In-Depth Information
The output signal power is
S
o
=
S
i
G
1
G
2
(1B.13)
The input and output noise powers are, respectively, given by
N
i
=
kT
o
B
(1B.14)
N
o
=
kT
0
BG
1
G
2
+
kT
e
1
BG
1
G
2
+
kT
e
2
BG
2
(1B.15)
where the three terms on the right-hand side of Eq. (1B.15), respectively, corre-
spond to the input noise power, thermal noise generated inside network 1, and
thermal noise generated inside network 2.
Now if we use the relation along with Eq. (1B.13) and Eq.
(1B.14), we can express the overall output noise power as
T
e
=
(
F
1
)
T
0
N
o
=
F
1
N
i
G
1
G
2
+
(
F
2
1
)
N
i
G
2
(1B.16)
It follows that the overall noise figure for the cascaded system is
(
S
i
⁄
N
i
)
F
2
G
1
1
F
=
--------------------
=
F
1
+
---------------
(1B.17)
(
S
o
⁄
N
o
)
In general, for an n-stage system we get
F
2
G
1
1
F
3
G
1
G
2
1
F
n
1
F
=
+
---------------
+
---------------
+
⋅
⋅
⋅
+
----------------------------------------------------------
(1B.18)
1
G
1
G
2
G
3
⋅
⋅
⋅
G
n
1
Also, the n-stage system effective temperatures can be computed as
T
e
2
G
1
T
e
3
G
1
G
2
T
en
T
e
=
T
e
1
++ +
--------
--------------
⋅⋅⋅
+
----------------------------------------------------------
(1B.19)
G
1
G
2
G
3
⋅
⋅
⋅
G
n
1
As suggested by Eq. (1B.18) and Eq. (1B.19), the overall noise figure is mainly
dominated by the first stage. Thus, radar receivers employ low noise power
amplifiers in the first stage in order to minimize the overall receiver noise fig-
ure. However, for radar systems that are built for low RCS operations every
stage should be included in the analysis.
Example:
A radar receiver consists of an antenna with cable loss
, an
L
=
1
dB
=
F
1
RF amplifier with
, and gain
, followed by a mixer
F
2
=
6
dB
G
2
=
20
dB
whose noise figure is
and conversion loss
, and finally,
F
3
=
10
dB
L
=
8
dB
an integrated circuit IF amplifier with
and gain
. Find
F
4
=
6
dB
G
4
=
60
dB
the overall noise figure.
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