Graphics Programs Reference
In-Depth Information
N
o
N
i
F
dB
=
10
log
---------------
(1B.5)
A
p
where
and
are, respectively, the noise power at the output and input of
N
o
N
i
the system.
If we define the input and output signal power by
and
, respectively,
S
i
S
o
then the power gain is
S
o
S
i
A
P
=
-----
(1B.6)
It follows that
S
i
⁄
Ni
S
i
N
i
S
o
N
o
----
dB
-----
dB
----------------
F
dB
=
10
log
=
(1B.7)
S
o
⁄
N
o
where
S
i
N
i
S
o
N
o
----
dB
-----
dB
>
(1B.8)
Thus, it can be said that the noise figure is the loss in the signal-to-noise ratio
due to the added thermal noise of the amplifier
.
(
(
SNR
)
o
=
(
SNR
)
i
FindB
)
We can also express the noise figure in terms of the systemÓs effective tem-
temperature be
T
e
. Assume the input noise temperature is
. Thus, the input
T
e
T
o
noise power is
N
i
=
kT
o
B
(1B.9)
and the output noise power is
N
o
=
kT
o
BA
p
+
kT
e
BA
p
(1B.10)
where the first term on the right-hand side of Eq. (1B.10) corresponds to the
input noise, and the latter term is due to thermal noise generated inside the sys-
tem. It follows that the noise figure can be expressed as
S
i
kT
o
B
T
o
+
S
o
T
e
(
SNR
)
i
T
e
T
o
------------
-----------------
F
=
------------------
=
kBA
p
=
1
+
-----
(1B.11)
(
SNR
)
o
Equivalently, we can write
T
e
=
(
F
1
)
T
o
(1B.12)
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