Page 382 - Satellite Communications, Fourth Edition

362 Chapter Twelve

The noise energy of amplifier 2 referred to its own input is simply kT .
e2
The noise input to amplifier 2 from the preceding stages is G k(T ant
1
T ), and thus the total noise energy referred to amplifier 2 input is
e1
G k(T T ) kT (12.20)
N 0,2 1 ant e1 e2
This noise energy may be referred to amplifier 1 input by dividing by
the available power gain of amplifier 1:

N 0,2
N 0,1
G 1 (12.21)
T e2
kaT ant T b
e1
G 1
A system noise temperature may now be defined as T by
S
N 0,1 kT S (12.22)
and hence it will be seen that T is given by
S
T e2
T T (12.23)
T S ant e1
G 1
This is a very important result. It shows that the noise temperature
of the second stage is divided by the power gain of the first stage when
referred to the input. Therefore, in order to keep the overall system
noise as low as possible, the first stage (usually an LNA) should have
high power gain as well as low noise temperature.
This result may be generalized to any number of stages in cascade,
giving
T e2 T e3
T T c (12.24)
T S ant e1
G 1 G G 2
1
12.5.4 Noise factor
An alternative way of representing amplifier noise is by means of its
noise factor, F. In defining the noise factor of an amplifier, the source is
taken to be at room temperature, denoted by T , usually taken as 290 K.
0
The input noise from such a source is kT , and the output noise from the
0
amplifier is
N 0,out FGkT 0 (12.25)

Here, G is the available power gain of the amplifier as before, and F is
its noise factor.