Page 383 - Satellite Communications, Fourth Edition

The Space Link 363

A simple relationship between noise temperature and noise factor
can be derived. Let T be the noise temperature of the amplifier, and let
e
the source be at room temperature as required by the definition of F.
This means that T ant T . Since the same noise output must be avail-
0
able whatever the representation, it follows that
T ) FGkT
Gk(T 0 e 0
or

T (F 1) T 0 (12.26)
e
This shows the direct equivalence between noise factor and noise tem-
perature. As a matter of convenience, in a practical satellite receiving
system, noise temperature is specified for low-noise amplifiers and con-
verters, while noise factor is specified for the main receiver unit.
The noise figure is simply F expressed in decibels:

Noise figure [F] 10 log F (12.27)

Example 12.6 An LNA is connected to a receiver which has a noise figure of 12
dB. The gain of the LNA is 40 dB, and its noise temperature is 120 K. Calculate
the overall noise temperature referred to the LNA input.
Solution 12 dB is a power ratio of 15.85:1, and therefore,
T e2 (15.85 1) 290 4306 K
4
A gain of 40 dB is a power ratio of 10 :1, and therefore,
4306
T in 120
10 4
120.43 K

In Example 12.6 it will be seen that the decibel quantities must be con-
verted to power ratios. Also, even though the main receiver has a very
high noise temperature, its effect is made negligible by the high gain of
the LNA.

12.5.5 Noise temperature
of absorptive networks
An absorptive network is one which contains resistive elements. These
introduce losses by absorbing energy from the signal and converting it
to heat. Resistive attenuators, transmission lines, and waveguides are
all examples of absorptive networks, and even rainfall, which absorbs
energy from radio signals passing through it, can be considered a form