563489578934

606
Wire and Wireless Communication Applications Chap. 8
where the available power from the source (antenna) is
f 0 +B>2
P as = 2 as (f) df
L
f 0 -B>2
(8–28)
Furthermore, the available power from the source might be characterized by its noise temperature,
T s , so that, using Eq. (8–17), we get
P as = kT s B
(8–29)
In satellite Earth station receiving applications, the antenna (source) noise temperature might
be T s = 32 K at 4 GHz for a parabolic antenna where the noise from the antenna is due to
cosmic radiation and to energy received from the ground as the result of the sidelobe beam
pattern of the antenna. (The Earth acts as a blackbody noise source with T = 280 K.) Note
that the T s = 32 K of the antenna is “caused” by radiation resistance, which is not the same as
a loss resistance (I 2 R losses) associated with a thermal source and that T s has no relation to the
physical temperature of the antenna.
In summary, two figures of merit have been defined: noise figure and effective inputnoise
temperature. By combining Eqs. (8–19) and (8–22), where T i = T 0 , a relationship
between these two figures of merit for the spot measures is obtained:
T es (f) = T 0 [F s (f) - 1]
(8–30a)
Here T i = T 0 is required, because T i = T 0 is used in the definition for the noise figure that precedes
Eq. (8–19).
Using Eqs. (8–21a) and (8–25), where T i = T 0 , we obtain the same relationship for the
average measures:
T e = T 0 (F - 1)
(8–30b)
Example 8–2 T e AND F FOR A TRANSMISSION LINE
The effective input-noise temperature, T e , and the noise figure, F, for a lossy transmission line
(a linear device) will now be evaluated. † This can be accomplished by terminating the transmission
line with a source and a load resistance (all having the same physical temperature) that are
both equal to the characteristic impedance of the line, as shown in Fig. 8–21. The gain of the
transmission line is G a = 1L, where L is the transmission line loss (power in divided by power
Lossy transmission line
Source R 0 Characteristic impedance=R 0
R 0 Load
Figure 8–21
Noise figure measurement of a lossy transmission line.
† These results also hold for the T e and F of (impedance) matched attenuators.