Page 384 - Satellite Communications, Fourth Edition

364 Chapter Twelve

of absorptive network. Because an absorptive network contains resist-
ance, it generates thermal noise.
Consider an absorptive network, which has a power loss L.The power
loss is simply the ratio of input power to output power and will always
be greater than unity. Let the network be matched at both ends, to a ter-
minating resistor, R , at one end and an antenna at the other, as shown
T
in Fig. 12.5, and let the system be at some ambient temperature T . The
x
noise energy transferred from R into the network is kT . Let the net-
T
x
work noise be represented at the output terminals (the terminals con-
nected to the antenna in this instance) by an equivalent noise
temperature T NW,0 . Then the noise energy radiated by the antenna is
kT x
kT (12.28)
N rad NW,0
L
Because the antenna is matched to a resistive source at temperature
T , the available noise energy which is fed into the antenna and radi-
x
ated is N rad kT . Keep in mind that the antenna resistance to which
x
the network is matched is fictitious, in the sense that it represents radi-
ated power, but it does not generate noise power. This expression for N rad
can be substituted into Eq. (12.28) to give

1
T a1 b (12.29)
T NW,0 x
L
This is the equivalent noise temperature of the network referred to
the output terminals of the network. The equivalent noise at the output
can be transferred to the input on dividing by the network power gain,
which by definition is 1/L. Thus, the equivalent noise temperature of the
network referred to the network input is

T NW,i T (L 1) (12.30)
x
Since the network is bilateral, Eqs. (12.29) and (12.30) apply for signal
flow in either direction. Thus, Eq. (12.30) gives the equivalent noise

Ambient temperature
T X

Lossy network
N RAD
power loss L : 1
R T

Figure 12.5 Network matched at both ends, to a terminating resistor R T at
one end and an antenna at the other.