563489578934

Sec. 8–6 Link Budget Analysis 609
which becomes
F = P x2 + G a2 (P x1 + G a1 P as )
(8–35)
G a1 G a2 P as
where P as = kT 0 B is the available power from the thermal source. P x1 and P x2 can be obtained
from the noise figures of the individual devices by using Fig. 8–19, so that for the ith device,
F i =
P aoi
G ai P as
= P xi + G ai P as
G ai P as
or
P xi = G ai P as (F i - 1)
Substituting this into Eq. (8–35) for P x1 and P x2 , we obtain
(8–36)
F = F 1 + F 2 - 1
G a1
which is identical to Eq. (8–34) for the case of two cascaded stages. In a similar way
Eq. (8–34) can be shown to be true for any number of stages.
Looking at Eq. (8–34), we see that if the terms G a1 , G a1 G a2 , G a1 G a2 G a3 , and so on, are
relatively large, F 1 will dominate the overall noise figure. Thus, in receiving system design, it
is important that the first stage have a low noise figure and a large available gain, so that the
noise figure of the overall system will be as small as possible.
The overall effective input-noise temperature of several cascaded stages can also be
evaluated.
THEOREM. The overall effective input-noise temperature for cascaded linear devices is
T e = T e1 +
T e2 T e3 T e4
+ +
+ (8–37)
G a1 G a1 G a2 G a1 G a2 G Á
a3
as shown in Fig. 8–22.
A proof of this result is left for the reader as an exercise.
For further study concerning the topics of effective input-noise temperature and noise
figure, the reader is referred to an authoritative monograph [Mumford and Scheibe, 1968].
Link Budget Evaluation
The performance of a communication system depends on how large the SNR is at the detector
input in the receiver. It is engineering custom to call the signal-to-noise ratio before detection
the carrier-to-noise ratio (CNR). Thus, in this section, we will use CNR to denote the signalto-noise
ratio before detection (bandpass case) and SNR to denote the signal-to-noise ratio
after detection (baseband case). Here we are interested in evaluating the detector input CNR