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Wire and Wireless Communication Applications Chap. 8
Overall system G a , F, T e
Device #1
G a1
F 1
T e1
Device #2
G a2
F 2
T e2
Device #3
G a3
F 3
T e3
Device #4
G a4
F 4
T e4
Figure 8–22
Cascade of four devices.
The overall available power gain is
G a (f) = G a1 (f) G a2 (f) G a3 (f) G a4 (f) Á
(8–33)
since, for example, for a four-stage system,
G a (f) = ao4
as
= a ao1
as
ba ao2
ao1
ba ao3
ao2
ba ao4
ao3
b
F = F 1 + F 2 - 1
+ F 3 - 1 F 4 - 1
+
G a1 G a1 G a2 G a1 G a2 G a3
(8–34)
THEOREM. The overall noise figure for cascaded linear devices is †
+ Á
as shown in Fig. 8–22 (for a four-stage system).
Proof. This result may be obtained by using an excess-noise model of Fig. 8–19 for
each stage. We will prove the result for a two-stage system as modeled in Fig. 8–23. The overall
noise figure is
F =
P ao2
(P ao2 ) ideal
= P x2 + P ao1 G a2
G a1 G a2 P as
Device #1 Device #2
P as P a o 1
G a 2
R s
G a 1
P x 1 P x 2
P a o2
R L =R o
Figure 8–23
Noise model for two cascaded devices.
† This is known as Friis’s noise formula.