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Sec. 7–8 Output Signal-to-Noise Ratios for Analog Systems 543
60
50
ı f =10
ı f =5
40
ı f =2
(S/N) out (dB)
30
20
ı f =1
Baseband
10
0
0
5 10 15 20 25 30 35
(S/N) baseband (dB)
Figure 7–24 Noise performance of a FM discriminator for a sinusoidal modulated FM signal
plus Gaussian noise (no deemphasis). (See Example7_10.m.)
FM Systems with Threshold Extension
Any one of several techniques may be used to lower the threshold below that provided by a
receiver that uses only a FM discriminator. For example, a PLL FM detector could be used to
extend the threshold below that provided by an FM discriminator. However, when the input
SNR is large, all the FM receiving techniques provide the same performance—namely, that
predicted by Eq. (7–129) or Eqs. (7–130).
An FM receiver with feedback (FMFB) is shown in Fig. 7–25. This is another threshold
extension technique. The FMFB receiver provides threshold extension by lowering the modulation
index for the FM signal that is applied to the discriminator input. That is, the modulation index of
'
e (t) is smaller than that for v in (t), as we will show. Thus, the threshold will be lower than that
illustrated in Fig. 7–24. The calculation of the exact amount of threshold extension that is realized
by an FMFB receiver is somewhat involved [Taub and Schilling, 1986]. However, we can easily
show that the FMFB technique does indeed reduce the modulation index of the FM signal at the
discriminator input. Referring to Fig. 7–25, we find that the FM signal at the receiver input is
v in (t) = A c cos[v c t + u i (t)]