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544
Performance of Communication Systems Corrupted by Noise Chap. 7
FM signal in
v in (t)
e(t)
IF
filter
Demodulated
output
~ ~
e(t)
m (t)
FM
discriminator
v 0 (t)
VCO
Figure 7–25
FMFB receiver.
where
The output of the VCO is
where
t
u i (t) = D f m(l) dl
L
With these representations for v in (t) and v 0 (t), the output of the multiplier (mixer) is
e(t) = A c A 0 cos[v c t + u i (t)] cos[v 0 t + u 0 (t)]
= 1 2 A cA 0 cos[(v c - v 0 )t + u i (t) - u 0 (t)]
+ 1 2 A cA 0 cos[(v c + v 0 ) t + u i (t) + u 0 (t)]
If the IF filter is tuned to pass the band of frequencies centered about f if ! f c - f 0 , the IF
output is
-q
y 0 (t) = A 0 cos [v 0 t + u 0 (t)]
u 0 (t) = D y
L
t
-q
m ' (l) dl
or
' A c A 0
e (t) =
2
' A c A 0
e (t) = cos[v
2 if t + u i (t) - u 0 (t)]
t
cose v if t + [D f m(l) - D y m ' (l)] dl f
L
-q
(7–133a)
(7–133b)
The FM discriminator output is proportional to the derivative of the phase deviation:
m ' (t) = K 2p
de
L
t
-q
[D f m(l) - D y m ' (l)] dl f
dt