563489578934

Sec. 5–4 Costas Loop and Squaring Loop 323
A 0 cos ( c t+¨e)
Baseband
LPF
(
1
v 1 (t)= A o A c cos ¨e m(t)
2
Demodulated
output
(
VCO
v 4 (t)
LPF
v 3 (t)
s(t)=A c m(t) cos c t
90°
phase shift
A 0 sin ( c t+¨e )
Baseband
LPF
v 2 (t)=( 1 A o A c sin ¨e m(t)
2
(
(a) Costas Phase-Locked Loop
s(t)=A c m(t) cos( c t)
1 2
s 2 (t)= A c m 2 (t)[1+cos(2 c t)]
2
1
A c m 2 (t) cos(2 c t)
2
A 0 cos(2 c t)
A 0 cos( c t)
Low-pass
filter
1
A c A 0 m(t)
2
Demodulated
output
Square-law
device
Bandpass
filter
f 0 =2f c
Limiter
Frequency
divider
÷ 2
(b) Squaring Loop
Figure 5–3
Carrier recovery loops for DSB-SC signals.
recover (i.e., demodulate) a BPSK signal, since the BPSK signal has the same mathematical
form as a DSB-SC signal, where m(t) is a polar NRZ data signal as given in Fig. 3–15c.
Both the Costas PLL and the squaring loop have one major disadvantage—a 180
phase ambiguity. For example, suppose that the input is -A c m(t) cos v c t instead of +A c m(t)
cos v c t. Retracing the steps in the preceding analysis, we see that the output would be
described by exactly the same equation that was obtained before. Then, whenever the loop is
energized, it is just as likely to phase lock such that the demodulated output is proportional
to -m(t) as it is to m(t). Thus, we cannot be sure of the polarity of the output. This is no problem
if m(t) is a monaural audio signal, because -m(t) sounds the same to our ears as m(t).