School of Engineering & Technology
DSBSC RECEIVER CIRCUIT COSTAS LOOP
Electronics & Communication Engg. Dept.
CUTM
Coherent Costas loop receiver for DSB-
SC :
3
I-channel:
After down converwsion,
At the output of the lowpass filter, with |H(0)| = 1,
Q-channel:
( ) ( )
( )
cos 2
cos )
2 (
cos cos
) ( )
(
+ +
=
+
=
t t
A m
t t
t m A t
v
c c
c c
c I
) ( 2 cos
)
( A m t
t
mI = c
( )
sin 2 sin
) 2 (
)
( = A m t t + +
t
vQ c c
) ( 2 sin
)
( A m t
t
mQ = c
Feedback path:
At the output of the multiplier,
At the output of the lowpass filter,
The purpose of hf(t) is to smooth out fast time variations of me(t) The output of the VCO is described by
2 sin ) 8 (
cos sin
) 4 (
) (
2 2
2 2
t A m
t A m
t m
c c e
=
=
− −= m h t d t
mef ( ) e( ) f ( )
(
+)
= t
t
xVCO ( ) cos c
5
Where c is the VCO’s reference frequency and is the residual phase angle due to the tracking error. The constant kv is the frequency sensitivity of the VCO in rad/s/volt
The instantaneous frequency in radians/sec of the VCO’s output is given by
Clearly, if (t) were small, then the instantaneous frequency would be close to c and the output of the I-path would also be proportional to m(t).
, ) ( )
(t = kv
0t mef d
), ) (
( k m t
dt t t
d
ef v c
c + = +
