Digital Signal Processing Reference
In-Depth Information
l
1
V
Tx
Rx
V
l
2
Signal at Tx
Signal at Rx
V
V
Differential
Signal
V
dm
Common Mode
Signal
V
cm
Figure 7-9
When asymmetry exists in the differential pair, part of the signal gets con-
verted to common mode at the receiver.
can be shown by calculating the voltage on each leg of the transmission line at
the receiver when the signals are launched 180
◦
(
π
) out of phase:
V(ω,l
1
)
=
v
1
e
−
αl
1
e
j(ωt
−
βl
1
)
(7-8a)
V(ω,l
2
)
=
v
2
e
−
αl
2
e
j(ωt
+
π
−
βl
2
)
(7-8b)
where
β
is the propagation constant as defined in equation (6-48c),
α
the atten-
uation constant as defined in equation (6-48b),
l
1
the length of line 1, and
l
2
the
length of line 2. Note that since there is no backward-propagating component
(
v
−
)
, all reflections are perfectly terminated in this example.
The differential-to-common mode conversion (ACCM) is calculated from
(7-8a) and (7-8b) with
α
=
0:
v
1
e
j(ωt
−
βl
1
)
+
v
2
e
j(ωt
+
π
−
βl
2
)
V(z
=
l
1
)
+
V(z
=
l
2
)
V(z
=
ACCM
=
0
)
=
v
1
e
j(ωt)
−
v
2
e
j(ωt
+
π)
0
)
−
V(z
=
v
1
e
−
jβl
1
+
v
2
e
−
jβl
2
=
(7-9)
v
1
−
v
2
where
V(z
=
l
1
)
and
V(z
=
l
2
)
are the voltages at the receiver, and
V(z
=
0
)
and
V(z
=
0
)
are the voltages at the driver.
At low frequencies where the wavelength is large, the phase delay difference
between lines 1 and 2 is small, so the numerator of (7-9) is approximately zero.
However, as the frequency increases, the phase difference becomes large. When
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