Digital Signal Processing Reference
In-Depth Information
Z
odd
50
50
∼
Odd mode
equivalent circuit
i
drive
Z
even
50
50
Even mode
equivalent circuit
i
drive
Figure 9-20
Modal decomposition of launch voltages when port 1 is driving as shown
in Figure 9-15.
Reverse (Near-End) Crosstalk
When the power is injected into port 1 and mea-
sured at port 3 for the circuit in Figure 9-15, it is called
reverse crosstalk
,as
described in detail in Chapter 4. Reverse crosstalk is often referred to as
near-end
crosstalk
. In terms of the scattering matrix, reverse crosstalk is defined as
v
3
/
√
R
v
1
/
√
R
=
a
2
=
0
=
v
3
v
1
b
3
a
1
S
31
=
(9-30)
To explain how reverse crosstalk behaves in the frequency domain, consider a
transmission-line pair built in a homogeneous dielectric that is perfectly termi-
nated with its characteristic impedance, so the forward crosstalk and reflections
can be neglected. At dc, the crosstalk is zero because the coupling mechanism is
dependent on
L
m
(∂i/∂t)
and
C
m
(∂v/∂t)
as described in Section 4.1. However,
as the frequency starts to increase, energy will be coupled onto a victim line. As
described in Section 9.1, the peak will occur when the imaginary part is zero as
described by
n
=
1
,
2
,
3
,
...
n
4
l
√
LC
f
(
real
)
=
(9-3b)
The peak value of the reverse crosstalk can be evaluated by decoupling the
circuit into odd- and even-mode equivalents and driving the system with a current
i
drive
as shown in Figure 9-20. The voltages propagating in the odd and even
modes are calculated with the modal impedances:
v
odd
=
i
drive
Z
odd
v
even
=
i
drive
Z
even
For the case where port 1 is driven and both odd and even modes are perfectly
terminated,
†
the line voltages propagating on each line when the imaginary part
†
This can be done with the appropriate T or pi termination network, as described by Hall [2000].
Another method is to choose the appropriate values of
Z
odd
and
Z
even
, so the network is terminated.
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