Digital Signal Processing Reference
In-Depth Information
9.5.1 Can the Odd- and Even-Mode Equations Be Used with More Than Two
Traces?
As demonstrated in the Problems, by summing all of the mutuals and using them
as
L
m
and
C
m
, (9.4) through (9.7) can be used to find the impedance and delay of a
victim trace when many neighbors switch.
9.5.2 Why Is the Even- and Odd-Mode Timing the Same for Stripline But Not
for Microstrip?
From Chapter 7, we know that in stripline the propagation delay is determined by
the laminate dielectric constant and not by the trace shape or impedance. This ap-
pears to conflict with (9.5) and (9.7) because they show that, in general, the timing
for even and odd modes is different.
We must turn to field theory to resolve this apparent paradox. It can be shown
[7, 8] that for the types of transmission lines of interest to us (lines where the elec-
tric and magnetic fields travel crosswise to the direction in which the signal is mov-
ing, called transverse electromagnetic, or TEM, transmission), the even-mode and
odd-mode propagation delays are the same. The significance of this is that because
striplines with low loss are true TEM lines, the even-mode propagation delay given
by (9.5) will be the same as the odd-mode propagation delay given in (9.7). In fact,
when used with striplines, they will give the same result as (7.5) where we used the
dielectric constant to find the delay. This is summarized in Figure 9.7 and explored
in the Problems.
However, the situation is very different in microstrips because even when they
are lossless, the two or more dielectrics involved means the signal propagation is
not truly TEM. In fact, microstrip delay is determined by how much of the signal
energy propagates in air and how much propagates in the laminate. This makes the
delay shorter when the victim and aggressors are out of phase because under those
conditions more of the signal energy travels in the air than in the laminate. The
Problems illustrate this further by showing that the odd-mode microstrip propaga-
tion time is smaller than the even-mode propagation times.
Stripline
Embedded
microstrip
tpd_odd = tpd_even
tpd_odd < tpd_even
ZZ
<
ZZ
<
oo
oe
oo
oe
Figure 9.7
Odd- and even-mode delays are the same in stripline traces but not in solder mask-cov-
ered microstrips.
