From: Jan Vercammen (email@example.com)
Date: Mon Aug 21 2000 - 05:47:09 PDT
the effect you are describing is due to differences in mode velocities.
Assuming you have a lossless muliconductor system with n+1 conductors, there
will be, in general, n linear independent propagation modes. In an homogeneous
medium (e.g. stripline or infinite large medium) all modes travel at the same
speed, however, in an inhomogeneous medium (microstrip, embedded microstrip)
the modes have different propagation speeds.
When a generator (or generators) excite(s) the multiconductor lines n modes
will be excited, each propagating at a different velocity. For a finite rise time
the modes will separate after covering some distance.
For example: consider a symmetric 2 conductor line + reference plane (return). This
2+1 conductor system has two propagating modes. In case of a symmetric system the
two modes are equivalent to the (better known) odd and even mode, which makes this
easier to discuss. For non-symmetric systems the situation is slightly more complex,
but quite similar to the symmetric system.
Depending on the (inhomogeneous) medium the odd mode velocity will be faster slower
than the even mode velocity. For microstrips (PCB technology) the difference is of the order
of several ps/cm. For a rise time of 200ps and a mode velocity difference of 5ps/cm
the modes will separate at a distance of 200/5=40cm. Before this distance the
propagating field and the associated voltages and currents will be a superposition of the
odd and even mode, after this distance the modes become more and more separated as
the covered distance grows.
The saturation occurs when the modes separate, before that you will see a mixture of
You can generalize the above discussion to an n+1 multiconductor system. In general you
will see n levels, the first level is due to mode k, the second level due to modes
k and l, ..., the final level due to all modes. Note that the level of the agressor
and culprit lines can take on various levels and it could swing positve or negative before
settling in the last final settings.
In a homogeneous system you will only see one level, that is, the superposition of all modes.
In most practical situations the details of the modes are very hard to observe, because (1)
differences in mode velocities are small (or coupling lengths are short) and (2) there is
If you want to go deeper into this matter then you should consult the following
reference: Analysis of multiconductor lines, author C.R. Paul (there are very likely other
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