From: Fethi Bellamine (email@example.com)
Date: Mon Aug 21 2000 - 12:38:13 PDT
Jan Vercammen wrote:
> 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
> both modes.
> 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
> good references).
> Jan Vercammen
> EMC Engineering
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The discussion in Paul's book is limited to a quasi-TEM mode. Dr. De Zutter of University of
Ghent and the folks at University of Colorado generalized to hybrid modes.
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