**From:** Fethi Bellamine (*fethi.bellamine@alcatel.com*)

**Date:** Mon Aug 21 2000 - 12:38:13 PDT

**Next message:**David Butler: "[SI-LIST] : differential pair separation"**Previous message:**Mike Jenkins: "Re: [SI-LIST] : x-talk saturation"**In reply to:**Jan Vercammen: "Re: [SI-LIST] : x-talk saturation"**Next in thread:**Mike Jenkins: "Re: [SI-LIST] : x-talk saturation"

Jan Vercammen wrote:

*> opamp,
*

*>
*

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

*> **** To unsubscribe from si-list or si-list-digest: send e-mail to
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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.

fethi bellamine

SI/EMC

alcatel

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**Next message:**David Butler: "[SI-LIST] : differential pair separation"**Previous message:**Mike Jenkins: "Re: [SI-LIST] : x-talk saturation"**In reply to:**Jan Vercammen: "Re: [SI-LIST] : x-talk saturation"**Next in thread:**Mike Jenkins: "Re: [SI-LIST] : x-talk saturation"

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