**From:** Jan Vercammen (*[email protected]*)

**Date:** Mon Aug 21 2000 - 05:47:09 PDT

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opamp,

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

attenuation.

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).

regrads,

Jan Vercammen

Agfa-Gevaert

EMC Engineering

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**Next message:**Pat Sharkey: "[SI-LIST] : FPGA Partial Plane"**Previous message:**Zabinski, Patrick J.: "RE: [SI-LIST] : Why CML for high-speed interfaces?"**Maybe in reply to:**opamps cybernetics: "[SI-LIST] : x-talk saturation"**Next in thread:**Fethi Bellamine: "Re: [SI-LIST] : x-talk saturation"**Reply:**Fethi Bellamine: "Re: [SI-LIST] : x-talk saturation"

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